Physics Exam Preparation

“Fail to prepare, prepare to fail”

R. Keane

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Contents

Contents PageExam Technique 3

Section A – Mandatory Experiments 8

Section B – Short Questions 57

Section B – Long Questions

Geometrical OpticsMechanicsAcceleration, Force, MomentumMoments and PressureTemperature and HeatWaves, Sound, LightCircular Motion and SHMStatic Electricity and CapacitanceResistanceSemiconductorsMagnetism and Magnetic FieldsEffects of an electric currentThe ElectronElectromagnetic inductionNuclear PhysicsParticle Physics

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8695112136140150166176187197200203209219226239

Solutions to all questions are in each section of the booklet.

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Exam Technique

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Exam Technique - Section A: Experiment Questions

You must know all mandatory experiments inside out:See the last page of the Real World Physics workbook for a full list of Experiments.

You will be given a set of results and each question generally consists of three parts:1. To calculate some quantity (e.g. Specific Heat Capacity) or to verify a Law (e.g. Conservation of Momentum,

Snell’s Law etc).2. At least one of the questions will require a graph to be drawn. In such cases the slope of the graph will usually

have to be calculated. The significance of the slope of the graph is determined by comparing it to a relevant formula (which links the two variables on the graph).

3. Some shorter questions on sources of error, precautions etc in relation to the performance of the experiment.

NoteThe data given will frequently have to be modified in some way (e.g. you may need to square one set of values or find the reciprocal etc) before the graph is drawn. This modification is determined by comparing it to the relevant formula which links the two variables.

When revising Section A make sure that you can do each of the following for every experiment: Draw a labelled diagram of the experimental set-up, including all essential apparatus. The first step in the

procedures should then read “we set up the apparatus as shown in the diagram”. Describe how to obtain values for both sets of variables Describe what needs to be adjusted to give a new set of data Say what goes on the graph, and which variable goes on which axis Know how to use the slope of the graph to obtain the desired answer (see below). List two or three precautions; if you are asked for two precautions, give three - if one is incorrect it will simply be

ignored. List two or three sources of error.

Misc Points The graph question is usually well worth doing. Learn the following line off by heart as the most common source of error: “parallax error associated with using a

metre stick to measure length / using a voltmeter to measure volts etc”. Make sure you understand the concept of percentage error; it’s the reason we try to ensure that what we’re

measuring is as large as possible. There is a subtle difference between a precaution and a source of error – know the distinction. When asked for a precaution do not suggest something which would result in giving no result, e.g. “Make sure the

power-supply is turned on” (a precaution is something which could throw out the results rather than something which negates the whole experiment).

To verify Joule's Law does not involve a Joulemeter To verify the Conservation of Momentum – the second trolley must be at rest. To verify the laws of equilibrium - the phrase ‘spring balance’ is not acceptable for ‘newton-metre’. To measure the Focal length of a Concave Mirror or a Convex Lens.

Note that when given the data for various values of u and v, you must calculate a value for f in each case, and only then find an average. (As opposed to averaging the u’s and the v’s and then just using the formula once to calculate f). Apparently the relevant phrase is “an average of an average is not an average”.

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Drawing the graph

You must use graph paper and fill at least THREE QUARTERS OF THE PAGE. Use a scale which is easy to work with i.e. the major grid lines should correspond to natural divisions of the

overall range. LABEL THE AXES with the quantity being plotted, including their units. Use a sharp pencil and mark each point with a dot, surrounded by a small circle (to indicate that the point is a

data point as opposed to a smudge on the page. Generally all the points will not be in perfect line – this is okay and does not mean that you should cheat by

putting them all on the line. Examiners will be looking to see if you can draw a best-fit line – you can usually make life easier for yourself by putting one end at the origin. The idea of the best-fit line is to imagine that there is a perfect relationship between the variables which should theoretically give a perfect straight line. Your job is to guess where this line would be based on the available points you have plotted.

Buy a TRANSPARENT RULER to enable you to see the points underneath the ruler when drawing the best-fit line.

DO NOT JOIN THE DOTS if a straight line graph is what is expected. Make sure that you know in advance which graphs will be curves.

BE VERY CAREFUL drawing a line if your ruler is too short to allow it all to be drawn at once. Nothing shouts INCOMPETENCE more than two lines which don’t quite match.

Note that examiners are obliged to check that each pint is correctly plotted, and you will lose marks if more than or two points are even slightly off.

When calculating the slope choose two points that are far apart; usually the origin is a handy point to pick (but only if the line goes through it).

When calculating the slope DO NOT TAKE DATA POINTS FROM THE TABLE of data supplied (no matter how tempting!) UNLESS the point also happens to be on the line. If you do this you will lose beaucoup de marks and can kiss goodbye any chance of an A grade.

What goes on what axis?Option oneTo show one variable is proportional to another, the convention is to put the independent variable on the x–axis, and the dependant variable on the y-axis, (from y = fn (x), meaning y is a function of x). The independent variable is the one which you control.

Option twoIf the slope of the graph needs to be calculated then we use a difference approach, one which often contradicts option one, but which nevertheless must take precedence. In this case we compare a formula (the one which connects the two variables in question) to the basic equation for a line: y = mx.See if you can work out what goes on what axis for each of the following examples (they get progressively trickier):1. To Show Force is proportional to Acceleration2. Ohm’s Law3. Snell’s Law4. Acceleration due to gravity by the method of free-fall5. Acceleration due to gravity using a Pendulum

There is usually a follow-up question like the following; “Draw a suitable graph on graph paper and explain how this verifies Snell’s Law”. There is a standard response to this; “The graph of Sin i against Sin r resulted in a straight line through the origin (allowing for experimental error), showing Sin i is directly proportional to Sin r, and therefore verifying Snell’s Law”.

If you are asked any questions to do with the information in the table, you are probably being asked to first find the slope of the graph, and use this to find the relevant information.

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Exam Technique - Section B

The most popular questions and also those which usually yield the highest marks: Question 5: do 8 from 10 Question 12: do 2 from 4 Question 10: Particle physics This leaves 2 more questions to be answered from 5

Question 5: 10 parts – do 8Attempt all parts – it’s not unusual to find that you did much better than expected in one part and much worse than expected in another, therefore it makes sense to have a reserve question, even if you think it’s of poor quality (once it doesn’t take a disproportionate amount of time).If you are looking for an A grade make sure you know all the relevant formulae and definitions before you tackle this question.

Question 10 (a): Particle Physics There will almost certainly be a question on Particle Physics (although there’s no rule which says there has to be one, and it doesn’t have to be Question 10 either). If it does come up it will appear together with the ‘Applied Electricity’ option [Question 10 (b)], but you can ignore this unless you have prepared for it by yourself.

Experiment Question in Section BOne of the questions in this section may require a description of an experiment although no detailed graph will be required.In describing the experiment ensure to include the following: A labelled diagram of the experimental set-up, including all essential apparatus. The first step in the procedures

should then be “we set up the apparatus as shown in the diagram”. A description of how to obtain values for both sets of variables A description of what needs to be adjusted to give a new set of data Reference to a relevant formula, graph etc

Comprehension QuestionThere will probably be one question which is very general in nature.This may seem easy but because it is non-mathematical in nature it can be hard to pick up top marks. Because it’s like a comprehension question it’s not always clear what information the question is looking for. In my opinion this question suits students looking for a D or C grade as there is not a whole lot of physics knowledge required to pick up 50/60%, but the questions can often be too vague to enable a student picking up full marks.

The RestThe format for the remaining questions generally require some or all of the following: Definition(s) Derivation of a formula Applications of a given concept Mathematical problem

It is important to note that for a given question some or all of the bullet points above can be asked. The definition at the beginning usually sets the scene for the question. Knowing this can help you to approach the mathematical part with greater confidence.

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Points to watch out for / Common Mistakes

Many questions require a specific phrase; avoid the temptation of putting things in your own words if a standard phrase exists. You check for this when revising by constantly cross-referencing your answers to past papers with their associated marking scheme. In particular ensure that your answer reads like a proper English sentence; if not then you won’t get full marks, despite having the relevant correct phrase embedded in it.

Think logically: Does your answer look right? e.g. a current of 1,000 Amps is not reasonable, nor is a focal length of 1,000 metres! If converting from kilometres to metres should your number get bigger or smaller. Why?

It is noticeable that many students often miss out on an A1 due to mis-reading a question or (more commonly) not noticing a question or definition. This isn’t helped by the exams commission refusing to number each sub-question. But there’s nothing you can do about that now. Just make sure that you read, re-read and then read again each question before and after you have attempted it.

Giving an example of something (e.g. for resonance) is not the same as giving an application of it. An expression is not the same as an equation, which in turn is not the same as a statement. When giving definitions, watch out for short phrases at the end such as "at constant temperature", or "if no

external forces act". Quite often the main part of the definition can be very long but still only merit the same amount of marks (three) as the bit that gets tagged on at the end. This is particularly important if you are giving a formula as an answer to a definition; the temptation is to think that it can all be represented mathematically.

When giving a formula as an answer to a definition, remember to explain all symbols. Similarly if are asked for a definition and you're unsure how something should be phrased, write it both ways -

you should only get marked on the best one. You may see the first part of a question as difficult and straight away write off the question - not a good idea. If you're unsure how much to write for a given question, look at the marking scheme. Definition of units – know how to express them in terms of their associated formulae, e.g. to define the Newton

refer to the F = ma equation). Ensure that you know how to use your calculator - don’t buy one on the day (or even the week) beforehand. And

make sure you can switch back from radians to degrees in case someone has accidentally put it on radians to begin with (or even worse – grads; who uses those things and why are they available on school calculators?).

Ask for Maths tables and be familiar with what information is available, particularly on pages 9 and 40. When giving a formula as an answer to a definition, remember to explain all symbols. Remember to include the relevant unit at the end of a maths question – you may not lose many marks but it is

unforgivable because you almost definitely know what the unit is. It’s also unforgivable because if you were in my class you will have spent two years losing half marks every time you left out in one of my tests and omitting it now would only serve to illustrate that you have learnt nothing in my class. In my opinion you should be heavily punished for this in the exam itself. After all if the required answer is two cm and you leave your answer as two it merely begs the question; is it two cm, two miles or two bananas?

Question: Name two devices that contain capacitors.‘Radios and cameras’ is probably too general to be accepted as an answer.A safer answer would be ‘rectifiers’ (used to convert a.c. to d.c.) or ‘in flashguns in cameras’.

Question: What is meant by the capacitance of a capacitor?The answer requires a definition of capacitance, not some vague, waffly, hand-wavy essay (so why don’t they just ask you to define capacitance? I don’t know).

Use the syllabus extracts in my chapter notes to double to check that you (and I) have everything covered.

Breakdown of Time Section A: Total time one hour. Five minutes to read over and pick your three questions, then 18 minutes for each question. Section B: 90 minutes for 5 questions. Five minutes to read over and pick your five questions, then 15 minutes each, 10 minutes at the end to read over your paper.

Obviously you’re not going to stick religiously to this time-scheme, but it is useful to at least have it in mind and perhaps write it down as soon as you start. It can also be useful to regard picking questions / looking over questions as a sort of ‘break’ from the main job of answering questions, so ration it out appropriately.

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Section A – Mandatory Experiments

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Section A: Theory questions

Most of the questions in Section A are repetitive and very straightforward once you have prepared properly.They include some or all of the following:

(i) Draw a fully labelled diagram which includes all essential apparatus (have you included the apparatus necessary to obtain values for both variables?)

(ii) State how the two sets of values were obtained.(iii) Describe what needs to be adjusted to give a new set of data(iv)Write down the relevant equation if there is one associated with the experiment(v) Be able to state how the data in the table will need to be adjusted.(vi)Be able to list three sources of error/precautions

If the experiment involves a graph:(vii) Know how the data provided will need to be adjusted(viii) Know what goes on each axis(ix)Know how to use the slope of the graph to obtain the desired answer

Usually these standard questions will then be followed by one or two tricky questions which are looking to test for a deeper understanding of what’s going on.

I have highlighted the most common of these below.

Note that some questions are common to many experiments and so the answers should be learned off like a mantra. Some examples:

Why is it important to keep (variable X) constant throughout the experiment?Answer:You can only investigate the relationship between two variables at any one time and variable X would be a third variable.

Why should room temperature be approximately half-way between initial and final temperature (for Heat experiments)?Answer:So that the heat lost to the environment when the system is above room temperature will cancel out the heat taken in from the environment when the system is below room temperature.

What is the advantage in keeping the length/time/mass as large as possible?Answer:A larger length/time/mass would result in a smaller percentage error.

All of the following are taken from past papers.Make sure when answering these that you check your answer against the appropriate marking scheme; knowing the answer in your head and writing it down in such a way that you get full marks in an exam are two very, very different things.

I was going to help you in this regard by including the appropriate answer, but I think the process of digging out the answer from your notes or marking schemes would actually result in you being more likely to remember it.

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Measurement of the focal length of a concave mirror(i) How was an approximate value for the focal length found?(ii) What was the advantage of finding the approximate value for the focal length?

Verification of Snell’s law of refraction / to measure the refractive index of a glass block(i) Why would smaller values lead to a less accurate result?

Measurement of the focal length of a convex lens(i) Why is it difficult to measure the image distance accurately?(ii) Give two precautions that should be taken when measuring the image distance.(iii) What difficulty would arise if the student placed the object 10 cm from the lens?

Measurement of acceleration due to gravity (g) using the freefall method(i) Indicate the distance s on your diagram.(ii) Describe how the time interval t was measured. (iii) Give two ways of minimising the effect of air resistance in the experiment. To show that acceleration is proportional to the force which caused it(i) How was the effect of friction reduced in the experiment?(i) Using your graph, find the mass of the body.(ii) On a trial run of this experiment, a student found that the graph did not go through the origin.

Suggest a reason for this.(iii) Describe how the apparatus should be adjusted, so that the graph would go through the origin. To verify the principle of conservation of momentum(i) How could the accuracy of the experiment be improved?(ii) How did the student know that body A was moving at constant velocity?(iii) How were the effects of friction and gravity minimised in the experiment? Verification of Boyle’s law(i) Why should there be a delay between adjusting the pressure of the gas and recording its value? (ii) Describe how the student ensured that the temperature of the gas was kept constant. Investigation of the laws of equilibrium for a set of co-planar forces(i) Describe how the centre of gravity of the metre stick was found. (ii) How did the student know that the metre stick was in equilibrium? (iii) Why was it important to have the spring balances hanging vertically?

Investigation of the relationship between periodic time and length for a simple pendulum and hence calculation of g(i) Give two factors that affect the accuracy of the measurement of the periodic time.(ii) Why did the student measure the time for 30 oscillations instead of measuring the time for one? (iii) How did the student ensure that the length of the pendulum remained constant when the pendulum

was swinging? (iv)Explain why a small heavy bob was used.(v) Explain why the string was inextensible.(vi)Describe how the pendulum was set up so that it swung freely about a fixed point.

Measurement of the specific heat capacity of water(i) Explain why adding a larger mass of copper would improve the accuracy of the experiment.

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Measurement of the specific latent heat of fusion of ice(i) Why was melting ice used? (ii) Why was dried ice used? (iii) Explain why warm water was used. (iv)What should be the approximate room temperature to minimise experimental error? (v) What was the advantage of having the room temperature approximately halfway between the initial

temperature of the water and the final temperature of the water?

Measurement of the specific latent heat of vaporisation of water(i) How was the water cooled below room temperature?(ii) How was the steam dried?(iii) Why was dry steam used? (iv)Why was a sensitive thermometer used?(v) A thermometer with a low heat capacity was used to ensure accuracy. Explain why.

To measure the speed of sound in air(i) How was it known that the air column was vibrating at its first harmonic?

Investigation of the variation of fundamental frequency of a stretched string with length(i) How did the student know that the string was vibrating at its fundamental frequency?

Investigation of the variation of fundamental frequency of a stretched string with tension(i) Why was it necessary to keep the length constant? (ii) How did the student know that the string was vibrating at its fundamental frequency? (iii) How did the student know that resonance occurred? (iv)Use your graph to calculate the mass per unit length of the string. Measurement of the wavelength of monochromatic light(i) What effect would each of the following changes have on the bright images formed: using a monochromatic light source of longer wavelength using a diffraction grating having 200 lines per mm using a source of white light instead of monochromatic light?(ii) Calculate the maximum number of images that are formed on the screen. (iii) The laser is replaced with a source of white light and a series of spectra are formed on the screen.

Explain how the diffraction grating produces a spectrum.(iv)Explain why a spectrum is not formed at the central (zero order) image. (v) The values for the angles on the left of the central image are smaller than the corresponding ones on the

right. Suggest a possible reason for this.

To measure the resistivity of the material of a wire(i) Why did the student measure the diameter of the wire at different places?(ii) The experiment was repeated on a warmer day. What effect did this have on the measurements?(iii) Give two precautions that should be taken when measuring the length of the wire.

To investigate the variation of the resistance of a thermistor with temperature(i) Use your graph to estimate the average variation of resistance per Kelvin in the range 45 °C – 55 °C.(ii) In this investigation, why is the thermistor usually immersed in oil rather than in water? To investigate the variation of current with potential difference for copper electrodes in a copper-sulphate solution (i) What was observed at the electrodes as current flowed through the electrolyte?(ii) Draw a sketch of the graph that would be obtained if inactive electrodes were used in this experiment.

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To investigate the variation of current with potential difference for a semiconductor diode(i) What is the function of the 330 Ω resistor in this circuit? (ii) The student continued the experiment with the connections to the semiconductor diode reversed.

What adjustments should be made to the circuit to obtain valid readings?(iii) Draw a sketch of the graph obtained for the diode in reverse bias.

To verify joule’s law(i) Why was a fixed mass of water used throughout the experiment?(ii) Given that the mass of water in the calorimeter was 90 g in each case, and assuming that all of the

electrical energy supplied was absorbed by the water, use the graph to determine the resistance of the heating coil. The specific heat capacity of water is 4200 J kg–1 K–1.

(iii) Explain why the current was allowed to flow for a fixed length of time in each case.

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Mandatory Experiments – Exam Questions and Solutions

This booklet contains every Section A exam question which has appeared on a Leaving Cert paper between 1992 and 2009, at both higher and ordinary level.

For each experiment check that you can do can do each of the following:(x)Draw a fully labelled diagram which includes all essential apparatus (have you included

the apparatus necessary to obtain values for both variables?).(xi) Be able to state how the two sets of values were obtained (this is a very common

question).(xii) Describe what needs to be adjusted to give a new set of data(xiii) Write down the relevant equation if there is one associated with the experiment.(xiv) Be able to state how the data in the table will need to be adjusted. (xv) Know what goes on each axis if there is a graph.(xvi) Know how to use the slope of the graph to obtain the desired answer.(xvii) Be able to list three sources of error/precautions.

Note that there is a more detailed guide to answering Section A questions in the Exam Technique document (all documents can be found in the revision page of www.thephysicsteacher.ie

Note that the only experiment which has yet to appear is: To investigate the variation of current (I) with p.d. (V) for a metallic conductor.

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Table of contents

ExperimentMeasurement of the Focal Length of a Concave Mirror

Snell’s Law of Refraction

Measurement of the Focal Length of a Convex Lens

Measurement of Acceleration

Measurement of Acceleration due To Gravity (g) Using the Freefall Method

To Show That Acceleration is Proportional To the Force which caused it

To Verify the Principle of Conservation Of Momentum

Verification of Boyle’s Law

Investigation of the Laws of Equilibrium for a set of Co-Planar Forces

Investigation of the Relationship between Periodic Time and Length for a Simple Pendulum and hence Calculation of g.To Calibrate a Thermometer using the Laboratory Mercury Thermometer as a Standard

Measurement of the Specific Heat Capacity of Water

Measurement of the Specific Latent Heat of Fusion of Ice

Measurement of the Specific Latent Heat of Vaporisation of Water

To Measure the Speed of Sound in Air

Investigation of the Variation of Fundamental Frequency of a Stretched String with LengthInvestigation of the Variation of Fundamental Frequency of a Stretched String with TensionMeasurement of the Wavelength of Monochromatic Light

To Measure the Resistivity of the Material of a Wire

To Investigate the Variation of Current (I) With P.D. (V) for a Filament Bulb

To Investigate the Variation of the Resistance of a Metallic Conductor with Temperature

To Investigate the Variation of Current (I) With P.D. (V) for Copper Electrodes in a Copper-Sulphate SolutionTo Verify Joule’s Law

To Investigate the Variation of the Resistance of a Thermistor with Temperature

To Investigate the Variation of Current (I) with P.D. (V) for a Semiconductor Diode

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MEASUREMENT OF THE FOCAL LENGTH OF A CONCAVE MIRROR

1. [2002 OL][2010 OL]A student carried out an experiment to measure the focal length of a concave mirror. The student placed an object at different positions in front of the mirror so that a real image was formed in each case. The table shows the measurements recorded by the student for the object distance u and the image distance v.

u/cm 20 30 40 50v/cm 64 43 41 35

(i) Draw a labelled diagram showing how the apparatus was arranged. (ii) Describe how the student found the position of the image. (iii) Show on your diagram the object distance u and the image distance v.

(iv)Using the formula or otherwise and the above data, find an average value for the focal length f of the mirror.

2. [2007]In an experiment to measure the focal length of a concave mirror, an approximate value for the focal length was found. The image distance v was then found for a range of values of the object distance u. The following data was recorded.

(i) How was an approximate value for the focal length found?

(ii) What was the advantage of finding the approximate value for the focal length? (iii) Describe, with the aid of a labelled diagram, how the position of the image was found. (iv)Calculate the focal length of the concave mirror by drawing a suitable graph based on the recorded data.

Solutions1.(i) See diagram(ii) The position of the screen was adjusted until the image of the

cross-wires came into focus.(iii) See diagram.(iv)1/f: 0.066, 0.057, 0.049, 0.049 f: 15.2, 17.67, 20.2, 20.6 average value for f = 18.4 cm.2.(i) An image of a distant object was focused on a screen.Measure the distance from the screen to the mirror.(ii) To avoid placing object inside f during the experiment) which

would have meant that the image couldn’t be formed on the screen.

(iii) Apparatus: object, concave mirror, screenAdjust the position of the the screen until a clear image of the crosswire is obtained. (iv)The question shouldn’t have specified the drawing of a graph as it

wasn’t specified on the syllabus. As a result marking scheme was adjusted and you could get 15 marks out of 18 by using the normal approach.

Focal length = 12.0 cm

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u/cm 15.0 20.0 25.0 30.0 35.0 40.0v/cm 60.5 30.0 23.0 20.5 18.0 16.5

u/cm 15.0 20.0 25.0 30.0 35.0 40.0v/cm 60.5 30.0 23.0 20.5 18.0 16.51/u 1/v

VERIFICATION OF SNELL’S LAW OF REFRACTIONOr

TO MEASURE THE REFRACTIVE INDEX OF A GLASS BLOCK

1. [2008 OL]An experiment was carried out to measure the refractive index of a substance.The experiment was repeated a number of times.(i) Draw a labelled diagram of the apparatus that could be used in this experiment. (ii) What measurements were taken during the experiment? (iii) How was the refractive index of the substance calculated? (iv)Why was the experiment repeated?

2. [2006 OL]A student carried out an experiment to verify Snell’s law of refraction by measuring the angle of incidence i and the angle of refraction r for a ray of light entering a glass block. The student repeated this procedure two more times. The data recorded by the student is shown in the table.(i) Draw a labelled diagram of the apparatus used

in the experiment. (ii) Describe how the student found the position of

the refracted ray. (iii) How did the student measure the angle of

refraction? (iv)Copy this table and complete it in your answer-book. (v) Use the data to verify Snell’s law of refraction.

3. [2010]In an experiment to verify Snell’s law, a student recorded the following data.

(ii) Draw a labelled diagram of the apparatus used. On your diagram, indicate an angle i and its corresponding angle r.

(iii) Using the recorded data, draw a suitable graph (iv)Explain how your graph verifies Snell’s law.(v) Using your graph, find the refractive index(vi)The student did not record any values of i below 30°, give two reasons why?

4. [2005]In an experiment to verify Snell’s law, a student measured the angle of incidence i and the angle of refraction r for a ray of light entering a substance. This was repeated for different values of the angle of incidence. The following data was recorded.

i/degrees 20 30 40 50 60 70r/degrees 14 19 26 30 36 40

(i) Describe, with the aid of a diagram, how the student obtained the angle of refraction. (ii) Draw a suitable graph on graph paper and explain how your graph verifies Snell’s law. (iii) From your graph, calculate the refractive index of the substance. (iv)The smallest angle of incidence chosen was 200. Why would smaller values lead to a less accurate result?

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angle of incidence i

angle of refraction

r

sin i sin i sin i/sin r

30o 19o

45o 28o

65o 37o

i / ° 30 40 50 55 60 65 70r / ° 19 26 30 33 36 38 40

SolutionsFor each of these diagrams you should include the ray box, the incident ray (from ray box), the normal and refracted rayAlso label the angles i and r

1.(i) As in diagram, plus a ray box and protractor.(ii) The angle of incidence and the angle of refraction.(iii) By using the formula n = sin i ÷ sin r.(iv)To increase the accuracy of the results.

2.(i) See diagram. Also include a protractor and raybox.(ii) Draw the incident ray going in, the emergent ray coming out, then remove the block

and join the two lines. This represents the refracted ray.(iii) By measuring the angle between the normal and the refracted ray using a

protractor.(iv)

(v) In each case sin i/sin r is (approximately) constant; therefore this verifies Snell’s Law.

3.(i) See diagram (see also the note at the top of the page).(ii) Correct sin i and sin r values for six points

Label axes correctly on graph paper Plot six points correctly Straight line showing good distribution

(iii) A straight line through the origin shows that sin i is proportional to sin r (iv)Correct slope method

(n = ) 1.41 [range: 1.38 – 1.52](v) To reduce the (percentage) error

Elaboration e.g. difficult to measure /read angles, r < i , etc.

4.(i) See diagram, plus ray-box.Mark the position of the incident and exit rays and also the outline of the block.Remove the block then measure the angle between the refracted ray and the normal using a protractor.

(ii)sin i 0.34 0.50 0.64 0.77 0.87 0.94sin r 0.24 0.33 0.44 0.50 0.59 0.64

(iii) Refractive index = slope = y2 – y1 / x2 – x1 n = 1.49 (iv)There would be a greater percentage error associated with

measuring smaller angles.

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angle of incidence i

angle of refraction r sin i sin i sin i/sin r

30o 19o 0.500 0.326 1.5345o 28o 0.707 0.469 1.5165o 37o 0.906 0.602 1.50

sin i 0.500 0.643 0.766 0.819 0.866 0.906 0.939sin r 0.325 0.438 0.500 0.544 0.588 0.615 0.643

MEASUREMENT OF THE FOCAL LENGTH OF A CONVEX LENS

1. [2005 OL]You carried out an experiment to measure the focal length of a converging lens.(i) Draw a labelled diagram of the apparatus that you used in the experiment. (ii) Describe how you found the position of the image formed by the lens.(iii) What measurements did you take?(iv)How did you get a value for the focal length of the converging lens from your measurements?(v) Give one precaution that you took to get an accurate result.

2. [2009]A student was asked to measure the focal length of a converging lens. The student measured the image distance v for each of three different object distances u. The student recorded the following data.

u/cm 20.0 30.0 40.0v/cm 65.2 33.3 25.1

(i) Describe how the image distance was measured.(ii) Give two precautions that should be taken when measuring the image distance.(iii) Use all of the data to calculate the focal length of the converging lens. (iv)What difficulty would arise if the student placed the object 10 cm from the lens?

3. [2003]The following is part of a student’s report of an experiment to measure the focal length of a converging lens.“I found the approximate focal length of the lens to be 15 cm. I then placed an object at different positions in front of the lens so that a real image was formed in each case.”The table shows the measurements recorded by the student for the object distance u and the image distance v.

u/cm 20.0 25.0 35.0 45.0v/cm 66.4 40.6 27.6 23.2

(i) How did the student find an approximate value for the focal length of the lens? (ii) Describe, with the aid of a labelled diagram, how the student found the position of the image. (iii) Using the data in the table, find an average value for the focal length of the lens. (iv)Give two sources of error in measuring the image distance and state how one of these errors can be

reduced.

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Solutions1.(i) See diagram. Include a metre-stick.(ii) We kept the ray-box and the lens fixed and moved the screen until there was a clear image formed on the

screen.(iii) We measured the distance from object (cross-wires) to the lens (u) and the distance from the lens to

the screen (v).

(iv)By substituting the values for u and v into the formula .(v) Ensure that the crosshairs are in focus, repeat and find the average, avoid error of parallax.

2.(i) Object, (converging) lens, screen /search pin Sharp image (state/imply) // no parallax (between image and search pin)Measure (distance) from image/screen to (centre of) lens(ii) Measure from the centre of the lens (to the screen) / measure

perpendicular distance /avoid parallax error (iii) 1/u + 1/v = 1/fCorrect substitution f = 15.3 cm, 15.8 cm, 15.4 cm fave = (15.5 ± 0.4) cm(iv)Object would be inside the focal point so an image cannot be formed on a screen Alternative (graphical method):Inverse values for u and for vPlot points Read intercept(s)f = (15.87 ± 0.40) cm

3.(i) Focus the image of a distant object on a screen.The distance from the lens to screen corresponds to the focal length.(ii) Set up as shown.Adjust the position of the screen until a sharp image is seen.(iii) 1/u+ 1/v = 1/fAverage = 15.4 cm

(iv)Image not sharp / parallax error in reading distance / not measuring to centre of lens / zero error in metre stick.

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1/u 0.050 0.033 0.0251/v 0.0153 0.0300 0.0398

u/cm 20.0 25.0 35.0 45.0v/cm 66.4 40.6 27.6 23.2f/cm 15.4 15.5 15.4 15.3

MEASUREMENT OF ACCELERATION1. [2004 OL]Describe an experiment to measure the velocity of a moving object.

2. [2008 OL]A student carried out an experiment to find the acceleration of a moving trolley.The student measured the velocity of the trolley at different times and plotted a graph which was then used to find its acceleration. The table shows the data recorded.

(i) Describe, with the aid of a diagram, how the student measured the velocity of the trolley. (ii) Using the data in the table, draw a graph on graph paper of the trolley’s velocity against time. Put time

on the horizontal axis (X-axis). (iii) Find the slope of your graph and hence determine the acceleration of the trolley.

Solutions

1. We set up as shown, turned on the ticker tape timer and released the trolley. We measured the distance between 11 dots on the tape. The time taken to cover that distance corresponded to the time

for 10 intervals, where each interval was 1/50th of a second. We calculated velocity using the formula velocity =

distance/time.

2.(i)

He measured the distance between 11 dots on the tape. The time taken to cover that distance corresponded to the time for 10 intervals, where each interval

was 1/50th of a second. He calculated velocity using the

formula velocity = distance/time. (ii) See graph

(iii) The acceleration corresponds to the slope of the velocity-time graph.Take any two points e.g. (0, 0.9) and (10, 4.9) and use the formula: slope = y2 – y1 / x2 – x1

Slope = acceleration = 0.4 m s-2

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Velocity/ m s-1 0.9 1.7 2.5 3.3 4.1 4.9Time/s 0 2 4 6 8 10

MEASUREMENT OF ACCELERATION DUE TO GRAVITY (g) USING THE FREEFALL METHOD

1. [2002 OL]You have carried out an experiment to measure g, the acceleration due to gravity.

(i) Draw a labelled diagram of the apparatus you used. (ii) Describe the procedure involved in measuring the time in this experiment.(iii) As well as measuring time, what other measurement did you take? (iv) Outline how you got a value for g from your measurements. (v) Name one precaution you took to get an accurate result.

2. [2009 OL]You carried out an experiment to measure g, the acceleration due to gravity.(i) Draw a labelled diagram of the apparatus you used. (ii) State what measurements you took during the experiment. (iii) Describe how you took one of these measurements. (iv)How did you calculate the value of g from your measurements? (v) Give one precaution that you took to get an accurate result.

3. [2009]In an experiment to measure the acceleration due to gravity, the time t for an object to fall from rest through a distance s was measured. The procedure was repeated for a series of values of the distance s. The table shows the recorded data.

(i) Draw a labelled diagram of the apparatus used in the experiment.(ii) Indicate the distance s on your diagram.(iii) Describe how the time interval t was measured. (iv) Calculate a value for the acceleration due to gravity by drawing a suitable graph based on the

recorded data. (v) Give two ways of minimising the effect of air resistance in the experiment.

4. [2004]In an experiment to measure the acceleration due to gravity g by a free fall method, a student measured the time t for an object to fall from rest through a distance s. This procedure was repeated for a series of values of the distance s.The table shows the data recorded by the student.

s/cm 30 40 50 60 70 80 90t/ms 244 291 325 342 371 409 420

(iv)Describe, with the aid of a diagram, how the student obtained the data. (v) Calculate a value for g by drawing a suitable graph. (vi)Give two precautions that should be taken to ensure a more accurate result.

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s/ cm 30 50 70 90 110 130 150t/ms 247 310 377 435 473 514 540

Solutions1. See diagram

(i) When we flicked the switched it turned on the timer and this remained on until the ball fell through the trap-door at the bottom. The time was then read from the timer.

(ii) The distance travelled by the ball.(iii) s = ut + ½ (g) t2 g = 2s/t2

(iv)For a given length repeat and use the smallest time value recorded for t.

2.(i) See diagram(ii) Distance s as shown on the diagram, time for the object to fall.(iii) Measure length from the bottom of the ball to the top of the trapdoor

as shown using a metre stick.The time is measured using the timer which switches on when the ball is released and stops when the ball hits the trap-door. (iv)Plot a graph of s against t2; the slope of the graph corresponds to g/2.Alternatively substitute (for t and s) into the equation s = (g/2) t2

(v) Use the smallest time value recorded for t, repeat the experiment a number of times

3.(i) Timer, ball, release mechanism, trap door(ii) (Perpendicular) distance indicated between bottom of ball and top of trap

door.(iii) Timer starts when ball leaves release mechanismTimer stops when ball hits trap door.(iv)

Axes correctly labelled points correctly plotted Straight line with a

good distribution Correct slope

method Slope = 5.02 // 0.198 g = (10.04 ± 0.20) m s–2

(v) Small (object)/ smooth(object)/ no draughts/ in vacuum/ distances relatively short / heavy (object) / dense / spherical/ aerodynamic .

4. [2004](i) The clock starts as sphere is released and stops when the sphere hits the trapdoor.S is the distance from solenoid to trap-door.Record distance s and the time t

(ii)Calculation of t2(at least five correct values) Axes s and t2 labelled At least five points correctly plotted

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s/ cm 30 50 70 90 110 130 150t/ms 247 310 377 435 473 514 540t 2 / s2 0.0610 0.0961 0.1421 0.1892 0.2237 0.2642 0.2916

s/cm 30 40 50 60 70 80 90t/ms 244 291 325 342 371 409 420t2 /s2

0.060 0.085 0.106 0.117 0.138 0.167 0.176

Straight line with good fit Method for slopeCorrect substitution g = 10.0 ± 0.2 m s−2

(iii) Measure from bottom of sphere; avoid parallax error; for each value of s take several values for t / min t reference;); adjust ‘sensitivity’ of trap door; adjust ‘sensitivity’ of electromagnet (using paper between sphere and core); use large values for s (to reduce % error); use millisecond timer

TO SHOW THAT ACCELERATION IS PROPORTIONAL TO THE FORCE WHICH CAUSED IT

1. [2003 OL]A student carried out an experiment to investigate the relationship between the force applied to a body and the acceleration of the body. The table shows the measurements recorded by the student.

Force /N 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Acceleration /cm s–2

8.4 17.6 25.4 35.0 43.9 51.5 60.4 70.0

(ii) Draw a labelled diagram of the apparatus used in the experiment.(iii) How was the effect of friction reduced in the experiment?(iv)Describe how the student measured the applied force.(v) Plot a graph, on graph paper, of the acceleration against the applied force. (vi)What does your graph tell you about the relationship between the acceleration of the body and the force

applied to it?

2. [2005 OL]In an experiment to investigate the relationship between force and acceleration a student applied a force to a body and measured the resulting acceleration. The table shows the measurements recorded by the student.

Force /N 0.1 0.2 0.3 0.4 0.5 0.6 0.7acceleration /m s–2

0.10 0.22 0.32 0.44 0.55 0.65 0.76

(i) Draw a labelled diagram of the apparatus used in the experiment.(ii) Outline how the student measured the applied force. (iii) Plot a graph, on graph paper of the acceleration against the applied force. Put acceleration on the

horizontal axis (X-axis). (iv)Calculate the slope of your graph and hence determine the mass of the body.(v) Give one precaution that the student took during the experiment.

3. [2010 OL]You carried out an experiment to investigate the relationship between the acceleration of a body and the force applied to it. You did this by applying a force to a body and measuring the resulting acceleration. The table shows the data recorded during the experiment.

(iv) Draw a labelled diagram of the apparatus you used

(v) How did you measure the applied force?(vi)How did you minimise the effect of friction during the experiment? (vii) Plot a graph on graph paper of the body’s acceleration against the force applied to it(viii) What does your graph tell you about the relationship between the acceleration of the body and the

force applied to it?

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Force / N 0.20 0.25 0.30 0.35 0.40 0.45 0.50acceleration / m s−2

0.4 0.5 0.6 0.7 0.8 0.9 1.0

4. [2010]In an experiment to investigate the relationship between the acceleration of a body and the force applied to it, a student recorded the following data.

(i) Describe the steps involved in measuring the acceleration of the body.(ii) Using the recorded data, plot a graph to show the relationship between the acceleration of the body and

the force (iii) What does your graph tell you about this relationship?(iv)Using your graph, find the mass of the body.(v) On a trial run of this experiment, a student found that the graph did not go through the origin.

Suggest a reason for this.(vi)Describe how the apparatus should be adjusted, so that the graph would go through the origin.

Solutions1.(i) See diagram in next question.(ii) Tilt the runway slightly, oil the track.(iii) By weighing the masses and hanger on an electronic

balance.(iv)See graph(v) Acceleration is directly proportional to the applied force.

2.(i) See diagram.(ii) The applied force corresponds to the weight of the hanger plus

weights; the value of the weights is written on the weights themselves.

(iii) See graph (below the diagram).

(iv)

Substituting in two values (from the graph, not the table) should give a slope of approximately 0.9.This means that the mass = 0.9 kg.(v) Oil the trolley wheels, dust the runway, oil the pulley.

3.(i) See diagram above(ii) Weighed the mass (and pan) / mg // from the (digital Newton)

balance (iii) Slant/clean the runway // oil (the trolley) wheels /

frictionless wheels (iv)See graph (v) They are proportional.

4.

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F/N 0.20 0.40 0.60 0.80 1.00 1.20 1.40a/m s–2 0.08 0.18 0.28 0.31 0.45 0.51 0.60

(i) Measure/calculate the initial velocity/speed Measure/calculate the velocity/speed again (t seconds later) Measure time interval from initial to final velocities / distance between light gates Use relevant formula Datalogging method:Align motion sensor with body (e.g. trolley) / diagram Select START and release body(Select STOP and) display GRAPH of ‘a vs. t’ // ‘v vs. t’(Use tool bar to) find average value for a // use slope (tool) to find a (= dv /dt)

(ii) Label axes correctly on graph paper Plot six points correctly Straight line Good distribution

(iii) Acceleration is proportional to the applied force.(iv)The mass of the body corresponds to the slope of the graph = 2.32 kg [range: 2.1 - 2.4 kg](v) Friction / dust on the track slowing down the trolley.(vi)Elevate/adjust the track/slope

TO VERIFY THE PRINCIPLE OF CONSERVATION OF MOMENTUM

1. [2006 OL]In a report of an experiment to verify the principle of conservation of momentum, a student wrote the following:I assembled the apparatus needed for the experiment. During the experiment I recorded the mass of the trolleys and I took measurements to calculate their velocities. I then used this data to verify the principle of conservation of momentum.(i) Draw a labelled diagram of the apparatus used in the experiment. (ii) How did the student measure the mass of the trolleys? (iii) Explain how the student calculated the velocity of the trolleys.(iv)How did the student determine the momentum of the trolleys? (v) How did the student verify the principle of conservation of momentum?

2. [2005]In an experiment to verify the principle of conservation of momentum, a body A was set in motion with a constant velocity. It was then allowed to collide with a second body B, which was initially at rest and the bodies moved off together at constant velocity.The following data was recorded.

Mass of body A = 520.1 gMass of body B = 490.0 gDistance travelled by A for 0.2 s before the collision = 10.1 cmDistance travelled by A and B together for 0.2 s after the collision = 5.1 cm

(vii) Draw a diagram of the apparatus used in the experiment. (viii) Describe how the time interval of 0.2 s was measured. (ix)Using the data calculate the velocity of the body A before and after the collision.(x) Show how the experiment verifies the principle of conservation of momentum. (xi)How were the effects of friction and gravity minimised in the experiment?

Solutions1.(i) See diagram(ii) By using an electronic balance.

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(iii) By taking a section of the tape and using the formula velocity = distance/time. We measured the distance between 11 dots and the time was the time for 10 intervals, where each interval was 1 50th of a second.

(iv)Using the formula momentum = mass × velocity.(v) By calculating the total momentum before and afterwards and showing that the total momentum before =

total momentum after.

2.(i) See diagram(ii) It corresponded to 10 intervals on the ticker-tape.(iii) Velocity before: v = s/t = 0.101/0.2 v = 0.505 m s-1 ≈ 0.51 m s-1

Velocity after: v = 0.051/0.2v = 0.255 m s-1 ≈ 0.26 m s-1

(iv)Momentum before:p = mv = (0.5201)(0.505) = 0.263 ≈ 0.26 kg m s-1

Momentum after:p = mv = (0.5201 + 0.4900)(0.255)p = 0.258 ≈ 0.26 kg m s-1

Momentum before ≈ momentum after (v) Friction: sloped runway // oil wheels or clean track Gravity: horizontal track // frictional force equal and // tilt track so that trolley moves with constant velocity

VERIFICATION OF BOYLE’S LAW1. [2004 OL]In an experiment to verify Boyle’s law, a student measured the volume of a gas at different pressures. The table shows the measurements recorded by the student.

(i) Draw a labelled diagram of the apparatus used in this experiment.(ii) Copy this table and fill in the last row by calculating 1/ volume for each measurement. (iii) Plot a graph on graph paper of pressure against 1/volume.(iv)Explain how your graph verifies Boyle’s law.(v) Give one precaution that the student took in carrying out the experiment.

2. [2003]In an experiment to verify Boyle’s law, a student measured the volume V of a gas at different values of the pressure p. The mass of the gas was not allowed to change and its temperature was kept constant.The table shows the data recorded by the student.

(i) Describe with the aid of a diagram how the student obtained this data. (ii) Draw a suitable graph on graph paper to show the relationship between the pressure of the gas and its

volume. (iii) Explain how your graph verifies Boyle’s law.(iv)Describe how the student ensured that the temperature of the gas was kept constant.

Solutions1.(i) See diagram.

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Pressure /kPa 100 111 125 143 167 200 250Volume /cm3 5.0 4.5 4.0 3.5 3.0 2.5 2.01/Volume /cm-3 0.25

p/ kPa 120 180 220 280 320 380 440V/cm3 9.0 6.0 5.0 4.0 3.5 3.0 2.5

(ii) See table

(iii)

See graph(iv)A straight line through the origin shows that pressure is proportional to 1/volume(v) After changing pressure wait a short time before taking readings / read the volume scale at eye level.

2.(i) See diagram.Note the pressure of the gas from the pressure-gauge and the volume from the graduated scale.Turn the screw to decrease the volume and increase the pressure. Note the new readings and repeat to get about seven readings.(ii)

p/ kPa 120 180 220 280 320 380 4401/V/cm-3 0.111 0.167 0.200 0.250 0.286 0.333 0.400

Axes labelled6 points plotted correctlyStraight lineGood fit(iii) A straight line through the origin verifies that pressure is inversely proportional to volume(iv)Release the gas pressure slowly, allow time between readings.

INVESTIGATION OF THE LAWS OF EQUILIBRIUM FOR A SET OF CO-PLANAR FORCES

1. [2007 OL]A student investigated the laws of equilibrium for a set of co-planar forces acting on a metre stick. The weight of the metre stick was 1.2 N and its centre of gravity was at the 50 cm mark.The student applied the forces shown to the metre stick until it was in equilibrium.(i) How did the student know the metre stick was in equilibrium? (ii) Copy the diagram and show all the forces acting on the metre stick. (iii) Find the total upward force acting on the metre stick.(iv)Find the total downward force acting on the metre stick.(v) Explain how these values verify one of the laws of equilibrium. (vi)Find the sum of the anticlockwise moments of the upward forces about the 0 mark.(vii) Find the sum of the clockwise moments of the downward forces about the 0 mark.(viii) Explain how these values verify the other law of equilibrium.

2. [2007]A student investigated the laws of equilibrium for a set of co-planar forces acting on a metre stick.The student found that the centre of gravity of the metre stick was at the 50.4 cm mark and its weight was 1.2 N.(i) How did the student find the centre of gravity?(ii) How did the student find the weight, of the metre stick?(iii) Why is the centre of gravity of the metre stick not at the 50.0 cm mark?

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Pressure /kPa 100 111 125 143 167 200 250Volume /cm3 5.0 4.5 4.0 3.5 3.0 2.5 2.01/Volume /cm-3 0.20 0.22 0.25 0.28 0.33 0.40 0.50

(iv)The student applied vertical forces to the metre stick and adjusted them until the metre stick was in equilibrium.

How did the student know that the metre stick was in equilibrium?

The student recorded the following data.

(v) Calculate the net force acting on the metre stick.(vi)Calculate the total clockwise moment about a vertical axis of the metre stick.(vii) Calculate the total anti-clockwise moment about a vertical axis of the metre stick.(viii) Use these results to verify the laws of equilibrium

3. [2002]A student investigated the laws of equilibrium for a set of co-planar forces acting on a metre stick. The weight of the metre stick was 1 N and its centre of gravity was found to be at the 50.5 cm mark. Two spring balances and a number of weights were attached to the metre stick. Their positions were adjusted until the metre stick was in horizontal equilibrium, as indicated in the diagram. The reading on the spring balance attached at the 20 cm mark was 2 N and the reading on the other spring balance was 4 N. The other end of each spring balance was attached to a fixed support.

(iv)Calculate the sum of the upward forces and the sum of the downward forces acting on the metre stick. (v) Explain how these experimental values verify one of the laws of equilibrium for a set of co-planar

forces. (vi)Calculate the sum of the clockise moments and the sum of the anticlockwise moments about an axis

through the 10 cm mark on the metre stick. (vii) Explain how these experimental values verify the second law of equilibrium for a set of co-planar

forces. (viii) Describe how the centre of gravity of the metre stick was found. (ix)Why was it important to have the spring balances hanging vertically?

Solutions1.(i) It was level / horizontal / no movement.(ii) As in the diagram, but there should also be the weight of the metre stick (1.2 N) shown at the 50 cm

mark.(iii) 20.2 N(iv)15 + 4 + 1.2 = 20.2 N(v) The sum of forces is zero / the upward forces = the downward forces(vi)Moment = F × d: (0.3 × 10) + (0.9 × 10.2) = 12.18 N m(vii) Moment = F × d: (0.27 × 4) + (0.5 × 1.2) + (0.7 × 15) = 12.18 N m(viii) The sum of the moments is zero (sum of clockwise moments = sum of anti-clockwise moments)

2.(i) By hanging the metre stick on a thread support and adjusting the position of the thread until the metre

stick remained horizontal.

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position on metre stick/cm 11.5 26.2 38.3 70.4 80.2magnitude of force/N 2.0 4.5 3.0 5.7 4.0direction of force down up down up down

(ii) By putting it on an electronic balance.(iii) The material is not of perfectly uniform density.(iv)The metre stick was at rest.(v) Fup = 4.5 + 5.7 = 10.2 N and Fdown = 2 + 3 +1.2 +4 = 10.2 N net force = 0 (vi)(through zero) Moment = 2(0.115) + 3(0.383) +1.2(0.504) +4.0(0.802) = 0.23+1.149+0.6048+3.208 =

5.2 N m (vii) (through zero) Moment = 4.5(0.262) +5.7(0.704) = 5.1918 N m = 5.2 N(viii) Fup = Fdown

Total clockwise moments = Total anti-clockwise moments

3.(i) Up = 2 +4 = 6 (N)Down = 2 +1 +1.8 + 1.2 = 6 (N)(ii) The vector sum of the forces in any direction is zero (forces up = forces down).(iii) Moment = force × distance Sum of anticlockwise moments = 2.8 N mSum of clockwise moments = 2.8 N m (iv)The sum of the moments about any point is zero.(v) Hang the metre stick on a string and adjust the position until the metre stick balances.Note the position.(vi)Moment of a force = force × perpendicular distance, so if the readings on the metre stick are to

correspond to these perpendicular distances then the metre stick must be perpendicular to the spring balances, and if the metre stick is horizontal then the spring balances should be vertical.

INVESTIGATION OF THE RELATIONSHIP BETWEEN PERIODIC TIME AND LENGTH FOR A SIMPLE PENDULUM AND HENCE CALCULATION OF g

Exam questions1. [2008]A student investigated the relationship between the period and the length of a simple pendulum. The student measured the length l of the pendulum. The pendulum was then allowed to swing through a small angle and the time t for 30 oscillations was measured. This procedure was repeated for different values of the length of the pendulum. The student recorded the following data:

l /cm 40.0 50.0 60.0 70.0 80.0 90.0 100.0 t /s 38.4 42.6 47.4 51.6 54.6 57.9 60.0

(i) Why did the student measure the time for 30 oscillations instead of measuring the time for one? (ii) How did the student ensure that the length of the pendulum remained constant when the pendulum was

swinging? (iii) Using the recorded data draw a suitable graph to show the relationship between the period and the

length of a simple pendulum. (iv)What is this relationship? (v) Use your graph to calculate the acceleration due to gravity.

2. [2006]In investigating the relationship between the period and the length of a simple pendulum, a pendulum was set up so that it could swing freely about a fixed point. The length l of the pendulum and the time t taken for 25 oscillations were recorded. This procedure was repeated for different values of the length.

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The table shows the recorded data.l/cm 40.0 50.0 60.0 70.0 80.0 90.0 100.0t/s 31.3 35.4 39.1 43.0 45.5 48.2 50.1

The pendulum used consisted of a small heavy bob attached to a length of inextensible string.(i) Explain why a small heavy bob was used.(ii) Explain why the string was inextensible.(iii) Describe how the pendulum was set up so that it swung freely about a fixed point.(iv)Give one other precaution taken when allowing the pendulum to swing.(v) Draw a suitable graph to investigate the relationship between the period of the simple pendulum and its

length. (vi)What is this relationship? (vii) Justify your answer.

Solutions1.(i) To reduce percentage error in measuring the periodic time.(ii) Use an inextensible string, string suspended at fixed point (e.g. split cork or two coins) (iii)

(iv)t2 is proportional to l (v) Slope = 0.25 (ms–2) [range: 0.24 – 0.25 m s–2] g = 9.72 m s–2 [range: 9.4 – 9.9 m s–2]

2.(i) To reduce air resistance and to keep the string taut

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l /cm 40.0 50.0 60.0 70.0 80.0 90.0 100.0 t /s 38.4 42.6 47.4 51.6 54.6 57.9 60.0 Time for 1 swing/ st2/ s2

l /m 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(ii) So that length remains constant because length would be another variable. (iii) The string was placed between two coins (or a split cork). (iv)Make sure that there are no draughts / make sure it oscillates in one plane only.(v) Draw a suitable graph

Values of t divided by 25 to get T Axes correctly labelled T2 vs. l At least six points plotted correctly Straight line drawn Good distribution (about straight line)

(vi)T2 is proportional to l (vii) The graph resulted in a straight line through the origin TO CALIBRATE A THERMOMETER USING THE LABORATORY MERCURY THERMOMETER AS A STANDARD

Exam question1. [2007 OL]A student carried out an experiment to obtain the calibration curve of a thermometer.The following is an extract from her report.I placed the thermometer I was calibrating in a beaker of water along with a mercury thermometer which I used as the standard. I recorded the value of the thermometric property of my thermometer and the temperature of the water as shown on the mercury thermometer. I repeated this procedure at different temperatures. The following is the table of results that I obtained.

(i) Draw a labelled diagram of the apparatus used in the experiment.(ii) Using the data in the table, draw a graph on graph paper of the value of the thermometric property

against its temperature. Put temperature on the horizontal axis (X-axis). (iii) Use your graph to estimate the temperature when the value of the thermometric property is 50.(iv)Give an example of a thermometric property. (v) How was the value of this thermometric property measured?

Solution

1. (i) See diagram(ii) See graph

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time for 25 swings /s 31.3 35.4 39.1 43.0 45.5 48.2 time for 1 swing/s 1.25 1.42 1.56 1.72 1.82 1.93 t2/s2 1.57 2.01 2.45 2.96 3.31 3.72 l/m .40 .50 .60 .70 .80 .90

Temperature/°C 0 20 40 60 80 100Value of thermometric property 4 12 24 40 64 150

(iii) 700 C {Accept 68 – 72 0C} (iv)Length of a column of liquid/ Resistance / emf / voltage / colour / volume / pressure, etc.(v) Metre stick/ / ohmmeter / multimeter etc.

MEASUREMENT OF THE SPECIFIC HEAT CAPACITY OF WATER

1. [2004 OL][2010 OL]In a report of an experiment to measure the specific heat capacity of a substance (e.g. water or a metal), a student wrote the following.“I assembled the apparatus needed for the experiment.During the experiment I took a number of measurements of mass and temperature.I used these measurements to calculate the specific heat capacity of the substance.”(i) Draw a labelled diagram of the apparatus used. (ii) What measurements of mass did the student take during the experiment?(iii) What temperature measurements did the student take during the experiment?(iv)Give a formula used to calculate the specific heat capacity of the substance. (v) Give one precaution that the student took to get an accurate result.

2. [2007]The specific heat capacity of water was found by adding hot copper to water in a copper calorimeter. This was not the method most students would have used to carry out the experiment so there was much annoyance when it appeared on the paper. Nevertheless it does differentiate between those students who understand the underlying principles and those who have just learned off a formula.The following data was recorded.(ii) Describe how the copper was heated and how its

temperature was measured. (iii) Using the data, calculate the energy lost by the hot

copper(iv)Using the data, calculate the specific heat capacity of water. (v) Give two precautions that were taken to minimise heat loss to the surroundings.(vi)Explain why adding a larger mass of copper would improve the accuracy of the experiment.

Solutions

1.(i) See diagram.(ii) Mass of calorimeter, mass of calorimeter +

water, (iii) Initial temperature of water, final

temperature of water.(iv)Energy supplied = (mcΔθ)cal + (mcΔθ)water

where Δθ is the change in temperature and ccal

is known.(v) Lagging, use sensitive thermometer, ensure

that heating coil is completely immersed in the liquid, stir the liquid, large temperature change, etc.

2.(i) It was heated using a hot-plate and temperature was measured using a thermometer.(ii) E = m c Δθ

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mass of calorimeter 55.7 gmass of calorimeter + water 101.2 g

mass of copper + calorimeter + water 131.4 g

initial temperature of water 16.5 oCtemperature of hot copper 99.5 oCfinal temperature of water 21.0 oC

E = (3.02 × 10-2)(390)(78.5) = 924.6 J(iii) Heat lost by hot copper = heat gained by calorimeter + water 924.57 = (0.0557)(390)(4.5) + (0.0455)(cw)(4.5) 924.57 = 97.75 + 0.2048 cw cw = 4.04 ×103 J kg-1 K-1

(iv)Insulate calorimeter /use lid /transfer copper pieces quickly / use cold water (below room temperature) / polish calorimeter / low heat capacity thermometer

(v) A larger mass of copper would result in a larger temperature change and therefore smaller percentage error.

MEASUREMENT OF THE SPECIFIC LATENT HEAT OF FUSION OF ICE1. [2009 OL]A student carried out an experiment to measure the specific latent heat of fusion of ice.The following is an extract from her report.“In my experiment, I prepared ice which was at 0 0C and I added it to warm water in a calorimeter. I waited for all the ice to melt before taking more measurements.I used my measurements to calculate the specific latent heat of fusion of ice.”(i) Draw a labelled diagram of the apparatus used in the experiment. (ii) What measurements did the student take in the experiment? (iii) How did the student prepare the ice for the experiment? (iv)How did the student know the ice was at 0 0C?(v) Why did the student use warm water in the experiment?

2.In a report of an experiment to measure the specific latent heat of fusion of ice, a student wrote the following.“Ice at 0 0C was added to water in a calorimeter.When the ice had melted measurements were taken.The specific latent heat of fusion of ice was then calculated.”(i) Draw a labelled diagram of the apparatus used.(ii) What measurements did the student take before adding the ice to the water?(iii) What did the student do with the ice before adding it to the water?(iv)How did the student find the mass of the ice?(v) Give one precaution that the student took to get an accurate result.

3. [2008]In an experiment to measure the specific latent heat of fusion of ice, warm water was placed in a copper calorimeter. Dried, melting ice was added to the warm water and the following data was recorded.

Mass of calorimeter 60.5 g Mass of calorimeter + water 118.8 g Temperature of warm water 30.5 oC Mass of ice 15.1 g Temperature of water after adding ice 10.2 oC

(vi)Explain why warm water was used. (vii) Why was dried ice used?(viii) Why was melting ice used? (ix)Describe how the mass of the ice was found.(x) What should be the approximate room temperature to minimise experimental error? (xi)Calculate the energy lost by the calorimeter and the warm water.(xii) Calculate the specific latent heat of fusion of ice.

4. [2002]

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In an experiment to measure the specific latent heat of fusion of ice, warm water was placed in an aluminium calorimeter. Crushed dried ice was added to the water. The following results were obtained.

Mass of calorimeter.......................................= 77.2 g

Mass of water.................................................= 92.5 g

Initial temperature of water...........................= 29.4 0C

Temperature of ice ........................................= 0 0CMass of ice.....................................................= 19.2

gFinal temperature of water.............................= 13.2 0CRoom temperature was 21 0C.

(i) What was the advantage of having the room temperature approximately halfway between the initial temperature of the water and the final temperature of the water?

(ii) Describe how the mass of the ice was found. (iii) Calculate a value for the specific latent heat of fusion of ice(iv)The accepted value for the specific latent heat of fusion of ice is 3.3 × 105 J kg-1; suggest two reasons

why your answer is not this value.Solutions

1.(i) See diagram

(ii) Mass of calorimeterMass of calorimeter and warm waterMass of calorimeter and warm water and iceTemperature of water beforeTemperature of water and melted ice after(iii) It was crushed and then dried.(iv)By using melting ice.(v) So that the heat lost to the environment when the system is above room temperature is balanced by the

heat taken in from the environment when the system is below room temperature.

2.(i) See diagram(ii) Mass of calorimeter, mass of water, mass of calorimeter + water, mass of ice, temperature of water(iii) The ice was crushed and dried.(iv)(mass of calorimeter + water + ice) – (mass of calorimeter + water)(v) Insulation, crush, dry, repeat and take average, use lots of ice, transfer ice quickly.

3.(i) To speed up the melting of the ice / in order to melt a larger mass of ice / (concept of) balancing energy

losses before and after the experiment.

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mass of calorimeter 55.7 gmass of calorimeter + water 101.2 gmass of copper + calorimeter + water 131.4 ginitial temperature of water 16.5 oCtemperature of hot copper 99.5 oCfinal temperature of water 21.0 oC

(ii) To remove any water/melted ice // melted ice would have already gained latent heat //so that only ice is added // so that no water is added

(iii) Melting ice is at 0 oC. (iv)Final mass of calorimeter + contents minus mass of calorimeter + water.(v) 20 0C / midway between initial and final temperatures (of the water in the calorimeter) (vi){energy lost = } (mcΔθ )cal + (mcΔθ )warm water = (0.0605)(390)(20.3) + (0.0583)(4200)(20.3) = 5449.6365 / 5449.6 J (vii) {Energy gained by ice and by melted ice =} (ml)ice + (mcΔθ )melted ice / (0.0151)l + (0.0151)(4200)(10.2) / 0.0151 l + 646.884 (equate:) 0.0151 l + 646.884 = 5449.6365 l = 3.181 × 105 ≈ 3.2 × 105 J kg–1

4. (i) Heat lost to surroundings when the system is above room temperature would cancel out the heat taken in

from the surroundings when the system was below room temperature.(ii) Final mass (of calorimeter + water + ice) - initial mass (of calorimeter + water)(iii) mcΔθAl + mcΔθwater = mlice +mcΔθmelted ice

Fall in temperature = 16.2 oC Ans = 3.2 × 105 J kg-1

(iv)Thermometer not sensitive enough, lack of insulation, lack of stirring, heat loss/gain to surroundings, too long for ice to melt, inside of calorimeter tarnished, splashing, heat capacity of thermometer

MEASUREMENT OF THE SPECIFIC LATENT HEAT OF VAPORISATION OF WATER

1. [2005 OL]In a report of an experiment to measure the specific latent heat of vaporisation of water, a student wrote the following.“Steam at 100 oC was added to cold water in a calorimeter.When the steam had condensed, measurements were taken.The specific latent heat of vaporisation of water was then calculated.”(i) Draw a labelled diagram of the apparatus used. (ii) List two measurements that the student took before adding the steam to the water.(iii) How did the student find the mass of steam that was added to the water?(iv)How did the student make sure that only steam, and not hot water, was added to the calorimeter?(v) Give one precaution that the student took to prevent heat loss from the calorimeter.

2. [2003]In an experiment to measure the specific latent heat of vaporisation of water, cold water was placed in a copper calorimeter. Steam was passed into the cold water until a suitable rise in temperature was achieved. The following results were obtained:

Mass of the calorimeter........................... = 73.4 gMass of cold water .................................. = 67.5 gInitial temperature of water..................... = 10 °CTemperature of the steam........................ = 100 °CMass of steam added ............................... = 1.1 gFinal temperature of water ...................... = 19 °C

(i) Describe how the mass of the steam was found.(ii) Using the data, calculate a value for the specific latent heat of vaporisation of water. (iii) Why is the rise in temperature the least accurate value? (iv)Give two ways of improving the accuracy of this value.

3. [2010]

35

In an experiment to measure the specific latent heat of vaporisation of water, a student used a copper calorimeter containing water and a sensitive thermometer. The water was cooled below room temperature before adding dry steam to it. The following measurements were recorded.

Mass of copper calorimeter = 34.6 gInitial mass of calorimeter and water = 96.4 gMass of dry steam added = 1.2 gInitial temperature of calorimeter and cooled water = 8.2 °CFinal temperature of calorimeter and water = 20.0 °C

(vi)How was the water cooled below room temperature?(vii) How was the steam dried?(viii) Describe how the mass of the steam was determined.(ix)Why was a sensitive thermometer used?(x) Using the data, calculate the specific latent heat of vaporisation of water.

4. [2005]In an experiment to measure the specific latent heat of vaporisation of water, cool water was placed in an insulated copper calorimeter. Dry steam was added to the calorimeter. The following data was recorded.

Mass of calorimeter = 50.5 gMass of calorimeter + water = 91.2 gInitial temperature of water = 10 oCTemperature of steam = 100 oCMass of calorimeter + water + steam = 92.3 gFinal temperature of water = 25 oC

(i) Calculate a value for the specific latent heat of vaporisation of water. (ii) Why was dry steam used? (iii) How was the steam dried? (iv)A thermometer with a low heat capacity was used to ensure accuracy. Explain why.

Solutions

1.(i) See diagram.(ii) Mass of calorimeter, mass of water, mass of calorimeter +

water, initial temperature of water, initial temperature of steam.

(iii) Final mass of water + calorimeter minus initial mass of water + calorimeter.

(iv)Allow steam to flow for some time before inserting it into water, slope delivery tube back to steam generator, use a steam trap.

(v) Lagging, insulation, lid, carry out measurements quickly.

2.(i) Final mass of (calorimeter + water + condensed steam) – Initial mass of (calorimeter + water)(ii) (ml) steam + (mc∆ϑ) steam = (mc∆ϑ) water + (mc∆ϑ) cal

∆ϑwater = 90C, ∆ϑcal= 90C∆ϑ) steam = 810CAnswer = 2.2 × 106 J kg-1

(iii) Read only to one significant figure {the concept of significant figures is not on the syllabus and shouldn’t have got asked. It hasn’t appeared since.]

(iv)Use a digital thermometer, use more steam, use less water, insulation, cover, stirring, steam trap

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3.(i) Ice was added to the water / the water was taken from fridge(ii) By using a steam trap (or ensure that the delivery tube is sloped upwards)(iii) Final mass of calorimeter plus contents – initial mass of calorimeter and contents(iv)For greater accuracy / to reduce (%) error / more significant figures / e.g. to read to 0.1 oC (v) ms = 1.2×10-3 kg

mw = 6.18 × 10-2 kgΔθs = 80 (K) and Δθw (= Δθcu) = 11.8 (K)

[heat lost by steam = heat gained by water and calorimeter] (ml)s + (mcΔθ )s = (mcΔθ )w + (mcΔθ )cu

(1.2×10-3)l + (1.2×10-3)(4180)(80) = (6.18 × 10-2)(4180)(11.8) + (3.46 × 10-2)(11.8)(390)(1.2×10-3)l + 401.3 = 3048.2 + 159.2

l = 2.34 × 106 J Kg-1

4.(i) mslw + mscwΔθs = mwcwΔθw+ mcccΔθc

Δθs = 75 0C and Δθw (= Δθc) = 15 0C (0.0011) lw + (0.0011)(4200)(75) = (0.0407)(4200)(15) + (0.0505)(390)(15) [(0.0011) lw + 346.5 = 2564.1 + 295.425] lw = 2.28 × 106 J kg-1

(ii) Calculations assume that only steam is added, not water.(iii) Use a steam trap / insulated delivery tube / sloped delivery tube / allow steam to issue freely initially(iv)It absorbs little heat from system in calorimeter and calculations assume that no energy is transferred to

the thermometer.

TO MEASURE THE SPEED OF SOUND IN AIR1. [2008 OL]You carried out an experiment to find the speed of sound in air, in which you measured the frequency and the wavelength of a sound wave.(i) With the aid of a diagram describe the adjustments you carried out during the experiment. (ii) How did you find the frequency of the sound wave? (iii) How did you measure the wavelength of the sound wave? (iv)How did you calculate the speed of sound in air? (v) Give one precaution you took to get an accurate result.

2. [2003 OL] In an experiment to measure the speed of sound in air, a student found the frequency and the wavelength of a sound wave.(i) Draw a labelled diagram of the apparatus used in the experiment. (ii) Describe how the student found the wavelength of the sound wave.(iii) How did the student find the frequency of the sound wave?(iv)How did the student calculate the speed of sound in air?(v) Give one precaution that the student took to get an accurate result.

3. [2006]A cylindrical column of air closed at one end and three different tuning forks were used in an experiment to measure the speed of sound in air. A tuning fork of frequency f was set vibrating and held over the column of air.The length of the column of air was adjusted until it was vibrating at its first harmonic and its length l was then measured. This procedure was repeated for each tuning fork.Finally, the diameter of the column of air was measured. The following data was recorded.

37f/Hz 512 480 426l/cm 16.0 17.2 19.4

Diameter of column of air = 2.05 cm.(ii) Describe how the length of the column of air was adjusted.(iii) Describe how the frequency of the column of air was measured.(iv)Describe how the diameter of the column of air was measured. (v) How was it known that the air column was vibrating at its first harmonic?(vi)Using all of the data, calculate the speed of sound in air.

Solutions1.(i) We adjusted the length of the inner tube until resonance occurred.(ii) We read it from the tuning fork which was used to create the sound wave.(iii) We measured the diameter of the inner tube using digital callipers.We measured the length of the inner tube above the water.We then used the formula λ = 4(l + 0.3d) to calculate the wavelength.(iv)We substituted the values for frequency and wavelength into the formula c = f λ(v) Repeat using different tuning forks and take an average, clamp tube to take measurements.2.(i) See diagram.(ii) We measured the diameter of the inner tube using digital callipers.We measured the length of the inner tube above the water.We then used the formula λ = 4(l + 0.3d) to calculate the wavelength.(iii) We read it from the tuning fork which was used to create the sound

wave.(iv)We substituted the values for frequency and wavelength into the formula

c = f λ(v) Repeat using different tuning forks and take an average, clamp tube to

take measurements.3.(i) The inner pipe was raised while immersed in water.(ii) The frequency was read from the tuning fork which caused the vibration.(iii) Using a digital calipers (iv)The inner tube was raised until a loud sound could be heard. (v) v = f λ λ = 4( l +0.3 d) v1 = 340(.3) m s-1; v2 = 342(.0) m s-1 ; v3 = 341(.1) m s-1

vavg = 341(.13) m s-1

INVESTIGATION OF THE VARIATION OF FUNDAMENTAL FREQUENCY OF A STRETCHED STRING WITH LENGTH

1. [2006 OL]A student carried out an experiment to investigate how the fundamental frequency of a stretched string varied with its length. The following is an extract from her report.I set the string vibrating and adjusted its length until it was vibrating at its fundamental frequency. I then recorded the length of the vibrating string and its fundamental frequency. I repeated this procedure for different lengths of the stretched string.Finally, I plotted a graph of the fundamental frequency of the vibrating string against the inverse of its length.(ii) Draw a labelled diagram of the apparatus used in the experiment. Indicate on your diagram the length of the string that was measured. (iii) Describe how the student set the string vibrating.(iv)How did the student know that the string was vibrating at its fundamental frequency?(v) Draw a sketch of the graph expected in this experiment.

2. [2002 OL)

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In a report of an experiment to investigate the variation of fundamental frequency of a stretched string with length, a student wrote the following. “The wire was set vibrating at a known frequency. The length of the wire was adjusted until it vibrated at its fundamental frequency. The length was recorded. A different frequency was applied to the wire and new measurements were taken. This procedure was repeated a few times.” (i) How was the wire set vibrating? (ii) How was the length adjusted?

The table shows the measurements recorded by the student.

Fundamental frequency (Hz)

650 395 290 260 192 174 163

length/ (m) 0.20 0.33 0.45 0.50 0.66 0.75 0.801/length (m-1)

(iii) Copy the table and complete the last row by calculating 1/ length1for each measurement. (iv) Plot a graph on graph paper of fundamental frequency against 1/ length. Put fundamental frequency

on the vertical axis. (v) What does the graph tell you about the relationship between fundamental frequency and length?

3. [2009 OL]In an experiment, a student investigated the variation of the fundamental frequency f of a stretched string with its length l. During the experiment the student kept the tension in the string constant. The table shows the data recorded by the student.

f/Hz 100 150 200 250 300 350 400l/m 0.50 0.33 0.25 0.20 0.166 0.142 0.1251/l (m− 1) 7.04

(i) Describe, with the aid of a diagram, how the student obtained the data. (ii) Why was the tension in the string kept constant during the experiment?(iii) Copy this table and fill in the last row by calculating 1/l for each measurement. (iv)Plot a graph on graph paper to show the relationship between the fundamental frequency and the length

of the stretched string (put 1/l on the X-axis). (v) What does your graph tell you about the relationship between the fundamental frequency of a stretched

string and its length?

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Solutions1.(i) See diagram.(ii) By turning on the signal generator.(iii) The paper rider starts to vibrate vigorously.(iv)See diagram.2.(i) Using a signal generator in series with a metal wire

which had a magnet around it.By moving the position of one of the bridges.

(ii)

(iii)

(iv)The straight line through the origin shows that frequency is inversely proportional to length.

3.(i) See diagram Adjust frequency until the paper rider falls off (resonance occurs)Record the frequency on the signal generator and measure the length between the bridges.Adjust the distance between the bridges and repeat.(ii) Because frequency also depends on tension and you can only investigate the relationship between two

variables at a time.(iii)

(iv)

(v) Fundamental frequency is inversely proportional to length

40

1/length (m-1) 5.0 3.0 2.2 2.0 1.5 1.3 1.25

f/Hz 100 150 200 250 300 350 400l/m 0.50 0.33 0.25 0.20 0.166 0.142 0.1251/l (m− 1) 2.00 3.03 4.00 5.00 6.02 7.04 8.00

INVESTIGATION OF THE VARIATION OF FUNDAMENTAL FREQUENCY OF A STRETCHED STRING WITH TENSION

1. [2004]A student investigated the variation of the fundamental frequency f of a stretched string with its length l.(v) Draw a labelled diagram of the apparatus used in this experiment. Indicate on the diagram the points

between which the length of the wire was measured.

The student drew a graph, as shown, using the data recorded in the experiment, to illustrate the relationship between the fundamental frequency of the string and its length.(vi)State this relationship and explain how the graph verifies it.(vii) The student then investigated the variation of the fundamental frequency f of

the stretched string with its tension T. The length was kept constant throughout this investigation.

How was the tension measured? (viii) What relationship did the student discover? (ix)Why was it necessary to keep the length constant? (x) How did the student know that the string was vibrating at its fundamental frequency?

2. [2009]A student investigated the variation of the fundamental frequency f of a stretched string with its tension T. The following is an extract of the student’s account of the experiment.“I fixed the length of the string at 40 cm. I set a tuning fork of frequency 256 Hz vibrating and placed it by the string. I adjusted the tension of the string until resonance occurred. I recorded the tension in the string. I repeated the experiment using different tuning forks.”(i) How was the tension measured? (ii) How did the student know that resonance occurred?

The following data were recorded.

(iii) Draw a suitable graph to show the relationship between the fundamental frequency of a stretched string and its tension.

(iv)State this relationship and explain how your graph verifies it.(v) Use your graph to estimate the fundamental frequency of the string when its tension is 11 N(vi)Use your graph to calculate the mass per unit length of the string.

3. [2002]A student obtained the following data during an investigation of the variation of the fundamental frequency f of a stretched string with its tension T. The length of the string was kept constant.

(i) Describe, with the aid of a diagram, how the student obtained the data.(ii) Why was the length of the string kept constant during the investigation? (iii) Plot a suitable graph on graph paper to show the relationship between fundamental frequency and

tension for the stretched string. From your graph, estimate the tension in the string when its fundamental frequency is 380 Hz.

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f /Hz 256 288 320 341 384 480 512T /N 2.4 3.3 3.9 4.3 5.7 8.5 9.8

T/N 15 20 25 30 35 40 45f /Hz 264 304 342 371 402 431 456

Solutions1.(i) See diagram(ii) f is proportional to 1/l.A straight line through the origin verifies this.(iii) Using a newton-balance / pan with weights /

suspended weights (iv)Frequency is proportional to Tension.(v) Because length is a third variable and you can

only investigate the relationship between two variables at a time.

(vi)The paper rider on the string falls off.

2.(i) A newton balance // weight of pan + contents (ii) Paper rider jumped vigorously / the string vibrated at maximum amplitude (iii)

Six correct values for T Both axes correctly labelled Six points correctly plotted Straight line with a good fit

(iv)f is proportional to square root of T because the graph was a straight line through the origin.(v) If tension is 11 N T = 3.32 Use the graph to get f = 542 Hz(vi)

Compare to the formula y = mx slope = 1/(2lμ), where l = 0.4 mMass per unit length (μ) = 5.86 × 10–5 kg m–1

3.(i)

Slowly increase the frequency on the signal generator until resonance occurs. Note the frequency on the signal generator and the tension on the Newton balance. Change tension and repeat. (ii) Because length is a third variable and you can only investigate the relationship between two variables at

a time.(iii) Square root of tension / frequency squared Label axes

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Plot 6 points correctlyStraight lineGood fit(iv)At a frequency of 380 the square root of tension = 5.6 T = 30.3 N

MEASUREMENT OF THE WAVELENGTH OF MONOCHROMATIC LIGHT

1. [2009](i) An interference pattern is formed on a screen when green light from a laser passes normally through a

diffraction grating. The grating has 80 lines per mm and the distance from the grating to the screen is 90 cm. The distance between the third order images is 23.8 cm.Calculate the wavelength of the green light.

(ii) Calculate the maximum number of images that are formed on the screen. (iii) The laser is replaced with a source of white light and a series of spectra are formed on the screen.

Explain how the diffraction grating produces a spectrum.(iv)Explain why a spectrum is not formed at the central (zero order) image.

2. [2007 OL]You carried out an experiment to measure the wavelength of a monochromatic light source using a diffraction grating. The diffraction grating had 600 lines per mm.(i) Draw a labelled diagram of the apparatus you used. (ii) Name a source of monochromatic light. (iii) State what measurements you took during the experiment. (iv)What is the distance between each line on the diffraction grating? (v) How did you determine the wavelength of the light? (vi)Give one precaution that you took to get an accurate result.

3. [2004 OL]You carried out an experiment to measure the wavelength of a monochromatic light source.(i) Name a monochromatic light source. (ii) Draw a labelled diagram of the apparatus that you used in the experiment. (iii) What readings did you take during the experiment?(iv)What formula did you use to calculate the wavelength of the light?(v) Give one precaution that you took to get an accurate result.

4. [2008]In an experiment to measure the wavelength of monochromatic light, a diffraction pattern was produced using a diffraction grating with 500 lines per mm. The angle between the first order images was measured. This was repeated for the second and the third order images. The table shows the recorded data:

(i) Draw a labelled diagram of the apparatus used in the experiment.

(ii) Explain how the first order images were identified. (iii) Describe how the angle between the first order images was measured. (iv)Use the data to calculate the wavelength of the monochromatic light.

5. [2004]In an experiment to measure the wavelength of monochromatic light, the angle θ between a central bright image (n = 0) and the first and second order images to the left and the right was measured.

43

Angle between first order images

Angle between second order images

Angle between third order images

34.20 71.60 121.60

A diffraction grating with 500 lines per mm was used.The table shows the recorded data.

n 2 1 0 1 2θ /degrees 36.2 17.1 0 17.2 36.3

(i) Describe, with the aid of a diagram, how the student obtained the data. (ii) Use all of the data to calculate a value for the wavelength of the light. (iii) Explain how using a diffraction grating with 100 lines per mm leads to a less accurate result.(iv)The values for the angles on the left of the central image are smaller than the corresponding ones on the

right. Suggest a possible reason for this.

6. [2006]In an experiment to measure the wavelength of monochromatic light, a narrow beam of the light fell normally on a diffraction grating. The grating had 300 lines per millimetre. A diffraction pattern was produced. The angle between the second order image to the left and the second order image to the right of the central bright image in the pattern was measured.The angle measured was 40.60.(i) Describe, with the aid of a labelled diagram, how the data was obtained. (ii) How was a narrow beam of light produced? (iii) Use the data to calculate the wavelength of the monochromatic light. (iv)Explain how using a diffraction grating of 500 lines per mm leads to a more accurate result. (v) Give another way of improving the accuracy of this experiment.

Solutions1.(i) d = 1/80000 = 1.25 × 10-5 m = tan-1 (0.238/0.90)n = 3n = d sin = d sin /n = 551 (± 5) × 10-9 m.(ii) For maximum number = 900 sin = 1n = d sin n = d n = d/

n = 22.7 so the greatest whole number of images is 22.But this is on one side only. In total there will be 22 on either side, plus one in the middle, so total = 45(iii) Different colours have different wavelengths so constructive interference occurs at different

positions for each separate wavelength.(iv)At central image = 0 so constructive interference occurs for all separate wavelengths at the same point

so no separation of colours.

2.(i) See diagram(ii) The laser(iii) Distance from grating to screen

Distance between dots on the screen(iv)600 lines per mm = 600000 lines per metre.

d = (1/ number of lines per metre) = (1/600000) = 1.67 × 10-6 m.(v) Using the formula nλ = d sin , where d was d was calculated

above, n was the order of the dots on either side and corresponded to the angle shown in the diagram.

(vi)Ensure that the diffraction grating is perpendicular to the (monochromatic) light, use a grating with a large number of lines, ensure D is large, repeat for different orders and take the average, etc.

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3.(i) A laser or a sodium lamp.(ii) See diagram.(iii) Distance from grating to screen

Distance between dots on the screen(iv)nλ = d sin (v) Ensure that the diffraction grating is perpendicular to the (monochromatic)

light, use a grating with a large number of lines, ensure D is large, repeat for different orders and take the average, etc.

4.(i) See diagram. Plus metre stick(ii) Nearest on either side of the central (zero order) image. (iii) Measure x between 1st order images

Measure D from screen to grating = tan-1 (x/D)

(iv)Use nλ = d sinθ(n=1) λ = sin (17.1)/[(5 × 105)(1)] = 5.8808 × 10-7 ≈ 5.88 × 10-7m(n=2) λ = sin (35.8)/[(5 × 105)(2)] = 5.8496 × 10-7 ≈ 5.85 × 10-7m(n=3) λ = sin (60.8)/[(5 × 105)(3)] = 5.8195 × 10-7 ≈ 5.82 × 10-7mλ = 5.85 × 10-7 m = 585 nm

5.(i) See diagram, plus metre stick.

Measure distance x from central fringe for n = ±1, ±2 Measure distance D from grating to screen and calculate θ in each case using tan θ = x/D

(ii) nλ = d sinθ d = 1/500000 d = 2 × 10-6

n=1, λL= 588.1 nm, λR= 591.4 nm n=2, λL= 590.6 nm, λR= 592.0 nmCalculated average wavelength = 590 nm.

(iii) It would result in a smaller value for which would mean larger percentage errors.(iv)The grating may not be perpendicular to the incident light

6.(i) The apparatus was set up as shown.

To get a value for the distance x was measured between the centre image and the second order image, then the distance D between grating and screen was measured. = Tan-1 (x/D)We did the same for the other side and got an average value for .

(ii) Use a laser. (iii) nλ = d sin θ

n = 2 d = 1/(3.00 x105) m = 3.33 x 10-6 m = 3.33 x 10-3 cm = 1/300 mmθ = 20.30

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λ = 5.78 x 10-7 m (= 578 ≈ 580 nm) (iv)This would result in a greater angle for each order image and therefore a smaller percentage error in

measuring the angle. (v) Repeat and get average value for the wavelength , repeat for higher orders.

TO MEASURE THE RESISTIVITY OF THE MATERIAL OF A WIRE

1. [2005 OL]In an experiment to measure the resistivity of the material of a wire, a student measured the length, diameter and the resistance of a sample of nichrome wire.The table shows the measurements recorded by the student.

resistance of the wire/ Ω 26.4length of the wire /mm 685diameter of the wire /mm 0.20 0.19 0.21

(i) Describe how the student measured the resistance of the wire.(ii) Name the instrument used to measure the diameter of the wire.(iii) Why did the student measure the diameter of the wire in three different places? (iv)Using the data, calculate the diameter of the wire.(v) Hence calculate the cross-sectional area of the wire. (A = πr2) (vi)Calculate the resistivity of nichrome using the formula ρ = RA/L(vii) Give one precaution that the student took when measuring the length of the wire.

2. [2010 OL]In an experiment to determine the resistivity of the material of a wire, a student measured the length, diameter and resistance of a sample of nichrome wire.

The table shows the data recorded by the student.(iv)Describe how the student measured the resistance of the wire.(v) Describe how the length of the wire was measured. (vi)What instrument did the student use to measure the diameter of the

wire? (vii) Why did the student measure the diameter of the wire at different places?(viii) Using the data, calculate the cross-sectional area of the wire. (ix)Find the resistivity of nichrome.

3. [2009]In an experiment to measure the resistivity of nichrome, the resistance, the diameter and appropriate length of a sample of nichrome wire were measured.The following data were recorded:Resistance of wire = 7.9 ΩLength of wire = 54.6 cmAverage diameter of wire = 0.31 mm

(i) Describe the procedure used in measuring the length of the sample of wire. (ii) Describe the steps involved in finding the average diameter of the wire. (iii) Use the data to calculate the resistivity of nichrome. (iv) The experiment was repeated on a warmer day. What effect did this have on the measurements?

4. [2004] The following is part of a student’s report of an experiment to measure the resistivity of nichrome wire.“The resistance and length of the nichrome wire were found. The diameter of the wire was then measured at several points along its length.”

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R/Ω 20.2l/cm 48.8d/mm 0.21 0.20 0.18

The following data was recorded.Resistance of wire = 32.1 ΩLength of wire = 90.1 cmDiameter of wire = 0.19 mm, 0.21 mm, 0.20 mm, 0.21 mm, 0.20 mm

(i) Name an instrument to measure the diameter of the wire and describe how it is used. (ii) Why was the diameter of the wire measured at several points along its length? (iii) Using the data, calculate a value for the resistivity of nichrome. (iv)Give two precautions that should be taken when measuring the length of the wire.

Solutions1.(i) Using an multimeter set to measure resistance, the ends of the multimeter wire were connected to the

ends of the wire in question.(ii) A digital callipers.(iii) To calculate an average diameter because the diameter of the wire is not uniform. (iv)Average diameter = (0.20 + 0.19 + 0.21)/3 diameter = 0.60 ÷ 30 diameter = 20 mm (v) r = 0.1 mm = 0.0001 m

A = πr2 A = π (0.0001)2

A = 3.14 × 10-8 m2

(vi)ρ = (26.4)( 3.14 × 10-8) ÷ 0.685 ρ = 1.21 × 10-6 Ω m.

(vii) Avoid parallax error when using metre stick, keep wire straight (no kinks), measure only the length of wire between leads to ohmmeter.

2.(i) Ohmmeter / (digital) multimeter / measure V and I and hence determine R (ii) Ensure the wire is taut and measure the length between the crocodile clips using a metre-stick.(iii) Micrometer / digital callipers(iv)To get average (diameter) as wire may not be uniform (v) Average diameter = 0.197 mm r = 0.0001m

A = π(0.1 × 10-3)2

A = 3.03 – 3.14 × 10-8 m2

(vi)Ƿ = RA/lǷ = (20.2)(3.14 × 10-8)/(0.488)Ƿ = 1.25 – 1.29 × 10-6 Ω m)

3.(i) Straighten the wire, clamp it to a bench and measure the distance between the points for which the

resistance was measured.(ii)

Zero the micrometer / digital callipers Place wire between jaws Tighten jaws and take reading Repeat at different points on wire Get average diameter

(iii) A = πr2 A = π(0.155 × 10-3)2 = 7.55 × 10-8 m2

= RA/l = (7.9)(7.55 × 10-8)/0.546) = 1.09 × 10-6 m(iv) Resistance increased / length increased (or wire expands) / diameter increased

4.(i) Digital callipers

Place the wire between the jaws

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Tighten the jawsRead the callipers

(ii) To get an average because the material is not of uniform density.(iii) Average diameter = 0.202 mm

A = πr 2 = 3.2 ×10−8 m2 ρ =RA/Lρ = (32.1)(3.2 × 10-8)/0.901)ρ = 1.1×10−6 Ω m

(iv)Ensure no kinks in wire, only measure length whose R value was measured, avoid parallax error, etc.

TO INVESTIGATE THE VARIATION OF CURRENT (I) WITH P.D. (V) FOR A FILAMENT BULB

1. [2003 OL]The diagram shows the circuit used by a student to investigate the variation of current with potential difference for a filament bulb.(i) Name the apparatus X. What does it measure? (ii) Name the apparatus Y. What does it do?

The table shows the values obtained for the current and the potential difference during the experiment.

Potential difference /V

2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

Current /A 1.0 1.5 1.9 2.3 2.6 2.9 3.2 3.5

(iii) Draw a graph, on graph paper, of the current against the potential difference. (iv)Use your graph to find the resistance of the bulb when the current is 3 A. (v) The resistance of the bulb is 2.0 Ω when the current is 1.5 A

Explain why the resistance of the bulb when the current is 1.5 A is different from its resistance when the current is 3 A.

2. [2005]A student investigated the variation of the current I flowing through a filament bulb for a range of different values of potential difference V.

(i) Draw a suitable circuit diagram used by the student. (ii) Describe how the student varied the potential difference. (iii) The student drew a graph, as shown, using data recorded in the

experiment.With reference to the graph, explain why the current is not proportional to the potential difference.

(iv)With reference to the graph, calculate the change in resistance of the filament bulb as the potential difference increases from 1 V to 5 V.

(v) Give a reason why the resistance of the filament bulb changes.

Solutions1.(i) X is an ammeter. It measures current.(ii) Y is a voltmeter. It measures volts.(iii) See graph(iv)When the current is 3 A the voltage is 7.2 V, so using

V = IR results in R = 2.4 .(v) Because the resistance of the bulb increases with

temperature, and temperature is greater when the current is greater.

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2.(i) See diagram(ii) By adjusting the voltage on the power supply.(iii) Because the graph is not a straight line.(iv)At 1 V: R = V/I = 1/0.028 = 35.7 Ω

At 5 V: R = (5/0.091) = 54.9 Ω Change in resistance (= 54.9 – 35.7) = 19.2 Ω

(v) As current increases the temperature of filament increases, therefore the filament gets hotter and it gets more difficult for electrons to pass through due to increased vibration of the metal atoms.

TO INVESTIGATE THE VARIATION OF THE RESISTANCE OF A METALLIC CONDUCTOR WITH TEMPERATURE

1. [2006 OL]In an experiment to investigate the variation of resistance with temperature for a metallic conductor in the form of a wire, a student measured the resistance of the conductor at different temperatures. The table shows the measurements recorded by the student.(i) How did the student measure the

resistance of the wire? (ii) Describe, with the aid of a diagram, how the student varied the temperature of the wire. (iii) Using the data in the table, draw a graph on graph paper of the resistance of the conductor against its

temperature. Put temperature on the horizontal axis (X-axis). (iv)Use the graph to estimate the temperature of the conductor when its resistance is 50 Ω.(v) What does your graph tell you about the relationship between the resistance of a metallic conductor and

its temperature?

2. [2008]A student investigated the variation of the resistance R of a metallic conductor with its temperature θ. The student recorded the following data.(i) Describe, with the aid of a labelled diagram, how the

data was obtained. (ii) Draw a suitable graph to show the relationship between

the resistance of the metal conductor and its temperature.

(iii) Use your graph to estimate the resistance of the metal conductor at a temperature of –20 oC.(iv)Use your graph to estimate the change in resistance for a temperature increase of 80 oC.(v) Use your graph to explain why the relationship between the resistance of a metallic conductor and its

temperature is linear.

Solutions1.(i) By using a multimeter set to measure resistance.(ii) See diagram.

The temperature was varied by allowing the wire to be heated.(iii) See graph

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Temperature / oC

20 30 40 50 60 70 80

Resistance / Ω 45.6 49.2 52.8 57.6 60.0 63.6 68.4

θ/oC

20 30 40 50 60 70 80

R/Ω

4.6 4.9 5.1 5.4 5.6 5.9 6.1

(iv)Use the graph to estimate the temperature of the conductor when its resistance is 50 Ω.(v) What does your graph tell you about the relationship between the resistance of a metallic conductor and

its temperature?

2.(i) The resistance was read from the ohmmeter, the

temperature was read from the thermometer and the readings were varied using the heat source. See diagram

(ii) See graph(iii) Continue (extrapolate) the graph on the left hand

side and then read off the resistance value that corresponds to the temperature of – 20 0C. R = 3.6 Ω

(iv)y-intercept value ≈ 4.12 Ω change in resistance ≈ 2 Ω

(v) A straight line is obtained.

TO INVESTIGATE THE VARIATION OF CURRENT (I) WITH P.D. (V) FOR COPPER ELECTRODES IN A COPPER-SULPHATE SOLUTION

1. [2004 OL]The diagram shows a circuit used to investigate the variation of current with potential difference for a copper sulfate solution.(i) Name the instrument used to measure the current.(ii) How was the potential difference measured in the experiment?(iii) Name the apparatus Y and give its function in the experiment.(iv)The following table shows the values recorded for the current and the

potential difference during the experiment.

Using the data in the table, draw a graph on graph paper of the current against the potential difference. Put current on the horizontal axis. (v) Calculate the slope of your graph and hence determine the resistance of the copper sulphate solution.

2. [2002]In an experiment to investigate the variation of current I with potential difference V for a copper sulfate solution, the following results were obtained.

(i) Draw a diagram of the apparatus used in this experiment, identifying the anode and the cathode. (ii) Draw a suitable graph on graph paper to show how the current varies with the potential difference. (iii) Using your graph, calculate the resistance of the copper sulfate solution. (Assume the resistance of

the electrodes is negligible.)(iv)Draw a sketch of the graph that would be obtained if inactive electrodes were used in this experiment.

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Potential Difference /V

0 0.5 1.0 1.5 2.0 2.5 3.0

Current /A 0 0.3 0.6 0.9 1.2 1.5 1.8

V /V 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0I /mA 24 48 79 102 120 143 185 195 215 263

Solutions1.(i) An ammeter(ii) Using a voltmeter.(iii) Y is a rheostat which is a variable resistor; by adjusting

it you vary the resistance which in turn varies the resistance and current.

(iv) See graph

(v) Take any two points and use the formula

Slope = resistance = 1.67 Ω.

2.(i) See diagram. Cathode = negative electrode, anode = positive electrode(ii) Axes labelled 6 points plotted correctly Straight line Good fit (iii) Resistance = slope of graph = 19.5 to 20.5 Ohms(iv)Straight line starting at v > 0

TO VERIFY JOULE’S LAW

1. [2007 OL]In an experiment to verify Joule’s law, a heating coil was placed in a fixed mass of water.

A current I was allowed to flow through the coil for a fixed length of time and the rise in temperature Δθ was recorded. This was repeated for different values of I.The table shows the data recorded.

(i) Draw a labelled diagram of the apparatus used. (ii) How was the current changed during the

experiment? (iii) Copy the table and complete it in your answerbook. (iv)Using the data in the completed table, draw a graph on graph paper of Δθ against I2.

Put I2 on the horizontal axis (X-axis). (v) Explain how your graph verifies Joule’s law (Δθ α I2).

2. [2006]In an experiment to verify Joule’s law a student passed a current through a heating coil in a calorimeter containing a fixed mass of water and measured the rise in temperature Δθ for a series of different values of the current I. The student allowed the current to flow for three minutes in each case.

(iii) Describe, with the aid of a labelled diagram, how the student arranged the apparatus.

(iv)Why was a fixed mass of water used throughout the experiment?

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I/A 1.0 1.5 2.0 2.5 3.0 3.5 4.0I 2/A2 4Δθ/°C 2.2 5.0 8.8 13.8 20.0 26.0 35.2

(v) The student drew a graph, as shown. Explain how this graph verifies Joule’s law.(vi)Given that the mass of water in the calorimeter was 90 g in each case, and assuming that all of the

electrical energy supplied was absorbed by the water, use the graph to determine the resistance of the heating coil. The specific heat capacity of water is 4200 J kg–1 K–1.

3. [2003]In an experiment to verify Joule’s law, a heating coil was placed in a fixed mass of water.The temperature rise Δθ produced for different values of the current I passed through the coil was recorded.

In each case the current was allowed to flow for a fixed length of time.The table shows the recorded data.(i) Describe, with the aid of a labelled diagram, how the apparatus was arranged in this experiment. (ii) Using the given data, draw a suitable graph on graph paper and explain how your graph verifies Joule’s

law. (iii) Explain why the current was allowed to flow for a fixed length of time in each case. (iv)Apart from using insulation, give one other way of reducing heat losses in the experiment. Solutions1.(i) See diagram below.(ii) Adjust the (variable) power supply // adjust the (variable) resistor(iii)

(iv)See graph(v) We got a straight line through the origin

showing that Δθ α I2

2.(i) See diagram.(ii)

The mass of water would be a third variable and you can only investigate the relationship between two variables at a time.

(iii) Straight line graph through origin Δθ α I2 P α I2 (iv)Electrical energy in = Heat energy out

RI2 t = mcΔθ Rt = mc(Δθ/ I2) Rt = mc(slope) R = mc(slope)/t = (.09)(4200)(3.8)/180R = (7.8 ↔ 8.2) Ω

3.(i) See diagram.(ii)

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I /A 1.5 2.0 2.5 3.0 3.5 4.0 4.5Δθ / °C 3.5 7.0 10.8 15.0 21.2 27.5 33.0

I/A 1.0 1.5 2.0 2.5 3.0 3.5 4.0I 2/A2 1 2.25 4 6.25 9 12.25 16Δθ/°C 2.2 5.0 8.8 13.8 20.0 26.0 35.2

I /A 1.5 2.0 2.5 3.0 3.5 4.0 4.5Δθ / °C 3.5 7.0 10.8 15.0 21.2 27.5 33.0I2 /A2 2.25 4.0 6.25 9.0 12.25 16.0 20.25

Label axesAt least 6 correct pointsStraight lineGood fitA straight line through origin shows that ∆ϑ ∝ I2 which verifies Joule’s Law.(iii) You can only investigate the relationship between two variables at a time and time is a third variable.(iv)Start with cold water, change the water for each run, use a lid, shorter time interval, polish calorimeter.

TO INVESTIGATE THE VARIATION OF THE RESISTANCE OF A THERMISTOR WITH TEMPERATURE

1. In an experiment to investigate the variation of the resistance R of a thermistor with its temperature θ, a student measured the resistance of the thermistor at different temperatures.The table shows the measurements recorded by the student.

θ/ 0C

20 30 40 50 60 70 80

R/Ω 2000 1300 800 400 200 90 40

(i) Draw a labelled diagram of the apparatus used in this experiment. (ii) How did the student measure the resistance of the thermistor? (iii) Plot a graph on graph paper to show the relationship between the resistance R of the thermistor and

its temperature θ (put θ on the X-axis). (iv)Use your graph to estimate the temperature of the thermistor when its resistance is 1000 Ω. (v) What does your graph tell you about the relationship between the resistance of a thermistor and its

temperature?

2. [2010]In an experiment to investigate the variation of the resistance R of a thermistor with its temperature θ, a student measured its resistance at different temperatures. The table shows the measurements recorded.

(iii) Draw a labelled diagram of the apparatus used.(iv)How was the resistance measured?(v) Describe how the temperature was varied.(vi)Using the recorded data, plot a graph to show the variation of the resistance of a thermistor with its

temperature.(vii) Use your graph to estimate the average variation of resistance per Kelvin in the range 45 °C – 55 °C.(viii) In this investigation, why is the thermistor usually immersed in oil rather than in water?

3. [2002 OL]The circuit diagram shows a thermistor connected to a meter M. A student used the circuit to measure the resistance R of the thermistor at different temperatures θ. (i) Name the meter M used to measure the resistance of the thermistor. (ii) Explain, with the aid of a labelled diagram, how the student varied the temperature of the

thermistor.(iii) How did the student measure the temperature of the thermistor?(iv)The table shows the measurements recorded by

the student.Draw a graph on graph paper of resistance R against temperature θ. Put temperature on the horizontal axis.(v) Using your graph, estimate the temperature of the thermistor when the meter M read 740 Ω.

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θ /°C 20 30 40 50 60 70 80R/Ω 2000 1300 800 400 200 90 40

/ 0C

20 30 40 50 60 70 80 90

R/ Ω

1300 900 640 460 340 260 200 150

Solutions1.(i) See diagram below(ii) Using an ohmmeter as shown(iii) See graph(iv)35 0C to 36.50 C(v) Resistance goes down with increased temperature and

the relationship is not linear.

2.(i) Thermistor, thermometer in waterbath/oil, thermistor

connected to labelled ohmmeter/(digital) multimeter(ii) The thermistor is connected to the ohmmeter and the value of

the resistance was read from the ohmmeter.(iii) By allowing the apparatus to heat up over a bunsen burner.(iv)Label axes correctly on graph paper

Plot six points correctlySmooth curve Good distribution

(v) Range: 28↔ 32 Ω (0C–1) or Ω (K–1) (vi)Oil is a better conductor of heat / water contains air / (impure)

water conducts electricity/good thermal contact

3.(i) Ohmmeter(ii) The apparatus was placed over a hot plate which heated

the water and then the glycerol and the thermistor.(iii) Using a thermometer.(iv)See graph(v) 35 0C.

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TO INVESTIGATE THE VARIATION OF CURRENT (I) WITH P.D. (V) FOR A SEMICONDUCTOR DIODE

1. [2008 OL]The diagram shows a circuit used to investigate the variation of current with potential difference for a semiconductor diode in forward bias.

(iv)Name the apparatus X. What does it measure?(v) Name the apparatus Y. What does it do?(vi)What is the function of the 330 Ω resistor in this circuit? (vii) The table shows the values of the potential difference used and its corresponding current recorded

during the experiment.Using the data in the table, draw a graph on graph paper of the current against the potential difference. Put potential difference on the horizontal axis (X-axis).

(viii) What does the graph tell you about the variation of current with potential difference for a semiconductor diode?

2. [2007]The following is part of a student’s report of an experiment to investigate of the variation of current I with potential difference V for a semiconductor diode.I put the diode in forward bias as shown in the circuit diagram. I increased the potential difference across the diode until a current flowed. I measured the current flowing for different values of the potential difference.I recorded the following data.

(i) Draw a circuit diagram used by the student.(ii) How did the student vary and measure the potential difference? (iii) Draw a graph to show how the current varies with the potential difference.(iv)Estimate from your graph the junction voltage of the diode. (v) The student then put the diode in reverse bias and repeated the experiment.

What changes did the student make to the initial circuit?(vi)Draw a sketch of the graph obtained for the diode in reverse bias.

Solutions1.(i) Ammeter. It measures amps.(ii) Rheostat / variable resistor / potential divider It changes the resistance which in turn changes the voltage.(iii) It protects the diode by limiting the current.(iv)See graph(v) They are not proportional because the current rises rapidly

after the potential difference reaches 0.6 V.

2.(i) See diagram(ii) Adjust rheostat / potential divider /variable power supply unit.

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potential difference/V

0 0.2 0.4 0.6 0.8 1.0

current/mA 0 3 6 14 50 100

V/V 0.60 0.64 0.68 0.72 0.76 0.80I /mA 2 4 10 18 35 120

To measure p.d. a voltmeter was used as shown in the diagram.(iii) See graph(iv)Junction voltage = 0.60 ↔0.78 V (very difficult to be more specific).(v) Reverse connections to the power supply, replace mA with μA.(vi)Correct shape (i.e. showing little or no current as V is increased negatively and maybe indicating a

breakdown.

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Section B – Short Questions

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Short questions from past papers

Reflection

1. State the laws of reflection of light. [2005 OL](i) The incident ray, the normal at the point of incidence and the reflected ray all lie on the same plane.(ii) The angle of incidence is equal to the angle of reflection (i = r).

2. Describe the image that is formed in a concave mirror when an object is placed inside the focus. [2003 OL] [2007 OL]The image is virtual, magnified and upright.

3. A concave mirror can produce a real or a virtual image, depending on the position of the object.Give one difference between a real image and a virtual image. [2004 OL]A real image can be obtained on a screen; a virtual image cannot.In a real image the light rays meet; in a virtual image they do not.A real image is always inverted/ a virtual is erect, a real image is in front / a virtual image is behind.

4. Give two uses for a concave mirror. [2004 OL]Torch, headlights, searchlight, dentist mirror, cosmetic mirror, solar furnace.

Refraction

1. What is meant by refraction of light? [2008] [2006][2009 OL][2005 OL][2002 OL]Refraction is the bending of light as it goes from one medium to another.

2. State the laws of refraction of light. [2002][2003 OL](i) The incident ray, the refracted ray and the normal all lie in the same plane.(ii) Sin i/ Sin r is a constant

3. State Snell’s law of refraction. [2008]The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.

4. Define the term total internal reflection. [2003 OL]Total internal reflection occurs when the angle of incidence in the denser of the two media is greater than the critical angle and light is reflected back into the denser medium.

5. Define the term critical angle. [2004 OL][2003 OL]The critical angle corresponds to the angle of incidence in the denser of two media which causes the angle of refraction to be 900.

6. Why is each fibre in an optical fibre cable coated with glass of lower refractive index? [2009]Because total internal reflection can only occur for rays travelling from a denser to a rarer medium.

7. What is meant by the refractive index of a material? [2004 OL]n = sin i/ sin r, where i is the angle of incidence and r is the angle of refraction.

8. Give two uses of total internal reflection. [2003 OL][2005 OL]Fibre optics, endoscopes, reflective road signs, telecommunications, binoculars, periscope.

9. How is the escape of light from the sides of an optical fibre prevented? [2004 OL]Total internal reflection occurs due to an outer cladding of lower refractive index.

10. An optical fibre has an outer less dense layer of glass. What is the role of this layer of glass? [2004][2009]

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Total internal reflection will only occur if the outer medium is of greater density. It also prevents damage to the surface of the core.

11. Give one use for optical fibres. [2004 OL]Endoscope, telecommunications, binoculars.

12. Give two reasons why the telecommunications industry uses optical fibres instead of copper conductors to transmit signals. [2004]Less interference, boosted less often, cheaper raw material, occupy less space, more information carried in the same space, flexible for inaccessible places, do not corrode, etc.

13. Name a material that is used in the manufacture of optical fibres. [2004 OL]Glass / plastic / sand / silicon

Lenses

1. A diverging lens cannot be used as a magnifying glass. Explain why. [2006]The image is always diminished

2. How does the eye bring objects at different distances into focus? [2002]It can change the shape of the lens which in turn changes the focal length of the lens.

Velocity and acceleration

1. Define velocity [2009 OL][2008 OL][2004 OL][2002 OL]Velocity is the rate of change of displacement with respect to time.

2. Define acceleration [2008 OL][2004 OL][2002 OL]Acceleration is the change in velocity with respect to time

3. Explain the term acceleration due to gravity, g. [2006 OL][2003 OL]It is the acceleration of an object which is in freefall due to the attraction of the earth.

Vectors

1. Give the difference between vector quantities and scalar quantities and give one example of each. [2003]A vector is a quantity which has magnitude and direction. Example: forceA scalar is a quantity which has magnitude only. Example: mass

2. Force is a vector quantity. Explain what this means. [2006 OL]A vector is a quantity which has magnitude and direction.

Force, Mass and Momentum

1. Define the Newton, the unit of force. [2008]The Newton is the force that gives a mass of 1 kg an acceleration of 1 m s-2.

2. Define Force [2004] [2008 OL][2006 OL]A force is something which causes an acceleration.

3. Define Momentum [2004][2004 OL]Momentum = mass × velocity

4. State Newton’s Second Law of Motion [2009][2004] [2003][2007 OL]Force is proportional to the rate of change of momentum.

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5. State Newton’s Third law of Motion. [2006]When body A exerts a force on body B, B exerts a force equal in magnitude (and) opposite in direction to A.

6. Name two forces acting on a cheetah while it is running. [2004 OL]Air resistance, gravity, friction

7. Why is the astronaut’s weight greater on earth than on the moon? [2006 OL]Because acceleration due to gravity is greater on the earth (because the mass of the earth is greater than the mass of the moon).

8. The earth is surrounded by a layer of air, called its atmosphere. Explain why the moon does not have an atmosphere. [2006 OL]Because gravity is less on the moon.

9. A powerful rocket is required to leave the surface of the earth.A less powerful rocket is required to leave the surface of the moon. Explain why. [2008 OL]The force of gravity is less on moon so less force is needed to escape.

10. Using Newton’s first law of motion, explain what would happen to the passengers in a plane if they were not wearing seatbelts while the aircraft was landing. [2002 OL]They would continue to move at the greater initial velocity and so would be ‘thrown’ forward.

11. Draw a diagram to show the forces acting on the ball when it is at position A. [2006]Weight (W) downwards; reaction (R) upwards; force to left (due to friction or curled fingers)

12. Use a diagram to show the forces acting on the skydiver and explain why he reaches a constant speed. [2003]Weight acting down.Air resistance / friction / buoyancy acting up.Air resistance = weight, therefore resultant force = 0 Therefore acceleration = 0

13. What is friction? [2007][2009 OL][2006 OL][2002 OL]Friction is a force that opposes the relative motion between two surfaces in contact.

14. State The Principle of Conservation of Momentum. [2002][2009 OL][2008 OL][2007 OL][2005 OL][2004 OL]In any interaction between two objects, the total momentum before the interaction is equal to the total momentum after the collision, provided no external forces act.

15. A rocket is launched by expelling gas from its engines. Use the principle of conservation of momentum to explain why a rocket rises. [2007 OL]The gas moves down (with a momentum) causing the rocket to move up (in the opposite direction with an equal momentum).

16. A spacecraft is approaching a space station at a constant speed. The spacecraft must slow for it to lock onto the space station. In what direction should the gas be expelled? [2002]Forward (toward the space station).

17. Explain how the principle of conservation of momentum is applied to changing the direction in which a spacecraft is travelling. [2002]As the gas is expelled with a momentum in one direction the rocket moves in the other direction with an equal momentum.

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Pressure

1. Define pressure. [2006][2009 OL][2007 OL][2005 OL][2002 OL]Pressure is Force per unit Area.

2. Give the unit of pressure. [2002 OL][2005 OL]The pascal

3. Name an instrument used to measure pressure. [2002 OL][2005 OL]A barometer

4. Is pressure a vector quantity or a scalar quantity? Justify your answer. [2006]It is a scalar quantity because it does not have a direction.

5. A balloon rises through the atmosphere while the temperature remains constant.What will happen to the balloon as it continues to rise? [2007 OL]It will expand.

6. When air is removed from a metal container it collapses. Explain why. [2002 OL]The pressure outside (due to atmospheric pressure) is greater than the pressure inside.

7. The earth is covered with a layer of air called the atmosphere. What holds this layer of air close to the earth? [2005 OL]Gravity.

8. The type of weather we get depends on the atmospheric pressure. Describe the kind of weather we get when the atmospheric pressure is high. [2005 OL]Good weather, dry, clear skies, little wind, settled.

9. State Boyle’s law. [2009][2006][2007 OL][2003 OL]For a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume.

10. State Archimedes Principle. [2007]When an object is immersed in a fluid, the upthrust it experiences is equal to the weight of the displaced fluid.

11. State the law of flotation. [2008]For a floating object, the weight of the object equals the weight of the fluid displaced.

Gravity

1. State Newton’s Law of Gravitation. [2008] [2005] [2004][2008 OL][2003 OL]Any two objects in the universe are attracted to each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.

2. Give two factors which affect the size of the gravitational force between two bodies. [2006 OL]The mass of the objects and the distance between them.

3. What is the relationship between the acceleration due to gravity g and the distance from the centre of the earth? [2003] g is proportional to 1/d2

4. The international space station (ISS) moves in a circular orbit around the equator at a height of 400 km. (i) What type of force is required to keep the ISS in orbit? (ii) What is the direction of this force? [2008]

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(i) Gravity(ii) Towards the centre of the orbit / inwards / towards the earth

5. An astronaut in the ISS appears weightless. Explain why. [2008]He is in a state of free-fall (the force of gravity cannot be felt).

6. Why is the acceleration due to gravity on the moon less than the acceleration due to gravity on the earth? [2003 OL]The earth has a greater mass than the moon.

7. The earth is covered with a layer of air called the atmosphere. What holds this layer of air close to the earth? [2005 OL]Gravity.

8. The earth is surrounded by a layer of air, called its atmosphere. Explain why the moon does not have an atmosphere. [2006 OL]Because gravity is less on the moon.

Moments

1. Define the moment of a force. [2006 OL][2003 OL]The moment of a force is equal to the force multiplied by the distance between the force and the fulcrum.

2. Why is it easier to turn a nut using a longer spanner than a shorter one? [2006]The distance from the fulcrum is greater therefore there is a greater turning effect.

3. Explain why the handle on a door is on the opposite side to the hinges of the door. [2003 OL]In order to maximise the distance between the force and the fulcrum.

4. A crane is an example of a lever. Give another example of a lever. [2006 OL]Crowbar / nailbar / nutcracker / wheelbarrow / tongs / door handle etc.

Work, Energy and Power1. Define energy [2005 OL]

Energy is defined as the ability to do work

2. Define work. [2007 OL]Work is the product of force by displacement

3. What is the difference between potential energy and kinetic energy? [2007 OL]Potential energy is energy a body has due to its position; kinetic energy is energy a body has due to its motion.

4. Name one method of producing electricity. [2005 OL]Solar, wind, wave, tidal, biomass, coal, oil, gas, hydroelectricity, geothermal, nuclear, uranium, turf.

5. What type of energy is associated with wind, waves and moving water? [2005 OL]Renewable energy.

6. Which of the following is not a renewable source of energy: wind, nuclear, solar, hydroelectric? [2007 OL]Nuclear

7. Give one disadvantage of non-renewable energy sources. [2005 OL]They will run out.

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8. How does the sun produce heat and light? [2005 OL]Through nuclear reactions.

9. State one energy conversion that takes place in an electrical generator. [2003 OL]Kinetic to electric.

10. What energy conversion takes place when a fuel is burnt? [2005 OL]Chemical to heat.

11. What energy conversion takes place in a solar panel? [2004 OL]Light to electricity, light to heat.

12. Why is a fluorescent tube an efficient source of light? [2008]Most of the (electrical) energy is converted to light (energy)

13. Why is a filament light bulb not an efficient source of light? [2007]Almost all of the energy is given off as heat.

14. What is the difference between potential energy and kinetic energy? [2007 OL]Potential energy is energy a body has due to its position; kinetic energy is energy a body has due to its motion.

15. Give one factor on which the potential energy of a body depends. [2005 OL]Mass, height, acceleration due to gravity (g).

16. State the Principle of Conservation of Energy. [2008] [2005]Energy cannot be created or destroyed; it can only be changed from one form to another.

17. Define Power [2006] [2002] [2007 OL]Power is the rate at which work is done.

18. What is the unit of power? [2005 OL][2007 OL]The watt.

Circular Motion

1. Define (i) velocity [2006] and (ii) angular velocity. [2006] [2005](i) Velocity is the rate of change of displacement.(ii) Angular velocity is the rate of change of angle.

2. Define ‘Centripetal Force’ [2005]Centripetal Force is the force - acting in towards the centre - required to keep an object moving in a circle.

3. The moon orbits the earth. What is the relationship between the period of the moon and the radius of its orbit? [2009]The period squared is proportional to the radius cubed.

4. Give an expression for centripetal force. [2004]

5. Centripetal force is required to keep the earth moving around the sun. [2004](i) What provides this centripetal force?(ii) In what direction does this centripetal force act?

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(i) Gravitational pull of the sun.(ii) Towards the centre.

Simple Harmonic Motion

1. State Hooke’s Law. [2009][2007] [2003] [2002]Hooke’s Law states that when an object is stretched the restoring force F is directly proportional to the displacement provided the elastic limit is not exceeded

2. A mass at the end of a spring is an example of a system that obeys Hooke’s Law. Give two other examples of systems that obey this law. [2002]Stretched elastic, pendulum, oscillating magnet, springs of car, vibrating tuning fork, object bobbing in water waves, ball in saucer, etc.

3. The equation F = – ks, where k is a constant, is an expression for a law that governs the motion of a body. Name this law and give a statement of it. [2002]Hooke’s Law states that when an object is stretched the restoring force is directly proportional to the displacement, provided the elastic limit is not exceeded.

4. Give the name for this type of motion and describe the motion. Simple harmonic motion; an object is said to be moving with Simple Harmonic Motion if its acceleration is directly proportional to its distance from a fixed point in its path, and its acceleration is directed towards that point.

Temperature and Thermometers

1. What is meant by the temperature of a body? [2009 OL][2008 OL]The Temperature of an object is a measure of the hotness or coldness of that object.

2. What does a thermometer measure? [2005 OL]Temperature

3. What is the unit of temperature? [2008 OL]The SI unit of temperature is the Kelvin (K)

4. What is heat? [2008 OL]Heat is a form of energy

5. What is the difference between heat and temperature? [2003]Heat is a form of energy.Temperature is a measure of the hotness of an object.

6. To calibrate a thermometer, a thermometric property and two fixed points are needed.What are the two fixed points on the Celsius scale? [2005 OL]The melting point and boiling point of water.

7. Name two scales that are used to measure temperature. [2009 OL]Celsius and Kelvin.

8. Give the equation that defines temperature on the Celsius scale. [2002]T (0C) = T(K) – 273

9. What is the boiling point of water on the Celsius scale? [2009 OL]100 °C

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10. The SI unit is named in honour of Lord Kelvin. What is the temperature of the boiling point of water in kelvin? [2008]273.15 + 100 = 373.15 K

11. The temperature of a body is 300 K. What is its temperature in degrees Celsius? [2003 OL]300 – 273 = 27 0C.

12. The temperature of a body is 34 °C. What is its temperature in kelvin? [2007 OL]273 + 34 = 307 (K)

13. Explain the term thermometric property. [2004] [2003][2005 OL][2004 OL][2002 OL]A thermometric property is a property which changes measurably with temperature.

14. Name the thermometric property used in a mercury thermometer. [2005 OL][2009 OL]Length (or volume) of the liquid.

15. What is the thermometric property of a thermocouple? [2005]emf

16. Name a thermometric property other than emf. [2003][2005 OL][2006 OL][2008 OL]Length, pressure, volume, resistance, colour

17. Name one other type of thermometer and state its thermometric property. [2009 OL]Thermistor – resistance, Thermocouple – emf, Liquid crystal - colour

18. Why is it necessary to have a standard thermometer? [2003][2009][2009 OL]Different thermometers have different thermometric properties at the same temperature.

Heat and Heat Transfer

1. Define specific heat capacity. [2006] [2004][2008 OL][2002 OL]Specific heat capacity is the heat energy required to raise the temperature of 1 kg of a substance by 1 K

2. Define specific latent heat. [2004] Specific latent heat is the heat energy required to change the state of 1 kg of a substance without a change in temperature.

3. What is heat? [2003][2008 OL]Heat is a form of energy

4. [2003 OL][2004 OL][2005 OL][2006 OL][2007 OL][2008 OL][2009]Name two methods by which heat can be transferred. Conduction, convection and radiation.

5. What is meant by conduction? [2004 OL]Conduction is the movement of heat energy through a substance by the passing on of molecular vibration from molecule to molecule, without any overall movement of the substance.

3. What is convection? [2006 OL]Convection is the transfer of heat through a fluid by means of circulating currents of fluid caused by the heat.

6. Why are the pipes in the solar panel usually made from copper? [2004 OL[It is a good heat conductor.

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7. What is the effect of increasing the U-value of a structure? [2002 OL]It means that the heat conductivity of the structure is increased.

8. The U-value of a house is a measure of the rate of heat loss to the surroundings.Give two ways in which the U-value of a house can be reduced. [2004 OL]Fibreglass in attic, insulation in cavity wall, double glazing, carpets

9. In an electric storage heater, bricks with a high specific heat capacity are heated overnight by passing an electric current through a heating coil in the bricks. The bricks are surrounded by insulation.Why is insulation used to surround the bricks? [2006 OL]To prevent heat-loss.

10. Name a material that could be used as insulation in a storage heater. [2006 OL]Fibre glass / rockwool / cotton wool.

11. What is convection? [2006 OL]Convection is the transfer of heat through a fluid by means of circulating currents of fluid caused by the heat.

12. Why is the heating element of an electric kettle near the bottom? [2002 OL]Because hot water rises.

13. Explain how the storage heater heats the air in a room. [2006 OL]The heater heats the air which is beside it. This hot air then rises and is replaced by cold air. This process then gets repeated.

14. Why does warm water rise to the top of the solar panel? [2004 OL]The water expands when heated and therefore has a lower density and gets replaced by water which has a higher density (cold water). This is convection.

15. An electric toaster heats bread by convection and radiation.What is the difference between convection and radiation as a means of heat transfer? [2008]Convection requires a medium, radiation does not.

16. Why are the pipes in the solar panel usually painted black? [2004]Black is a good absorber of radiation.

17. Storage heaters have a large heat capacity. Explain why. [2004]They are heated only at night but must release energy slowly during the day.

18. Why does the temperature of an athlete reduce when she perspires? [2007]As the water evaporates it takes heat energy from the body.

Waves and Wave Motion

1. Explain what is meant by the frequency of a wave? [2007 OL]The frequency of a wave is the number of waves passing a fixed point per second.

2. What is meant by the amplitude of a wave? [2005 OL]Amplitude corresponds to the height of the wave.

3. Explain the difference between Transverse and Longitudinal waves. [2005][2006 OL]A Transverse wave is a wave where the direction of vibration is perpendicular to the direction in which the wave travels.

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A Longitudinal Wave is a wave where the direction of vibration is parallel to the direction in which the wave travels.

4. Explain the term diffraction [2009][2005 OL][2004 OL][2002 OL]Diffraction is the spreading out of a wave when it passes through a gap or passes by an obstacle.

5. Explain the term interference. [2005 OL][2004 OL]Interference occurs when waves from two sources meet to produce a wave of different amplitude.

6. Explain the term constructive interference. [2003]Constructive interference occurs when two waves combine to produce a wave of greater amplitude.

7. Explain the term coherent sources. [2003]Coherent sources are waves which have the same frequency and are at in phase.

8. What is the Doppler effect? [2008] [2007] [2006] [2003] [2002]The Doppler Effect is the apparent change in frequency due to relative motion between source and observer.

Sound1. Define Sound Intensity [2007] [2002]

Sound Intensity is defined as power per unit area.

2. Explain the term resonance. [2007 OL]Resonance is the transfer of energy between two objects which have the same natural frequency.

3. Explain the term natural frequency. [2007 OL]Natural frequency is the frequency at which an object will vibrate if free to do so.

4. The sound intensity level at a concert increases from 85 dB to 94 dB when the concert begins. By what factor has the sound intensity increased? [2009]If sound intensity doubles intensity level increases by 3 dB, so if intensity has increased by 9 dB then the sound intensity must have increased by a factor of 8.

The wave nature of Light

1. Explain the term dispersion. [2009][2007 OL]Dispersion is the splitting up of white light into its constituent colours.

2. Explain what is meant by a spectrum. [2007 OL]A spectrum refers to the range of colours present in white light.

3. Explain the term monochromatic light. [2009 OL]Monochromatic light is light of one wavelength only.

4. Explain the term diffraction grating. [2009 OL]A diffraction grating consists of a piece of transparent material on which a very large number of opaque (black) parallel lines are engraved.

5. Explain how the diffraction grating produces a spectrum. [2009]Different colours have different wavelengths so constructive interference occurs at different positions for each separate wavelength.

6. What are complementary colours? [2003 OL]Complementary colours are pairs of colours consisting of a primary and a secondary colour, such that when combined they give white light.

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Static Electricity

1. State Coulomb’s law of force between electric charges. [2005] [2003] [2007 OL]Coulomb’s Law states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

2. Define electric field strength. [2009][2007] [2005] [2003] [2002]Electric field strength is defined as force per unit charge.

3. Give the unit of electric field strength. [2007][2003]The unit of electric field strength is the newton per coulomb (N C-1).

4. Give one effect of static electricity? [2008 OL]Lightning, static discharge, receive shock after walking across carpets, attracts objects, can damage electronics.

5. Identify two hazards caused by static electricity. [2004]Electric shock / explosion in flour mills /explosion when fuelling aircraft/ damage to electronic devices / electrical storm / static cling, etc.

6. The build-up of electric charge can lead to explosions. Give two examples where this could happen. [2003 OL]Dust e.g. flour mill explosions, inflammable vapours e.g. fuelling aircraft, lightning

7. How can the build-up of electric charge on an object be reduced? [2003 OL]By earthing the object (i.e. using a conductor to connect the object to the earth which allows the charge to flow to earth).

8. Explain why the gold leaf on the electroscope diverges when a positively charged rod is brought

close to the metal cap. [2005 OL]Some of the electrons at the bottom of the electroscope are attracted to the top due to the positive charge on the rod and as a result there is an excess of positive charge on the bottom, including on the gold leaf. Because similar charges repel the gold leaf moves away from the main section.

9. Give one use of an electroscope. [2005 OL]To detect charge

10. Why is Coulomb’s law an example of an inverse square law? [2006][2005]Force is inversely proportional to distance squared.

11. Give two differences between the gravitational force and the electrostatic force between two electrons. [2005]Gravitational force is much smaller than the electrostatic force. Gravitational force is attractive, electrostatic force (between two electrons) is repulsive.

12. All the charge resides on the surface of a Van de Graff generator’s dome. Explain why. [2007]Like charges repel and the charges are a maximum distance apart on the outside surface of dome.

13. Give an application of the fact that all charge resides on the outside of a conductor. [2007]Electrostatic shielding / co-axial cable / TV (signal) cable / to protect persons or equipment, enclose them in hollow conductors /Faraday cages (there is no electric field inside a closed conductor), etc.

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Electric Current

1. What is an electric current? [2006] [2008 OL][2006 OL][2004 OL][2003 OL][2002 OL]An electric current is a flow of charge.

2. What is the unit of electric charge? [2003 OL]The ampere.

Potential Difference and Capacitance1. Define potential difference. [2009][2005] [2004][2002 OL]

Potential difference is the work done in moving a charge of 1 Coulomb from one point to another.

2. Explain the term emf. [2003]The term emf is used to describe a potential difference when it applies to a full circuit.

3. Name a source of potential difference. [2008 OL]Battery, generator, thermocouple.

4. Name an instrument used to measure potential difference. [2007 OL]A voltmeter

5. Define capacitance. [2009][2008] [2004][2002 OL]The capacitance of a conductor is the ratio of the charge on the conductor to its potential.

6. Give one use of a capacitor. [2006 OL][2006 OL][2007 OL]Store charge / (radio) tuning / smoothing / store energy / flash guns for cameras, phone charger, blocks d.c.

7. List the factors that affect the capacitance of a parallel plate capacitor. [2006]Common area of plates, distance apart, permittivity of dielectric between plates.

8. How would you demonstrate that the capacitance of a parallel plate capacitor depends on the distance between its plates? [2008]Connect the two parallel plates to a digital multi-meter (DMM) set to read capacitance. Note the capacitance.Increase the distance between them – note that the capacitance decreases.

Resistance1. Define resistance. [2007] [2005]

The resistance of a conductor is the ratio of the potential difference across the conductor to the current flowing through it.

2. State Ohm’s Law [2007 OL][2006 OL][2005 OL]Ohm’s Law states that the current flowing through a conductor is directly proportional to the potential difference across it, assuming constant temperature.

3. Define resistivity. [2008] [2007] [2002]Resistivity is defined as the resistance of a cube of material of side one metre.

4. Give the unit of resistivity. [2008]The ohm-metre

5. Give two uses for the multimeter. [2008 OL]It can function as a voltmeter, ammeter or ohmmeter.

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6. Explain why the resistance of the bulb is different when it is not connected to the mains. [2006]Cold filament has lower resistance

Effects of an Electric Current

1. Give one use for electricity in the home. [2006 OL]Heating / cooking / lighting /named electrical appliance etc.

2. List three effects of an electric current. [2004 OL][2008 OL]Magnetic effect, heating effect and chemical effect.

3. Describe an experiment that demonstrates the heating effect of an electric current. [2002][2004 OL]Connect a electrical calorimeter containing water to a power supply and notice the increase in temperature using a thermometer.

4. State two factors on which the heating effect of an electric current depends. [2004 OL]Size of current, length of coil.

5. Explain why high voltages are used in the transmission of electrical energy. [2005]High voltages result in smaller currents therefore less energy is lost as heat.

6. Suggest a method of reducing the energy “lost” in ESB power lines. [2002]Transfer the electrical energy at a higher voltage which would result in a lower current, therefore less energy lost as heat.

7. Name two safety devices that are used in domestic electric circuits. [2004 OL][2005 OL][2007 OL]Fuse, miniature circuit breaker, residual current device, earthing, 3 pin plug etc.

8. What is the colour of the earth wire in an electric cable? [2006 OL]Green and yellow

9. What is the colour of the wire that should be connected to the fuse in a plug? [2009 OL]Brown

10. Give the standard colour of the insulation on the wires connected to each of the terminals L, N and E on the 3 pin plug. [2003 OL]L (live) is brown, N (neutral) is blue, E (earth) is green-yellow

11. What is the purpose of the wire connected to the terminal E on the plug? [2003 OL]The earth wire protects from electrocution / shock by conducting the current to earth.

12. Name and give the colour of the wire that should be connected to the fuse in a standard three-pin plug. [2004] [2008 OL]Live, brown

13. Give one safety precaution that should be taken when wiring a plug. [2006 OL]Screw connections are fully tightened / fit the correct size fuse / ensure to match the colour codes

14. Explain why a fuse is used in a plug. [2003 OL][2009 OL]It ‘blows’ and breaks the circuit if too large a current flows, preventing possible electrocution.

15. Explain how a fuse works. [2009 OL]

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When too high a current flows the thin wire heats up and melts which breaks the circuit.

16. What will happen when a current of 20 A flows through a fuse marked 13 A? [2006 OL]The fuse blows which stops the current.

17. Why would it be dangerous to use a fuse with too high a rating? [2009 OL]It would allow too large a current to flow so the device could overheat.

18. Explain why replacing a fuse with a piece of aluminium foil is dangerous. [2004]If a very large current flows the foil may still not break and so may start a fire.

19. Name a common material used to conduct electricity in electric cables. [2006 OL]Copper

20. Some electrical appliances are supplied with two-pin plugs. Why is an earth wire not required in these devices? [2004][2006 OL]They have a plastic housing so even if they are in contact with a live wire the current will not travel along the cover.

21. Why is the coating on electric cables made from plastic? [2006 OL]It is an insulator.

22. A toaster has exposed metal parts. How is the risk of electrocution minimised? [2008]The metal parts are earthed.

23. Bonding is a safety precaution used in domestic electric circuits. [2003 OL]How does bonding improve safety in the home?Bonding is where all metal pipes are connected to earth preventing accidental electrocution.

24. Name another device with the same function as a fuse. [2009 OL]Circuit breaker, trip switch, RCD, MCB

25. What is the purpose of a miniature circuit breaker (MCB) in an electric circuit? [2003][2002 OL]It behaves as a fuse when too large a current flows

26. When will an RCD (residual current device) disconnect a circuit? [2009]When the magnitude of the current flowing in is different from that flowing out.

27. An RCD is rated 30 mA. Explain the significance of this current. [2006]The RCD trips the circuit if the current reaches 30 mA.

28. What is the purpose of a residual current device (RCD) in an electrical circuit? [2004][2002]It acts as a safety device by breaking the circuit if there is a difference between the live and the neutral in a circuit.

29. Name a device that is often used nowadays in domestic electric circuits instead of fuses. [2003 OL]Miniature circuit breakers (MCBs) or residual current devices (RCDs).

30. Give one advantage of a Residual Current Device (RCD) over a Miniature Circuit Breaker (MCB). [2004]RCD responds v. Quickly, RCD responds to tiny currents

31. What are the charge carriers when an electric current passes through an electrolyte? [2008]Ions

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MCBs and RCDs

32. How would the VI graph for a metal differ if its temperature were increasing? [2003]If temperature was increasing it would no longer be linear; instead there would be a curve to the right because resistance would increase.

33. What is the kilowatt-hour? [2004 OL]The kilo-watt hour is the amount of energy used by a 1000 Watt appliance in one hour.

34. What is the function of the ESB meter? [2006 OL]It records the amount of units used.

Semiconductors3. What is a semiconductor? [2003 OL][2006 OL][2009 OL]

A semiconductor is a material whose resistivity is between that of a conductor and insulator.

4. Name a material used in the manufacture of semiconductors. [2003 OL][2006 OL]Silicon, germanium

5. Why is silicon a semiconductor? [2007]It has a resistivity between that of a conductor and an insulator.

6. Give one difference between conduction in metals and conduction in semiconductors. [2002 OL]There are two types of charge carriers (holes and electrons) in semiconductors, whereas with metals electrons are the only charge carriers.Conduction increases with temperature for semiconductors whereas conduction decreases with temperature for metals.

7. As the temperature of a room increases, explain why the resistance of a thermistor decreases. [2005]More energy is added to the thermistor therefore more electrons are released and are available for conduction.

8. Give two uses of semiconductors. [2002 OL]Rectifiers, transistors, diodes, thermistors, thermometers, radios/TV, etc.

9. Give a use for a thermistor. [2005 OL]Thermometer, heat sensor, temperature control.

10. What is doping? [2004][2003 OL][2009 OL]Doping is the addition of a small amount of atoms of another element to a pure semiconductor to increase its conductivity.

11. Semiconductors can be made p-type or n-type. How is a semiconductor made p-type? [2002 OL]By doping it with Boron.

12. Explain how the presence of phosphorus and boron makes silicon a better conductor. [2009]When phosphorus is added more electrons become available as charge carriers. When boron is added more positive holes become available as charge carriers.

13. Give one difference between a p-type semiconductor and an n-type semiconductor. [2003 OL]P-type material contains more holes than n-type material.N-type material contains more free electrons than p-type material.

14. What are the charge carriers when an electric current passes through a semiconductor? [2008][2003 OL] Electrons and (positive) holes

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15. What is a p-n junction? [2003 OL][2006 OL]A p-n junction is the region connecting the p-type semiconductor to the n-type semiconductor

16. What happens at the boundary of the two adjacent layers? [2009]Electrons and holes cross the junction cancelling each other out and recombine and as a result there are no free charge carriers.A depletion layer is therefore formed between the n-type and p-type regions and as a result a junction voltage is created.

17. A p-n junction is formed by taking a single crystal of silicon and doping separate but adjacent layers of it. A depletion layer is formed at the junction. Explain how a depletion layer is formed at the junction. [2004][2009 OL]Electrons from n-type and holes from p-type cross the junction and recombine cancelling each other out and as a result there are no free charge carriers across this narrow insulating region.A depletion layer is therefore formed which now acts as a ‘barrier’ between the n-type and p-type regions and as a result a junction voltage is created.

18. [2009](i) Describe what happens at the boundary when the semiconductor diode is forward biased.(ii) Describe what happens at the boundary when the semiconductor diode is reverse biased.

The depletion layer breaks down and the diode conducts.The width of depletion layer gets increased and the region acts as an insulator.

19. Why does the p-n junction become a good conductor as the potential difference exceeds 0.6 Volts? [2004]The depletion layer is overcome and as a result a large current flows.

20. What is a diode? [2003 OL]A diode is a device that allows current to flow in one direction only.

21. Give a use of a semiconductor diode. [2009]A rectifier

22. Give an example of a device that contains a rectifier. [2003 OL]Radio, television, computer, battery charger, mobile phone charger.

Magnets and magnetic fields

1. What is a magnetic field? [2003 OL][2005 OL][2006 OL][2009 OL]A Magnetic Field is any region of space where magnetic forces can be felt.

2. Give one use of the earth’s magnetic field. [2004][2003 OL]Navigation, protective layer around the earth which deflects dangerous cosmic rays (sometimes called solar winds).

3. Why does a magnet that is free to rotate point towards the North? [2007]It is the north end of the magnet which is being attracted to the south-end of the Earth’s magnetic field (which is located at what we call the north pole).

4. A solenoid carrying a current and containing an iron core is known as an electromagnet.Give one use of an electromagnet. [2006 OL]Electric bell / scrap yard crane / speaker / doorbell.

5. State one advantage of an electromagnet over an ordinary magnet. [2006 OL]

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It can be turned on and off.

Current in a Magnetic Field

1. A current-carrying conductor experiences a force when placed in a magnetic field. Name two factors that affect the magnitude of the force. [2002][2002 OL][2005 OL]Strength of magnetic field, size of current flowing, length of conductor in magnetic field.

2. Name two devices that are based on the principle that a current-carrying conductor in a magnetic field experiences a force. [2002 OL][2002 OL][2006 OL]Motor, galvanometer, loudspeaker.

3. State the principle on which the definition of the ampere is based. [2007]A current-carrying conductor in a magnetic field experiences a force.

4. Define the ampere, the SI unit of current. [2006][2003]The ampere is the amount of charge which, if flowing in two very long parallel wires one metre apart in a vacuum will experience a force of 2 × 10-7 N per metre length.

5. Give an expression for the force acting on a charge q moving at a velocity v at right angles to a magnetic field of flux density B. [2003]F = Bqv

Electromagnetic Induction

1. Explain the term emf[2003]emf stands for electromotive force. It is a potential difference applied to a full circuit.

2. What is electromagnetic induction? [2008][2004][2002][2002 OL][2004 OL][2007 OL][2008 OL]Electromagnetic Induction occurs when an emf is induced in a coil due to a changing magnetic flux.

3. State Faraday’s law of electromagnetic induction. [2007][2005]Faraday’s Law states that the size of the induced emf is proportional to the rate of change of flux.

4. State Lenz’s law of electromagnetic induction. [2002]Lenz’s Law states that the direction of the induced emf is always such as to oppose the change producing it.

5. State the laws of electromagnetic induction. [2008][2003]

6. Define magnetic flux. [2006][2005]Magnetic flux is defined as the product of magnetic flux density multiplied by area.

7. Electricity produced in a generating station is a.c. What is meant by a.c.? [2008 OL]Alternating current

8. What is a diode? [2003 OL] A diode is a device that allows current to flow in one direction only.

9. Give an example of a device that contains a rectifier. [2003 OL]Radio, television, computer, battery charger, mobile phone charger.

10. Name a device that is based on electromagnetic induction. [2004 OL][2005 OL]Dynamo, generator, induction motor, transformer, dynamo

11. What is a transformer used for? [2003 OL]

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To increase or decrease voltage.

12. The transformer is a device based on the principle of electromagnetic induction. Name two devices that use transformers. [2002 OL][2007 OL]Computer, radio, TV, doorbell, washing machine, mobile phone chargers, power supply, etc.

13. How is the iron core in a transformer designed to make the transformer more efficient? [2002 OL]It has a laminated core.

14. The efficiency of a transformer is 90%. What does this mean? [2002 OL]10% of the power in is lost.

15. State one energy conversion that takes place in an electrical generator. [2003 OL]Kinetic to electric.

The Electron

1. List two properties of the electron. [2003][2003 OL][2005 OL][2006 OL][2008 OL]Negative charge, negligible mass , orbits nucleus, no internal structure, deflected by electric / magnetic field etc.

2. Name another subatomic particle. [2005 OL]Proton, neutron.

3. Name the Irishman who gave the electron its name in the nineteenth century. [2003]George Stoney

4. What is thermionic emission? [2002 OL][2009 OL]Thermionic emission is the emission of electrons from the surface of a hot metal.

5. Give two ways of deflecting a beam of electrons. [2008] [2002 OL][2005 OL]By means of an electric field and a magnetic field.

6. What are cathode rays? [2009 OL]Cathode rays are streams of high speed electrons.

7. Give a use of a cathode ray tube. [2002 OL][2005 OL][2009 OL]Old-style televisions/ computer monitor, X-ray machine/oscilloscope /heart monitor/ECG.

8. How are electrons accelerated in a cathode ray tube? [2007]By a the high positive voltage at the anode.

9. What happens when the electrons hit the screen? [2005 OL][2009 OL]Light is emitted (the screen fluoresces).

10. What happens to the energy of the electron when it hits the screen of the CRT? [2003]It gets converted to light.

11. Which one of the following is emitted from a metal surface when suitable light shines on the metal? protons, neutrons, electrons, atoms [2004 OL]Electrons

12. Distinguish between photoelectric emission and thermionic emission. [2004]Photoelectric Effect: Emission of electrons when light of suitable frequency falls on a metal.

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Thermionic Emission: Emission of electrons from the surface of a hot metal.

13. What is the photoelectric effect? [2008][2005][2003][2005 OL][2008 OL]The Photoelectric Effect is the emission of electrons from a metal due to light of a suitable frequency falling upon it.

14. Give one application of the photoelectric effect. [2005][2006 OL][2009 OL]Sound track in film, photography, counters, photocell, burglar alarm, automatic doors, etc.

15. What is a photon? [2003 OL][2009]A photon is a packet of electromagnetic radiation.

16. Why as the quantum theory of light revolutionary? [2008]Light has a particle nature (as well as a wave nature)

17. A freshly cleaned piece of zinc metal is placed on the cap of a negatively charged gold leaf electroscope and illuminated with ultraviolet radiation. [2004]

(i) Explain why the leaves of the electroscope collapse. Photoelectric emission occurs (electrons get emitted from the surface of the metal). The leaves become uncharged and therefore collapse.

(ii) Explain why the leaves do not collapse when the zinc is covered by a piece of ordinary glass.Ordinary glass does not transmit UV light

(iii) Explain why the leaves do not collapse when the zinc is illuminated with green light.The energy associated with photons of green light is too low for the photoelectric effect does not occur, so no electrons are emitted from the electroscope.

(iv)Explain why the leaves do not collapse when the electroscope is charged positively. Any electrons emitted are attracted back to the positive electroscope.

18. In an experiment to demonstrate the photoelectric effect, a piece of zinc is placed on a gold leaf electroscope. The zinc is given a negative charge causing the gold leaf to deflect. [2006 OL]

(i) Explain why the gold leaf deflects when the zinc is given a negative charge.Some of the excess electrons flow down to the bottom and the gold leaf moves away from the main section because similar charges repel.

(ii) Ultraviolet radiation is then shone on the charged zinc and the gold leaf falls. Explain why. Many electrons are emitted from the zinc as a result of the ultraviolet radiation shining on it. Electrons from the main part of the electroscope flow up to replace this so there aren’t as many electrons on the gold leaf to feel the repulsion.

(iii) What is observed when the experiment is repeated using infrared radiation? Infrared radiation will not have sufficient energy to release electrons so the gold leaf will not diverge to begin with.

19. Give two applications of a photocell. [2003 OL] [2002 ][2008 OL]Burglar alarm, smoke alarms, safety switch, light meters, automatic lights, counters, automatic doors, control of central heating burners, sound track in films, scanner reading bar codes, stopping conveyer belt, solar cells etc.

20. What are X-rays? [2006][2004 OL][2007 OL]High frequency electromagnetic radiation.

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21. Give one use of X-rays. [2004 OL][2007 OL]To photograph bones/ internal organs, to treat cancer, to detect flaws in materials.

22. Who discovered X-rays? [2006]X-rays were discovered by Wilhelm Röntgen in 1895 (shouldn’t have got asked – not on the syllabus).

23. How are X-rays produced? [2009]Accelerated (fast moving) electrons strike a (heavy) metal target causing electrons in the target to rise to a high orbital level. When these electrons fall back down to a lower lever they emit they energy as X-rays.

24. How are the electrons emitted from the cathode? [2006][2005][2004 OL][2007 OL]The electrons are emitted from the cathode due to thermionic emission because the filament is hot.

25. How are the electrons accelerated? [2006]By the high voltage between the anode and cathode.

26. What is the function of the high voltage across the X-ray tube? [2004 OL][2007 OL]To accelerate the electrons.

27. Name a suitable material for the target T in the X-ray tube. [2004 OL][2007 OL]Tungsten

28. What happens when the electrons hit part B? [2007 OL]Some inner electrons in the tungsten target get bumped up to a high orbital, then quickly fall back down to a lower lever, emitting X-rays in the process.

29. Why is a lead-shield normally put around an X-ray tube? [2002 OL]For protection (to prevent X-rays entering the body).

30. Give one safety precaution when using X-rays. [2007 OL]Use a lead shield, lead apron, lead glass, monitor dosage.

31. Justify the statement “X-ray production may be considered as the inverse of the photoelectric effect.” [2002]X-ray: Electrons in, electromagnetic radiation is emitted.Photoelectric: electromagnetic radiation in and electrons are emitted.

The Atom, the Nucleus and Radioactivity1. Rutherford had bombarded gold foil with alpha particles. What conclusion did he form about the

structure of the atom? [2005]The atom was mostly empty space with a dense positively-charged core and with negatively-charged electrons in orbit around it.

2. What is the structure of an alpha particle? [2009][2005][2008 OL]An alpha particle is identical to a helium nucleus (composed of 2 protons and 2 neutrons).

3. How are the electrons arranged in the atom? [2008 OL]They orbit the nucleus at discrete levels.

4. Describe the Bohr model of the atom. [2006]A dense positively-charged nucleus with the negatively-charged electrons in orbit at discrete levels around it.

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5. Describe how an emission line spectrum is produced. [2007]When the gas is heated the electrons in the gas are move up to higher orbital level and as they fall back down they emit electromagnetic radiation of a specific frequency.

6. When the toaster is on, the coil emits red light. [2008]Explain, in terms of movement of electrons, why light is emitted when a metal is heated. Electrons gain energy and jump to higher energy. Then when they fall back down they emit electromagnetic radiation in the form of light.

7. What is an isotope? [2007][2003][2009 OL]Isotopes are atoms which have the same atomic number but different mass numbers.

8. Give two examples of radioisotopes. [2002 OL]Iodine, caesium, radon, carbon 14, etc.

9. How many neutrons are in a 14C nucleus? [2003]Eight

10. What is radioactive decay? [2003][2003 OL]Radioactive decay is the breakup of unstable nuclei with the emission of one or more types of radiation.

11. What is radioactivity? [2004 OL][2005 OL][2007 OL]Radioactivity is the breakup of unstable nuclei with the emission of one or more types of radiation.

12. Name the three types of radiation. [2009 OL]Alpha (α), beta (β) and gamma (γ).

13. Which radiation is negatively charged? [2009 OL]Beta (β)

14. Which radiation has the shortest range? [2009 OL]Alpha (α)

15. Which radiation is not affected by electric fields? [2009 OL]Gamma (γ)

16. Name the French physicist who discovered radioactivity in 1896. [2004 OL]Henri Becquerel (you shouldn’t have been asked this).

17. What is measured in becquerels? [2002 OL]Rate of decay, activity of a radioactive substance.

18. Apart from “carbon dating”, give two other uses of radioactive isotopes. [2003][2002 OL][2005 OL]Medical imaging, (battery of) heart pacemakers, sterilization, tracers, irradiation of food, killing cancer cells, measuring thickness, smoke detectors, nuclear fuel, detect disease, detect leaks.

19. Give two examples of radioisotopes. [2002 OL]Iodine, caesium, radon, carbon 14, etc.

20. Name an instrument used to detect radiation/ alpha particles/ measure the activity of a sample. [2008][2007][2003 OL][2004 OL][2005 OL][2007 OL][2008 OL][2009 OL]

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Radioactivity

Geiger Muller tube.

21. What is the principle of operation of this instrument? [2008][2007][2004 OL]Incoming radiation causes ionisation of the gas.

22. Give an application of radioactivity. [2005]Smoke detectors, carbon dating, tracing leaks, cancer treatment, sterilising, etc.

23. Give one use of a radioactive source. [2004 OL]Carbon dating, radiotherapy, sterilising medical equipment, killing bacteria in food, smoke alarm

24. Distinguish between radioactivity and fission. [2005]Radioactivity is the breakup of unstable nuclei with the emission of one or more types of radiation.Nuclear Fission is the break-up of a large nucleus into two smaller nuclei with the release of energy (and neutrons).

25. Radioactivity causes ionisation in materials. What is ionisation? [2005]Ionisation occurs when a neutral atom loses or gains an electron.

26. Explain the term half-life. [2007][2002 OL][2005 OL]Time for half the radioactive nuclei in a sample to decay

27. 14C decays to 14N. Write an equation to represent this nuclear reaction. [2003]

28. Cobalt−60 is a radioactive isotope and emits beta particles. Write an equation to represent the decay of cobalt−60. [2005]

29. Write a nuclear equation to represent the decay of carbon-14 by beta emission. [2007]14

6C → 714N + -1

0e ( accept e in lieu of β)

30. 14C decays to 14N. Write an equation to represent this nuclear reaction. [2003]14

6C → 714N + -1

0e

31. Cobalt−60 is a radioactive isotope and emits beta particles. [2005]Write an equation to represent the decay of cobalt−60.

32. Why does the 12C in dead tissue remain “undisturbed”? [2003]It is not radioactive / it is not exchanging with the atmosphere / it is stable.

33. What is meant by background radiation? [2002 OL]Radiation which is in the environment due to rocks/cosmic radiation.

34. Give two precautions that are taken when storing the plutonium / dealing with radioactive sources. [2003 OL][2004 OL]Use thick shielding, use a tongs, use protective clothing, etc.

35. Give two effects of radiation on the human body. [2004 OL][2002 OL]Cancer, skin burns, sickness, cataracts, cause sterility, genetic, etc.

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Fission, Fusion and Nuclear Energy

1. What is meant by nuclear fission? [2007][2004][2002][2002 OL][2003 OL][2004 OL][2006 OL][2009 OL]Nuclear Fission is the break-up of a large nucleus into two smaller nuclei with the release of energy (and neutrons).

2. Name a material in which fission occurs. [2006 OL]Uranium, Plutonium.

3. In 1939 Lise Meitner discovered that the uranium isotope U–238 undergoes fission when struck by a slow neutron. Barium–139 and krypton–97 nuclei are emitted along with three neutrons. Write a nuclear reaction to represent the reaction. [2008]

4. Name two parts of a nuclear fission reactor. Fuel rods, control rods, shielding, moderator, coolant.

5. Name a fuel used in a nuclear reactor. [2009 OL]Plutonium or uranium.

6. What is the function of the moderator in a fission reactor? [2007][2004]To slow down fast neutrons to facilitate fission.

7. What is the role of neutrons in nuclear fission? [2009 OL]To make the nucleus unstable which causes fission.

8. In a nuclear fission reactor, neutrons are slowed down after being emitted. [2008]Why are the neutrons slowed down?Only slow neutrons can cause (further) fission.

9. How are fast neutrons slowed down? [2008]They collide with the molecules in the moderator.

10. In a nuclear reactor, how can the fission be controlled or stopped? [2009 OL]Dropping the control rods absorbs the neutrons and prevents further fission

11. How do cadmium rods control the rate of fission? [2004]They absorbed neutrons which would otherwise cause fission.

12. Describe what happens to the coolant when the reactor is working. [2006 OL]It gets hot.

13. What is the purpose of the shielding? [2006 OL]It prevents radiation from escaping and harming humans.

14. Name a material used as shielding in a nuclear reactor. [2005 OL][2006 OL]Lead, concrete.

15. What is a chain reaction? [2003 OL]This occurs when at least one neutron gets released during fission causing more fission to occur in another nucleus and this then becomes a self-sustaining reaction.

16. Describe how a chain reaction occurs in the fuel rods. [2006 OL]

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A neutron is fired into the material and this splits the nucleus of one of the atoms releasing more energy and neutrons. This process then continues.

17. Explain how the chain reaction is controlled. [2006 OL]The control rods can move up and down and when they are lowered they absorb the neutrons which prevents further fission.

18. How is the energy produced in a nuclear reactor used to generate electricity? [2009 OL]The energy produced is converted to heat. This is used to generate steam which drives a generator.

19. Give one advantage and one disadvantage of a nuclear reactor as a source of energy. [2009 OL]Advantage; abundant fuel / cheap fuel / no greenhouse gases / no global warming , etc.Disadvantage; risk of nuclear contamination / fallout / difficulty of dealing with waste / dangerous, etc.

20. Name three types of radiation that are present in a nuclear reactor. [2003 OL]Alpha, beta and gamma.

21. Give one effect of a nuclear fission reactor on the environment. [2006 OL]It can cause pollution due to nuclear waste.

22. Give one positive and one negative environmental impact of fission reactors. [2008]Positive: no CO2 emissions / no greenhouse gases / no gases to result in acid rain / less dependence on fossil fuels.Negative: radioactive waste / potential for major accidents etc.

23. Distinguish between radioactivity and fission. [2005]Radioactivity is the breakup of unstable nuclei with the emission of one or more types of radiation.Nuclear Fission is the break-up of a large nucleus into two smaller nuclei with the release of energy (and neutrons).

24. Give an application of fission. [2005]Generating electrical energy, bombs

25. Give one precaution that should be taken when storing radioactive materials. [2006 OL]Store in lead or use a tongs when handling.

In Einstein’s equation E = mc2, what does c represent? [2005 OL]26. The speed of light.

27. Distinguish between fission and fusion. [2006]Nuclear Fission is the break-up of a large nucleus into two smaller nuclei with the release of energy (and neutrons).Nuclear Fusion is the combining of two small nuclei to form one large nucleus with the release of energy.

28. What is meant by nuclear fusion? [2003] [2008 OL]Nuclear fusion is the combining of two small nuclei to form one large nucleus with the release of energy.

29. What is the source of the sun’s energy? [2007][2009 OL]Nuclear fusion

30. How does the sun produce heat and light? [2005 OL]Through nuclear reactions.

31. The core of our sun is extremely hot and acts as a fusion reactor. Why are large temperatures required for fusion to occur? [2006]

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Nuclei are positively charged so enormous energy is required to overcome the very large repulsion.

32. In the sun a series of different fusion reactions take place. In one of the reactions, 2 isotopes of helium, each with a mass number of 3, combine to form another isotope of helium with the release of 2 protons. [2006]Write an equation for this nuclear reaction.

33. Give one benefit of a terrestrial fusion reactor under each of the following headings: [2006](a) fuel; (b) energy; (c) pollution.

a) Fuel: plentiful / cheap b) Energy: vast energy releasedc) Pollution: little (radioactive) waste / few greenhouse gases

34. Controlled nuclear fusion has been achieved on earth using the following reaction.

What condition is necessary for this reaction to take place on earth? [2006]Very large energy/temperature is necessary.

Particle Physics1. In the Cockcroft and Walton experiment how were the protons accelerated? [2009]

They were accelerated by the very large potential difference which existed between the top and the bottom

2. In the Cockcroft and Walton experiment how were the alpha particles detected? [2009]They collide with a zinc sulphide screen, where they cause a flash and get detected by microscopes.

3. Explain why. High voltages can be used to accelerate alpha particles and protons but not neutrons. [2005]Alpha particles and protons are charged, neutrons are not.

4. Most of the accelerated protons did not split a lithium nucleus. Explain why. [2009]The atom is mostly empty space so the protons passed straight through.

5. Write a nuclear equation to represent the splitting of a lithium nucleus by a proton. [2009] [2007] [2005][2002]

+ + K.E.

6. Circular particle accelerators were later developed. [2005][2009]Give an advantage of circular accelerators over linear accelerators. Circular accelerators result in progressively increasing levels of speed/energy and occupy much less space than an equivalent linear accelerator.

7. In beta decay, a neutron decays into a proton with the emission of an electron. Write a nuclear equation for this decay. [2004]

8. Give two reasons why it is difficult to detect a neutrino. [2008]Neutrinos have no charge and very small mass.

9. In beta decay it appeared that momentum was not conserved. How did Fermi’s theory of radioactive decay resolve this? [2007]

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Fermi (and Pauli) realised that another particle must be responsible for the missing momentum , which they called the neutrino.

10. Momentum and energy do not appear to be conserved in beta decay. Explain how the existence of the neutrino, which was first named by Enrico Fermi, resolved this. [2004]Momentum and energy are conserved when the momentum and energy of the (associated) neutrino are taken into account.

Antimatter14. Compare the properties of an electron with that of a positron. [2007]

Both have equal mass / charges equal / charges opposite (in sign) / matter and anti-matter

15. What happens when an electron meets a positron? [2007]Pair annihilation occurs.

16. Give one contribution made to Physics by Paul Dirac. [2003] Dirac predicted antimatter.

Pair Production17. In an accelerator, two high-speed protons collide and a series of new particles are produced, in

addition to the two original protons. Explain why new particles are produced. [2005]The kinetic energy of the two protons gets converted into mass.

18. What is the effect on the products of a pair production reaction if the frequency of the γ-ray photon exceeds the minimum value? [2003]The electrons which were created would move off with greater speed.There may also be more particles produced.

19. Write a reaction that represents pair annihilation. [2003]e+ + e- → 2γ

20. Explain how the principle of conservation of charge and the principle of conservation of momentum apply in pair annihilation. [2003]Total charge on both sides is zero Momentum of positron + electron = momentum of photons

Fundamental Forces

21. Baryons and mesons are made up of quarks and experience the four fundamental forces of nature. List the four fundamental forces and state the range of each one. [2008]Strong (short range), Weak (short range), Gravitational (infinite range), Electromagnetic (infinite range).

22. List the fundamental forces of nature that pions experience. [2006]Electromagnetic, strong, weak , gravitational

23. Name the fundamental force of nature that holds the nucleus together. [2005]The strong nuclear force.

24. Beta decay is associated with the weak nuclear force. List two fundamental forces of nature and give one property of each force. [2004]Strong: acts on nucleus/protons + neutrons/hadrons/baryons/mesons, short rangeGravitational: attractive force, inverse square law/infinite range, all particlesElectromagnetic: acts on charged particles, inverse square law/infinite range

25. Name the four fundamental forces of nature. [2002]

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Gravitational, Electromagnetic, Strong (nuclear), Weak (nuclear)

26. Which force is responsible for binding the nucleus of an atom? [2002]Strong

27. Arrange the fundamental forces of nature in increasing order of strength. [2009]Gravitational, weak, electromagnetic, strong.

28. Give two properties of the strong force. [2002]Short range, strong(est), act on nucleons, binds nucleus

Quark Composition and Particle Classification

29. Name the three positively charged quarks. [2008]Up, top, charm

30. What is the difference in the quark composition of a baryon and a meson? [2008]Baryon: three quarks Meson: one quark and one antiquark

31. What is the quark composition of the proton? [2008]Up, up, down

32. A kaon consists of a strange quark and an up anti-quark. What type of hadron is a kaon? [2007]It is a meson.

33. Pions are mesons that consist of up and down quarks and their antiquarks. Give the quark composition of (i) a positive pion, (ii) a negative pion. [2006]π+ = up and anti-down π- = down and anti-up

34. Name the three negatively charged leptons. [2006]Electron (e) , muon (μ), tau (τ )

35. Give the quark composition of the neutron. [2004]Up, down, down

36. A huge collection of new particles was produced using circular accelerators. The quark model was proposed to put order on the new particles. List the six flavours of quark. [2005]Up, down, strange, charm, top and bottom.

37. Give the quark composition of the proton. [2005]Up, up, down.

38. Leptons, baryons and mesons belong to the “particle zoo”.Give (i) an example, (ii) a property, of each of these particles. [2003]LEPTONS; electron, positron, muon , tau, neutrinoNot subject to strong force BARYONS; proton, neutronSubject to all forces, three quarksMESONS pi(on), kaonSubject to all forces, mass between electron and proton, quark and antiquark

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Section B – Long Questions

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Geometrical Optics

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Leaving Cert Physics long questions: Geometrical OpticsPlease remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the

photocopier.

2012 - 2002Solutions (to higher level questions only) begin on page 7

2012 no.12 (b) [Ordinary Level](i) State the laws of reflection of light. (ii) How would you estimate the focal length of a concave mirror? (iii) The diagram shows an object O in front of a concave mirror, whose

focus is at F.Copy and complete the diagram to show the formation of the image of the object O.

(iv)Give one use for a concave mirror.

2004 Question 12 (b) [Ordinary Level] (i) Explain how a concave mirror can produce a real or a virtual image, depending on the position of the

object.(ii) Give one difference between a real image and a virtual image.(iii) Use a ray diagram to show the formation of a real image by a concave mirror.(iv)A concave mirror has a focal length of 20 cm. An object is placed 30 cm in front of the mirror. How far

from the mirror will the image be formed? (v) Give two uses for a concave mirror.

Refraction2005 Question 7 [Ordinary Level] (i) Reflection and refraction can both occur to rays of light.

What is meant by the reflection of light?(ii) State the laws of reflection of light. (iii) Describe an experiment to demonstrate one of the laws of reflection of

light. (iv)The diagram shows a ray of light travelling from glass to air.

At B the ray of light undergoes refraction.Explain what is meant by refraction.

(v) What special name is given to the angle of incidence i, when the effect shown in the diagram occurs?(vi)In the diagram the value of the angle i is 41.80.

Calculate a value for the refractive index of the glass.(vii) Draw a diagram to show what happens to the ray of light when the angle of incidence i is increased

to 450.(viii) Give one application of the effect shown in the diagram you have drawn.

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2003 Question 7 [Ordinary Level](i) State the laws of refraction of light.(ii) Explain, with the aid of a labelled diagram, (i) total internal reflection, (ii) critical angle. (iii) The diagram shows a 45o prism made of glass.

The critical angle for the glass is 42o.(iv)Calculate the refractive index of the glass. (v) The diagram shows a ray of light entering the prism from air.

Copy the diagram and show the path of the ray through the prism and back into the air.

(vi)Explain why the ray follows the path that you have shown. (vii) Give two uses of total internal reflection.2012 Question 12 (b) [Higher Level]The diagram shows a ray of light as it leaves a rectangular block of glass. As the ray of light leaves the block of glass, it makes an angle θ with the inside surface of the glass block and an angle of 30o when it is in the air, as shown.

(i) If the refractive index of the glass is 1.5, calculate the value of θ. (ii) What would be the value of the angle θ so that the ray of light emerges parallel to the side of the glass

block? (iii) Calculate the speed of light as it passes through the glass.

2011 Question 12 (b) [Higher Level](i) State the laws of refraction of light.

(ii) A lamp is located centrally at the bottom of a large swimming pool, 1.8 m deep.Draw a ray diagram to show where the lamp appears to be, as seen by an observer standing at the edge of the pool.

(iii) At night, when the lamp is switched on, a disc of light is seen at the surface of the swimming pool. Explain why the area of water surrounding the disc of light appears dark.

(iv)Calculate the area of the illuminated disc of water. (refractive index of water = 1.33)

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Optical Fibres2004 Question 11 [Ordinary Level]Read the following passage and answer the accompanying questions.Optical fibres are made of very transparent glass or plastic. The fibres contain at least two layers. Guiding light in an optical fibre depends on how light travels through different media. Light waves are bent, or refracted, as they pass between materials of different refractive index. The amount of bending depends on the refractive index and the angle at which light strikes the surface.Sometimes light cannot leave the material of higher refractive index. If it strikes the surface at a large enough angle, it is reflected back into the material. The critical angle, for what is called total internal reflection, depends on the difference in refractive indexes. An optical fibre guides light by using total internal reflection.(Adapted from New Scientist, 13 October 1990)(a) Draw a diagram to show how a ray of light is transmitted through an optical fibre.(b) How is the escape of light from the sides of an optical fibre prevented? (c) Name a material that is used in the manufacture of optical fibres. (d) What is the bending of light as it moves from one medium to another called? (e) What is meant by the refractive index of a material?(f) Define the critical angle.(g) When will total internal reflection occur?(h) Give one use for optical fibres.

2011 Question 7 [Ordinary Level]Light rays can undergo reflection and refraction. Both of these can occur when light is travelling from a denser medium, such as glass, to a less dense medium, such as air.

(i) Explain the underlined terms.(ii) Give a practical application of the reflection of light.(iii) State the laws of reflection of light.(iv)Explain, with the aid of a diagram, how total internal reflection can occur.(v) What is meant by the ‘critical angle’ in total internal reflection?(vi)The photo shows an optical fibre which is used for the transmission of data

using light waves.Draw a diagram to show how light waves travel along an optical fibre.

(vii) Give two advantages of using optical fibres instead of copper wires when transmitting data.(viii) Optical fibres are also used in medicine. Give an example of their use in medicine.

2004 Question 12 (b) [Higher Level](i) Give two reasons why the telecommunications industry uses optical fibres instead of copper conductors

to transmit signals.(ii) Explain how a signal is transmitted along an optical fibre. (iii) An optical fibre has an outer less dense layer of glass. What is the role of this layer of glass? (iv)An optical fibre is manufactured using glass of refractive index of 1.5.

Calculate the speed of light travelling through the optical fibre.Speed of light in air = 3.0 × 108 m s–1

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2009 Question 12 (c) [Higher Level]Information is transmitted over long distances using optical fibres in which a ray of light is guided along a fibre. Each fibre consists of a core of high quality glass with a refractive index of 1.55 and is coated with glass of a lower refractive index.(i) Explain, with the aid of a labelled diagram, how a ray of light is guided along a fibre. (ii) Why is each fibre coated with glass of lower refractive index? (iii) What is the speed of the light as it passes through the fibre? (iv)Light passing through optical fibres must travel through an enormous length of glass. Impurities in the

glass reduce the power transmitted by half every 2 km.The initial power being transmitted by the light is 10 W.What is the power being transmitted by the light after it has travelled 8 km through the fibre?

(speed of light in air = 3.0 × 108 m s–1)

Lenses2008 Question 9 [Higher Level](i) What is meant by refraction of light? (ii) State Snell’s law of refraction.

An eye contains a lens system and a retina, which is 2.0 cm from the lens system. The lens system consists of the cornea, which acts as a fixed lens of power 38 m–1, and a variable internal lens just behind the cornea. The maximum power of the eye is 64 m–1.

(iii) Calculate how near an object can be placed in front of the eye and still be in focus; (iv)Calculate the maximum power of the internal lens.

(v) Light is refracted as it enters the cornea from air as shown in the diagram. Calculate the refractive index of the cornea.

(vi)Draw a diagram to show the path of a ray of light as it passes from water of refractive index 1.33 into the cornea.

A swimmer cannot see properly when she opens her eyes underwater. When underwater: (vii) Why does the cornea not act as a lens? (viii) What is the maximum power of the eye? (ix)Why do objects appear blurred? (x) Explain how wearing goggles allows objects to be seen clearly.

2006 Question 7 [Higher Level](i) What is meant by the refraction of light? (ii) A converging lens is used as a magnifying glass.

Draw a ray diagram to show how an erect image is formed by a magnifying glass. (iii) A diverging lens cannot be used as a magnifying glass. Explain why.(iv)The converging lens has a focal length of 8 cm.

Determine the two positions that an object can be placed to produce an image that is four times the size of the object?

(v) The power of an eye when looking at a distant object should be 60 m–1. A person with defective vision has a minimum power of 64 m–1. Calculate the focal length of the lens required to correct this defect.

(vi)What type of lens is used? (vii) Name the defect.

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2002 Question 12 (b) [Higher Level](i) State the laws of refraction of light. (ii) Draw a labelled diagram showing the optical structure of the eye. (iii) How does the eye bring objects at different distances into focus? (iv)The power of a normal eye is +60 m-1. A short-sighted person’s eye has a power of +65 m-1.

Calculate the power of the contact lens required to correct the person’s short-sightedness.(v) Calculate the focal length of the contact lens required to correct the person’s short-sightedness.

Solutions to higher level questions

2012 Question 12 (b)(i) If the refractive index of the glass is 1.5, calculate the value of θ.

i = 600

r = 35.260

θ = 54.740

(ii) What would be the value of the angle θ so that the ray of light emerges parallel to the side of the glass block?

c = 41.820

θ = 48.20

(iii) Calculate the speed of light as it passes through the glass.

= 2 ×108 m s-1

2011 Question 12 (b) (i) State the laws of refraction of light.

The incident ray, refracted ray and normal all lie in same plane sin i/sinr is a constant

(ii) Draw a ray diagram to show where the lamp appears to be, as seen by an observer standing at the edge of the pool.

(iii) Explain why the area of water surrounding the disc of light appears dark.No light emerges from this area of the pool due to total internal reflection

(iv)Calculate the area of the illuminated disc of water.

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η = 1.33ic = 48.760

radius of disc = r = 1.8 tan(48.76)r = 2.053 marea = πr2 = 13.24 m2

2009 Question 12 (c) Information is transmitted over long distances using optical fibres in which a ray of light is guided along a fibre. Each fibre consists of a core of high quality glass with a refractive index of 1.55 and is coated with glass of a lower refractive index.(i) Explain, with the aid of a labelled diagram, how a ray of light is guided along a fibre.

1. An optical fibre consists of a glass pipe coated with a second material of lower refractive index.

2. Light enters one end of the fibre and strikes the boundary between the two materials at an angle greater than the critical angle, resulting in total internal reflection at the interface.

3. This reflected light now strikes the interface on the opposite wall and gets totally reflected again.4. This process continues all along the glass pipe until the light emerges at the far end.

(ii) Why is each fibre coated with glass of lower refractive index? Because total internal reflection can only occur for rays travelling from a denser to a rarer medium.

(iii) What is the speed of the light as it passes through the fibre? n = cair/cglass cglass = 3.0 × 108/1.55cglass = 1.94 × 108 m s-1

(iv)What is the power being transmitted by the light after it has travelled 8 km through the fibre?After 2 km power has dropped to 5 W; after 4 km power has dropped to 2.5 W; after 6 km power has dropped to 1.25 W; after 8 km power has dropped to 0.625 W.

2008 Question 9(i) What is meant by refraction of light?

Refraction is the bending of light as it passes from one medium to another (of different refractive index).(ii) State Snell’s law of refraction.

The ratio of the sin of the sin of the angle of incidence to the sin of the angle of refraction is a constant.(iii) Calculate how near an object can be placed in front of the eye and still be in focus.

Pmax = 64 m-1 = 1/ff = 0.0156 m = 1.56 cm1/u = 1/v +1/f 1/u = 1/2 = 1/1.56 u = 7.14 cm

(iv)Calculate the maximum power of the internal lens. Pmax = P1 + P2 64 = 38 + P2 P2 = 26 m-1

(v) Light is refracted as it enters the cornea from air as shown in the diagram. Calculate the refractive index of the cornea.

n = sin 37/sin 27 n = 1.33

(vi)Draw a diagram to show the path of a ray of light as it passes from water of refractive index 1.33 into the cornea. Both media have the same refractive index so there is no bending of light.Draw a straight line passing from one medium to the other without bending.

(vii) A swimmer cannot see properly when she opens her eyes underwater. When underwater why does the cornea not act as a lens? Because light does not refract at the cornea since there is no change in refractive index.

(viii) What is the maximum power of the eye when underwater?

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The maximum power of the eye is 64 m–1, but this includes the focusing power of the cornea (38 m-1) which doesn’t work underwater, so maximum power = 64 – 38 = 26 m–1.

(ix)Why do objects appear blurred when underwater? Because the internal lens by itself is not powerful enough to focus light on retina.

(x) Explain how wearing goggles allows objects to be seen clearly. Because light which hits the cornea is coming from air and so there will be refraction here (the cornea will now act as a lens).

2006 Question 7(i) What is meant by the refraction of light?

Refraction is the bending of light as it passes from one medium to another.(ii) A converging lens is used as a magnifying glass.

Draw a ray diagram to show how an erect image is formed by a magnifying glass. Object inside focal point Two (appropriate) rays from object to lens Two rays emerge correctly from lens Rays produced back to form upright virtual image (on same side as object)

(iii) A diverging lens cannot be used as a magnifying glass. Explain why.The image is always dimished.

(iv)The converging lens has a focal length of 8 cm. Determine the two positions that an object can be placed to produce an image that is four times the size of the object? 1/u + 1/v = 1/f Magnification = v /u = 4 v = 4uFor real image: 1/u + 1/4u = 1/8 u = 10 cm For virtual image: 1 /u - 1/4u = 1/8 u = 6 cm

(v) The power of an eye when looking at a distant object should be 60 m–1. A person with defective vision has a minimum power of 64 m–1. Calculate the focal length of the lens required to correct this defect. P = P1 + P2 60 = 64 + P1 P1 = -4 ( m-1) P = 1/f f = 1/P 1/f = (-)4 f = (-)¼ m = (-)25 cm

(vi)What type of lens is used? Diverging / concave lens

(vii) Name the defect.Short sight / myopia

2004 Question 12 (b) (i) Give two reasons why the telecommunications industry uses optical fibres instead of copper

conductors to transmit signals.Less interference, boosted less often, cheaper raw material, occupy less space, more information carried in the same space, flexible for inaccessible places, do not corrode, etc

(ii) Explain how a signal is transmitted along an optical fibre. Light ray introduced at one end of fibre and strikes the interface at an angle greater than the internal angle so total internal reflection occurs.This continues all along the fibre.

(iii) An optical fibre has an outer less dense layer of glass. What is the role of this layer of glass? Total internal reflection will only occur if the outer medium is of greater density. It also prevents damage to the surface of the core.

(iv)An optical fibre is manufactured using glass of refractive index of 1.5. Calculate the speed of light travelling through the optical fibre.

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ng = ca /cg

1.5 = 3 × 108/ vg

vg = 2.0 × 108 (m s-1)

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2002 Question 12 (b)(i) State the laws of refraction of light.

The incident ray, the normal and the refracted ray all lie on the same plane.The ratio of the sin of the sin of the angle of incidence to the sin of the angle of refraction is a constant.

(ii) Draw a labelled diagram showing the optical structure of the eye. See diagram.

(iii) How does the eye bring objects at different distances into focus? It can change the shape of the lens which in turn changes the focal length of the lens.

(iv)The power of a normal eye is +60 m-1. A short-sighted person’s eye has a power of +65 m-1. Calculate the power of the contact lens required to correct the person’s short-sightedness.PTotal = P1 + P2

60 = P1 + 65Power = - 5 m

(v) Calculate the focal length of the contact lens required to correct the person’s short-sightedness. P = 1/f f = - 0.2 m

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Mechanics

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Leaving Cert Physics Mechanics long questions2011 - 2002

Two Common Topics Year of appearanceSatellite Motion (Circular Motion plus Gravity) 2010 no.6, 2008 no.6, 2005 no.6, 2004 12 (a)Simple Harmonic Motion (and Hooke’s Law) 2011 12 (a), 2009 12 (a), 2007 no 6, 2002 no. 6

2011 Question 6(a)Define the moment of a force.A toy, such as that shown, has a heavy hemispherical base and its centre of gravity is located at C. When the toy is knocked over, it always returns to the upright position. Explain why this happens.

(b)State the conditions necessary for the equilibrium of a body under a set of co-planar forces.Three children position themselves on a uniform see-saw so that it is horizontal and in equilibrium. The fulcrum of the see-saw is at its centre of gravity. A child of mass 30 kg sits 1.8 m to the left of the fulcrum and another child of mass 40 kg sits 0.8 m to the right of the fulcrum.Where should the third child of mass 45 kg sit, in order to balance the see-saw?

(c) A simple merry-go-round consists of a flat disc that is rotated horizontally. A child of mass 32 kg stands at the edge of the merry-go-round, 2.2 metres from its centre. The force of friction acting on the child is 50 N.Draw a diagram showing the forces acting on the child as the merry-go-round rotates.

What is the maximum angular velocity of the merry-go-round so that the child will not fall from it, as it rotates?If there was no force of friction between the child and the merry-go-round, in what direction would the child move as the merry-go-round starts to rotate?

2011 Question 12 (a)State Hooke’s law.

A body of mass 250 g vibrates on a horizontal surface and its motion is described by the equation a = – 16 s, where s is the displacement of the body from its equilibrium position. The amplitude of each vibration is 5 cm.(a)Why does the body vibrate with simple harmonic motion?(b)Calculate the frequency of vibration of the body?(c)What is the magnitude of (i) the maximum force, (ii) the minimum force, which causes the body’s

motion?

2010 Question 6(Radius of the earth = 6.36 × 106 mAcceleration due to gravity at the earth’s surface = 9.81 m s−2

Distance from the centre of the earth to the centre of the moon = 3.84 × 108 m

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Assume the mass of the earth is 81 times the mass of the moon.)

(i) State Newton’s law of universal gravitation.(ii) Use this law to calculate the acceleration due to gravity at a height above the surface of the earth, which

is twice the radius of the earth.Note that 2d above surface is 3d from earth’s centre

(iii) A spacecraft carrying astronauts is on a straight line flight from the earth to the moon and after a while its engines are turned off. Explain why the spacecraft continues on its journey to the moon, even though the engines are turned off.

(iv)Describe the variation in the weight of the astronauts as they travel to the moon.(v) At what height above the earth’s surface will the astronauts experience weightlessness?

Gravitational pull of earth = gravitational pull of moon (vi)The moon orbits the earth every 27.3 days. What is its velocity, expressed in metres per second?(vii) Why is there no atmosphere on the moon?

2009 Question 6(i) State Newton’s laws of motion. (ii) Show that F = ma is a special case of Newton’s second law.

A skateboarder with a total mass of 70 kg starts from rest at the top of a ramp and accelerates down it. The ramp is 25 m long and is at an angle of 200 to the horizontal. The skateboarder has a velocity of 12.2 m s–1 at the bottom of the ramp.

(iii) Calculate the average acceleration of the skateboarder on the ramp.(iv) Calculate the component of the skateboarder’s weight that is parallel to the ramp.(v) Calculate the force of friction acting on the skateboarder on the ramp.(vi) The skateboarder then maintains a speed of 10.5 m s–1 until he enters a circular ramp of radius 10 m.

What is the initial centripetal force acting on him?(vii) What is the maximum height that the skateboarder can reach? (viii) Sketch a velocity-time graph to illustrate his motion.

(acceleration due to gravity = 9.8 m s–2)

2009 Question 12 (a)(i) State Hooke’s law. (ii) When a sphere of mass 500 g is attached to a spring of length 300 mm, the length of the spring increases

to 330 mm.Calculate the spring constant.

(iii) The sphere is then pulled down until the spring’s length has increased to 350 mm and is then released.

(iv)Describe the motion of the sphere when it is released. (v) What is the maximum acceleration of the sphere?

(acceleration due to gravity = 9.8 m s-2)

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2008 Question 6(i) State Newton’s law of universal gravitation. (ii) The international space station (ISS) moves in a circular orbit around the equator at a height of 400 km.

What type of force is required to keep the ISS in orbit? (iii) What is the direction of this force? (iv)Calculate the acceleration due to gravity at a point 400 km above the surface of the earth. (v) An astronaut in the ISS appears weightless. Explain why. (vi)Derive the relationship between the period of the ISS, the radius of its orbit and the mass of the earth.(vii) Calculate the period of an orbit of the ISS.(viii) After an orbit, the ISS will be above a different point on the earth’s surface. Explain why. (ix)How many times does an astronaut on the ISS see the sun rise in a 24 hour period?

(gravitational constant = 6.6 × 10–11 N m2 kg–2; mass of the earth = 6.0 × 1024 kg; radius of the earth = 6.4 × 106 m)

2008 Question 12 (a)(i) State the principle of conservation of energy. (ii) In a pole-vaulting competition an athlete, whose centre of gravity is 1.1 m above the ground, sprints

from rest and reaches a maximum velocity of 9.2 ms–1 after 3.0 seconds. He maintains this velocity for 2.0 seconds before jumping. Draw a velocity-time graph to illustrate the athlete’s horizontal motion.

(iii) Use your graph to calculate the distance travelled by the athlete before jumping. (iv)What is the maximum height above the ground that the athlete can raise his centre of gravity?

2007 Question 6(i) State Hooke’s law. (ii) A stretched spring obeys Hooke’s law.

When a small sphere of mass 300 g is attached to a spring of length 200 mm, its length increases to 285 mm.Calculate its spring constant.

(iii) The sphere is pulled down until the length of the spring is 310 mm.The sphere is then released and oscillates about a fixed point.Derive the relationship between the acceleration of the sphere and its displacement from the fixed point.

(iv)Why does the sphere oscillate with simple harmonic motion? (v) Calculate the period of oscillation of the sphere(vi)Calculate the maximum acceleration of the sphere(vii) Calculate the length of the spring when the acceleration of the sphere is zero. (acceleration due to gravity = 9.8 m s–2)

2007 Question 12 (a)(i) What is friction? (ii) A car of mass 750 kg is travelling east on a level road. Its engine exerts a constant force of 2.0 kN

causing the car to accelerate at 1.2 m s–2 until it reaches a speed of 25 m s–1.(iii) Calculate (i) the net force, (ii) the force of friction, acting on the car. (iv)If the engine is then turned off, calculate how far the car will travel before coming to rest.

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2006 Question 6(i) Define velocity.(ii) Define angular velocity. (iii) Derive the relationship between the velocity of a particle travelling in

uniform circular motion and its angular velocity. (iv)A student swings a ball in a circle of radius 70 cm in the vertical plane as

shown. The angular velocity of the ball is 10 rad s–1.What is the velocity of the ball?

(v) How long does the ball take to complete one revolution? (vi)Draw a diagram to show the forces acting on the ball when it is at

position A.(vii) The student releases the ball when is it at A, which is 130 cm above the ground, and the ball travels

vertically upwards. Calculate the maximum height, above the ground, the ball will reach.(viii) Calculate the time taken for the ball to hit the ground after its release from A.

(acceleration due to gravity = 9.8 m s–2)

2006 Question 12 (a)(i) Define pressure. (ii) Is pressure a vector quantity or a scalar quantity? Justify your answer.(iii) State Boyle’s law. (iv)A small bubble of gas rises from the bottom of a lake. The volume of the bubble increases threefold

when it reaches the surface of the lake where the atmospheric pressure is 1.01 × 105 Pa. The temperature of the lake is 4 oC. Calculate the pressure at the bottom of the lake;

(v) Calculate the depth of the lake. (acceleration due to gravity = 9.8 m s–2; density of water = 1.0 × 103 kg m–3)

2005 Question 6(i) Define angular velocity.(ii) Define centripetal force.(iii) State Newton’s Universal Law of Gravitation.(iv)A satellite is in a circular orbit around the planet Saturn.

Derive the relationship between the period of the satellite, the mass of Saturn and the radius of the orbit. (v) The period of the satellite is 380 hours. Calculate the radius of the satellite’s orbit around Saturn. (vi)The satellite transmits radio signals to earth. At a particular time the satellite is 1.2 × 1012 m from earth.

How long does it take the signal to travel to earth? (vii) It is noticed that the frequency of the received radio signal changes as the satellite orbits Saturn.

Explain why.

Gravitational constant = 6.7 × 10–11 N m2 kg–2; mass of Saturn = 5.7 × 1026 kg; speed of light = 3.0 × 108 m s–1

2005 Question 12 (a)(i) State the principle of conservation of energy. (ii) A basketball of mass 600 g which was resting on a hoop falls to the ground 3.05 m below.

What is the maximum kinetic energy of the ball as it falls? (iii) On bouncing from the ground the ball loses 6 joules of energy.

What happens to the energy lost by the ball? (iv)Calculate the height of the first bounce of the ball. (acceleration due to gravity = 9.8 m s–2)

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2004 Question 6(i) Define force.(ii) Define momentum. (iii) State Newton’s second law of motion.(iv)Hence, establish the relationship: force = mass × acceleration. (v) A pendulum bob of mass 10 g was raised to a height of 20 cm and allowed to

swing so that it collided with a block of mass 8.0 g at rest on a bench, as shown. The bob stopped on impact and the block subsequently moved along the bench.Calculate the velocity of the bob just before the collision.

(vi)Calculate the velocity of the block immediately after the collision. (vii) The block moved 2.0 m along the bench before stopping.

What was the average horizontal force exerted on the block while travelling this distance? (acceleration due to gravity = 9.8 m s–2)

2004 Question 12 (a)(iii) State Newton’s universal law of gravitation. (iv)Centripetal force is required to keep the earth moving around the sun.

What provides this centripetal force?(v) In what direction does this centripetal force act?(vi)Give an expression for centripetal force. (vii) The earth has a speed of 3.0 × 104 m s–1 as it orbits the sun.

The distance between the earth and the sun is 1.5 × 1011 m. Calculate the mass of the sun.

(gravitational constant, G = 6.7 × 10–11 m3 kg–1 s–2)

2003 Question 6(i) Give the difference between vector quantities and scalar quantities and give one

example of each.(ii) Describe an experiment to find the resultant of two vectors. (iii) A cyclist travels from A to B along the arc of a circle of radius 25 m as shown.(iv)Calculate (i) the distance travelled by the cyclist.(v) Calculate the displacement undergone by the cyclist.

(vi)A person in a wheelchair is moving up a ramp at a constant speed. Their total weight is 900 N. The ramp makes an angle of 10o with the horizontal.Calculate the force required to keep the wheelchair moving at a constant speed up the ramp. (You may ignore the effects of friction.)

(vii) The ramp is 5 m long. Calculate the power exerted by the person in the wheelchair if it takes her 10 s to travel up the ramp.

2003 Question 12 (a)(i) State Newton’s second law of motion. (ii) A skydiver falls from an aircraft that is flying horizontally.

He reaches a constant speed of 50 m s–1 after falling through a height of 1500 m. Calculate the average vertical acceleration of the skydiver.

(iii) If the mass of the skydiver is 90 kg, what is the magnitude and direction of the average resultant force acting on him?

(iv)Use a diagram to show the forces acting on the skydiver and explain why he reaches a constant speed.

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2002 Question 6(i) State Newton’s second law of motion. (ii) The equation F = – ks, where k is a constant, is an expression for a law that governs the motion of a

body. Name this law and give a statement of it.

(iii) Give the name for this type of motion and describe the motion. (iv)A mass at the end of a spring is an example of a system that obeys this law.

Give two other examples of systems that obey this law. (v) The springs of a mountain bike are compressed vertically by 5 mm when a cyclist of mass 60 kg sits on

it. When the cyclist rides the bike over a bump on a track, the frame of the bike and the cyclist oscillate up and down.Using the formula F = – ks, calculate the value of k, the constant for the springs of the bike.

(vi)The total mass of the frame of the bike and the cyclist is 80 kg. Calculate (i) the period of oscillation of the cyclist, (ii) the number of oscillations of the cyclist per second. (acceleration due to gravity, g = 9.8 m s-2)

2002 Question 12 (a)(i) State the principle of conservation of momentum. (ii) A spacecraft of mass 50 000 kg is approaching a space station at a constant speed of 2 m s-1. The

spacecraft must slow to a speed of 0.5 m s-1 for it to lock onto the space station. Calculate the mass of gas that the spacecraft must expel at a speed 50 m s-1 for the spacecraft to lock onto the space station. (The change in mass of the spacecraft may be ignored.)

(iii) In what direction should the gas be expelled? (iv)Explain how the principle of conservation of

momentum is applied to changing the direction in which a spacecraft is travelling.

Solutions2011 Question 6

(a) Define the moment of a force.Moment of a force = force × perpendicular distance between the force and the fulcrum

When the toy is knocked over, it always returns to the upright position. Explain why this happens.(toy non-vertical) c.g. has a (turning) moment about fulcrum / point of support/contact /(c.g. has) zero turning moment when toy is in vertical position

(b) State the conditions necessary for the equilibrium of a body under a set of co-planar forces.Algebraic sum of the forces = zeroSum of the moments about any point = zero

Three children position themselves on a uniform see-saw so that it is horizontal and in equilibrium. The fulcrum of the see-saw is at its centre of gravity. A child of mass 30 kg sits 1.8 m to the left of the fulcrum and another child of mass 40 kg sits 0.8 m to the right of the fulcrum. Where should the third child of mass 45 kg sit, in order to balance the see-saw?30g(1.8) = 40g(0.8) + 45g(x)x = 0.488 m / 0.49 m / 49 cm

(c) A simple merry-go-round consists of a flat disc that is rotated horizontally. A child of mass 32 kg stands at the edge of the merry-go-round, 2.2 metres from its centre. The force of friction acting on the child is 50 N. Draw a diagram showing the forces acting on the child as the merry-go-round rotates.

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What is the maximum angular velocity of the merry-go-round so that the child will not fall from it, as it rotates?

F = mω2r50 = 30 ω2(2.2)ω = 0.842 rad s-1

If there was no force of friction between the child and the merry-go-round, in what direction would the child move as the merry-go-round starts to rotate?The child would remain stationary / any appropriate answer.

2011 Question 12 (a)State Hooke’s law.For a stretched string the restoring force is proportional to displacement

A body of mass 250 g vibrates on a horizontal surface and its motion is described by the equationa = – 16 s, where s is displacement of the body from its equilibrium position. The amplitude of each vibration is 5 cm. Why does the body vibrate with simple harmonic motion?The acceleration is proportional to the displacement

Calculate the frequency of vibration of the body?ω2 = 16ω = 4f = ω/2πf = 0.64 Hz s-1

What is the magnitude of (i) the maximum force, (ii) the minimum force, which causes the body’s motion?a max = (–)16(0.05) = 0.80 (Fmax occurs when acceleration / displacement is a maximum)Fmax = (0.250)(0.80) = 0.20 N Fmin = 0

2010 Question 6(i) State Newton’s law of universal gravitation.

Force between any two point masses is proportional to product of masses and inversely/indirectly proportional to square of the distance between them.

(ii) Use this law to calculate the acceleration due to gravity at a height above the surface of the earth, which is twice the radius of the earth.Note that 2d above surface is 3d from earth’s centre

where d = 6.36 × 106 m

gnew = 1.09 m s-2

(iii) A spacecraft carrying astronauts is on a straight line flight from the earth to the moon and after a while its engines are turned off. Explain why the spacecraft continues on its journey to the moon, even though the engines are turned off.

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There are no external forces acting on the spacecraft so from Newton’s 1st law of motion the object will maintain its velocity.

(iv)Describe the variation in the weight of the astronauts as they travel to the moon.Weight decreases as the astronaut moves away from the earth and gains (a lesser than normal) weight as she/he approaches the moon

(v) At what height above the earth’s surface will the astronauts experience weightlessness?Gravitational pull of earth = gravitational pull of moon

=

dE = 9 dm and dE + dm = 3.84 × 108 m

10 dm = 3.84 × 108

dm = 3.84 × 107

dE = 3.356 × 108

Height above the earth = (3.356 × 108) – (6.36 × 106) = 3.39 × 108 m

(vi)The moon orbits the earth every 27.3 days. What is its velocity, expressed in metres per second?

v = 1022.9 m s-1

(vii) Why is there no atmosphere on the moon?The gravitational force is too weak to sustain an atmosphere.

2009 Question 6(i) State Newton’s laws of motion.

Newton’s First Law of Motion states that every object will remain in a state of rest or travelling with a constant velocity unless an external force acts on it.Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to the force which caused it, and takes place in the direction of the force.Newton’s Third Law of Motion states that when body A exerts a force on body B, B exerts a force equal in magnitude (but) opposite in direction (on A).

(ii) Show that F = ma is a special case of Newton’s second law. From Newton II: Force is proportional to the rate of change of momentumForce rate of change of momentumF (mv – mu)/tF m(v-u)/tF maF = k (ma) [but k = 1]F = ma

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A skateboarder with a total mass of 70 kg starts from rest at the top of a ramp and accelerates down it. The ramp is 25 m long and is at an angle of 200 to the horizontal. The skateboarder has a velocity of 12.2 m s–1 at the bottom of the ramp.

(iii) Calculate the average acceleration of the skateboarder on the ramp.v2= u2 + 2as (12.2)2 = 0 +2a(25) a = 2.98 m s–2

(iv)Calculate the component of the skateboarder’s weight that is parallel to the ramp.W = mgsin = mgsin20 = 234.63 N

(v) Calculate the force of friction acting on the skateboarder on the ramp.Force down (due to gravity) – Resistive force (due to friction) = Net forceForce down (due to gravity) = 234.63 NNet force= 70(2.98) = 208.38 NFriction force = 234.63 – 208.38 = 26.25 N

(vi)The skateboarder then maintains a speed of 10.5 m s–1 until he enters a circular ramp of radius 10 m.What is the initial centripetal force acting on him?

= 70 (10.5)2/10 = 771.75 N

(vii) What is the maximum height that the skateboarder can reach? (acceleration due to gravity = 9.8 m s–2) v2= u2 + 2as u2 = 2g(s) s = 5.63 m

(viii) Sketch a velocity-time graph to illustrate his motion. Velocity on vertical axis, time on horizontal axis, with appropriate numbers on both axes.

2009 Question 12 (a)(i) State Hooke’s law.

When a string is stretched the restoring force is proportional to the displacement.(ii) When a sphere of mass 500 g is attached to a spring of length 300 mm, the length of the spring

increases to 330 mm. Calculate the spring constant. When the mass of 500 g is attached the new force down = mg = (0.5)(g).Because the spring is in equiblibrium this must be equal to the force up (which is the restoring force).Hooke’s law in symbols: F = k x (0.5)(g) = kx k = F/x = 0.5g/0.030 k = 163.3 N m-1

(iii) The sphere is then pulled down until the spring’s length has increased to 350 mm and is then released.Describe the motion of the sphere when it is released. It executes simple harmonic motion because the displacement is proportional to t he acceleration.

(iv)What is the maximum acceleration of the sphere? F = ma = kxa = kx/m = (163.3)(0.02)/(0.5) = 6.532 m s-2

ORa = 2 x 2 = k/m = 163.3/0.5 a = 6.532 m s-2

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2008 Question 6(i) State Newton’s law of universal gravitation.

Newton’s Law of Gravitation states that any two point masses in the universe attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

(ii) The international space station (ISS) moves in a circular orbit around the equator at a height of 400 km. What type of force is required to keep the ISS in orbit? Gravity

(iii) What is the direction of this force? Towards the centre of the orbit / inwards / towards the earth

(iv)Calculate the acceleration due to gravity at a point 400 km above the surface of the earth.

= mg g = (6.6 × 10–11)( 6.0 × 1024) / (400 000 + 6.4 × 106)2

g = 8.6 m s-2

(v) An astronaut in the ISS appears weightless. Explain why. He is in a state of free-fall (the force of gravity cannot be felt).

(vi)Derive the relationship between the period of the ISS, the radius of its orbit and the mass of the earth.

See notes Circular Motion chapter for a more detailed derivation.

(vii) Calculate the period of an orbit of the ISS.

T2 = 3.1347 × 107 T = 5.6 × 103 s

(viii) After an orbit, the ISS will be above a different point on the earth’s surface. Explain why. The ISS has a different period to that of the earth’s rotation (it is not in geostationary orbit).

(ix)How many times does an astronaut on the ISS see the sun rise in a 24 hour period? (24 ÷ 1.56 + 1) = 16 ( sunrises).

2008 Question 12 (a)(i) State the principle of conservation of energy.

The Principle of Conservation of Energy states that energy cannot be created or destroyed but can only be converted from one form to another.

(ii) In a pole-vaulting competition an athlete, whose centre of gravity is 1.1 m above the ground, sprints from rest and reaches a maximum velocity of 9.2 ms–1 after 3.0 seconds. He maintains this velocity for 2.0 seconds before jumping. Draw a velocity-time graph to illustrate the athlete’s horizontal motion.See diagram

(iii) Use your graph to calculate the distance travelled by the athlete before jumping. Distance (s) = area under curve s = ½ (3)(9.2) + 2 (9.2) / 13.8 + 18.4 / 32.2 m

(iv)What is the maximum height above the ground that the athlete can raise his centre of gravity?K.E. = P.E.½ mv2 = mghh = v2/2g = (9.2)2/2(9.8) = 4.32Max height above the ground = 4.32 + 1.1 = 5.42 m.

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2007 Question 6(i) State Hooke’s law.

For a stretched string the restoring force is proportional to the extension.(ii) A stretched spring obeys Hooke’s law.

When a small sphere of mass 300 g is attached to a spring of length 200 mm, its length increases to 285 mm.Calculate its spring constant. F = mg = ks (0.30)(9.8) = (k)(0.085) k = 34.6 N m-1

(iii) The sphere is pulled down until the length of the spring is 310 mm.The sphere is then released and oscillates about a fixed point.Derive the relationship between the acceleration of the sphere and its displacement from the fixed point.F = - ks ma = - ks a = - (k/m)s a α -s a = - k s

(iv)Why does the sphere oscillate with simple harmonic motion? Its acceleration is proportional to its displacement from a fixed point.

(v) Calculate the period of oscillation of the sphere.From above:ω2 = k/m ω2 = 34.6 / 0.3 ω = 10.7 T = 2π/ω = 2π/10.7 = 0.58 ≈ 0.6 T = 0.6 s

(vi)Calculate the maximum acceleration of the sphere.This occurs when s is a maximum, i.e. when s = amplitude = 0.310 – 0.285 = 0.025 m.a = -ω2s a = - (10.7)2 (0.025) a = (-) 2.89 m s-2

(vii) Calculate the length of the spring when the acceleration of the sphere is zero. This occurs at the fixed point when l = 0.285 m

2007 Question 12 (a)(i) What is friction?

Friction is a force which opposes the relative motion between two objects.(ii) A car of mass 750 kg is travelling east on a level road. Its engine exerts a constant force of 2.0 kN

causing the car to accelerate at 1.2 m s–2 until it reaches a speed of 25 m s–1.Calculate the net force acting on the car. Fnet = ma = (750)(1.2) = 900 N east.

(iii) Calculate the force of friction acting on the car.Fnet = Fcar - Ffriction

900 = 2000 - Ffriction Ffriction = 1100 N west(iv)If the engine is then turned off, calculate how far the car will travel before coming to rest?

Friction causes deceleration: a = F ÷ ma = (-1100) ÷ 750 = - 1.47 ms-2

v 2 = u 2 + 2as0 = 252 +2(-1.47) s or s = 213 m

2006 Question 6(i) Define velocity.

Velocity is the rate of change of displacement with respect to time.(ii) Define angular velocity.

Angular velocity is the rate of change of angle with respect to time.(iii) Derive the relationship between the velocity of a particle

travelling in uniform circular motion and its angular velocity. θ = s /r θ /t = s/rt ω = v /r v = ω r

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(iv)A student swings a ball in a circle of radius 70 cm in the vertical plane as shown. The angular velocity of the ball is 10 rad s–1. What is the velocity of the ball? v = ω r = (10)(0.70) = 7.0 m s-1

(v) How long does the ball take to complete one revolution? T= 2πr/v = 2π(0.70)/v = 0.63 s

(vi)Draw a diagram to show the forces acting on the ball when it is at position A.Weight (W) downwards; reaction (R) upwards; force to left (due to friction or curled fingers)

(vii) The student releases the ball when is it at A, which is 130 cm above the ground, and the ball travels vertically upwards. Calculate the maximum height, above the ground, the ball will reach.v2 = u2+ 2as 0 = (7)2 + 2(-9.8) s / s = 2.5(0) m max. height = 2.5 + 1.30 / 3.8 m

(viii) Calculate the time taken for the ball to hit the ground after its release from A. s = ut + ½ at2

-1.30 = 7t – ½ (9.8)t2

t = 1.59 s

2006 Question 12 (a)(i) Define pressure.

Pressure = Force divided by area.(ii) Is pressure a vector quantity or a scalar quantity? Justify your answer.

It is a scalar because it has no direction.(iii) State Boyle’s law.

Boyle’s Law states that pressure is inversely proportional to volume if temperature is constant.(iv)A small bubble of gas rises from the bottom of a lake. The volume of the bubble increases

threefold when it reaches the surface of the lake where the atmospheric pressure is 1.01 × 105 Pa. The temperature of the lake is 4 oC. Calculate the pressure at the bottom of the lake.Pressure at bottom = 3 × pressure at top = 3.03 × 105 Pa

(v) Calculate the depth of the lake. Pressure at bottom due to water = 2.02 × 105 Pa P= hρg h = P/ρg = 2.02 × 105 / (1.0 × 103)( 9.8 ) = 20.61 m

2005 Question 6(i) Define angular velocity.

Angular velocity is the rate of change of displacement with respect to time.(ii) Define centripetal force.

The force - acting in towards the centre - required to keep an object moving in a circle is called Centripetal Force.

(iii) State Newton’s Universal Law of Gravitation.Newton’s Law of Gravitation states that any two point masses in the universe attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

(iv)A satellite is in a circular orbit around the planet Saturn. Derive the relationship between the period of the satellite, the mass of Saturn and the radius of the orbit.

See notes on the Circular Motion chapter for a more detailed derivation.

(v) The period of the satellite is 380 hours. Calculate the radius of the satellite’s orbit around Saturn. T = 380 × 60 × 60 = 1.37 × 106 s

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r3 = T2GM/4π2 r3 = (1.37 × 106)2(6.7 × 10–11)( 5.7 × 1026)/ 4π2 r = 1.2 × 109 m

(vi)The satellite transmits radio signals to earth. At a particular time the satellite is 1.2 × 1012 m from earth. How long does it take the signal to travel to earth? v = s/t (3.0 × 108) = (1.2 × 1012)/t t = 4000 s

(vii) It is noticed that the frequency of the received radio signal changes as the satellite orbits Saturn. Explain why. Doppler Effect due to relative motion between source of signal and the detector

2005 Question 12 (a)(v) State the principle of conservation of energy.

Energy cannot be created or destroyed but it can only be changed from one form to another .(vi)A basketball of mass 600 g which was resting on a hoop falls to the ground 3.05 m below.

What is the maximum kinetic energy of the ball as it falls? KE = PE (at height of 3.05 m) v2 = u2 +2as v2 = 0 + 2(9.8)(3.05) v2 = 59.78 {you could also have use P.E. = mgh}Ek = ½mv2 = ½ (0.60)(59.78) Ek = 17.9 J

(vii) On bouncing from the ground the ball loses 6 joules of energy. What happens to the energy lost by the ball? It changes into sound and heat.

(viii) Calculate the height of the first bounce of the ball. [retained energy = 17.9 – 6] E = 11.9 JE = mgh h = E / mg h = 11.9 /(0.600)(9.8) h = 2.02 m

2004 Question 6(i) Define force.

Force is that which causes an acceleration.(ii) Define momentum.

Momentum is the defined as the product of mass multiplied by velocity.(iii) State Newton’s second law of motion.

Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to the force which caused it, and takes place in the direction of the force.

(iv)Hence, establish the relationship: force = mass × acceleration. From Newton II: Force is proportional to the rate of change of momentumF (mv – mu)/t F m(v-u)/t F ma F = k (ma) F = ma

(v) A pendulum bob of mass 10 g was raised to a height of 20 cm and allowed to swing so that it collided with a block of mass 8.0 g at rest on a bench, as shown. The bob stopped on impact and the block subsequently moved along the bench.Calculate the velocity of the bob just before the collision.Loss in P.E = gain in K.Emgh = ½ mv2 v2 = 2gh = 2(9.8)(0.2) v = 1.98 m s-1

(vi)Calculate the velocity of the block immediately after the collision. m1u1 + m2u2 = m1v1 + m2v2

(0.01)(2) = (0.008) v2 v2= 2.48 m s-1

(vii) The block moved 2.0 m along the bench before stopping. What was the average horizontal force exerted on the block while travelling this distance? v2 = u2 + 2as / 0 = (2.5)2 + 2a(2)

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a = 1.56 m s-2

F = ma = (0.008)(1.6) = 0. 0.013 N

2004 Question 12 (a)(i) State Newton’s universal law of gravitation.

Newton’s Law of Gravitation states that any two point masses in the universe attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

(ii) Centripetal force is required to keep the earth moving around the sun.What provides this centripetal force?Gravitational pull of the sun.

(iii) In what direction does this centripetal force act?Towards the centre.

(iv)Give an expression for centripetal force.

(v) The earth has a speed of 3.0 × 104 m s–1 as it orbits the sun. The distance between the earth and the sun is 1.5 × 1011 m. Calculate the mass of the sun.

and Equating gives v2 Ms = v2R/G

Ms = (3.0 × 104)2 ( 1.5 × 1011)/ 6.7 × 10–11 = 2.0 × 1030 kg.

2003 Question 6Give the difference between vector quantities and scalar quantities and give one example of each.

A vector has both magnitude and direction whereas a scalar has magnitude only.(i) Describe an experiment to find the resultant of two vectors.

1. Attach three Newton Balances to a knot in a piece of thread.2. Adjust the size and direction of the three forces until the

knot in the thread remains at rest.3. Read the forces and note the angles.4. The resultant of any two of the forces can now be shown to be

equal to the magnitude and direction of the third force.

(ii) A cyclist travels from A to B along the arc of a circle of radius 25 m as shown.Calculate the distance travelled by the cyclist.The displacement is equivalent to one quarter of the circumference of a circle = 2πr/4 = 25π/2 = 12.5π = 39.3 m.

(iii) Calculate the displacement undergone by the cyclist.Using Pythagoras: x2 = 252 + 252 x = 35.3 m. Direction is NW

(iv)A person in a wheelchair is moving up a ramp at a constant speed. Their total weight is 900 N. The ramp makes an angle of 10o with the horizontal.Calculate the force required to keep the wheelchair moving at a constant speed up the ramp. (You may ignore the effects of friction.)If the wheelchair is moving at constant speed then the force up must equal the force down. So to calculate the size of the force up, we just need to calculate the force down:F = mgSinϑ= 900 Sin 10o

= 156.3 N(v) The ramp is 5 m long. Calculate the power exerted by the person in the wheelchair if it takes her

10 s to travel up the ramp.

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Power = work/timeWork = Force × displacement = 156.3 × 5 = 780 JPower = 780/10 = 78 W

2003 Question 12 (a)(i) State Newton’s second law of motion.

Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to the force which caused it, and takes place in the direction of the force.

(ii) A skydiver falls from an aircraft that is flying horizontally. He reaches a constant speed of 50 m s–1

after falling through a height of 1500 m. Calculate the average vertical acceleration of the skydiver.v 2= u2+2as (50)2 = 0 + 2(a)(1500) a = 0.83 m s-2

(iii) If the mass of the skydiver is 90 kg, what is the magnitude and direction of the average resultant force acting on him?F = ma = 90 × 0.83 = 75 N Down

(iv)Use a diagram to show the forces acting on the skydiver and explain why he reaches a constant speed. Weight acting down on diagramAir resistance / friction / buoyancy acting up on diagramAir resistance = weight, therefore resultant force = 0 Therefore acceleration = 0

2002 Question 6(i) State Newton’s second law of motion.

Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to the force which caused it, and takes place in the direction of the force.

(ii) The equation F = – ks, where k is a constant, is an expression for a law that governs the motion of a body. Name this law and give a statement of it.Hooke’s Law states that when an object is stretched the restoring force is directly proportional to the displacement, provided the elastic limit is not exceeded.

(iii) Give the name for this type of motion and describe the motion. Simple harmonic motion; an object is said to be moving with Simple Harmonic Motion if its acceleration is directly proportional to its distance from a fixed point in its path, and its acceleration is directed towards that point.

(iv)A mass at the end of a spring is an example of a system that obeys this law. Give two other examples of systems that obey this law. Stretched elastic, pendulum, oscillating magnet, springs of car, vibrating tuning fork, object bobbing in water waves, ball in saucer, etc.

(v) The springs of a mountain bike are compressed vertically by 5 mm when a cyclist of mass 60 kg sits on it. When the cyclist rides the bike over a bump on a track, the frame of the bike and the cyclist oscillate up and down.Using the formula F = – ks, calculate the value of k, the constant for the springs of the bike.F = – ks mg = – ks 60 × 9.8 = -k (.005) 588 = -k (.005) k = 1.2 × 105 N m-1

(vi)The total mass of the frame of the bike and the cyclist is 80 kg. Calculate the period of oscillation of the cyclist.k/m = ω2

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ω = 38 s-1

T = 2π/ω = 0.16 s

(vii) Calculate the number of oscillations of the cyclist per second. f = 1/T approximately = 6

2002 Question 12 (a)(i) State the principle of conservation of momentum.

The principle of conservation of momentum states that in any collision between two objects, the total momentum before impact equals total momentum after impact, provided no external forces act on the system.

(ii) A spacecraft of mass 50 000 kg is approaching a space station at a constant speed of 2 m s-1. The spacecraft must slow to a speed of 0.5 m s-1 for it to lock onto the space station. Calculate the mass of gas that the spacecraft must expel at a speed 50 m s-1 for the spacecraft to lock onto the space station. (The change in mass of the spacecraft may be ignored.)m1u1 + m2u2 = m1v1 + m2v2

(50000 × 2) = (50000 × 0.5) + (50m)m =1500 kg

(iii) In what direction should the gas be expelled? Forward (toward the space station).

(iv)Explain how the principle of conservation of momentum is applied to changing the direction in which a spacecraft is travelling. As the gas is expelled in one direction the rocket moves in the other direction.

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Acceleration, Force and Momentum

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Velocity

2010 Question 12 (a) [Higher Level](i) A student holds a motion sensor attached to a data-logger and its calculator. List the instructions you should give the student so that the calculator will display the graph shown in Fig 1.

(ii) The graph in Figure 2 represents the motion of a cyclist on a journey.Using the graph, calculate the distance travelled by the cyclist and the average speed for the journey.

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Equations of motion (vuast)2004 Question 6 [Ordinary Level](i) Define velocity.(ii) Define acceleration. (iii) Describe an experiment to measure the velocity of a moving object. (iv)A cheetah can go from rest up to a velocity of 28 m s−1 in just 4 seconds and stay running at this velocity

for a further 10 seconds.Sketch a velocity−time graph to show the variation of velocity with time for the cheetah during these 14 seconds.

(v) Calculate the acceleration of the cheetah during the first 4 seconds. (vi)Calculate the resultant force acting on the cheetah while it is accelerating.

The mass of the cheetah is 150 kg.(vii) Name two forces acting on the cheetah while it is running.

2008 Question 12 (a) [Ordinary Level](i) Define velocity.(ii) Define acceleration.(iii) A speedboat starts from rest and reaches a velocity of 20 m s−1 in 10 seconds.

It continues at this velocity for a further 5 seconds.The speedboat then comes to a stop in the next 4 seconds.Draw a velocity-time graph to show the variation of velocity of the boat during its journey.

(iv)Use your graph to estimate the velocity of the speedboat after 6 seconds. (v) Calculate the acceleration of the boat during the first 10 seconds. (vi)What was the distance travelled by the boat when it was moving at a constant velocity?

2010 Question 12 (a) [Ordinary Level](i) A cyclist on a bike has a combined mass of 120 kg.

The cyclist starts from rest and by pedalling applies a net force of 60 N to move the bike along a horizontal road. Calculate the acceleration of the cyclist

(i) Calculate the maximum velocity of the cyclist after 15 seconds.(ii) Calculate the distance travelled by the cyclist during the first 15 seconds.(iii) The cyclist stops peddling after 15 seconds and continues to freewheel for a further 80 m before

coming to a stop. Why does the bike stop? (iv)Calculate the time taken for the cyclist to travel the final 80 m.

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Force, gravity and acceleration

2002 Question 6 [Ordinary Level](i) Define (i) velocity, (ii) acceleration.(ii) Copy and complete the following statement of Newton’s first law of motion.

“An object stays at rest or moves with constant velocity (i.e. it does not accelerate) unless………………..” The diagram shows the forces acting on an aircraft travelling horizontally at a constant speed through the air.

L is the upward force acting on the aircraft. W is the weight of the aircraft. T is the force due to the engines. R is the force due to air resistance.

(iii) What happens to the aircraft when the force L is greater than the weight of the aircraft?(iv)What happens to the aircraft when the force T is greater than the force R?(v) The force T exerted by the engines is 20 000 N.

Calculate the work done by the engines while the aircraft travels a distance of 500 km.(vi)The aircraft was travelling at a speed of 60 m s-1 when it landed on the runway. It took two minutes to

stop. Calculate the acceleration of the aircraft while coming to a stop.(vii) The aircraft had a mass of 50 000 kg. What was the force required to stop the aircraft?(viii) Using Newton’s first law of motion, explain what would happen to the passengers if they were not

wearing seatbelts while the aircraft was landing.

2003 Question 6 [Ordinary Level] (i) Copy and complete the following statement of Newton’s law of universal gravitation.

“Any two point masses attract each other with a …….… which is proportional to the product of their …….... and inversely proportional to the ……..………...…………. between them.”

(ii) What is meant by the term acceleration due to gravity? (iii) An astronaut of mass 120 kg is on the surface of the moon, where the

acceleration due to gravity is 1.6 m s–2. What is the weight of the astronaut on the surface of the moon?

(iv)The astronaut throws a stone straight up from the surface of the moon with an initial speed of 25 m s–1. Describe how the speed of the stone changes as it reaches its highest point.

(v) Calculate the highest point reached by the stone. (vi)Calculate how high the astronaut can throw the same stone with the same initial speed of 25 m s–1 when

on the surface of the earth, where the acceleration due to gravity is 9.8 m s–2.(vii) Why is the acceleration due to gravity on the moon less than the acceleration due to gravity on the

earth?

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2006 Question 6 [Ordinary Level] (i) Define the term force and give the unit in which force is measured. (ii) Force is a vector quantity. Explain what this means. (iii) Newton’s law of universal gravitation is used to calculate the force between two bodies such as the

moon and the earth.Give two factors which affect the size of the gravitational force between two bodies.

(iv)Explain the term acceleration due to gravity, g. (v) An astronaut carries out an experiment to measure the acceleration due to gravity on the surface of the

moon.He drops an object from a height of 1.6 m above the surface of the moon and the object takes 1.4 s to fall.Use this data to show that the acceleration due to gravity on the surface of the moon is 1.6 m s–2.

(vi)The astronaut has a mass of 120 kg. Calculate his weight on the surface of the moon. (vii) Why is the astronaut’s weight greater on earth than on the moon? (viii) The earth is surrounded by a layer of air, called its atmosphere. Explain why the moon does not have

an atmosphere.

2008 Question 6 [Ordinary Level] The weight of an object is due to the gravitational force acting on it.Newton investigated the factors which affect this force.(i) Define force and give the unit of force.(ii) State Newton’s law of universal gravitation. (iii) Calculate the acceleration due to gravity on the moon.

The radius of the moon is 1.7 × 106 m and the mass of the moon is 7 × 1022 kg. (iv)A lunar buggy designed to travel on the surface of the moon had a mass of 2000 kg when built on the

earth.What is the weight of the buggy on earth?

(v) What is the mass of the buggy on the moon?(vi)What is the weight of the buggy on the moon? (vii) A powerful rocket is required to leave the surface of the earth.

A less powerful rocket is required to leave the surface of the moon.Explain why.

2012 Question 6 [Ordinary Level](i) What is meant by the term ‘acceleration due to gravity’? (ii) A spacecraft of mass 800 kg is on the surface of the moon, where the

acceleration due to gravity is 1.6 m s−2.Compare the weight of the spacecraft on the surface of the moon with its weight on earth, where the acceleration due to gravity is 9.8 m s–2.

(iii) The module of the spacecraft has a mass of 600 kg, when it is launched vertically from the surface of the moon with its engine exerting an upward force of 2000 N.Draw a diagram showing the forces acting on the module at lift-off.

(iv)What is the resultant force on the module?(v) Calculate the acceleration of the module during lift-off. (vi)Calculate the velocity of the module, 20 seconds after lift-off.(vii) Would the engine of the module be able to lift it off the earth’s surface?(viii) Justify your answer in terms of the forces acting on the module. (ix)Why is the acceleration due to gravity on the moon less than the acceleration due to gravity on earth?(x) Suggest a reason why the module of the spacecraft when launched from the moon does not need a

streamlined shape like those that are launched from earth.

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2007 Question 12 (a) [Higher Level](v) What is friction? (vi)A car of mass 750 kg is travelling east on a level road. Its engine exerts a constant force of 2.0 kN

causing the car to accelerate at 1.2 m s–2 until it reaches a speed of 25 m s–1.(vii) Calculate (i) the net force, (ii) the force of friction, acting on the car. (viii) If the engine is then turned off, calculate how far the car will travel before coming to rest.

2012 Question 6 [Higher Level]On 16 August, 1960, Joseph Kittinger established a record for the highest altitude parachute jump. This record remains unbroken. Kittinger jumped from a height of 31 km. He fell for 13 seconds and then his 1.8-metre canopy parachute opened. This stabilised his fall. Only four minutes and 36 seconds more were needed to bring him down to 5 km, where his 8.5-metre parachute opened, allowing him to fall at constant velocity, until he reached the surface of the earth.(Adapted from http://www.centennialofflight.gov)

(i) Calculate the acceleration due to gravity at a height of 31 km above the surface of the earth.(ii) What was the downward force exerted on Kittinger and his equipment at 31 km, taking their total mass

to be 180 kg?(iii) Estimate how far he fell during the first 13 seconds.

What assumptions did you take in this calculation?(iv)What was his average speed during the next 4 minutes and 36 seconds?(v) Assuming that the atmospheric pressure remains constant, how much was the force on a hemispherical

parachute of diameter 8.5 m greater than that on a similar parachute of diameter 1.8 m?(vi)Calculate the upthrust that acted on Kittinger when he reached constant velocity in the last stage of his

descent (assume g = 9.81 m s–2 during this stage).(radius of earth =6.36 × 106 m; mass of earth = 5.97 × 1024 kg)

2003 Question 12 (a) [Higher Level](v) State Newton’s second law of motion. (vi)A skydiver falls from an aircraft that is flying horizontally.

He reaches a constant speed of 50 m s–1 after falling through a height of 1500 m. Calculate the average vertical acceleration of the skydiver.

(vii) If the mass of the skydiver is 90 kg, what is the magnitude and direction of the average resultant force acting on him?

(viii) Use a diagram to show the forces acting on the skydiver and explain why he reaches a constant speed.

2010 Question 6 [Higher Level](Radius of the earth = 6.36 × 106 m, acceleration due to gravity at the earth’s surface = 9.81 m s−2

Distance from the centre of the earth to the centre of the moon = 3.84 × 108 mAssume the mass of the earth is 81 times the mass of the moon.)

(viii) State Newton’s law of universal gravitation.(ix)Use this law to calculate the acceleration due to gravity at a height above the surface of the earth, which

is twice the radius of the earth.Note that 2d above surface is 3d from earth’s centre

(x) A spacecraft carrying astronauts is on a straight line flight from the earth to the moon and after a while its engines are turned off. Explain why the spacecraft continues on its journey to the moon, even though the engines are turned off.

(xi)Describe the variation in the weight of the astronauts as they travel to the moon.(xii) At what height above the earth’s surface will the astronauts experience weightlessness?(xiii) The moon orbits the earth every 27.3 days. What is its velocity, expressed in metres per second?(xiv) Why is there no atmosphere on the moon?

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Momentum2007 Question 12 (a) [Ordinary Level] (i) State the principle of conservation of momentum.(ii) A rocket is launched by expelling gas from its engines.

Use the principle of conservation of momentum to explain why a rocket rises.

(iii) The diagram shows two shopping trolleys each of mass 12 kg on a smooth level floor.Trolley A moving at 3.5 m s−1 strikes trolley B, which is at rest.After the collision both trolleys move together in the same direction.Calculate the initial momentum of trolley A

(iv)Calculate the common velocity of the trolleys after the collision.

2004 Question 12 (a) [Ordinary Level](i) Define momentum. Give the unit of momentum. (ii) State the principle of conservation of momentum. (iii) The diagram shows a child stepping out of a boat onto a pier.

The child has a mass of 40 kg and steps out with an initial velocity of 2 m s−1 towards the pier. The boat, which was initially at rest, has a mass of 50 kg. Calculate the initial velocity of the boat immediately after the child steps out.

2004 Question 6 [Higher Level](viii) Define force.(ix)Define momentum. (x) State Newton’s second law of motion.(xi)Hence, establish the relationship: force = mass × acceleration. (xii) A pendulum bob of mass 10 g was raised to a height of 20 cm and allowed

to swing so that it collided with a block of mass 8.0 g at rest on a bench, as shown. The bob stopped on impact and the block subsequently moved along the bench.Calculate the velocity of the bob just before the collision.

(xiii) Calculate the velocity of the block immediately after the collision. (xiv) The block moved 2.0 m along the bench before stopping.

What was the average horizontal force exerted on the block while travelling this distance? (acceleration due to gravity = 9.8 m s–2)

2002 Question 12 (a) [Higher Level](v) State the principle of conservation of momentum. (vi)A spacecraft of mass 50 000 kg is approaching a space station at a constant speed of 2 m s-1. The

spacecraft must slow to a speed of 0.5 m s-1 for it to lock onto the space station. Calculate the mass of gas that the spacecraft must expel at a speed 50 m s-1 for the spacecraft to lock onto the space station. (The change in mass of the spacecraft may be ignored.)(vii) In what direction should the gas be expelled? Explain how the principle of conservation of momentum is applied to changing the direction in which a spacecraft is travelling.

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Work, Energy and Power2005 Question 11 [Ordinary Level] Read the following passage and answer the accompanying questions.There are different forms of energy. Fuels such as coal, oil and wood contain chemical energy. When these fuels are burnt, the chemical energy changes into heat and light energy. Electricity is the most important form of energy in the industrialised world, because it can be transported over long distances via cables. It is produced by converting the chemical energy from coal, oil or natural gas in power stations.In a hydroelectric power station the potential energy of a height of water is released as the water flows through a turbine, generating electricity.Energy sources fall into two broad groups: renewable and non-renewable. Renewable energy sources are those which replenish themselves naturally and will always be available – hydroelectric power, solar energy, wind and wave power, tidal energy and geothermal energy. Non-renewable energy sources are those of which there are limited supplies and once used are gone forever. These include coal, oil, natural gas and uranium.(Adapted from the Hutchinson Encyclopaedia of Science, 1998).(a) Define energy. (b) What energy conversion takes place when a fuel is burnt? (c) Name one method of producing electricity. (d) Give one factor on which the potential energy of a body depends. (e) What type of energy is associated with wind, waves and moving water? (f) Give one disadvantage of non-renewable energy sources. (g) How does the sun produce heat and light? (h) In Einstein’s equation E = mc2, what does c represent?

2011 Question 6 [Ordinary Level](i) State Newton’s first law of motion.(ii) A car of mass 1400 kg was travelling with a constant speed of 15 m s-1 when

it struck a tree and came to a complete stop in 0.4 s.Draw a diagram of the forces acting on the car before it hit the tree.

(iii) Calculate the acceleration of the car during the collision.(iv)Calculate the kinetic energy of the moving car before it struck the tree.(v) What happened to the kinetic energy of the moving car?(vi)A back seat passenger could injure other occupants during a collision.

Explain, with reference to Newton’s laws of motion, how this could occur.(vii) How is this risk of injury minimised?

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2009 Question 6 [Ordinary Level] (i) Define velocity.(ii) Define friction. (iii) The diagram shows the forces acting on a

train which was travelling horizontally.A train of mass 30000 kg started from a station and accelerated at 0.5 m s−2 to reach its top speed of 50 m s−1 and maintained this speed for 90 minutes.As the train approached the next station the driver applied the brakes uniformly to bring the train to a stop in a distance of 500 m.Calculate how long it took the train to reach its top speed.

(iv)Calculate how far it travelled at its top speed. (v) Calculate the acceleration experienced by the train when the brakes were applied. (vi)What was the force acting on the train when the brakes were applied? (vii) Calculate the kinetic energy lost by the train in stopping. (viii) What happened to the kinetic energy lost by the train? (ix)Name the force A and the force B acting on the train, as shown in the diagram. (x) Describe the motion of the train when the force A is equal to the force T. (xi)Sketch a velocity-time graph of the train’s journey.

2007 Question 6 [Ordinary Level] (i) Define work and give the unit of measurement.(ii) Define power and give the unit of measurement. (iii) What is the difference between potential energy and kinetic energy? (iv)An empty lift has a weight of 7200 N and is powered by an electric motor.

The lift takes a person up 25 m in 40 seconds. The person weighs 800 N.Calculate the total weight raised by the lift’s motor.

(v) Calculate the work done by the lift’s motor. (vi)Calculate the power output of the motor.(vii) Calculate the energy gained by the person in taking the lift. (viii) If instead the person climbed the stairs to the same height in 2 minutes, calculate the

power generated by the person in climbing the stairs. (ix)Give two disadvantages of using a lift.

2008 Question 12 (a) [Higher Level](v) State the principle of conservation of energy. (vi)In a pole-vaulting competition an athlete, whose centre of gravity is 1.1 m above the ground, sprints

from rest and reaches a maximum velocity of 9.2 ms–1 after 3.0 seconds. He maintains this velocity for 2.0 seconds before jumping. Draw a velocity-time graph to illustrate the athlete’s horizontal motion.

(vii) Use your graph to calculate the distance travelled by the athlete before jumping. (viii) What is the maximum height above the ground that the athlete can raise his centre of gravity?

2005 Question 12 (a) [Higher Level](ix)State the principle of conservation of energy. (x) A basketball of mass 600 g which was resting on a hoop falls to the ground 3.05 m below.

What is the maximum kinetic energy of the ball as it falls? (xi)On bouncing from the ground the ball loses 6 joules of energy. What happens to the energy lost by the ball? (xii) Calculate the height of the first bounce of the ball.

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Kinetic Energy and Momentum

2012 Question 12 (a) [Ordinary Level](i) State the principle of conservation of momentum.(ii) A cannon of mass 1500 kg containing a cannonball of mass 80 kg

was at rest on a horizontal surface as shown. The cannonball was fired from the cannon with an initial horizontal velocity of 60 m s–1 and the cannon recoiled.Calculate the recoil velocity of the cannon

(iii) Calculate the kinetic energy of the cannon as it recoils. (iv)Why did the cannon recoil? (v) Why will the cannon come to a stop in a shorter distance that the

cannonball?

2010 Question 6 [Ordinary Level] (i) Define momentum (ii) Define kinetic energy (iii) State the principle of conservation of momentum. (iv)Explain how this principle applies in launching a spacecraft. (v) An ice skater of mass 50 kg was moving with a speed of 6 m s−1 then she collides with another skater of

mass 70 kg who was standing still. The two skaters then moved off together.Calculate the momentum of each skater before the collision?

(vi)What is the momentum of the combined skaters after the collision? (vii) Calculate the speed of the two skaters after the collision. (viii) Calculate the kinetic energy of each skater before the collision. (ix)Calculate the kinetic energy of the pair of skaters after the collision.(x) Comment on the total kinetic energy values before and after the collision.

Force and Vectors2009 Question 6 [Higher Level](i) State Newton’s laws of motion. (ii) Show that F = ma is a special case of Newton’s second law.

A skateboarder with a total mass of 70 kg starts from rest at the top of a ramp and accelerates down it. The ramp is 25 m long and is at an angle of 200 to the horizontal. The skateboarder has a velocity of 12.2 m s–1 at the bottom of the ramp.

(iii) Calculate the average acceleration of the skateboarder on the ramp.(iv)Calculate the component of the skateboarder’s weight that is parallel to the ramp.(v) Calculate the force of friction acting on the skateboarder on the ramp.(vi)The skateboarder then maintains a speed of 10.5 m s–1 until he enters a circular ramp of radius 10 m.

What is the initial centripetal force acting on him?(vii) What is the maximum height that the skateboarder can reach? (viii) Sketch a velocity-time graph to illustrate his motion.

(acceleration due to gravity = 9.8 m s–2)

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2003 Question 6 [Higher Level](viii) Give the difference between vector quantities and scalar quantities and give one

example of each.(ix)Describe an experiment to find the resultant of two vectors. (x) A cyclist travels from A to B along the arc of a circle of radius 25 m as shown.(xi)Calculate (i) the distance travelled by the cyclist.(xii) Calculate the displacement undergone by the cyclist.

(xiii) A person in a wheelchair is moving up a ramp at a constant speed. Their total weight is 900 N. The ramp makes an angle of 10o with the horizontal.Calculate the force required to keep the wheelchair moving at a constant speed up the ramp. (You may ignore the effects of friction.)

(xiv) The ramp is 5 m long. Calculate the power exerted by the person in the wheelchair if it takes her 10 s to travel up the ramp.

Solutions to Ordinary Level questions

2012 Question 12 (a) [Ordinary Level](i) State the principle of conservation of momentum.

The Principle of Conservation of Momentum states that in any collision between two objects, the total momentum before impact equals total momentum after impact, provided no external forces act on the system.

(ii) Calculate the recoil velocity of the cannon0 = m1 v1 + m2 v2

0 = (1500)( v1) + (80)(60)v1 = (-) 3.2 m s-1

(ii) Calculate the kinetic energy of the cannon as it recoils. (½(1500)(3.2)2 = 7680 J

(iii) Why did the cannon recoil? For momentum to be conserved (because initially there was no momentum and the cannonball went forward).

(iv)Why will the cannon come to a stop in a shorter distance that the cannonball?Because the cannon has a bigger mass / the resistance of the ground (friction) is bigger than that of air / the cannon had a smaller recoil velocity

2012 Question 6 (i) What is meant by the term ‘acceleration due to gravity’?

Acceleration caused by the (gravitational pull of the) earth (ii) Compare the weight of the spacecraft on the surface of the moon with its weight on earth, where

the acceleration due to gravity is 9.8 m s–2. Weight on moon = mgm= (800)(1.6) = 1280 N Weight on earth = mge = (800)(9.8) = 7840 N So the spacecraft is (7840/1280) = 6.1 times heavier on the earth than on the moon.

(iii) Draw a diagram showing the forces acting on the module at lift-off.Weight acting down, thrust acting up.

(iv)What is the resultant force on the module?Fnet = (Fbig – Fsmall) = (F - mgm) = [2000 - (600)(1.6)] = 1040 N

(v) Calculate the acceleration of the module during lift-off. Fnet =ma 1040 = (600)(a) a = 1.73 m s-2

(vi)the velocity of the module, 20 seconds after lift-off.(v = u + at ) i.e. v = 0 + (1.73)(20) = 34.6 m s-1

(vii) Would the engine of the module be able to lift it off the earth’s surface?

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No. The force of gravity on the earth is 5880 N (600 × 9.8) and the upward thrust of the spacecraft is only 2000 N.

(viii) Why is the acceleration due to gravity on the moon less than the acceleration due to gravity on earth?Because the mass of the moon is less than the mass of the earth

(ix)Suggest a reason why the module of the spacecraft when launched from the moon does not need a streamlined shape like those that are launched from earth.There is no atmosphere on the moon so no air resistance / drag / friction

2011 [Ordinary Level] 6.(i) State Newton’s first law of motion.

A body will remain at rest or moving at a constant velocity unless acted on by an (external) force,

(ii) Draw a diagram of the forces acting on the car before it hit the tree.

(iii) Calculate the acceleration of the car during the collision.v = u + at

a = 37.5 m s-2

(iv)Calculate the net force acting on the car during the collision.F= ma F =1400 × 37.5 = 52500 N

(v) Calculate the kinetic energy of the moving car before it struck the tree.(E = ½ mv2 E = ½ (1400)(15)2 = 157500 J

(vi)What happened to the kinetic energy of the moving car?It got converted to heat and sound and also deformed the tree

(vii) Explain, with reference to Newton’s laws of motion, how this could occur.Even though the car comes to a stop the back-seat passenger will continue to move forward (from Newton’s first law of motion) and so could collide with someone in the front.

(viii) How is this risk of injury minimised?By wearing a seat belt.

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2010 Question 12 (a)(i) Calculate the acceleration of the cyclist

F = ma, a = 60/120a = 0.5 m s–2

(ii) Calculate the maximum velocity of the cyclist after 15 seconds.v = u + at. v = u + (0.5)(15) = 7.5 m s–1

(iii) Calculate the distance travelled by the cyclist during the first 15 seconds.s = ut + ½ at2

s = ut + ½ (0.5)(15)2 = 56.25 m.(iv)The cyclist stops peddling after 15 seconds and continues to freewheel for a further 80 m before

coming to a stop. Why does the bike stop? Due to friction / air resistance.

(v) Calculate the time taken for the cyclist to travel the final 80 m?v2 = u2 + 2as0 = (7.5)2 + 2a(80)a = - (7.5)2/(2)(80)a = - 0.35Then use v = u + at0 = 7.5 – (0.35)(t)t = - 7.5/- 0.35 = 21.43s

Alternatively we could just have used s = (u +v)t/280 = (7.5 + 0)t/2t = 21.33 s

2010 Question 6(i) Define momentum

Momentum = (mass)(velocity) // p = mv (ii) Define kinetic energy

Kinetic energy is energy that an object has due to being in motion.(iii) State the principle of conservation of momentum.

The Principle of Conservation of Momentum states that in any collision between two objects, the total momentum before impact equals total momentum after impact, provided no external forces act on the system.

(iv)Explain how this principle applies in launching a spacecraft. The momentum of the rocket is equal but opposite to rocket exhaust

(v) Calculate the momentum of each skater before the collision50 × 6 = 300 kg m s−1

70 × 0 = 0 kg m s−1

(vi)What is the momentum of the combined skaters after the collision? 300 kg m s−1

(vii) Calculate the speed of the two skaters after the collision. 300 = (50 + 70) vv = 2.5 m s−1

(viii) Calculate the kinetic energy of each skater before the collision. Ek = ½mv2

Ek = ½ 50 × 62 = 900 JEk = ½ 70 × 0 = 0 J

(ix)Calculate the kinetic energy of the pair of skaters after the collision.Ek = ½ 120 × (2.5)2 = 375 (J)

(x) Comment on the total kinetic energy values before and after the collision.Kinetic energy not conserved in collision because some of the energy was given off as heat and sound.

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2009 Question 6 (i) Define velocity.

Velocity is the rate of change of displacement with respect to time.(ii) Define friction.

Friction is a force which resists relative motion between surfaces in contact.(iii) Calculate how long it took the train to reach its top speed.

v = u + at50 = 0 + 0.5tt = 50/0.5 = 100 s

(iv)Calculate how far it travelled at its top speed. s = ut + ½ at2 (but a = 0)s = 50 × (90×60) = 270000 m

(v) Calculate the acceleration experienced by the train when the brakes were applied. v2 = u2 + 2as0 = 502 + 2a(500)a = −2500/1000 = − 2.5 m s-1

(vi)What was the force acting on the train when the brakes were applied? F = maF = 30000× (−)(2.5) = - 75000 N = 75 kN

(vii) Calculate the kinetic energy lost by the train in stopping. Ek = ½mv2

Ek = ½ (30000)(50)2 = 37500000 J = 37.5 MJ(viii) What happened to the kinetic energy lost by the train?

It was converted to other forms of energy such as heat, sound and light (from sparks).(ix)Name the force A and the force B acting on the train, as shown in the diagram.

A = friction/retardation / resistance to motion B = weight / force of gravity

(x) Describe the motion of the train when the force A is equal to the force T. The train will move at constant speed.

(xi)Sketch a velocity-time graph of the train’s journey. See diagram

2008 Question 12 (a) (i) Define velocity

Velocity is the change in displacement with respect to time.(ii) Define acceleration.

Acceleration is the change in velocity with respect to time(iii) Draw a velocity-time graph to show the variation of velocity of the boat during its journey.

See diagram(iv)Use your graph to estimate the velocity of the speedboat after 6

seconds.12 m s-1

(v) Calculate the acceleration of the boat during the first 10 seconds. v= u + at, so cross multiply to get a = v - u/t = 20 - 0/10 = 2 m s-2.

(vi)What was the distance travelled by the boat when it was moving at a constant velocity? Constant velocity so can use vel = distance/time Cross-multiply to get s = vt = 20×5 = 100 m

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2008 Question 6 (i) Define force and give the unit of force.

A Force is anything which can cause an object to accelerate.The unit of force is the newton.

(ii) State Newton’s law of universal gravitation. Newton’s Law of Gravitation states that any two point masses in the universe attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

(iii) Calculate the acceleration due to gravity on the moon.The radius of the moon is 1.7 × 106 m and the mass of the moon is 7 × 1022 kg.

(iv)What is the weight of the buggy on earth?W = mg = 2000 × 9.8 = 19600 N

(v) What is the mass of the buggy on the moon?2000 kg

(vi)What is the weight of the buggy on the moon?W = mg = 2000 × 1.6 = 3200 N

(vii) A less powerful rocket is required to leave the surface of the moon. Explain why. Gravity is less on moon so less force is needed to escape.

2007 Question 12 (a)(i) State the principle of conservation of momentum.

The Principle of Conservation of Momentum states that in any collision between two objects, the total momentum before impact equals total momentum after impact, provided no external forces act on the system.

(ii) Use the principle of conservation of momentum to explain why a rocket rises. The gas moves down (with a momentum) causing the rocket to move up (in the opposite direction with an equal momentum)

(iii) Calculate the initial momentum of trolley A (mu = ) 12×3.5 = 42 kg m s-1

(iv)Calculate the common velocity of the trolleys after the collision. Momentum before = Momentum after 42 = m3v3 v3 = 42/m3 v = 42/24 = 1.75 ( m s-1)

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2007 Question 6(i) Define work and give the unit of measurement.

Work is the product of force by displacement (distance). Unit: joule(ii) Define power and give the unit of measurement.

Power is the rate at which work is done. Unit: watt(iii) What is the difference between potential energy and kinetic energy?

Potential energy is energy a body has due to its position; kinetic energy is energy a body has due to its motion,

(iv)Calculate the total weight raised by the lift’s motor.7200 + 800 = 8000 (N)

(v) Calculate the work done by the lift’s motor. Work = Force × distance = 8000 × 25 = 200,000 J (200 kJ)

(vi)Calculate the power output of the motor.Power = work/time =200,000/40 = 5000 W

(vii) Calculate the energy gained by the person in taking the lift. Energy = Force × distance = 800 × 25 = 20,000 J

(viii) Calculate the power generated by the person in climbing the stairs. Power = work/time = (800 × 25)/120 = 166.6 W

(ix)Give two disadvantages of using a lift.Needs more energy / uses energy / no exercise so not good for health /cost involved / can be dangerous

2006 Question 6(i) Define the term force and give the unit in which force is measured.

A force is something which causes an acceleration.The unit of force is the newton.

(ii) Force is a vector quantity. Explain what this means. A vector is a quantity which has magnitude and direction.

(iii) Give two factors which affect the size of the gravitational force between two bodies. The mass of the objects and the distance between them.

(iv)Explain the term acceleration due to gravity, g. It is the acceleration of an object which is in freefall due to the attraction of the earth.

(v) Use this data to show that the acceleration due to gravity on the surface of the moon is 1.6 m s–2.s = 1.6 m, t = 1.4 s, u = 0. Substitute into the equation s = ut + ½ at2 to get a = 1.6 m s-2.

(vi)The astronaut has a mass of 120 kg. Calculate his weight on the surface of the moon. w = mg w = (120)(1.6) = 192 N.

(vii) Why is the astronaut’s weight greater on earth than on the moon? Because acceleration due to gravity is greater on the earth (or because the mass of the earth is greater than the mass of the moon).

(viii) Explain why the moon does not have an atmosphere. Because gravity is less on the moon.

2004 Question 12 (a) (i) Define momentum. Give the unit of momentum.

Momentum = mass × velocity.The unit of momentum is the kg m s-1

(ii) State the principle of conservation of momentum. The Principle of Conservation of Momentum states that in any collision between two objects, the total momentum before impact equals total momentum after impact, provided no external forces act on the system.

(iii) Calculate the initial velocity of the boat immediately after the child steps out.m1u1 + m2u2 = m1v1 + m2v2 0 = (40)(2) + (50)x x = - 1.6 m s-1

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2004 Question 6(i) Define velocity.

Velocity is the rate of change of displacement with respect to time.(ii) Define acceleration.

Acceleration is the rate of change of velocity with respect to time.(iii) Describe an experiment to measure the velocity of a

moving object. We measured the distance between 11 dots and the time was the time for 10 intervals, where each interval was 1 50th of a second. We then used the formula velocity = distance/time to calculate the velocity.

(iv)Sketch a velocity−time graph to show the variation of velocity with time for the cheetah during these 14 seconds. See graph

(v) Calculate the acceleration of the cheetah during the first 4 seconds. v = u + at 28 = 0 + a (4) a = a = 7 m s-2

(vi)Calculate the resultant force acting on the cheetah while it is accelerating. The mass of the cheetah is 150 kg.F = ma F = 150 × 7 = 1050 N

(vii) Name two forces acting on the cheetah while it is running. Gravity (or weight), friction, air resistance.

2003 Question 6(i) “Any two point masses attract each other with a force which is proportional to the product of their

masses and inversely proportional to the square of the distance between them.” (ii) What is meant by the term acceleration due to gravity?

It is the acceleration which objects in freefall experience due to the pull of the earth.(iii) What is the weight of the astronaut on the surface of the moon?

W = mg = 120 × 1.6 = 192 N.(iv)The astronaut throws a stone straight up from the surface of the moon with an initial speed of 25

m s–1. Describe how the speed of the stone changes as it reaches its highest point.It slows down as it rises until at the highest point its speed is 0.

(v) Calculate the highest point reached by the stone. v2 = u2 + 2as 0 = (25)2 + 2 (-1.6) s s = 195.3 m.

(vi)Calculate how high the astronaut can throw the same stone with the same initial speed of 25 m s–1 when on the surface of the earth, where the acceleration due to gravity is 9.8 m s–2.v2 = u2 + 2as 0 = (25)2 + 2 (-9.8) s s = 31.9 m.

(vii) Why is the acceleration due to gravity on the moon less than the acceleration due to gravity on the earth?The earth has a greater mass than the moon.

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2002 Question 6(i) Define velocity.

Velocity is the rate of change of displacement with respect to time.(ii) Define acceleration.

Acceleration is the rate of change of velocity with respect to time(iii) “An object stays at rest or moves with constant velocity (i.e. it does not accelerate) unless an

external force acts on it”.(iv)What happens to the aircraft when the force L is greater than the weight of the aircraft?

It accelerates upwards.(v) What happens to the aircraft when the force T is greater than the force R?

It accelerates forward.(vi)Calculate the work done by the engines while the aircraft travels a distance of 500 km.

Work = Force × displacement 20000 × 500 000 = 1 × 1010 (J)(vii) Calculate the acceleration of the aircraft while coming to a stop.

v = u + at 0 = 60 + a (120) a = - 0.5 m s-2

(viii) The aircraft had a mass of 50 000 kg. What was the force required to stop the aircraft?F = ma F = 50 000 × 0.5 = 25 000 N.

(ix)Using Newton’s first law of motion, explain what would happen to the passengers if they were not wearing seatbelts while the aircraft was landing. They would continue to move at the greater initial velocity and so would be ‘thrown’ forward.

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Solutions to Higher Level questions2012 Question 6(i) Calculate the acceleration due to gravity at a height of 31 km above the surface of the earth.

d = (6.36 × 106) + (31 × 103) =

g = 9.76 m s-2 (ii) What was the downward force exerted on Kittinger and his equipment at 31 km, taking their total

mass to be 180 kg?W = F = mg F = 180(9.715) = 1748.7 N

(iii) Estimate how far he fell during the first 13 seconds.What assumptions did you take in this calculation?s = ut + ½ at2

s = ½ (9.715)(13)2

s = 820.92 mu taken as zero / g is constant / no atmospheric resistance / no buoyancy due to atmosphere

(iv)What was his average speed during the next 4 minutes and 36 seconds?Average speed = distance ÷ timeDistance = 31000 – 820.92 –5000 = 25180 mAverage speed = 25180 ÷ 276 = 91.23 m s–1

(v) How much was the force on a hemispherical parachute of diameter 8.5 m greater than that on a similar parachute of diameter 1.8 m?

Or F = 22.3 N

(vi)Calculate the upthrust that acted on Kittinger when he reached constant velocity in the last stage of his descent (assume g = 9.81 m s–2 during this stage).Pressure = force / areaUpthrust (U) = mg = (180)(9.81) = 1766 N

2010 Question 12 (a)(i) List the instructions . . .

Stand 1 m from wall (and select START) Stationary for 5 s Move back to 3 m (from wall) in 6 s / accept specific velocity and time/distance Stationary for 7 s Approach to 1 m in 4 s

(ii) Using the graph, calculate the distance travelled by the cyclist and the average speed for the journey.Distance travelled = area under the graph18 km h-1 = 18000/60 m s-1 = 300 m min-1

S1 = 150 × 6 = 900 mS2 = 300 × 8 = 2400 mS3 = 150 × 5 = 750 mTotal distance = 4050 m

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Average speed = total distance divided by total time = 4050/19 = 213.2 m min-1 = 3.55 m s-1

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2010 Question 6(viii) State Newton’s law of universal gravitation.

Force between any two point masses is proportional to product of masses and inversely/indirectly proportional to square of the distance between them.

(ix)Use this law to calculate the acceleration due to gravity at a height above the surface of the earth, which is twice the radius of the earth.Note that 2d above surface is 3d from earth’s centre

where d = 6.36 × 106 m

gnew = 1.09 m s-2

(x) Explain why the spacecraft continues on its journey to the moon, even though the engines are turned off.There are no external forces acting on the spacecraft so from Newton’s 1st law of motion the object will maintain its velocity.

(xi)Describe the variation in the weight of the astronauts as they travel to the moon.Weight decreases as the astronaut moves away from the earth and gains (a lesser than normal) weight as she/he approaches the moon

(xii) At what height above the earth’s surface will the astronauts experience weightlessness?Gravitational pull of earth = gravitational pull of moon

=

dE = 9 dm and dE + dm = 3.84 × 108 m10 dm = 3.84 × 108

dm = 3.84 × 107

dE = 3.356 × 108

Height above the earth = (3.356 × 108) – (6.36 × 106) = 3.39 × 108 m

(xiii) The moon orbits the earth every 27.3 days. What is its velocity, expressed in metres per second?

v = 1022.9 m s-1

(xiv) Why is there no atmosphere on the moon?The gravitational force is too weak to sustain an atmosphere.

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2009 Question 6(i) State Newton’s laws of motion.

Newton’s First Law of Motion states that every object will remain in a state of rest or travelling with a constant velocity unless an external force acts on it.Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to the force which caused it, and takes place in the direction of the force.Newton’s Third Law of Motion states that when body A exerts a force on body B, B exerts a force equal in magnitude (but) opposite in direction (on A).

(ii) Show that F = ma is a special case of Newton’s second law. From Newton II: Force is proportional to the rate of change of momentumForce rate of change of momentumF (mv – mu)/tF m(v-u)/tF maF = k (ma) [but k = 1]F = ma

(iii) Calculate the average acceleration of the skateboarder on the ramp.v2= u2 + 2as (12.2)2 = 0 +2a(25) a = 2.98 m s–2

(iv)Calculate the component of the skateboarder’s weight that is parallel to the ramp.W = mgsin = mgsin20 = 234.63 N

(v) Calculate the force of friction acting on the skateboarder on the ramp.Force down (due to gravity) – Resistive force (due to friction) = Net forceForce down (due to gravity) = 234.63 NNet force= 70(2.98) = 208.38 NFriction force = 234.63 – 208.38 = 26.25 N

(vi)What is the initial centripetal force acting on him?

= 70 (10.5)2/10 = 771.75 N(vii) What is the maximum height that the skateboarder can reach?

v2= u2 + 2as u2 = 2g(s) s = 5.63 m(viii) Sketch a velocity-time graph to illustrate his motion.

Velocity on vertical axis, time on horizontal axis, with appropriate numbers on both axes.

2008 Question 12 (a)(v) State the principle of conservation of energy.

The Principle of Conservation of Energy states that energy cannot be created or destroyed but can only be converted from one form to another.

(vi)Draw a velocity-time graph to illustrate the athlete’s horizontal motion.See diagram

(vii) Use your graph to calculate the distance travelled by the athlete before jumping. Distance (s) = area under curve s = ½ (3)(9.2) + 2 (9.2) / 13.8 + 18.4 / 32.2 m

(viii) What is the maximum height above the ground that the athlete can raise his centre of gravity?K.E. = P.E.½ mv2 = mghh = v2/2g = (9.2)2/2(9.8) = 4.32Max height above the ground = 4.32 + 1.1 = 5.42 m.

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2007 Question 12 (a)(v) What is friction?

Friction is a force which opposes the relative motion between two objects.(vi)Calculate the net force acting on the car.

Fnet = ma = (750)(1.2) = 900 N east.(vii) Calculate the force of friction acting on the car.

Fnet = Fcar - Ffriction

900 = 2000 - Ffriction Ffriction = 1100 N west(viii) If the engine is then turned off, calculate how far the car will travel before coming to rest?

Friction causes deceleration: a = F ÷ ma = (-1100) ÷ 750 = - 1.47 ms-2

v 2 = u 2 + 2as0 = 252 +2(-1.47) s or s = 213 m

2005 Question 12 (a)(i) State the principle of conservation of energy.

Energy cannot be created or destroyed but it can only be changed from one form to another .(ii) What is the maximum kinetic energy of the ball as it falls?

KE = PE (at height of 3.05 m) v2 = u2 +2as v2 = 0 + 2(9.8)(3.05) v2 = 59.78 {you could also have use P.E. = mgh}Ek = ½mv2 = ½ (0.60)(59.78) Ek = 17.9 J

(iii) On bouncing from the ground the ball loses 6 joules of energy. What happens to the energy lost by the ball? It changes into sound and heat.

(iv)Calculate the height of the first bounce of the ball. [retained energy = 17.9 – 6] E = 11.9 JE = mgh h = E / mg h = 11.9 /(0.600)(9.8) h = 2.02 m

2004 Question 6(viii) Define force.

Force is that which causes an acceleration.(ix)Define momentum.

Momentum is the defined as the product of mass multiplied by velocity.(x) State Newton’s second law of motion.

Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to the force which caused it, and takes place in the direction of the force.

(xi)Hence, establish the relationship: force = mass × acceleration. From Newton II: Force is proportional to the rate of change of momentumF (mv – mu)/t F m(v-u)/t F ma F = k (ma) F = ma

(xii) Calculate the velocity of the bob just before the collision.Loss in P.E = gain in K.Emgh = ½ mv2 v2 = 2gh = 2(9.8)(0.2) v = 1.98 m s -1

(xiii) Calculate the velocity of the block immediately after the collision. m1u1 + m2u2 = m1v1 + m2v2

(0.01)(2) = (0.008) v2 v2= 2.48 m s-1

(xiv) What was the average horizontal force exerted on the block while travelling this distance? v2 = u2 + 2as / 0 = (2.5)2 + 2a(2) a = 1.56 m s-2

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F = ma = (0.008)(1.6) = 0. 0.013 N2003 Question 12 (a)(v) State Newton’s second law of motion.

Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to the force which caused it, and takes place in the direction of the force.

(vi)Calculate the average vertical acceleration of the skydiver.v 2= u2+2as (50)2 = 0 + 2(a)(1500) a = 0.83 m s-2

(vii) What is the magnitude and direction of the average resultant force acting on him?F = ma = 90 × 0.83 = 75 N Down

(viii) Use a diagram to show the forces acting on the skydiver and explain why he reaches a constant speed. Weight acting down on diagramAir resistance / friction / buoyancy acting up on diagramAir resistance = weight, therefore resultant force = 0 Therefore acceleration = 0

2003 Question 6Give the difference between vector quantities and scalar quantities and give one example of each.A vector has both magnitude and direction whereas a scalar has magnitude only.(vi)Describe an experiment to find the resultant of two vectors.

5. Attach three Newton Balances to a knot in a piece of thread.6. Adjust the size and direction of the three forces until the knot in the thread remains at rest.7. Read the forces and note the angles.8. The resultant of any two of the forces can now be shown to be equal to the magnitude and direction

of the third force.(vii) Calculate the distance travelled by the cyclist.

The displacement is equivalent to one quarter of the circumference of a circle = 2πr/4 = 25π/2 = 12.5π = 39.3 m.

(viii) Calculate the displacement undergone by the cyclist.Using Pythagoras: x2 = 252 + 252 x = 35.3 m. Direction is NW

(ix)Calculate the force required to keep the wheelchair moving at a constant speed up the ramp. (You may ignore the effects of friction.)If the wheelchair is moving at constant speed then the force up must equal the force down. So to calculate the size of the force up, we just need to calculate the force down:F = mgSinϑ= 900 Sin 10o

= 156.3 N(x) The ramp is 5 m long. Calculate the power exerted by the person in the wheelchair if it takes her

10 s to travel up the ramp.Power = work/timeWork = Force × displacement = 156.3 × 5 = 780 JPower = 780/10 = 78 W

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2002 Question 12 (a)(v) State the principle of conservation of momentum.

The principle of conservation of momentum states that in any collision between two objects, the total momentum before impact equals total momentum after impact, provided no external forces act on the system.

(vi)Calculate the mass of gas that the spacecraft must expel at a speed 50 m s-1 for the spacecraft to lock onto the space station. (The change in mass of the spacecraft may be ignored.)m1u1 + m2u2 = m1v1 + m2v2

(50000 × 2) = (50000 × 0.5) + (50m)m =1500 kg

(vii) In what direction should the gas be expelled? Forward (toward the space station).

(viii) Explain how the principle of conservation of momentum is applied to changing the direction in which a spacecraft is travelling. As the gas is expelled in one direction the rocket moves in the other direction.

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Moments and Pressure

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2012 - 2002

2011 Question 6 (a) [Higher Level](i) Define the moment of a force.(ii) A toy, such as that shown, has a heavy hemispherical base and its centre of gravity is

located at C. When the toy is knocked over, it always returns to the upright position. Explain why this happens.

2006 Question 12 (a) [Ordinary Level](i) Define the moment of a force. (ii) The diagram shows a crane in equilibrium.

Give one condition that is necessary for the crane to be in equilibrium.

(iii) What is the moment of the 9000 N concrete slab about the axis of the crane?

(iv)Calculate the value of the load marked X. (v) A crane is an example of a lever.

Give another example of a lever.

2003 Question 12 (a) [Ordinary Level](i) Define the moment of a force.(ii) Explain why the handle on a door is on the opposite side

to the hinges of the door.(iii) A metre stick is suspended by a thread at the 20 cm

mark as shown in the diagram. The weight W of the metre stick acts through the 50 cm mark. A weight of 2 N is placed at the 15 cm mark.

(iv)Calculate the moment of the 2 N weight about the 20 cm mark.

(v) What is the moment of W about the 20 cm mark?(vi)If the metre stick is in equilibrium, find the value of W.

2011 Question 6 (b) [Higher Level](i) State the conditions necessary for the equilibrium of a body under a set of co-planar forces.(ii) Three children position themselves on a uniform see-saw so that it is horizontal and in equilibrium.

The fulcrum of the see-saw is at its centre of gravity. A child of mass 30 kg sits 1.8 m to the left of the fulcrum and another child of mass 40 kg sits 0.8 m to the right of the fulcrum.Where should the third child of mass 45 kg sit, in order to balance the see-saw?

Pressure

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2011 Question 12 (a) [Ordinary Level] (i) State Boyle’s law. (ii) Describe an experiment to demonstrate that the atmosphere exerts a pressure.

(iii) Atmospheric pressure at the top of Mount Everest is very low at 3.0 × 104 Pa, which is why climbers need oxygen tanks.

A climber uses a 5.0 litre tank with an internal gas pressure of 4.2 × 106 Pa to supply oxygen.What volume of gas will be available at the top of Mount Everest, when the gas is released from the tank?

2009 Question12 (a) [Ordinary Level](i) Define pressure. (ii) Describe an experiment to show that the pressure in a liquid increases with

depth. (iii) A diver is swimming in a lake at a depth of 5 m.

He then dives deeper until he reached a depth of 30 m.Calculate the increase in pressure on the diver at this new depth.

(density of water = 1000 kg m−3 ; g = 9.8 m s−2)

2007 Question 12 (b) [Ordinary Level](i) Define pressure.(ii) Describe an experiment to demonstrate that the atmosphere exerts pressure. (iii) State Boyle’s law.(iv)A balloon rises through the atmosphere while the temperature remains constant.

The volume of the balloon is 2 m3 at ground level where the pressure is 1000 hPa.Find the volume of the balloon when it has risen to a height where the atmospheric pressure is 500 hPa.

(v) What will happen to the balloon as it continues to rise?

2005 Question 6 [Ordinary Level] (i) Define pressure and give the unit of pressure. (ii) Name an instrument used to measure pressure. (iii) The earth is covered with a layer of air called the atmosphere.

What holds this layer of air close to the earth? (iv)Describe an experiment to show that the atmosphere exerts pressure. (v) The type of weather we get depends on the atmospheric pressure.

Describe the kind of weather we get when the atmospheric pressure is high.(vi)The African elephant is the largest land animal.

An elephant weighs 40 000 N and is standing on all four feet each of area 0.2 m2. Calculate the pressure exerted on the ground by the elephant.

(vii) Why would the pressure on the ground be greater if the elephant stood up on just two feet?

2002 Question 12 (a) [Ordinary Level](i) What is meant by pressure? Give the unit of pressure.(ii) Name an instrument used to measure pressure.(iii) When air is removed from the metal container shown in the diagram, it

collapses. Explain why.(iv)The wind exerts a horizontal force of 1000 N on a wall of area 20 m2.

Calculate the pressure at the wall.2006 Question 12 (a) [Higher Level](vi)Define pressure.

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(vii) Is pressure a vector quantity or a scalar quantity? Justify your answer.(viii) State Boyle’s law. (ix)A small bubble of gas rises from the bottom of a lake. The volume of the bubble increases threefold

when it reaches the surface of the lake where the atmospheric pressure is 1.01 × 105 Pa. The temperature of the lake is 4 oC. Calculate the pressure at the bottom of the lake;

(x) Calculate the depth of the lake. (acceleration due to gravity = 9.8 m s–2; density of water = 1.0 × 103 kg m–3)Solutions2011 Question 6 (a)(i) Define the moment of a force.

Moment of a force = force × perpendicular distance between the force and the fulcrum(ii) When the toy is knocked over, it always returns to the upright position. Explain why this happens.

(toy non-vertical) c.g. has a (turning) moment about fulcrum / point of support/contact /(c.g. has) zero turning moment when toy is in vertical position

2011 Question 6 (b) (i) State the conditions necessary for the equilibrium of a body under a set of co-planar forces.

Algebraic sum of the forces = zeroSum of the moments about any point = zero

(ii) Where should the third child of mass 45 kg sit, in order to balance the see-saw?30g(1.8) = 40g(0.8) + 45g(x)x = 0.488 m / 0.49 m / 49 cm

2006 Question 12 (a)(vi)Define pressure.

Pressure = Force divided by area.(vii) Is pressure a vector quantity or a scalar quantity? Justify your answer.

It is a scalar because it has no direction.(viii) State Boyle’s law.

Boyle’s Law states that pressure is inversely proportional to volume if temperature is constant.(ix)A small bubble of gas rises from the bottom of a lake. The volume of the bubble increases

threefold when it reaches the surface of the lake where the atmospheric pressure is 1.01 × 105 Pa. The temperature of the lake is 4 oC. Calculate the pressure at the bottom of the lake.Pressure at bottom = 3 × pressure at top = 3.03 × 105 Pa

(x) Calculate the depth of the lake. Pressure at bottom due to water = 2.02 × 105 Pa P= hρg h = P/ρg = 2.02 × 105 / (1.0 × 103)( 9.8 ) = 20.61 m

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Temperature and Heat

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Temperature2011 Question 8 (a) [Ordinary Level](i) What is meant by a thermometric property? (ii) Name two different thermometric properties.(iii) Name two different thermometers. (iv)Describe how to calibrate a thermometer. (v) Why is there a need for a standard thermometer?

2009 Question 12 (b) [Ordinary Level] (i) What is meant by the temperature of a body?(ii) Name two scales that are used to measure temperature.(iii) What is the boiling point of water on each of these scales?(iv)The diagram shows a laboratory thermometer, what is its thermometric property? (v) Name one other type of thermometer and state its thermometric of property. (vi)Why is there a need for a standard thermometer?

2008 Question 7 (a) [Ordinary Level]The temperature of an object is measured using a thermometer, which is based on the variation of its thermometric property.(i) What is meant by temperature?(ii) What is the unit of temperature?(iii) Give an example of a thermometric property.

2005 12 (a) [Ordinary Level]To calibrate a thermometer, a thermometric property and two fixed points are needed.

(i) What does a thermometer measure? (ii) What are the two fixed points on the Celsius scale? (iii) Explain the term thermometric property.(iv)Name the thermometric property used in a mercury thermometer. (v) Give an example of another thermometric property.

2003 Question 12 (b) [Higher Level](i) What is the difference between heat and temperature? (ii) The emf of a thermocouple can be used as a thermometric property.

Explain the underlined terms. (iii) Name a thermometric property other than emf. (iv)Explain why it is necessary to have a standard thermometer.

2011 Question 7 (c) [Higher Level](i) A thermocouple is used to measure the temperature of the steam.

How would you demonstrate the principle of operation of a thermocouple?(ii) Describe how to establish a calibration curve for a thermocouple.

Heat: Theory Questions2012 Question 9 (a) [Ordinary Level](i) The temperature of an object is a measure of its hotness or coldness.

What is the SI unit of temperature? (ii) The Celsius scale is the practical temperature scale.

How is the degree Celsius (°C) related to the SI unit of temperature?

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(iii) When heat is transferred to a substance, it causes a rise in temperature or a change in state of the substance, or both.What is heat?

(iv)Name the three methods of heat transfer.(v) What is meant by the change in state of a substance? (vi)Define specific latent heat.

2010 Question 8 (a) [Ordinary Level](i) What is heat?(ii) Explain how heat is transferred in a solid.(iii) Describe an experiment to compare the rates of heat transfer through different solids.(iv)Explain the term U-value(v) How can the U-value of the walls of a house be reduced?

2010 Question 8 (b) [Ordinary Level]The diagram shows a solar heating system.(i) How is the sun’s energy transferred to the solar collector? (ii) Why is the solar collector normally painted black? (iii) How is the heat transferred from the solar panel to the hot water

tank?(iv)The heating coil for the hot water tank are placed at the bottom,

explain why.(v) Give an advantage and a disadvantage of a solar heating system.

2008 Question 7 (c) [Ordinary Level]The rise in temperature of an object depends on the amount of heat transferred to it and on its specific heat capacity.(i) What is heat?(ii) Name three ways in which heat can be transferred.(iii) Define specific heat capacity.

2006 Question 7 (a) [Ordinary Level] (i) Heat can be transferred in a room by convection.(ii) What is convection? (iii) Name two other ways of transferring heat. (iv)Describe an experiment to demonstrate convection in a liquid.

(v) In an electric storage heater, bricks with a high specific heat capacity are heated overnight by passing an electric current through a heating coil in the bricks. The bricks are surrounded by insulation.Why is insulation used to surround the bricks?

(vi)Name a material that could be used as insulation. (vii) Explain how the storage heater heats the air in a room.

2004 Question 7 [Ordinary Level](i) Heat can be transferred by conduction. What is meant by conduction?(ii) Name two other ways of transferring heat.(iii) Describe an experiment to show how different solids conduct heat

at different rates.

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(iv)The U-value of a house is a measure of the rate of heat loss to the surroundings.Give two ways in which the U-value of a house can be reduced.

(v) The diagram shows a solar panel (solar heater) which can be used in the heating of a house.What energy conversion takes place in a solar panel?

(vi)Why are the pipes in the solar panel usually made from copper? (vii) Why are the pipes in the solar panel usually painted black?(viii) Why does warm water rise to the top of the solar panel?

Heat: Maths Questions2012 Question 9 (b) [Ordinary Level]

20 g of ice cubes at 0 °C are added to a glass of warm water.All the ice melts quickly and cools the water to 5 °C.Assuming no heat transfer to the surroundings or to the glass,

(i) Calculate the energy required to melt the ice.(ii) Calculate the energy required to warm the melted ice to 5 °C.(iii) Why is it important to stir the mixture? (specific heat capacity of water = 4180 J kg−1 K−1 ; specific latent heat of fusion of ice = 3.34 × 105 J kg−1)

2011 8 (b) [Ordinary Level] An electric kettle is filled with 500 g of water and is initially at a temperature of 15 0C.The kettle has a power rating of 2 kW.(i) Calculate the energy required to raise the temperature of the water to 100 0C. (ii) How much energy is supplied by the kettle every second? (iii) How long will it take the kettle to heat the water to 100 0C? (iv)Name a suitable material for the handle of the kettle. Justify your answer.

(specific heat capacity of water = 4180 J Kg−1 K−1)

2008 Question 7 (c) [Ordinary Level]A saucepan containing 500 g of water at a temperature of 20 °C is left on a 2 kW ring of an electric cooker until it reaches a temperature of 100 °C.All the electrical energy supplied is used to heat the water.

(i) Calculate the rise in temperature of the water;(ii) Calculate the energy required to heat the water to 100 °C;(iii) Calculate the amount of energy the ring supplies every second;(iv)Calculate the time it will take to heat the water to 100 °C.

2006 Question 7 (b) [Ordinary Level] The total mass of the bricks in a storage heater is 80 kg and their specific heat capacity is 1500 J kg–1 K–1. During a ten-hour period the temperature of the bricks rose from 15 oC to 300 oC.(i) Calculate the energy gained by the bricks;(ii) Calculate the power of the heating coil.

2002 Question 12 (b) [Ordinary Level](i) Define specific heat capacity. (ii) An electric kettle contains 1.5 kg of water. The specific heat capacity of water is 4180 J kg-1 K-1.

Calculate the amount of energy required to raise the temperature of the water from 15 0C to 100 0C. (iii) The kettle takes 4 minutes to heat the water from 15 0C to 100 0C. Calculate the power of the kettle.

(Assume all the energy supplied is used to heat the water).(iv)Why is the heating element of an electric kettle near the bottom?

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2011 Question 7 (a) [Higher Level](i) When making a hot drink, steam at 100 °C is added to 160 g of milk at 20 °C.

If the final temperature of the drink is to be 70 °C, what mass of steam should be added?You may ignore energy losses to the surroundings.

(ii) A metal spoon, with an initial temperature of 20 °C, is then placed in the hot drink, causing the temperature of the hot drink to drop to 68 °C. What is the heat capacity of the spoon? You may ignore other possible heat transfers.

(cmilk = 3.90 × 103 J kg–1 K–1, cwater = 4.18 × 103 J kg–1 K–1, chot drink = 4.05 × 103 J kg–1 K–1

specific latent heat of vaporisation of water = 2.34 × 106 J kg–1)

2006 Question 12 (c) [Higher Level](i) Define power.(ii) Define specific heat capacity. (iii) 400 g of water at a temperature of 15 oC is placed in an electric kettle.

The power rating of the kettle is 3.0 kW.Calculate the energy required to raise the temperature of the water to 100 oC.

(iv)Calculate the energy supplied by the kettle per second.(v) Calculate the least amount of time it would take to heat the water to 100 oC. (vi)In reality, the time taken to heat the water will be greater. Explain why.

(specific heat capacity of water = 4200 J kg–1 K–1)

2004 Question 7 [Higher Level](i) Define specific heat capacity.(ii) Define specific latent heat. (iii) 500 g of water at a temperature of 15 0C is placed in a freezer.

The freezer has a power rating of 100 W and is 80% efficient.Calculate the energy required to convert the water into ice at a temperature of –20 oC.

(iv)How much energy is removed every second from the air in the freezer?(v) How long will it take the water to reach a temperature of –20 oC? (vi)Allowing a liquid to evaporate in a closed pipe inside the freezer cools the air in the freezer. The vapour

is then pumped through the pipe to the outside of the freezer, where it condenses again.Explain how this process cools the air in the freezer.

(vii) The freezer causes the room temperature to rise. Explain why.

specific heat capacity of ice = 2100 J kg–1 K–1; specific heat capacity of water = 4200 J kg–1 K–1;specific latent heat of fusion of ice = 3.3 × 105 J kg–1

2011 Question 7 (b) [Higher Level](i) Name two processes by which a hot drink cools. (ii) How is the energy lost by each of these processes reduced for a hot drink supplied in a disposable cup?

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2012 Question 12 (c) [Higher Level]The graph shows the variation in temperature θ of 150 g of crushed ice when it was supplied with energy ΔE at a constant rate.

(i) Explain the shape of the graph.(ii) Describe how energy could have been supplied at a constant rate.(iii) Using the graph, estimate the specific latent heat of fusion of ice.

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2009 Question 11[Higher Level]Read the following passage and answer the accompanying questions.The sun is a major source of ‘green’ energy. In Ireland solar heating systems and geothermal systems are used to get energy from the sun.There are two main types of solar heating systems, flat-plate collectors and vacuum-tube collectors.1.A flat-plate collector is usually an aluminium box with a glass cover on top and a blackened plate on the bottom. A copper pipe is laid on the bottom of the box, like a hose on the ground; water is passed through the pipe and transfers the absorbed heat to the domestic hot water system.

2.In a vacuum-tube collector, each tube consists of an evacuated double-walled silvered glass tube in which there is a hollow copper pipe containing a liquid. The liquid inside the copper pipe is vaporised and expands into the heat tip. There the vapour liquefies and the latent heat released is transferred, using a heat exchanger, to the domestic hot water system. The condensed liquid returns to the copper pipe and the cycle is repeated.In a geothermal heating system a heat pump is used to extract solar energy stored in the ground and transfer it to the domestic hot water system.

(a) What is the maximum energy that can fall on an area of 8 m2 in one hour if the solar constant is 1350 W m–2? (b) Why is the bottom of a flat-plate collector blackened? (c) How much energy is required to raise the temperature of 500 litres of water from 20 0C to 50 0C?(d) The liquid in a vacuum-tube solar collector has a large specific latent heat of vaporisation. Explain why. (e) Name the three ways that heat could be lost from a vacuum-tube solar collector.(f) How is the sun’s energy trapped in a vacuum-tube solar collector? (g) Describe, in terms of heat transfer, the operation of a heat pump. (h) Give an advantage of a geothermal heating system over a solar heating system.(specific heat capacity of water = 4200 J kg–1 K–1; density of water = 1000 kg m–3; 1 litre = 10–3 m3)

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Solutions - Ordinary Level Maths Questions2012 Question 9(ii) t = T - 273(.15)(i) E = ml = (20 ×10-3)(3.34 ×105) = 6.68 ×103 J (ii) E = mcΔθ = (20×10-3)(4.18 ×103)(5) = ) 418 J

2008 Question 7(i) 100 – 20 = 80 °C(ii) Q = m cΔθ = 0.5 × 4200 × 80 = 168 000 J(iii) 2 kW = 2,000 W = 2,000 J per second.(iv)P = W/t so t = W/P t = 168 000/2,000 = 84 secs.

2006 Question 7(i) Q = mcΔθ Q = (80)(1500)(285) = 34 200 000 J = 4.2 MJ(ii) P = W/ t P = 34 200 000 / (10×60×60) = 950 W

2002 Question 12 (b)(ii) Q = mcΔθ Q = 1.5 × 4180 × 85 = 532 950 J.(iii) P=W/t P = 532 950/240 P = 2221 W.

Solutions – Higher Level

2012 Question 12 (c)(i) Explain the shape of the graph.

Temperature of ice increased from –3o to 0o as energy is added.Ice temperature stays at 0 0C while ice is melting / changing state.The heat taken in at this stage is known as latent heat.Once melted the water temperature increases to 1oC.

(ii) Describe how energy could have been supplied at a constant rate.(heating) coil/element joulemeter / ammeter + rheostat (water bath … 6 marks; hotplate …3 marks)

(iii) Using the graph, estimate the specific latent heat of fusion of ice.Energy required to melt 0.15 kg of ice = (59 – 10) = 49 kJE = mL

L = 3.27 × 105 J Kg-1

2011 Question 7 (a) (i) If the final temperature of the drink is to be 70 °C, what mass of steam should be added?

You may ignore energy losses to the surroundings.energy gained by the milk = energy lost by the steam when condensing

+ energy lost by this condensed water cooling down(mcΔθ)m = (ml)steam + (mcΔθ)cond

(0.160)(3.90×103)(50) = ms(2.34×106) + ms(4.18×103)(30)

= 12.655×10-3 kg = 12.66 g

(ii) What is the heat capacity of the spoon?

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It looks like we are missing a value for the mass of the spoon, but we are being asked to calculate the heat capacity (C), not the specific heat capacity (c). The relationship between the two is as follows: C = mc

Energy gained by the spoon = energy lost be the hot drink(CΔθ)spoon = (mcΔθ)hot drink

48C = (0.17266)(4.05×103)(2) = 1.3985×103

C = 29.14 J K-1

(b)(i) Name two processes by which a hot drink cools. (ii) How is the energy lost by each of these processes reduced for a hot drink supplied in a disposable

cup?Conduction – The material the cup is made from is a good insulatorEvaporation – use a lidConvection – Use a lid /insulation

2011 Question 7 (c) (i) A thermocouple is used to measure the temperature of the steam.

How would you demonstrate the principle of operation of a thermocouple?One junction (the reference junction) is held in cold water.The other junction is then heated Observation: e.g. emf /voltage is observed.

(ii) Describe how to establish a calibration curve for a thermocouple. Hold one junction at constant temperature, Hold the other junction in water with beside an (already calibrated) thermometer. Heat the water (in steps of 10 oC approx) and note temperature and emf values each time. Plot a graph of emf vs. Temperature.

2009 Question 11(a) What is the energy that can fall on an area of 8 m2 in one hour if the solar constant is 1350 W m–2?

1350 × 8 × 3600 Emax = 3.9 × 107 J

(b) Why is the bottom of a flat-plate collector blackened?Dark surfaces are good absorbers of heat/energy/radiation

(c) How much energy is required to raise the temperature of 500 litres of water from 20 0C to 50 0C?Density = mass/volume mass = (density)(volume) m = (1000)(500 × 10–3) = 500 kg.E = mc = (500)(4200)(30) = 6.3 × 107 J

(d) Explain why.So that a lot of energy gets absorbed (and then released) per kg in the heat exchanger during a change of state.

(e) Name the three ways that heat could be lost from a vacuum-tube solar collector.Conduction, convection, radiation

(f) How is the sun’s energy trapped in a vacuum-tube solar collector? Silvered walls prevent radiation and evacuated walls prevent conduction and convection

(g) Describe, in terms of heat transfer, the operation of a heat pump. Energy is taken from one place (making it colder) by allowing the liquid to change state to a gas.Then in another place the gas condenses to a liquid releasing the heat to another place making it hotter.

(h) Give an advantage of a geothermal heating system over a solar heating system.Geothermal system functions all the time whereas a solar heating system works only during sunshine.

2006 Question 12 (c)(i) Define power.

Power is defined as energy divided by time.

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(ii) Define specific heat capacity. The specific heat capacity of a substance is the heat energy needed to change one kilogram of the substance by one Kelvin.

(iii) Calculate the energy required to raise the temperature of the water to 100 oC.E = m cΔθ E = (0.40)(4200)(85) = 1.428 x 105 J

(iv)Calculate the energy supplied by the kettle per second.3000 J per second = 3000 W

(v) Calculate the least amount of time it would take to heat the water to 100 oC. Time taken = 1.428 × 105 / 3000 = 47.6 s

(vi)In reality, the time taken to heat the water will be greater. Explain why. Energy will be lost to the surroundings.

2004 Question 7(i) Define specific heat capacity.

The specific heat capacity of a substance is the heat energy needed to change one kilogram of the substance by one Kelvin.

(ii) Define specific latent heat. The Specific Latent of a substance is the amount of heat energy need to change the state of 1 kg of the substance without a change in temperature.

(iii) Calculate the energy required to convert the water into ice at a temperature of –20 oC.Cooling from 15 0C to 0 0C: Q = mcΔθ = (0.5)(4200)(15) = 31500 JChange of state: Q = ml = (0.5)(3.3 × 105) =165000 JCooling ice from 0 oC to -20 oC: Q = (0.5)(2100)(20) =21000 JTotal energy required = Qt = Q1 +Q2 +Q3 =217500 = 2.2 × 105 J

(iv)How much energy is removed every second from the air in the freezer?80% efficiency ⇒ 80 W ⇒ 80 J (per second)

(v) How long will it take the water to reach a temperature of –20 oC? Power = Q ÷ time t = (217500 ÷ 80) = 2700 s

(vi)Explain how this process cools the air in the freezer. This change of state requires energy (latent heat) which is taken from inside the freezer and this lowers the temperature .

(vii) The freezer causes the room temperature to rise. Explain why. Condensation (vapour to liquid) releases latent heat

2003 Question 12 (b)(i) What is the difference between heat and temperature?

Heat is a form of energy, temperature is a measure of hotness.(ii) The emf of a thermocouple can be used as a thermometric property. Explain the underlined terms.

An emf is a voltage applied to a full circuit.A thermometric property is any property which changes measurably with temperature.

(iii) Name a thermometric property other than emf. Length, pressure, volume, resistance, colour

(iv)Explain why it is necessary to have a standard thermometer. Two different types of thermometer will give slightly different readings at the same temperature

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Waves, Sound and Light

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Waves2004 Question 8 [Ordinary Level](i) Sound from a vibrating object can cause diffraction and interference.Explain the underlined terms.(ii) Describe an experiment to demonstrate the interference

of sound.(iii) The diagram shows a stationary wave (standing

wave) on a vibrating stretched string.What is the name given to the points on the string marked (i) X, (ii) Y?(iv)How many wavelengths are contained in the distance marked L? (v) State two factors on which the natural frequency of a stretched string depends. (vi)A note of wavelength 1.4 m is produced from a stretched string. If the speed of sound in air is 340 m s−1,

calculate the frequency of the note.

2006 Question 8 [Ordinary Level](i) Describe, using diagrams, the difference between transverse waves and longitudinal waves. (ii) The speed of sound depends on the medium through which the sound is travelling.

Explain how sound travels through a medium. (iii) Describe an experiment to demonstrate that sound requires a medium to travel. (iv)A ship detects the seabed by reflecting a pulse of high frequency sound from the seabed.

The sound pulse is detected 0.4 s after it was sent out and the speed of sound in water is 1500 m s–1.Calculate the time taken for the pulse to reach the seabed.

(v) Calculate the depth of water under the ship.(vi)Calculate the wavelength of the sound pulse when its frequency is 50 000 Hz. (vii) Why is the speed of sound greater in water than in air?

2010 Question 7 [Ordinary Level] The diagram shows a waveform.(i) What is the name given to the distance X and Y?(ii) What is meant by the frequency of a wave? (iii) Explain the term natural frequency.(iv)If the natural frequency of a string is 250 Hz calculate the

wavelength of the sound wave produced (speed of sound = 340 m s-1).(v) State the wave property on which the loudness, the pitch, of a musical note depends.(vi)An opera singer, singing a high pitched note, can shatter a glass. Explain why. (vii) Describe a laboratory experiment to demonstrate resonance.

2007 Question 7 [Ordinary Level] Resonance occurs when a vibrating object causes vibrations in nearby objects which have the same natural frequency.(i) Explain the underlined terms.(ii) Describe an experiment to demonstrate resonance. (iii) The diagram shows the waveform of a musical note.(iv)What is the name given to (i) the distance A, (ii) height B? (v) Explain what is meant by the frequency of a wave. (vi)State the wave property on which (i) the loudness, (ii) the pitch, of a note depends.(vii) A tin-whistle produces a note of 256 Hz. Calculate the wavelength of this note.The speed of sound in air is 340 m s−1

2005 Question 12 (c) (i) The frequency of a stretched string depends on its length.

Give two other factors that affect the frequency of a stretched string. (ii) The diagram shows a guitar string stretched between supports 0.65 m

apart.

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The string is vibrating at its first harmonic. The speed of sound in the string is 500 m s–1. What is the frequency of vibration of the string?

(iii) Draw a diagram of the string when it vibrates at its second harmonic. (iv)What is the frequency of the second harmonic?

2011 Question 8 (a) Destructive interference can occur when waves from coherent sources meet.(i) Explain the underlined term.(ii) Give two other conditions necessary for total destructive interference to

occur. (iii) The diagram shows a standing wave in a pipe closed at one end.

The length of the pipe is 90 cm.Name the points on the wave labelled P and Q.

(iv)Calculate the frequency of the standing wave.(v) What is the fundamental frequency of the pipe? (vi)The clarinet is a wind instrument based on a pipe that is closed at one end.

What type of harmonics is produced by a clarinet?

2002 Question 7(i) “Constructive interference and destructive interference take place when waves from two coherent

sources meet.” Explain the underlined terms in the above statement.

(ii) What is the condition necessary for destructive interference to take place when waves from two coherent sources meet?

(iii) Describe an experiment that demonstrates the wave nature of light.

(iv)Radio waves of frequency 30 kHz are received at a location 1500 km from a transmitter.The radio reception temporarily “fades” due to destructive interference between the waves travelling parallel to the ground and the waves reflected from a layer (ionosphere) of the earth’s atmosphere, as indicated in the diagram.Calculate the wavelength of the radio waves.

(v) What is the minimum distance that the reflected waves should travel for destructive interference to occur at the receiver?

(vi)The layer at which the waves are reflected is at a height h above the ground. Calculate the minimum height of this layer for destructive interference to occur at the receiver. (speed of light, c = 3.0 × 108 m s-1)

The Doppler Effect2012 Question 12 (c) [Ordinary Level]The pitch of the sound emitted by the siren of a moving fire engine appears to change as it passes a stationary observer.(i) Name this phenomenon. (ii) Explain, with the aid of a diagram, how this phenomenon occurs. (iii) Will the crew in the fire engine notice this phenomenon?(iv)Give a reason for your answer. (v) Give an application of this phenomenon.

2008 Question12 (b)

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(i) The pitch of a musical note depends on its frequency. (ii) On what does (i) the quality, (ii) the loudness, of a musical note depend? (iii) What is the Doppler Effect? (iv)A rally car travelling at 55 m s–1 approaches a stationary observer. As the car passes, its engine is

emitting a note with a pitch of 1520 Hz. What is the change in pitch observed as the car moves away? (v) Give an application of the Doppler Effect.

2003 Question 7 (i) Describe an experiment to show that sound is a wave motion. (ii) What is the Doppler Effect? (iii) Explain, with the aid of labelled diagrams, how this phenomenon occurs. (iv)Bats use high frequency waves to detect obstacles. A bat emits a wave of frequency 68 kHz and

wavelength 5.0 mm towards the wall of a cave. It detects the reflected wave 20 ms later.Calculate the speed of the wave and the distance of the bat from the wall.

(v) If the frequency of the reflected wave is 70 kHz, what is the speed of the bat towards the wall? (vi)Give two other applications of the Doppler Effect.

2007 Question 7(i) What is the Doppler Effect?(ii) Explain, with the aid of labelled diagrams, how this phenomenon occurs. (iii) The emission line spectrum of a star was analysed using the Doppler Effect.

Describe how an emission line spectrum is produced. (iv)The red line emitted by a hydrogen discharge tube in the laboratory has a wavelength of 656 nm.

The same red line in the hydrogen spectrum of a moving star has a wavelength of 720 nm.Is the star approaching the earth? Justify your answer.

(v) Calculate the frequency of the red line in the star’s spectrum.(vi)Calculate the speed of the moving star. (speed of light = 3.00 × 108 m s–1)

2010 Question 7(i) What is the Doppler effect?(ii) Explain, with the aid of labelled diagrams, how this phenomenon occurs.(iii) Describe a laboratory experiment to demonstrate the Doppler effect.(iv)What causes the red shift in the spectrum of a distant star?(v) The yellow line emitted by a helium discharge tube in the laboratory has a wavelength of 587.

The same yellow line in the helium spectrum of a star has a measured wavelength of 590 nm.(vi)What can you deduce about the motion of the star?(vii) Calculate the speed of the moving star.(viii) Give another application of the Doppler effect.

Sound2008 Question 8 [Ordinary Level]The diagram shows a signal generator connected to two loudspeakers emitting the same note.A person walks slowly along the line AB.(i) What will the person notice?(ii) Why does this effect occur?(iii) What does this tell us about sound? (iv)Describe an experiment to demonstrate that sound requires a medium to travel. (v) The pitch of a note emitted by the siren of a fast moving ambulance appears to change as

it passes a stationary observer.Name this phenomenon.

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(vi)Explain how this phenomenon occurs.(vii) Give an application of this phenomenon.

2005 Question 12 (b) [Ordinary Level](i) What is meant by (i) diffraction, (ii) interference, of a wave? (ii) In an experiment, a signal generator was connected to two

loudspeakers, as shown in the diagram. Both speakers are emitting a note of the same frequency and same amplitude.

(iii) A person walks along the line XY. Describe what the person hears.

(iv)What does this experiment demonstrate about the nature of sound? (v) What is meant by the amplitude of a wave?

2011 Question 8 (b) An audio speaker at a concert emits sound uniformly in all directions at a rate of 100 W. Calculate the sound intensity experienced by a listener at a distance of 8 m from the speaker.The listener moves back from the speaker to protect her hearing. At what distance from the speaker is the sound intensity level reduced by 3 dB?(speed of sound in air = 340 m s–1)

2007 Question 12 (b) (i) Define sound intensity. (ii) A loudspeaker has a power rating of 25 mW.

What is the sound intensity at a distance of 3 m from the loudspeaker?(iii) The loudspeaker is replaced by a speaker with a power rating of 50 mW.

What is the change in the sound intensity?(iv)What is the change in the sound intensity level? (v) The human ear is more sensitive to certain frequencies of sound.

How is this taken into account when measuring sound intensity levels?

2010 12 (c)(i) Explain the term resonance and describe a laboratory experiment to demonstrate it.(ii) Give two characteristics of a musical note and name the physical property on which each characteristic

depends.(iii) Explain why a musical tune does not sound the same when played on different instruments.

2011 Question 12 (b) [Ordinary Level](i) Loudness, pitch and quality are characteristics of a musical note.

Name the physical property of a sound wave on which each characteristic depends.

(ii) A bat detector allows us to hear the sounds emitted by bats. The detector is needed as humans cannot hear the sounds emitted by bats as they are outside our frequency limits of audibility.What is meant by the frequency limits of audibility?

(iii) What name is given to a sound whose frequency is greater than our upper frequency limit of audibility?

(iv)A bat emitted a sound wave and detected its reflection from a wall 0.02 s later.Calculate the distance of the bat from the wall. (speed of sound in air = 340 m s−1)

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The Wave nature of Light2009 Question 7 [Ordinary Level] (i) In an experiment a beam of monochromatic light passes through a diffraction grating and strikes a

screen.(ii) Explain the underlined terms. (iii) Describe what is observed on the screen. (iv)Explain, with the aid of a diagram, how this phenomenon occurs. (v) What does this experiment tell us about the nature of light?(vi)Name the property of light that can be determined in this experiment. (vii) What measurements must be taken to determine the property you named?

2009 Question 7(i) When light shines on a compact disc it acts as a diffraction grating causing diffraction and dispersion of

the light. Explain the underlined terms. (ii) Derive the diffraction grating formula.(iii) An interference pattern is formed on a screen when green light from a laser passes normally through

a diffraction grating. The grating has 80 lines per mm and the distance from the grating to the screen is 90 cm. The distance between the third order images is 23.8 cm.Calculate the wavelength of the green light.

(iv)Calculate the maximum number of images that are formed on the screen. (v) The laser is replaced with a source of white light and a series of spectra are formed on the screen.

Explain how the diffraction grating produces a spectrum.(vi)Explain why a spectrum is not formed at the central (zero order) image.

2005 Question 7A student used a laser, as shown, to demonstrate that light is a wave motion.(i) Name the two phenomena that occur when the light passes through the pair of narrow slits. (ii) A pattern is formed on the screen. Explain how the pattern is formed. (iii) What is the effect on the pattern when the wavelength of the light is increased?(iv)What is the effect on the pattern when the distance between the slits is increased?(v) Describe an experiment to demonstrate that sound is also a wave motion. (vi)Sound travels as longitudinal waves while light travels as transverse waves. Explain

the difference between longitudinal and transverse waves.(vii) Describe an experiment to demonstrate that light waves are transverse waves.

2010 Question 12 (b) [Ordinary Level](i) What is meant by dispersion of light?(ii) Describe an experiment to demonstrate the dispersion of light.(iii) Give an example of the dispersion of light occurring in nature.(iv)Only red, green and blue lights are needed to create most lighting effects.

Explain why

2012 Question 7 [Ordinary Level](i) Under certain conditions, light can undergo diffraction and interference.

Explain the underlined terms. (ii) Describe an experiment to demonstrate the wave nature of light. (iii) The photograph shows Polaroid sunglasses which reduce glare caused by

sunlight.Explain the term ‘polarisation’.

(iv)Describe an experiment to demonstrate the polarisation of light.

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(v) What type of wave motion does light have as indicated by the experiment in part (iv)? (vi)Why are Polaroid sunglasses more effective than non-Polaroid sunglasses at reducing glare?

The Electromagnetic Spectrum2008 Question 12 (b) [Ordinary Level]

Sunlight is made up of different colours and invisible radiations.(i) How would you show the presence of the different colours in light?(ii) Name two radiations in sunlight that the eye cannot detect. (iii) Describe how to detect one of these radiations. (iv)Give a use for this radiation.

2007 Question 8 [Ordinary Level] Dispersion occurs when a beam of white light passes through a prism forming a spectrum on a screen, as shown in the diagram.(i) What is meant by the terms dispersion and spectrum? (ii) What happens to the white light when it enters the prism at Z? (iii) Name the invisible radiation formed on the screen at (i) region X, (ii) region Y. (iv)Describe how to detect one of these invisible radiations. (v) Give a use for one of these invisible radiations.(vi)The colour on a TV screen is made by mixing the primary colours.

Name the primary colours. (vii) How is a secondary colour (e.g. yellow) produced on a TV screen?

2006 Question 12 (b) [Ordinary Level]The diagram shows the relative positions of electromagnetic radiations in terms of their wavelength.

gamma rays A UV light IR microwaves B(i) Name the radiations marked A and B. (ii) Give one property which is common to all electromagnetic radiations. (iii) Which one of the radiations has the shortest wavelength? (iv) Describe how IR radiation is detected.(i) Give one use for microwaves.

2003 Question 12 (b) [Ordinary Level](i) Name two primary colours.(ii) What are complementary colours?(iii) White light is made up of light of different colours. Describe an experiment to demonstrate this.(iv)The diagram shows a simple form of the electromagnetic spectrum, with wavelength increasing from left

to right.Copy this diagram and indicate on it the positions of the following:microwaves; infrared; ultraviolet; X-rays.

2002 Question 7 [Ordinary Level] (i) The dispersion of white light can be produced by refraction or diffraction. Explain the underlined terms.(ii) Describe an experiment to demonstrate the dispersion of white light.(iii) The following table gives examples of electromagnetic waves and their typical wavelengths.

(iv)Name one property that all of these waves have in common.(v) What is the frequency of the radio waves? The speed of light is 3 × 108 m s-1.(vi)Describe how infrared radiation can be detected.

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(vii) Give two uses of microwaves.

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2012 Question 7

(i) The diagram shows a simplified version of the electromagnetic spectrum.Name the sections labelled A and B in the diagram.

(ii) Describe how to detect each of these radiations.(iii) An electromagnetic radiation has a wavelength of 4 m.

Name the section of the electromagnetic spectrum in which this radiation is located. (iv)Distinguish between interference and diffraction.(v) Can a diffraction grating which diffracts light also diffract X-rays? Justify your answer.(vi)Light travels as a transverse wave.

Name another type of wave motion and give two differences between these two types of wave motion.

2010 Question 11Read the following passage and answer the accompanying questions.

A person’s exposure to radiation when using a mobile phone is measured in terms of the Specific Absorption Rate (SAR). This is a measure of the rate at which radio frequency energy is absorbed by a person’s body during a phone call and is expressed in watts per kilogram.A radio frequency wave penetrates the body to a depth that depends on its frequency. At mobile phone frequencies the wave energy is absorbed by about one centimetre of body tissue. The energy absorbed is converted into heat and is carried away by the body. Any adverse health effects from radio frequency waves are due to heating. Current scientific evidence indicates that exposure to radiation from mobile phones is unlikely to induce cancer.(Adapted from a Dept. of Communications, Energy and Natural Resources Press Release of 22 March 2007.)

(i) Give two properties of radio waves.(ii) In a three-minute phone call, 10 g of head tissue absorbs 0.36 J of radio frequency energy.

Calculate the SAR value.(iii) What happens to the radio frequency energy absorbed by the body?(iv)Why are radio frequency waves not very penetrating?(v) A mobile phone converts the received radio frequency waves to sound waves.

What are the audible frequency limits for sound waves?(vi)Give two safety precautions you should take when using a mobile phone.(vii) A mobile phone transmits at 1200 MHz from its antenna.

Calculate the length of its antenna, which is one quarter of the wavelength that it transmits.(viii) Name an electromagnetic wave which may induce cancer. Justify your answer.

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Solutions2012 Question 7(i) Name the sections labelled A and B in the diagram.

A: infra red /I.R B: ultra violet / U.V

(ii) Describe how to detect each of these radiations.A: thermometer (with blackened bulb) / temperature sensor /photographic plate / mobile phone camera/ eEffect e.g. rise in temperatureB: (shine on) Vaseline/detergents / phosphor Effect e.g. fluorescence / glows

(iii) Name the section of the electromagnetic spectrum in which this radiation is located. c = f λf = 7.5 × 107 Hz short wave radio / TV FM radio

(iv)Distinguish between interference and diffraction.Interference occurs when waves from different sources overlap to form a resultant wave of greater or lower amplitude.Diffraction occurs when a wave spreads around an obstacle or passes through an aperture.

(v) Can a diffraction grating which diffracts light also diffract X-rays? Justify your answer.No.Line spacing must be similar to the wavelength of the radiation (for diffraction to occur) / the spacing between lines in (such) a grating is too large (for diffraction to occur) / for x-ray diffraction, gratings in which lines are separated by infinitesimal distances are required.

(vi)Name another type of wave motion and give two differences between these two types of wave motion.Longitudinal.Transverse can be polarized – longitudinal cannot.Transverse waves vibrate perpendicular to the direction in which the wave travels.Longitudinal waves vibrate parallel to the direction (longitudinal) in which the wave travels.

2011 Question 8 (a)Explain the underlined term.Coherent waves are waves which are the same frequency (or wavelength) and are in phase.Give two other conditions necessary for total destructive interference to occur.The waves must have the same amplitude and be out of phase by 1800 (crests over troughs).(i) Name the points on the wave labelled P and Q.P represents a node, Q represents an anti-node.(ii) Calculate the frequency of the standing wave.

λ = 0.720 mv = fλ

f = 472.2 Hz(iii) What is the fundamental frequency of the pipe?

= 0.90 λ = 3.60 m

f0 = 94.44 HzWhat type of harmonics is produced by a clarinet?Odd harmonics

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2011 Question 8 (b) An audio speaker at a concert emits sound uniformly in all directions at a rate of 100 W.Calculate the sound intensity experienced by a listener at a distance of 8 m from the speaker.

SI = 0.124 W m-2

The listener moves back from the speaker to protect her hearing. At what distance from the speakeris the sound intensity level reduced by 3 dB? (speed of sound in air = 340 m s–1)SIL decreased by 3dB means SI was halved.

R = 11.33 m

2010 Question 7(i) What is the Doppler effect?

The Doppler effect is the apparent change in frequency due to the relative motion between a source and an observer.

(ii) Explain, with the aid of labelled diagrams, how this phenomenon occurs.Diagram:Labelled moving source of waves Shorter wavelength approaching observerLonger wavelength recedingCorrect reference to frequency change

(iii) Describe a laboratory experiment to demonstrate the Doppler effect.Attach a string to a buzzer.Swing the buzzer over your head.An observer will note a frequency change as the buzzer approaches then recedes from source the observer.

(iv)What causes the red shift in the spectrum of a distant star?Distant stars are moving away from us therefore the wavelengths increase.

(v) The yellow line emitted by a helium discharge tube in the laboratory has a wavelength of 587 nm. The same yellow line in the helium spectrum of a star has a measured wavelength of 590 nm.What can you deduce about the motion of the star?The star is moving away from earth

(vi)Calculate the speed of the moving star.

Substitution: c = 3 × 108, f = 5.11073 × 1014 and f’ = 5.08475 × 1014

Answer: u = 1.5333 × 106 m s-1

(vii) Give another application of the Doppler effect.Radar, medical imaging, blood flow measurement (echocardiogram), temperature measurement, etc.

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2010 Question 11(i) Give two properties of radio waves.

They travel at speed of light, electromagnetic radiation, travel through vacuum, can be reflected, refracted, polarized etc.

(ii) In a three-minute phone call, 10 g of head tissue absorbs 0.36 J of radio frequency energy.Calculate the SAR value.Power = Energy/time = 0.36 / (3 × 60) = 0.002 WSAR = Power/mass = 0.36/(3 × 60)(10 ×10-3) = 0.20 W kg-1

(iii) What happens to the radio frequency energy absorbed by the body?It is converted into heat in the body.

(iv)Why are radio frequency waves not very penetrating?They have a low frequency / long wavelength / low energy.

(v) A mobile phone converts the received radio frequency waves to sound waves.What are the audible frequency limits for sound waves?20 Hz to 20 000 Hz

(vi)Give two safety precautions you should take when using a mobile phone.Keep phone at distance, use loudspeaker function, ‘no hands, brief calls only, direct antenna away from your head etc.

(vii) A mobile phone transmits at 1200 MHz from its antenna.Calculate the length of its antenna, which is one quarter of the wavelength that it transmits.λ = c/fλ = (3 × 108)/(1.2 × 109)λ = 0.25 mLength of antenna = 0.25/4 = 0.0625 m.

(viii) Name an electromagnetic wave which may induce cancer. Justify your answer.Gamma rays / X-rays / UV - they can all cause ionization of body cells.

2010 Question 12 (c)(i) Explain the term resonance and describe a laboratory experiment to demonstrate it.

Resonance is the transfer of energy so that a body vibrates at its natural frequency.Exemplar:Apparatus: tuning fork, length of pipe (with means of varying length)Procedure: hold vibrating fork over (open) end of pipe and vary length (of air column)Observation: loud sound is heard (at certain length)

(ii) Give two characteristics of a musical note and name the physical property on which each characteristic depends.Pitch: frequency Loud: amplitude / intensity Quality/timbre: harmonics / overtones

(iii) Explain why a musical tune does not sound the same when played on different instruments.Different instruments emit (a fundamental frequency plus) different (combinations of) overtones/harmonics.

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2009 Question 7When light shines on a compact disc it acts as a diffraction grating causing diffraction and dispersion of the light.

(i) Explain diffractionDiffraction is the spreading out of a wave when it passes through a gap or passes by an obstacle.

(ii) Explain dispersion. Dispersion is the splitting up of white light into its constituent colours.

(iii) Derive the diffraction grating formula.For constructive interference path difference = n, where n is an integerFrom diagram we can see that path difference = d sin n = d sin

(iv)An interference pattern is formed on a screen when green light from a laser passes normally through a diffraction grating. The grating has 80 lines per mm and the distance from the grating to the screen is 90 cm. The distance between the third order images is 23.8 cm.Calculate the wavelength of the green light.d = 1/80000 = 1.25 × 10-5 m = tan-1 (0.238/0.90)n = 3n = d sin = d sin /n = 551 (± 5) × 10-9 m.

(v) Calculate the maximum number of images that are formed on the screen. For maximum number = 900 sin = 1n = d sin n = d n= d/n = 22.7 so the greatest whole number of images is 22.But this is on one side only. In total there will be 22 on either side, plus one in the middle, so total = 45

(vi)The laser is replaced with a source of white light and a series of spectra are formed on the screen.Explain how the diffraction grating produces a spectrum.Different colours have different wavelengths so constructive interference occurs at different positions for each separate wavelength.

(vii) Explain why a spectrum is not formed at the central (zero order) image. At central image = 0 so constructive interference occurs for all separate wavelengths at the same point so no separation of colours.

2008 Question 12 (b)(i) The pitch of a musical note depends on its frequency.

On what does (i) the quality, (ii) the loudness, of a musical note depend? Quality depends on number and relative strengths of overtones.Loudness depends on amplitude of the wave.

(ii) What is the Doppler Effect? The Doppler Effect is the apparent change in the frequency of a wave due to the relative motion between the source of the wave and the observer.

(iii) A rally car travelling at 55 m s–1 approaches a stationary observer. As the car passes, its engine is emitting a note with a pitch of 1520 Hz. What is the change in pitch observed as the car moves away?

f1 = 1308.35 Hz

change in frequency = 1520 – 1308.35 = 211.65 Hz.(iv)Give an application of the Doppler Effect.

Calculate speeds of stars or galaxies, speed traps.

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2007 Question 7(i) What is the Doppler Effect?

The Doppler Effect is the apparent change in the frequency of a wave due to the relative motion between the source of the wave and the observer.

(ii) Explain, with the aid of labelled diagrams, how this phenomenon occurs. Non-concentric circles ( labelled as waves )Source and direction of motion (stated/implied) Position of observer indicatedShorter wavelength / higher frequency on approaching observer (or vice versa)

(iii) The emission line spectrum of a star was analysed using the Doppler Effect.Describe how an emission line spectrum is produced. When the gas is heated the electrons in the gas are move up to higher orbital level and as they fall back down they emit electromagnetic radiation of a specific frequency.

(iv)The red line emitted by a hydrogen discharge tube in the laboratory has a wavelength of 656 nm. The same red line in the hydrogen spectrum of a moving star has a wavelength of 720 nm.Is the star approaching the earth? Justify your answer. NoThe wavelength has increased therefore it must be moving away.

(v) Calculate the frequency of the red line in the star’s spectrumf’ = c / λ’f’ = 3×108 / 720×10-9 f’ = 4.17 × 1014 Hz

(vi)Calculate the speed of the moving starFormula: f’ = fc/c+uSubstitution: 4.17 ×1014 = (4.57 ×1014)(3 ×108) / (3.00×108 + u)Answer: u = 2.92 × 10 7 ms-1

2007 Question 12 (b) (i) Define sound intensity.

Sound Intensity is defined as power per unit area.(ii) A loudspeaker has a power rating of 25 mW.

What is the sound intensity at a distance of 3 m from the loudspeaker?Surface area of sphere = 4π r2 S.I at 3 m = (25 × 10-3 ) ÷ 4 π (3)2 S.I = 2.21 × 10-4 W m-2

(iii) The loudspeaker is replaced by a speaker with a power rating of 50 mW. What is the change in the sound intensity?Increased by: 2.21 × 10-4 W m-2

(iv)What is the change in the sound intensity level? Increased by: 0.30 B or 3 dB

(v) The human ear is more sensitive to certain frequencies of sound.How is this taken into account when measuring sound intensity levels? dBA / decibel adapted / a frequency weighted scale is used // sound level meter (modified so that it) responds more to sounds between 2kHz and 4 kHz / just like the ear

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2005 Question 7A student used a laser, as shown, to demonstrate that light is a wave motion.(i) Name the two phenomena that occur when the light passes through the pair of

narrow slits. Diffraction and Interference

(ii) A pattern is formed on the screen. Explain how the pattern is formed. The slits act as sources of two coherent waves which overlap to give areas of constructive interference (bright lines) and destructive interference (dark lines)

(iii) What is the effect on the pattern when the wavelength of the light is increased?The pattern becomes more spread out.

(iv)What is the effect on the pattern when the distance between the slits is increased?The pattern becomes less spread out.

(v) Describe an experiment to demonstrate that sound is also a wave motion. Walking slowly from X to Y, you will notice the loudness of the sound

increasing and decreasing at regular intervals. This is because sound waves from the two speakers will interfere both

constructively and destructively, along the path XY.(vi)Sound travels as longitudinal waves while light travels as transverse waves.

Explain the difference between longitudinal and transverse waves.Longitudinal waves: the direction of the vibrations is parallel to the direction of propagation of the wave.Transverse wave: the direction of the vibrations is perpendicular to the direction of the wave.

(vii) Describe an experiment to demonstrate that light waves are transverse waves. Light source and two pieces of polaroid as shown.Rotate one polaroid relative to the other and note that the light intensity increases and decreasesOnly transverse waves can be polarised, so light is a transverse wave.

2005 Question 12 (c) (i) The frequency of a stretched string depends on its length.

Give two other factors that affect the frequency of a stretched string. Tension and mass per unit length

(ii) The diagram shows a guitar string stretched between supports 0.65 m apart. The string is vibrating at its first harmonic. The speed of sound in the string is 500 m s–1. What is the frequency of vibration of the string? λ = 2 × 0.65 = 1.3 mv = fλ f = v/ λ = 500 / 1.3 f = 384.6 Hz

(iii) Draw a diagram of the string when it vibrates at its second harmonic.

(iv)What is the frequency of the second harmonic? f2nd = 2f1st = 769.2 Hz

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2003 Question 7 (i) Describe an experiment to show that sound is a wave motion.

1. Walking slowly from X to Y, you will notice the loudness of the sound increasing and decreasing at regular intervals.

2. This is because sound waves from the two speakers will interfere both constructively and destructively, along the path XY.

(ii) What is the Doppler Effect? The Doppler Effect is the apparent change in the frequency of a wave due to the relative motion between the source of the wave and the observer.

(iii) Explain, with the aid of labelled diagrams, how this phenomenon occurs. Non concentric circles, stated or implied as wavesClose parts of circles show high frequency / short wavelengthCentres show direction of movement of source

(iv)Bats use high frequency waves to detect obstacles. A bat emits a wave of frequency 68 kHz and wavelength 5.0 mm towards the wall of a cave. It detects the reflected wave 20 ms later.Calculate the speed of the wave. v = fλ340 m s-1

(v) Calculate the distance of the bat from the wall.v = s/t vt = s = 6.8 m.Divide by two to get the distance going one way only = 3.4 m.

(vi)If the frequency of the reflected wave is 70 kHz, what is the speed of the bat towards the wall? f ' = fc / c± u70000 = (68000)(340)/340 - uu = 9.7 m s-1

(vii) Give two other applications of the Doppler Effect. Speed traps , speed of stars (red shift), landing aircraft, ultrasound (blood movement or heartbeat of foetus), weather forecasting.

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2002 Question 7(i) Constructive interference and destructive interference take place when waves from two coherent

sources meet. Explain the underlined terms in the above statement. Constructive Interference occurs when waves from two coherent sources meet to produce a wave of greater amplitude.Coherent Waves: Two waves are said to be coherent if they have the same frequency and are in phase.

(ii) What is the condition necessary for destructive interference to take place when waves from two coherent sources meet? They must be out of phase by half a wavelength (this means that the crest of one wave will be over the trough of the other.

(iii) Describe an experiment that demonstrates the wave nature of light. Shine a laser through a diffraction grating; an interference pattern will be produced on a screen, caused by interference of the light waves

(iv)Radio waves of frequency 30 kHz are received at a location 1500 km from a transmitter.The radio reception temporarily “fades” due to destructive interference between the waves travelling parallel to the ground and the waves reflected from a layer (ionosphere) of the earth’s atmosphere, as indicated in the diagram.Calculate the wavelength of the radio waves.c = f λ λ = c/f = (3.0 × 108)/ (30000) = 104 m = 10 km

(v) What is the minimum distance that the reflected waves should travel for destructive interference to occur at the receiver? For destructive interference to occur the reflected wave must arrive out of phase, i.e. it must have travelled half a wavelength more than the regular wave.The regular wave will have travelled 1500 km and half a wavelength is 5 km therefore the reflected wave must travel1500 km + 5 km = 1505 km.

(vi)The layer at which the waves are reflected is at a height h above the ground. Calculate the minimum height of this layer for destructive interference to occur at the receiver. Use Pythagoras: h = 61000 m

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Circular Motion and SHM

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Circular Motion

2012 Question 12 (a)An Olympic hammer thrower swings a mass of 7.26 kg at the end of a light inextensible wire in a circular motion. In the final complete swing, the hammer moves at a constant speed and takes 0.8 s to complete a circle of radius 2.0 m.(i) What is the angular velocity of the hammer during its final swing? (ii) Even though the hammer moves at a constant speed, it accelerates. Explain. (iii) Calculate the acceleration of the hammer during its final swing(iv)Calculate the kinetic energy of the hammer as it is released.

2011 Question 6 (c) A simple merry-go-round consists of a flat disc that is rotated horizontally. A child of mass 32 kg stands at the edge of the merry-go-round, 2.2 metres from its centre. The force of friction acting on the child is 50 N.Draw a diagram showing the forces acting on the child as the merry-go-round rotates.

What is the maximum angular velocity of the merry-go-round so that the child will not fall from it, as it rotates?If there was no force of friction between the child and the merry-go-round, in what direction would the child move as the merry-go-round starts to rotate?

2006 Question 6(ix)Define velocity.(x) Define angular velocity. (xi)Derive the relationship between the velocity of a particle travelling in

uniform circular motion and its angular velocity. (xii) A student swings a ball in a circle of radius 70 cm in the vertical

plane as shown. The angular velocity of the ball is 10 rad s–1.What is the velocity of the ball? (xiii) How long does the ball take to complete one revolution? (xiv) Draw a diagram to show the forces acting on the ball when it is at

position A.(xv) The student releases the ball when is it at A, which is 130 cm above the ground, and the ball travels

vertically upwards. Calculate the maximum height, above the ground, the ball will reach.(xvi) Calculate the time taken for the ball to hit the ground after its release from A.

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Circular Motion and Gravity2008 Question 6(x) State Newton’s law of universal gravitation. (xi)The international space station (ISS) moves in a circular orbit around the equator at a height of 400 km. What type of force is required to keep the ISS in orbit? (xii) What is the direction of this force? (xiii) Calculate the acceleration due to gravity at a point 400 km above the surface of the earth. (xiv) An astronaut in the ISS appears weightless. Explain why. (xv) Derive the relationship between the period of the ISS, the radius of its orbit and the mass of the earth.(xvi) Calculate the period of an orbit of the ISS.(xvii) After an orbit, the ISS will be above a different point on the earth’s surface. Explain why. (xviii) How many times does an astronaut on the ISS see the sun rise in a 24 hour period?

(gravitational constant = 6.6 × 10–11 N m2 kg–2; mass of the earth = 6.0 × 1024 kg; radius of the earth = 6.4 × 106 m)

2005 Question 6(viii) Define angular velocity.(ix)Define centripetal force.(x) State Newton’s Universal Law of Gravitation.(xi)A satellite is in a circular orbit around the planet Saturn. Derive the relationship between the period of the satellite, the mass of Saturn and the radius of the orbit. (xii) The period of the satellite is 380 hours. Calculate the radius of the satellite’s orbit around Saturn. (xiii) The satellite transmits radio signals to earth. At a particular time the satellite is 1.2 × 1012 m from

earth. How long does it take the signal to travel to earth? (xiv) It is noticed that the frequency of the received radio signal changes as the satellite orbits Saturn.

Explain why.

Gravitational constant = 6.7 × 10–11 N m2 kg–2; mass of Saturn = 5.7 × 1026 kg; speed of light = 3.0 × 108 m s–1

2004 Question 12 (a)(viii) State Newton’s universal law of gravitation. (ix)Centripetal force is required to keep the earth moving around the sun.What provides this centripetal force?(x) In what direction does this centripetal force act?(xi)Give an expression for centripetal force. (xii) The earth has a speed of 3.0 × 104 m s–1 as it orbits the sun. The distance between the earth and the sun is 1.5 × 1011 m. Calculate the mass of the sun. (gravitational constant, G = 6.7 × 10–11 m3 kg–1 s–2)

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Simple Harmonic Motion2011 Question 12 (a)State Hooke’s law.A body of mass 250 g vibrates on a horizontal surface and its motion is described by the equation a = – 16 s, where s is the displacement of the body from its equilibrium position. The amplitude of each vibration is 5 cm.(d)Why does the body vibrate with simple harmonic motion?(e)Calculate the frequency of vibration of the body?(f) What is the magnitude of (i) the maximum force, (ii) the minimum force, which causes the body’s

motion?

2009 Question 12 (a)(vi)State Hooke’s law. (vii) When a sphere of mass 500 g is attached to a spring of length 300 mm, the length of the spring

increases to 330 mm.Calculate the spring constant. (viii) The sphere is then pulled down until the spring’s length has increased to 350 mm and is then

released.(ix)Describe the motion of the sphere when it is released. (x) What is the maximum acceleration of the sphere?

(acceleration due to gravity = 9.8 m s-2)

2007 Question 6(viii) State Hooke’s law. (ix)A stretched spring obeys Hooke’s law. When a small sphere of mass 300 g is attached to a spring of length 200 mm, its length increases to 285 mm.Calculate its spring constant. (x) The sphere is pulled down until the length of the spring is 310 mm.The sphere is then released and oscillates about a fixed point.Derive the relationship between the acceleration of the sphere and its displacement from the fixed point.(xi)Why does the sphere oscillate with simple harmonic motion? (xii) Calculate the period of oscillation of the sphere(xiii) Calculate the maximum acceleration of the sphere(xiv) Calculate the length of the spring when the acceleration of the sphere is zero. (acceleration due to gravity = 9.8 m s–2)

2002 Question 6(vii) State Newton’s second law of motion. (viii) The equation F = – ks, where k is a constant, is an expression for a law that governs the motion of a

body. Name this law and give a statement of it. (ix)Give the name for this type of motion and describe the motion. (x) A mass at the end of a spring is an example of a system that obeys this law. Give two other examples of systems that obey this law. (xi)The springs of a mountain bike are compressed vertically by 5 mm when a cyclist of mass 60 kg sits on

it. When the cyclist rides the bike over a bump on a track, the frame of the bike and the cyclist oscillate up and down.Using the formula F = – ks, calculate the value of k, the constant for the springs of the bike.(xii) The total mass of the frame of the bike and the cyclist is 80 kg. Calculate (i) the period of oscillation of the cyclist, (ii) the number of oscillations of the cyclist per second. (acceleration due to gravity, g = 9.8 m s-2)

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Solutions2012 Question 12 (a)(i) What is the angular velocity of the hammer during its final swing?

= 7.85 rad s-1

(ii) Even though the hammer moves at a constant speed, it accelerates. Explain. The direction changes (continuously)

(iii) Calculate the acceleration of the hammer during its final swing.a = ω2ra = (7.85)2(2)a = 123.37 m s-2 towards the centre of orbit

(iv)Calculate the kinetic energy of the hammer as it is released.K.E. = ½ mv2

K.E. = ½ m(r ω) 2

K.E. = 896 J

2011 Question 6 (c) (i) Draw a diagram showing the forces acting on the child as the merry-go-round rotates.

(ii) What is the maximum angular velocity of the merry-go-round so that the child will not fall from it, as it rotates?F = mω2r50 = 30 ω2(2.2)ω = 0.842 rad s-1

(iii) If there was no force of friction between the child and the merry-go-round, in what direction would the child move as the merry-go-round starts to rotate?The child would remain stationary / any appropriate answer.

2011 Question 12 (a)(i) State Hooke’s law.

For a stretched string the restoring force is proportional to displacement

(ii) Why does the body vibrate with simple harmonic motion?The acceleration is proportional to the displacement

(iii) Calculate the frequency of vibration of the body?ω2 = 16ω = 4f = ω/2π

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f = 0.64 Hz s-1

(iv)What is the magnitude of (i) the maximum force, (ii) the minimum force, which causes the body’s motion?a max = (–)16(0.05) = 0.80 (Fmax occurs when acceleration / displacement is a maximum)Fmax = (0.250)(0.80) = 0.20 N Fmin = 0

2010 Question 6(xv) State Newton’s law of universal gravitation.

Force between any two point masses is proportional to product of masses and inversely/indirectly proportional to square of the distance between them.

(xvi) Use this law to calculate the acceleration due to gravity at a height above the surface of the earth, which is twice the radius of the earth.Note that 2d above surface is 3d from earth’s centre

where d = 6.36 × 106 m

gnew = 1.09 m s-2

(xvii) A spacecraft carrying astronauts is on a straight line flight from the earth to the moon and after a while its engines are turned off. Explain why the spacecraft continues on its journey to the moon, even though the engines are turned off.There are no external forces acting on the spacecraft so from Newton’s 1st law of motion the object will maintain its velocity.

(xviii) Describe the variation in the weight of the astronauts as they travel to the moon.Weight decreases as the astronaut moves away from the earth and gains (a lesser than normal) weight as she/he approaches the moon

(xix) At what height above the earth’s surface will the astronauts experience weightlessness?Gravitational pull of earth = gravitational pull of moon

=

dE = 9 dm and dE + dm = 3.84 × 108 m

10 dm = 3.84 × 108

dm = 3.84 × 107

dE = 3.356 × 108

Height above the earth = (3.356 × 108) – (6.36 × 106) = 3.39 × 108 m

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(xx) The moon orbits the earth every 27.3 days. What is its velocity, expressed in metres per second?

v = 1022.9 m s-1

(xxi) Why is there no atmosphere on the moon?The gravitational force is too weak to sustain an atmosphere.

2009 Question 12 (a)(v) State Hooke’s law.

When a string is stretched the restoring force is proportional to the displacement.(vi)When a sphere of mass 500 g is attached to a spring of length 300 mm, the length of the spring

increases to 330 mm. Calculate the spring constant. When the mass of 500 g is attached the new force down = mg = (0.5)(g).Because the spring is in equiblibrium this must be equal to the force up (which is the restoring force).Hooke’s law in symbols: F = k x (0.5)(g) = kx k = F/x = 0.5g/0.030 k = 163.3 N m-1

(vii) The sphere is then pulled down until the spring’s length has increased to 350 mm and is then released.Describe the motion of the sphere when it is released. It executes simple harmonic motion because the displacement is proportional to t he acceleration.

(viii) What is the maximum acceleration of the sphere? F = ma = kxa = kx/m = (163.3)(0.02)/(0.5) = 6.532 m s-2

OR a = 2 x 2 = k/m = 163.3/0.5 a = 6.532 m s-2

2008 Question 6(x) State Newton’s law of universal gravitation.

Newton’s Law of Gravitation states that any two point masses in the universe attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

(xi)What type of force is required to keep the ISS in orbit? Gravity

(xii) What is the direction of this force? Towards the centre of the orbit / inwards / towards the earth

(xiii) Calculate the acceleration due to gravity at a point 400 km above the surface of the earth.

= mg g = (6.6 × 10–11)( 6.0 × 1024) / (400 000 + 6.4 × 106)2

g = 8.6 m s-2

(xiv) An astronaut in the ISS appears weightless. Explain why. He is in a state of free-fall (the force of gravity cannot be felt).

(xv) Derive the relationship between the period of the ISS, the radius of its orbit and the mass of the earth.See notes Circular Motion chapter for a derivation.

(xvi) Calculate the period of an orbit of the ISS.

T2 = 3.1347 × 107 T = 5.6 × 103 s

(xvii) After an orbit, the ISS will be above a different point on the earth’s surface. Explain why.

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The ISS has a different period to that of the earth’s rotation (it is not in geostationary orbit). (xviii) How many times does an astronaut on the ISS see the sun rise in a 24 hour period?

(24 ÷ 1.56 + 1) = 16 ( sunrises).

2007 Question 6(viii) State Hooke’s law.

For a stretched string the restoring force is proportional to the extension.(ix)A stretched spring obeys Hooke’s law.

When a small sphere of mass 300 g is attached to a spring of length 200 mm, its length increases to 285 mm.Calculate its spring constant. F = mg = ks (0.30)(9.8) = (k)(0.085) k = 34.6 N m-1

(x) The sphere is pulled down until the length of the spring is 310 mm.The sphere is then released and oscillates about a fixed point.Derive the relationship between the acceleration of the sphere and its displacement from the fixed point.F = - ks ma = - ks a = - (k/m)s a α -s a = - k s

(xi)Why does the sphere oscillate with simple harmonic motion? Its acceleration is proportional to its displacement from a fixed point.

(xii) Calculate the period of oscillation of the sphere.From above:ω2 = k/m ω2 = 34.6 / 0.3 ω = 10.7 T = 2π/ω = 2π/10.7 = 0.58 ≈ 0.6 T = 0.6 s

(xiii) Calculate the maximum acceleration of the sphere.This occurs when s is a maximum, i.e. when s = amplitude = 0.310 – 0.285 = 0.025 m.a = -ω2s a = - (10.7)2 (0.025) a = (-) 2.89 m s-2

(xiv) Calculate the length of the spring when the acceleration of the sphere is zero. This occurs at the fixed point when l = 0.285 m

2006 Question 6(ix)Define velocity.

Velocity is the rate of change of displacement with respect to time.(x) Define angular velocity.

Angular velocity is the rate of change of angle with respect to time.(xi)Derive the relationship between the velocity of a particle travelling in

uniform circular motion and its angular velocity. θ = s /r θ /t = s/rt ω = v /r v = ω r

(xii) A student swings a ball in a circle of radius 70 cm in the vertical plane as shown. The angular velocity of the ball is 10 rad s–1. What is the velocity of the ball? v = ω r = (10)(0.70) = 7.0 m s-1

(xiii) How long does the ball take to complete one revolution? T= 2πr/v = 2π(0.70)/v = 0.63 s

(xiv) Draw a diagram to show the forces acting on the ball when it is at position A.Weight (W) downwards; reaction (R) upwards; force to left (due to friction or curled fingers)

(xv) The student releases the ball when is it at A, which is 130 cm above the ground, and the ball travels vertically upwards. Calculate the maximum height, above the ground, the ball will reach.v2 = u2+ 2as 0 = (7)2 + 2(-9.8) s / s = 2.5(0) m max. height = 2.5 + 1.30 / 3.8 m

(xvi) Calculate the time taken for the ball to hit the ground after its release from A. s = ut + ½ at2

-1.30 = 7t – ½ (9.8)t2

t = 1.59 s

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2005 Question 6(viii) Define angular velocity.

Angular velocity is the rate of change of displacement with respect to time.(ix)Define centripetal force.

The force - acting in towards the centre - required to keep an object moving in a circle is called Centripetal Force.

(x) State Newton’s Universal Law of Gravitation.Newton’s Law of Gravitation states that any two point masses in the universe attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

(xi)A satellite is in a circular orbit around the planet Saturn. Derive the relationship between the period of the satellite, the mass of Saturn and the radius of the orbit. See notes on the Circular Motion chapter for the derivation.

(xii) The period of the satellite is 380 hours. Calculate the radius of the satellite’s orbit around Saturn. T = 380 × 60 × 60 = 1.37 × 106 sr3 = T2GM/4π2 r3 = (1.37 × 106)2(6.7 × 10–11)( 5.7 × 1026)/ 4π2 r = 1.2 × 109 m

(xiii) The satellite transmits radio signals to earth. At a particular time the satellite is 1.2 × 1012 m from earth. How long does it take the signal to travel to earth? v = s/t (3.0 × 108) = (1.2 × 1012)/t t = 4000 s

(xiv) It is noticed that the frequency of the received radio signal changes as the satellite orbits Saturn. Explain why. Doppler Effect due to relative motion between source of signal and the detector

2004 Question 12 (a)(vi)State Newton’s universal law of gravitation.

Newton’s Law of Gravitation states that any two point masses in the universe attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of the distance between them.

(vii) Centripetal force is required to keep the earth moving around the sun.What provides this centripetal force?Gravitational pull of the sun.

(viii) In what direction does this centripetal force act?Towards the centre.

(ix)Give an expression for centripetal force.

(x) The earth has a speed of 3.0 × 104 m s–1 as it orbits the sun. The distance between the earth and the sun is 1.5 × 1011 m. Calculate the mass of the sun.

and Equating gives v2 Ms = v2R/G Ms = (3.0 × 104)2 ( 1.5 × 1011)/ 6.7 × 10–11 = 2.0 × 1030 kg.

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2002 Question 6(viii) State Newton’s second law of motion.

Newton’s Second Law of Motion states that the rate of change of an object’s momentum is directly proportional to the force which caused it, and takes place in the direction of the force.

(ix)The equation F = – ks, where k is a constant, is an expression for a law that governs the motion of a body. Name this law and give a statement of it.Hooke’s Law states that when an object is stretched the restoring force is directly proportional to the displacement, provided the elastic limit is not exceeded.

(x) Give the name for this type of motion and describe the motion. Simple harmonic motion; an object is said to be moving with Simple Harmonic Motion if its acceleration is directly proportional to its distance from a fixed point in its path, and its acceleration is directed towards that point.

(xi)A mass at the end of a spring is an example of a system that obeys this law. Give two other examples of systems that obey this law. Stretched elastic, pendulum, oscillating magnet, springs of car, vibrating tuning fork, object bobbing in water waves, ball in saucer, etc.

(xii) The springs of a mountain bike are compressed vertically by 5 mm when a cyclist of mass 60 kg sits on it. When the cyclist rides the bike over a bump on a track, the frame of the bike and the cyclist oscillate up and down.Using the formula F = – ks, calculate the value of k, the constant for the springs of the bike.F = – ks mg = – ks 60 × 9.8 = -k (.005) 588 = -k (.005) k = 1.2 × 105 N m-1

(xiii) The total mass of the frame of the bike and the cyclist is 80 kg. Calculate the period of oscillation of the cyclist.k/m = ω2

ω = 38 s-1

T = 2π/ω = 0.16 s

(xiv) Calculate the number of oscillations of the cyclist per second. f = 1/T approximately = 6

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Static Electricity and Capacitance

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Static Electricity

2010 Question 9 (a) [Ordinary Level](i) State Coulomb’s law of force between electric charges. (ii) How would you detect the presence of an electric field?(iii) What is the unit of electric charge? (iv)How does the lightning conductor prevent damage to the building?(v) Suggest a suitable material for a lightning conductor.

2007 Question 9 (a) [Ordinary Level](i) State Coulomb’s law of force between charges. (ii) The diagram shows a positively charged gold leaf electroscope.

Describe how an electroscope is given a positive charge.(iii) What is observed when the cap of an electroscope is earthed? (iv)Why does this happen?(v) How is the cap of the electroscope earthed?

2005 Question 12 (c) [Ordinary Level]The diagram shows a gold leaf electroscope.(i) Name the parts labelled A and B. (ii) Give one use of an electroscope. (iii) Explain why the gold leaf diverges when a positively charged rod is

brought close to the metal cap. (iv)The positively charged rod is held close to the electroscope and the metal

cap is then earthed. Explain why the gold leaf collapses.

2003 Question 12 (c) [Ordinary Level](i) What is the unit of electric charge?(ii) Describe, with the aid of a labelled diagram, how you would charge a conductor by induction.(iii) The build-up of electric charge can lead to explosions. Give two examples where this could happen.(iv)How can the build-up of electric charge on an object be reduced?

Higher Level Questions2011 Question 9 (b)(i) Draw a labelled diagram of an electroscope.(ii) Why should the frame of an electroscope be earthed?(iii) Describe how to charge an electroscope by induction.

2011 Question 9 (c) (i) How does a full-body metal-foil suit protect an operator when working on high voltage

power lines?(ii) Describe an experiment to investigate the principle by which the operator is protected.

2002 Question 11Read the following passage and answer the accompanying questions. Benjamin Franklin designed the lightning conductor. This is a thick copper strip running up the outside of a tall building. The upper end of the strip terminates in one or more sharp spikes above the highest point of the

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building. The lower end is connected to a metal plate buried in moist earth. The lightning conductor protects a building from being damaged by lightning in a number of ways. During a thunderstorm, the value of the electric field strength in the air can be very high near a pointed lightning conductor. If the value is high enough, ions, which are drawn towards the conductor, will receive such large accelerations that, by collision with air molecules, they will produce vast additional numbers of ions. Therefore the air is made much more conducting and this facilitates a flow of current between the air and the ground. Thus, charged clouds become neutralised and lightning strikes are prevented. Alternatively, in the event of the cloud suddenly discharging, the lightning strike will be conducted through the copper strip, thus protecting the building from possible catastrophic consequences. Raised umbrellas and golf clubs are not to be recommended during thunderstorms for obvious reasons. On high voltage electrical equipment, pointed or roughly-cut surfaces should be avoided. (Adapted from “Physics – a teacher’s handbook”, Dept. of Education and Science.)

(a) Why is a lightning conductor made of copper?(b) What is meant by electric field strength? (c) Why do the ions near the lightning conductor accelerate? (d) How does the presence of ions in the air cause the air to be more conducting? (e) How do the charged clouds become neutralised? (f) What are the two ways in which a lightning conductor prevents a building from being damaged by

lightning? (g) Why are raised umbrellas and golf clubs not recommended during thunderstorms? (h) Explain why pointed surfaces should be avoided when using high voltage electrical equipment.

Electric Fields / Electric Field Strength

2003 Question 12 (c)(i) State Coulomb’s law of force between electric charges.(ii) Define electric field strength and give its unit. (iii) How would you demonstrate an electric field pattern? (iv)The diagram shows a negative charge – Q at a point X.

Copy the diagram and show on it the direction of the electric field strength at Y.

2005 Question 10(i) Define electric field strength.(ii) State Coulomb’s law of force between electric charges. (iii) Why is Coulomb’s law an example of an inverse square law? (iv)Give two differences between the gravitational force and the

electrostatic force between two electrons. (v) Describe an experiment to show an electric field pattern. (vi)Calculate the electric field strength at the point B, which is

10 mm from an electron.(vii) What is the direction of the electric field strength at B?(viii) A charge of 5 μC is placed at B. Calculate the electrostatic force exerted on this charge. (permittivity of free space = 8.9 × 10–12 F m–1; charge on the electron = 1.6 × 10–19 C)

2010 Question 12 (d)(i) Define electric field strength and give its unit of measurement.(ii) Copy the diagram into your answerbook and show on it the direction of the electric field at point P.

(iii) Calculate the electric field strength at P.(iv)Under what circumstances will point discharge occur?

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(permittivity of free space = 8.9 × 10–12 F m–1)

2007 Question 8(i) Define electric field strength and give its unit of measurement. (ii) Describe how an electric field pattern may be demonstrated in the laboratory. (iii) The dome of a Van de Graff generator is charged.

The dome has a diameter of 30 cm and its charge is 4 C. A 5 μC point charge is placed 7 cm from the surface of the dome.Calculate the electric field strength at a point 7 cm from the dome

(iv)Calculate the electrostatic force exerted on the 5 μC point charge. (v) All the charge resides on the surface of a Van de Graff generator’s dome. Explain why.(vi)Describe an experiment to demonstrate that total charge resides on the outside of a conductor.(vii) Give an application of this effect. (permittivity of free space = 8.9 × 10–12 F m–1)

2011 Question 9 (a) {part (ii) was ridiculous}(i) State Coulomb’s law.(ii) Two identical spherical conductors on insulated stands are placed a certain distance apart.

One conductor is given a charge Q while the other conductor is given a charge 3Q and they experience a force of repulsion F. The two conductors are then touched off each other and returned to their original positions. What is the new force, in terms of F, between the spherical conductors?Capacitance

2012 no.12 (d) [Ordinary Level]A capacitor is connected to a switch, a battery and a bulb as shown in the diagram.When the switch is changed from position A to position B, the bulb lights briefly.(i) What happens to the capacitor when the switch is in position A? (ii) Why does the bulb light when the switch is in position B? (iii) Why does the bulb light only briefly? (iv)The capacitor has a capacitance of 200 μF. Calculate its charge

when connected to a 6 V battery. (v) Give a use for a capacitor.

2007 Question 9 (b) [Ordinary Level]A capacitor is connected to a switch, a battery and a bulb as shown in the diagram. When the switch is moved from position A to position B, the bulb lights briefly.(i) What happens to the capacitor when the switch is in position A?(ii) Why does the bulb light when the switch is in position B? (iii) When the switch is in position A the capacitor has a charge of

0.6 C, calculate its capacitance. (iv)Give a use for a capacitor.

2002 Question12 (c) [Ordinary Level](i) Define capacitance. (ii) Diagram A shows a capacitor connected to a bulb and a

12 V a.c. supply. (iii) Diagram B shows the same capacitor connected to

the bulb, but connected to a 12 V d.c. supply. (iv)What happens in each case when the switch is closed?

Explain your answer.

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(v) Describe an experiment to demonstrate that a capacitor can store energy.

Higher Level Questions2008 Question 12 (d) (i) Define capacitance. (ii) Describe how an electroscope can be charged by induction. (iii) How would you demonstrate that the capacitance of a parallel plate capacitor depends on the

distance between its plates?

2006 Question 12 (b)(i) List the factors that affect the capacitance of a parallel plate capacitor. (ii) The plates of an air filled parallel plate capacitor have a common area of 40 cm2 and are 1 cm apart.

The capacitor is connected to a 12 V d.c. supply. Calculate the capacitance of the capacitor.(iii) Calculate the magnitude of the charge on each plate. (iv)What is the net charge on the capacitor?(v) Give a use for a capacitor. (permittivity of free space = 8.85 × 10–12 F m–1)

2009 Question 9(i) Define potential difference.(ii) Define capacitance. (iii) A capacitor stores energy.

Describe an experiment to demonstrate that a capacitor stores energy.

(iv) The ability of a capacitor to store energy is the basis of a defibrillator. During a heart attack the chambers of the heart fail to pump blood because their muscle fibres contract and relax randomly. To save the victim, the heart muscle must be shocked to re-establish its normal rhythm. A defibrillator is used to shock the heart muscle.A 64 μF capacitor in a defibrillator is charged to a potential difference of 2500 V.The capacitor is discharged through electrodes attached to the chest of a heart attack victim.Calculate the charge stored on each plate of the capacitor.

(v) Calculate the energy stored in the capacitor.(vi) Calculate the average current that flows through the victim when the capacitor discharges in a time of

10 ms.(vii) Calculate the average power generated as the capacitor discharges.

2004 Question 8 {you should have the Resistance chapter covered before trying the maths part of this question}(i) Define potential difference. (ii) Define capacitance. (iii) Describe an experiment to demonstrate that a capacitor can store energy.

(iv)The circuit diagram shows a 50 μF capacitor connected in series with a 47 kΩ resistor, a 6 V battery and a switch. When the switch is closed the capacitor starts to charge and the current flowing at a particular instant in the circuit is 80 μA.Calculate the potential difference across the resistor and hence the potential difference across the capacitor when the current is 80 μA.

(v) Calculate the charge on the capacitor at this instant.(vi)Calculate the energy stored in the capacitor when it is fully charged.(vii) Describe what happens in the circuit when the 6 V d.c. supply is replaced with a 6 V a.c. supply.

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Solutions2011 Question 9(a) (i) State Coulomb’s law.

The force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

(ii) What is the new force, in terms of F, between the spherical conductors?

(b)(i) Draw a labelled diagram of an electroscope.

A = insulated joint, B = metal case (ii) Why should the frame of an electroscope be earthed?

If the frame was charged it would affect the degree of deflection of the leaf.(iii) Describe how to charge an electroscope by induction.1. Bring a charged rod near the electroscope (the positive and negative charges become separated on it).2. Keeping the charged rod in place, earth the cap by touching it with your finger.

Some of the negative charge on the metal flows through you to earth.3. Remove your finger, then and only then remove the rod.4. The conductor will now be positively charged.

(c) (i) How does a full-body metal-foil suit protect an operator when working on high voltage power

lines?All charges will reside on the outside of the conducting suit (because the suit blocks out external electrical fields) so he won’t get shocked.

(ii) Describe an experiment to investigate the principle by which the operator is protected.1. Charge the conductor (a metal can will do fine).2. Using a proof plane, touch the inside of the can and bring it up to the GLE.

Notice that there is no deflection.3. Touch the proof plane off the outside of the can and bring it up to the GLE.

Notice that there is a deflection.4. Conclusion: charge resides on outside only

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2010 Question 12 (d)(i) Define electric field strength and give its unit of measurement.

Electric field strength is defined as force per unit charge.Its unit is the N C–1

(ii) Copy the diagram into your answerbook and show on it the direction of the electric field at point P.

(iii) Calculate the electric field strength at P.The electric field strength at P is the sum of the electric fields acting on P from the other two charges. The electric field strength is towards the left in both cases (attracted to the negative charge and repelled from the positive charge). Because they are both in the same direction the individual field strengths can simply be added together.

Etotal = 3.77 × 106 N C-1

(iv)Under what circumstances will point discharge occur?Large electric field strength /potential at a point / high charge density at a point.

2009 Question 9 (i) Define potential difference

Potential difference is the work done in moving unit charge from one place to another.(ii) Define capacitance

The capacitance of a conductor is the ratio of the charge on the conductor to its potential.(iii) A capacitor stores energy.

Describe an experiment to demonstrate that a capacitor stores energy. 1. Set up as shown.2. Close the switch to charge the capacitor.3. Remove the battery and connect the terminals together to ‘short’ the circuit.4. The bulb will flash as the capacitor discharges, showing that it stores energy.

The ability of a capacitor to store energy is the basis of a defibrillator. During a heart attack the chambers of the heart fail to pump blood because their muscle fibres contract and relax randomly. To save the victim, the heart muscle must be shocked to re-establish its normal rhythm. A defibrillator is used to shock the heart muscle.A 64 μF capacitor in a defibrillator is charged to a potential difference of 2500 V.The capacitor is discharged through electrodes attached to the chest of a heart attack victim.

(iv) Calculate the charge stored on each plate of the capacitor.q = CV q = (64 × 10-6)(2500) q = 0.16 C

(v) Calculate the energy stored in the capacitor.E = ½ CV2 = ½ (64 × 10-6)(2500)2 = 200 J

(vi) Calculate the average current that flows through the victim when the capacitor discharges in a time of 10 ms.I = q/t = (64 × 10-6)/(10 × 10-3) = 16 A

(vii) Calculate the average power generated as the capacitor discharges. P = W/t = (200)/(10 × 10-3) = 20000 W

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2008 Question 12 (d) (i) Define capacitance.

The Capacitance of a conductor is the ratio of the charge on the conductor to its potential.(ii) Describe how an electroscope can be charged by induction. 1. Bring a charged rod near the electroscope (the positive and negative charges become separated on it).2. Keeping the charged rod in place, earth the cap by touching it with your finger.

Some of the negative charge on the metal flows through you to earth.3. Remove your finger, then and only then remove the rod.4. The conductor will now be positively charged. (iii) How would you demonstrate that the capacitance of a parallel plate capacitor depends on the

distance between its plates? Connect the two parallel plates to a digital multi-meter (DMM) set to read capacitance. Note the capacitance.Increase the distance between them – note that the capacitance decreases.

2007 Question 8(i) Define electric field strength and give its unit of measurement.

Electric field strength at a point is the force per unit charge at that point.The unit is the N C-1

(ii) Describe how an electric field pattern may be demonstrated in the laboratory. Apparatus: oil, metal plates, container, semolina, H.T. Arrangement: correct arrangement Procedure: switch on powerObservation: semolina particles line up to show field pattern.

(iii) The dome of a Van de Graff generator is charged. (iv)The dome has a diameter of 30 cm and its charge is 4 C.

A 5 μC point charge is placed 7 cm from the surface of the dome.Calculate the electric field strength at a point 7 cm from the dome.

The key here is to note that d corresponds to the distance from the charge to the centre of the dome, i.e. 0.07 + 0.15 (radius of the dome) = 0.22 m

Answer: E = 7.39 x 1011 N C-1

(v) Calculate the electrostatic force exerted on the 5 μC point charge.F = E q F = (7.39 × 1011)(5 × 10-6) or F = 3.69 × 106 N

(vi)All the charge resides on the surface of a Van de Graff generator’s dome. Explain why.Like charges repel and the charges are a maximum distance apart on the outside surface of dome.

(vii) Describe an experiment to demonstrate that total charge resides on the outside of a conductor.Apparatus: metal can, gold leaf electroscope, proof plane.Procedure: charge metal can and use proof plane to test inside and outside.Observation: leaves on g.l.e. deflect for outside sample only. Conclusion: charge resides on outside only .

(viii) Give an application of this effect. Electrostatic shielding / co-axial cable / TV (signal) cable / to protect persons or equipment, enclose them in hollow conductors /Faraday cages (there is no electric field inside a closed conductor), etc.

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2006 Question 12 (b)(i) List the factors that affect the capacitance of a parallel plate capacitor.

Common area of plates, distance apart, permittivity of dielectric between plates.(ii) The plates of an air filled parallel plate capacitor have a common area of 40 cm2 and are 1 cm

apart. The capacitor is connected to a 12 V d.c. supply. Calculate the capacitance of the capacitor.C=εA/dC = [(8.85 × 10-12)(40 × 10-4)] / (0.01) C = 3.54 × 10-12 F

(iii) Calculate the magnitude of the charge on each plate. Q = C V Q = (3.54 x 10-12)(12) = 4.2(5) x 10-11 C

(iv)What is the net charge on the capacitor?zero

(v) Give a use for a capacitor. blocks d.c. /smoothing /tuning circuits / timing circuits / flash guns for cameras.

2005 Question 10(i) Define electric field strength.

Electric field strength is defined as force per unit charge.(ii) State Coulomb’s law of force between electric charges.

The force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

(iii) Why is Coulomb’s law an example of an inverse square law? Force is inversely proportional to distance squared.

(iv)Give two differences between the gravitational force and the electrostatic force between two electrons. Gravitational force is much smaller than the electrostatic force. Gravitational force is attractive, electrostatic force (between two electrons) is repulsive.

(v) Describe an experiment to show an electric field pattern. High voltage and two metal plates /electrodesSemolina and oil in containerConnect a (high) voltage to the plates in container Semolina lines up in the field

(vi)Calculate the electric field strength at the point B, which is 10 mm from an electron.E = Q/4πεd2

= (1.6 × 10-19)/4π(8.9 × 10-12)(0.01)2 E = 1.4 × 10-5 N C-1

(vii) What is the direction of the electric field strength at B?Towards the electron / to the right

(viii) A charge of 5 μC is placed at B. Calculate the electrostatic force exerted on this charge. F = Eq or F = (1.4 × 10-5)(5 × 10-6) = 7.2 × 10-11 N Towards the electron

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2004 Question 8(i) Define potential difference.

The Potential difference (p.d.) between two points is the work done in bringing a charge of 1 Coulomb from one point to the other.

(ii) Define capacitance. The Capacitance of a conductor is the ratio of the charge on the conductor to its potential.

(iii) Describe an experiment to demonstrate that a capacitor can store energy. 1. Set up as shown.2. Close the switch to charge the capacitor.3. Remove the battery and connect the terminals together to ‘short’ the circuit.4. The bulb will flash as the capacitor discharges, showing that it stores energy.

(iv)Calculate the potential difference across the resistor and hence the potential difference across the capacitor when the current is 80 μA.V = IR V (across 47 kΩ resistor) = (80 ×10−6 )(47 ×103 ) = 3.76 V V (across the capacitor) = 6 − 3.76 = 2.24 V

(v) Calculate the charge on the capacitor at this instant.C = Q/V Q = CV = (50 ×10−6 )(2.24) = 1.12 × 10-4 C

(vi)Calculate the energy stored in the capacitor when it is fully charged.E = ½ CV2 = ½ (50 ×10− 6)(6 )2 = 9 ×10−4 J

(vii) Describe what happens in the circuit when the 6 V d.c. supply is replaced with a 6 V a.c. supply. The current will flow continually.

2003 Question 12 (c)(i) State Coulomb’s law of force between electric charges.

Coulomb’s Law states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

(ii) Define electric field strength and give its unit. Electric field strength at a point is the force per unit charge at that point.The unit of electric field strength is the Newton per Coulomb (NC-1).

(iii) How would you demonstrate an electric field pattern? Oil and semolina or seeds High tension / high voltage Lines of semolina show field

(iv)The diagram shows a negative charge – Q at a point X. Copy the diagram and show on it the direction of the electric field strength at Y. Arrow towards X

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2002 Question 11(a) Why is a lightning conductor made of copper?

It is a good conductor.(b) What is meant by electric field strength?

Electric field strength is defined as force per unit charge.(c) Why do the ions near the lightning conductor accelerate?

They experience a large force(d) How does the presence of ions in the air cause the air to be more conducting?

The ions act as charge carriers.(e) How do the charged clouds become neutralised?

Electrons flow to or from the ground through the air.(f) What are the two ways in which a lightning conductor prevents a building from being damaged by

lightning? Neutralises charged clouds It conducts charges to earth.

(g) Why are raised umbrellas and golf clubs not recommended during thunderstorms? Because they act as lightning conductors.

(h) Explain why pointed surfaces should be avoided when using high voltage electrical equipment.Sparking is more likely to occur from these points due to point discharge.

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Resistance

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Circuit Diagrams – Maths Questions

2007 Question 12 (c) [Ordinary Level]The circuit diagram shows two resistors connected in series with a 6 V battery.(v) State Ohm’s law. (vi)Calculate the total resistance of the circuit.(vii) Calculate the current in the circuit.(viii) Calculate the potential difference across the 9 Ω resistor. (ix)Name an instrument used to measure potential difference.

2002 Question 8 [Ordinary Level](i) Explain potential difference(ii) Explain electric current.(iii) Give one difference between conduction in metals and conduction in semiconductors. (iv)A circuit consists of a 3 Ω resistor and a 6 Ω resistor connected in

parallel to a 1.5 V d.c. supply as shown. Calculate the total resistance of the two resistors.

(v) Calculate the current flowing in the circuit. (vi)What is the current in the 3 Ω resistor?(vii) Semiconductors can be made p-type or n-type.

How is a semiconductor made p-type?(viii) Draw a diagram showing a p-n junction connected in forward bias

to a d.c. supply. (ix)Give two uses of semiconductors.

2008 Question 9 [Ordinary Level] (i) An electric current flows in a conductor when there is a potential difference between its ends.

What is an electric current?(ii) Give two effects of an electric current. (iii) Name a source of potential difference. (iv)Describe an experiment to investigate if a substance is a conductor or an insulator. (v) The two headlights of a truck are connected in parallel to a 24 V supply.

Draw a circuit diagram to show how the headlights are connected to the supply.(vi)What is the advantage of connecting them in parallel? (vii) Why should a fuse be included in such a circuit?(viii) The resistance of each headlight is 20 Ω.

Calculate the total resistance in the circuit.(ix)Calculate the current flowing in the circuit.

2010 Question 9 (b) [Ordinary Level](i) State Ohm’s law(ii) The diagram shows a number of resistors connected to a

12 V battery and a bulb whose resistance is 4 Ω.Calculate the combined resistance of the 15 Ω and 30 Ω resistors in parallel.

(iii) Calculate the total resistance of the circuit (iv)Calculate the current flowing in the circuit

2005 Question 8 [Ordinary Level](i) State Ohm’s Law.

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(ii) The graphs show how current (I ) varies with potential difference (V) for (a) a metal, (b) a filament bulb.Which conductor obeys Ohm’s law?

(iii) Explain your answer.

(iv)The circuit diagram shows a 100 Ω resistor and a thermistor connected in series with a 6 V battery. At a certain temperature the resistance of the thermistor is 500 Ω.Calculate the total resistance of the circuit.

(v) Calculate the current flowing in the circuit.(vi)Calculate the potential difference across the 100 Ω resistor.(vii) As the thermistor is heated, what happens to the resistance of the

circuit?(viii) As the thermistor is heated, what happens to the potential difference

across the 100 Ω resistor? (ix)Give a use for a thermistor.

2005 Question 9 [Higher Level](i) Define potential difference.(ii) Define resistance. (iii) Two resistors, of resistance R1 and R2 respectively, are connected in

parallel. Derive an expression for the effective resistance of the two resistors in terms of R1 and R2.

(iv)In the circuit diagram, the resistance of the thermistor at room temperature is 500 Ω.At room temperature calculate the total resistance of the circuit.

(v) At room temperature calculate the current flowing through the 750 Ω resistor. (vi)As the temperature of the room increases, explain why the resistance of the thermistor decreases.(vii) As the temperature of the room increases, explain why the potential at A increases.

Resistivity Problems2002 Question 8 [Higher Level](i) Define power. (ii) Define resistivity.(iii) Describe an experiment that demonstrates the heating effect of an electric current. (iv)The ESB supplies electrical energy at a rate of 2 MW to an industrial park from a local power station,

whose output voltage is 10 kV. The total length of the cables connecting the industrial park to the power station is 15 km. The cables have a diameter of 10 mm and are made from a material of resistivity 5.0 × 10-8 Ω m. Calculate the total resistance of the cables.

(v) Calculate the current flowing in the cables.(vi)Calculate the rate at which energy is “lost” in the cables.(vii) Suggest a method of reducing the energy “lost” in the cables.

2008 Question 7 [Higher Level](i) Define resistivity and give its unit of measurement. (ii) An electric toaster heats bread by convection and radiation.

What is the difference between convection and radiation as a means of heat transfer?(iii) A toaster has a power rating of 1050 W when it is connected to the mains supply.

Its heating coil is made of nichrome and it has a resistance of 12 Ω.The coil is 40 m long and it has a circular cross-section of diameter 2.2 mm.Calculate the resistivity of nichrome.

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(iv)Calculate the heat generated by the toaster in 2 minutes if it has an efficiency of 96%. (v) The toaster has exposed metal parts. How is the risk of electrocution minimised? (vi)When the toaster is on, the coil emits red light.

Explain, in terms of movement of electrons, why light is emitted when a metal is heated.

2011 Question 12 (c) [Higher Level](i) List the factors that affect the heat produced in a current-carrying conductor.

An electric cable consists of a single strand of insulated copper wire. The wire is of uniform cross-sectional area and is designed to carry a current of 20 A. To preserve the insulation, the maximum rate at which heat may be produced in the wire is 2.7 W per metre length.

(ii) Calculate the maximum resistance per metre of the wire(iii) Calculate the minimum diameter of the wire.

(resistivity of copper = 1.7 × 10–8 Ω m)

2010 Question 8 [Higher Level]A hair dryer with a plastic casing uses a coiled wire as a heat source. When an electric current flows through the coiled wire, the air around it heats up and a motorised fan blows the hot air out.

(i) What is an electric current?(ii) Heating is one effect of an electric current.

Give two other effects of an electric current.(iii) The diagram shows a basic electrical circuit for a hair dryer.

Describe what happens when switch A is closed and the rheostat is adjusted(iv)Describe what happens when switch A and switch B are closed.(vi)Calculate the current that flows through the coil when the dryer is turned on.

The maximum power generated in the heating coil is 2 kW.(v) What is the initial resistance of the coil?(vii) A length of nichrome wire of diameter 0.17 mm is used for the coil.

Calculate the length of the coil of wire. (resistivity of nichrome = 1.1 × 10–6 Ω m)(viii) Explain why the current through the coil would decrease if the fan developed a fault and stopped

working.Wheatstone Bridge and Metre Bridge

2007 Question 9 [Higher Level](i) Define resistance.(ii) Define resistivity.

A metre bridge was used to measure the resistance of a sample of nichrome wire.The diagram indicates the readings taken when the metre bridge was balanced.The nichrome wire has a length of 220 mm and a radius of 0.11 mm.

(i) Calculate the resistance of the nichrome wire(iii) Calculate the resistivity of nichrome. (iv)Sketch a graph to show the relationship between the temperature and the resistance of the nichrome wire

as its temperature is increased. (v) What happens to the resistance of the wire as its temperature falls below 0oC?(vi)What happens to the resistance of the wire as its length is increased?(vii) What happens to the resistance of the wire if its diameter is increased? (viii) Name another device, apart from a metre bridge, that can be used to measure resistance.(ix)Give one advantage and one disadvantage of using this device instead of a metre bridge.

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2012 Question 9 [Higher Level](i) Define resistance.(ii) Two resistors of resistance R1 and R2 are connected in series.

Derive an expression for the effective resistance of the two resistors in terms of R1 and R2. (iii) Two 4 Ω resistors are connected in parallel.

Draw a circuit diagram to show how another 4 Ω resistor could be arranged with these two resistors to give an effective resistance of 6 Ω.

(iv)A fuse is a resistor used as a safety device in a circuit. How does a fuse operate?

A Wheatstone bridge circuit is used to measure the resistance of an unknown resistor R.The bridge ABCD is balanced when X = 2.2 kΩ, Y = 1.0 kΩ and Z = 440 Ω.

(v) What test would you use to determine that the bridge is balanced? (vi)What is the resistance of the unknown resistor R? (vii) When the unknown resistor R is covered by a piece of black paper, the bridge goes out of balance.What type of resistor is it? Give a use for this type of resistor.

Solutions to Ordinary Level questions

2010 Question 9 (b) [Ordinary Level](i) State Ohm’s law

Ohm’s Law states that the current flowing through a conductor is directly proportional to the potential difference across it, assuming constant temperature.

(ii) Calculate the combined resistance of the 15 Ω and 30 Ω resistors in parallel. 1/R15,30 = 1/15 + 1/30R15,30 = 10 Ω

(iii) Calculate the total resistance of the circuit T total = 10 + 10 + 4 = 24 Ω

(iv)Calculate the current flowing in the circuitI = V/R = 12/24 = 0.5 A

2008 Question 9 [Ordinary Level](i) What is an electric current?

An electric current is a flow of charge.(ii) Give two effects of an electric current.

Heating, magnetic, chemical.(iii) Name a source of potential difference.

Battery, generator, thermocouple.(iv)Describe an experiment to investigate if a substance is a conductor or an insulator.

Apparatus: circuit to show power source, ammeter/ bulb, leads, Procedure: connect the circuit and place item between contacts Observation: If the bulb lights then the item is a conductor; if the bulb does not light then the item is an insulator.

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(v) The two headlights of a truck are connected in parallel to a 24 V supply.Draw a circuit diagram to show how the headlights are connected to the supply.Circuit diagram showing battery and two bulbs connected in parallel.

(vi)What is the advantage of connecting them in parallel? If one goes the other still works, they are brighter.

(vii) Why should a fuse be included in such a circuit?To prevent too high a current flowing.

(viii) The resistance of each headlight is 20 Ω. Calculate the total resistance in the circuit.For resistors in parallel we use the formulaR = 10 Ω

(ix)Calculate the current flowing in the circuit.V = IR I = V/R I = 24/10 = 2.4 A.

2007 Question 12 (c) [Ordinary Level](i) State Ohm’s law.

Ohm’s Law states that the current flowing through a conductor is directly proportional to the potential difference across it, assuming constant temperature.

(ii) Calculate the total resistance of the circuit.R = 3 + 9 = 12 Ω

(iii) Calculate the current in the circuit.V=IR I = V/R = 6/12 = 0.5 A

(iv)Calculate the potential difference across the 9 Ω resistor. V = I R = 0.5×9 = 4.5 V

(v) Name an instrument used to measure potential difference. A voltmeter

2005 Question 8 [Ordinary Level](i) State Ohm’s Law.

Ohm’s Law states that the current flowing through a conductor is directly proportional to the potential difference across it, assuming constant temperature.

(ii) Which conductor obeys Ohm’s law? The metal.

(iii) Explain your answer. Graph (a) results in a straight line through the origin, therefore I is proportional to V

The circuit diagram shows a 100 Ω resistor and a thermistor connected in series with a 6 V battery. At a certain temperature the resistance of the thermistor is 500 Ω.

(iv)Calculate the total resistance of the circuit.RTotal = R1 + R2 RTotal = 100 + 500 = 600 Ω.

(v) Calculate the current flowing in the circuit.V = I R I = V/R I = 6/600 = 0.01A

(vi)Calculate the potential difference across the 100 Ω resistor.V = I R V = (0.01)×(100) V = 1 V.

(vii) As the thermistor is heated, what happens to the resistance of the circuit?It decreases.

(viii) As the thermistor is heated, what happens to the potential difference across the 100 Ω resistor?It increases, because the total voltage is still 6 V is still the potential difference across both resistors, so if the potential difference decreases across the thermistor, it must increase across the 100 Ω resistor.

(ix)Give a use for a thermistor.Thermometer, heat sensor, temperature control.

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2002 Question 8 [Ordinary Level](i) Explain potential difference.

The Potential difference between two points is the work done in bringing a charge of 1 Coulomb from one point to the other.

(ii) Explain electric current.An electric current is a flow of charge.

(iii) Give one difference between conduction in metals and conduction in semiconductors. There are two types of charge carriers (holes and electrons) in semiconductors, whereas with metals electrons are the only charge carriers.Conduction increases with temperature for semiconductors whereas conduction decreases with temperature for metals.

(iv)A circuit consists of a 3 Ω resistor and a 6 Ω resistor connected in parallel to a 1.5 V d.c. supply as shown. Calculate the total resistance of the two resistors.1/R = 1/3 + 1/6 1/R = 1/2 R = 2 Ω.

(v) Calculate the current flowing in the circuit. V = IR I = V/R I = 1.5/2 = 0.75 A

(vi)What is the current in the 3 Ω resistor?Voltages in parallel are the same and the supply voltage is in parallel with the 3 Ω resistor, so the voltage across the 3 Ω resistor is also 1.5 Volts I = 1.5/3 = 0.5 A

(vii) Semiconductors can be made p-type or n-type. How is a semiconductor made p-type?By doping it with Boron.

(viii) Draw a diagram showing a p-n junction connected in forward bias to a d.c. supply.

(ix)Give two uses of semiconductors. Rectifiers, transistors, diodes, thermistors, thermometers, radios/TV, etc.

Solutions to Higher Level questions

2011 Question 12 (c) [Higher Level](i) List the factors that affect the heat produced in a current-carrying conductor.

resistance, current (squared), time, (any valid answer)(ii) Calculate the maximum resistance per metre of the wire

R = 6.75 × 10-3 Ω(iii) Calculate the minimum diameter of the wire (resistivity of copper = 1.7 × 10–8 Ω m).

r = 9.0 × mdiameter = 1.8 ×10-3 m

2010 Question 8 [Higher Level](i) What is an electric current?

An electric current is a flow of charge (ii) Heating is one effect of an electric current. Give two other effects of an electric current.

Magnetic and chemical (iii) Describe what happens when switch A is closed and the rheostat is adjusted

The fan operates and its speed of rotation changes.(iv)Describe what happens when switch A and switch B are closed.

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Current flows through coil and the coil gets hot.The fan blows hot air

(v) Calculate the current that flows through the coil when the dryer is turned on.P = VII = P/V = 2000/230I = 8.7 A

(vi)What is the initial resistance of the coil?V = RIR = 230/8.7 = 26.4 Ω

(vii) Calculate the length of the coil of wire.A = πr2

A = (3.14)(0.085 × 10-3)2

A = 2.27 × 10-8 m2

ƿ = RA/ll = RA/ ƿ l = (26.4)( 2.27 × 10-8)/(1.1 × 10-6)l = 0.545 m

(viii) Explain why the current through the coil would decrease if the fan developed a fault and stopped working.The coil gets hot therefore its resistance increases (or any correct statement explaining why Rcct or Rcoil has increased)

2008 Question 7 [Higher Level](i) Define resistivity and give its unit of measurement.

Resistivity is defined as the resistance of a cube of material of side 1 m.(ii) What is the difference between convection and radiation as a means of heat transfer?

Convection requires a medium, radiation does not.(iii) Calculate the resistivity of nichrome.

= 12 × π (1.1 × 10-3)2 / 40 = 1.14 × 10-6 Ω m.

(iv)Calculate the heat generated by the toaster in 2 minutes if it has an efficiency of 96%. Heat generated = power × timeH = 1050 × 120 / 1.26 × 105 96% = 1.21 × 105 J

(v) The toaster has exposed metal parts. How is the risk of electrocution minimised? The metal parts are earthed.

(vi)Explain, in terms of movement of electrons, why light is emitted when a metal is heated. Electrons gain energy and jump to higher energy. Then when they fall back down they emit electromagnetic radiation in the form of light.

2007 Question 9 [Higher Level] (i) Define resistance.

The resistance of a conductor is the ratio of the potential difference across it to the current flowing through it.

(ii) Define resistivity.The resistivity of a material is defined as the resistance of a cube of material of side 1 m.

(iii) Calculate the resistance of the nichrome wireR1/R2= L1/L2 R/20 = 282/718

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R = 7.86 Ω(iv) Calculate the resistivity of nichrome

ρ =RA/L ρ = (7.844)(3.801× 10-8)/ 0.220ρ = 1.36 × 10-6 Ω m

(v) Sketch a graph to show the relationship between the temperature and the resistance of the nichrome wire as its temperature is increased.Axes labelled R and T (or θ)Correct linear graph with intercept showing R greater than zero.

(vi)What happens to the resistance of the wire as its temperature falls below 0oC?R decreases

(vii) What happens to the resistance of the wire as its length is increased?R increases

(viii) What happens to the resistance of the wire if its diameter is increased?R decreases

(ix)Name another device, apart from a metre bridge, that can be used to measure resistance. Ohmmeter / wheatstone bridge /multimeter.

(x) Give one advantage and one disadvantage of using this device instead of a metre bridge.Ohmmeter: compact, portable, faster method, etc. less accurate, fragile, difficult to calibrate/checWheatstone bridge: compact, portable, more accurate etc. ‘black box’ difficult to comprehend, expensive.

2005 Question 9 [Higher Level](i) Define potential difference.

Potential difference is the work done in bringing unit charge from one point to another.(ii) Define resistance.

Resistance of a conductor is the ratio of the potential difference across it to the current passing through it.

(iii) Derive an expression for the effective resistance of the two resistors in terms of R1 and R2.IT = I1 + I2

(apply Ohm’s law ) V = IR V/RT= V/R1+ V/R2

1/RT= 1/R1+ 1/R2

(iv)At room temperature calculate the total resistance of the circuit.1/Rp = 1/500 + 1/750 Rp = 300 Ω RTot = 600 Ω

(v) At room temperature calculate the current flowing through the 750 Ω resistor. ITotal = (VTot / RTot)/ = 6 ÷ 600 / = 0.01 A V300 = (0.01)(300) = 3 V Vp = 6 – 3 = 3 V.I750 = 3 ÷ 750 = 4 × 10-3 A = 4 mA

(vi)As the temperature of the room increases, explain why the resistance of the thermistor decreases.More energy is added to the thermistor therefore more electrons are released and are available for conduction.

(vii) As the temperature of the room increases, explain why the potential at A increases. The resistance of thermistor (and 750 Ω combination) decreases Therefore potential difference across thermistor and 750 Ω combination decreases Therefore potential at A increases

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2002 Question 8 [Higher Level](i) Define power.

Power is the rate at which work is done.(ii) Define resistivity.

Resistivity is the resistance of a cube of material of side one metre.(iii) Describe an experiment that demonstrates the heating effect of an electric current.

Connect a electrical calorimeter containing water to a power supply and notice the increase in temperature using a thermometer.

(iv)Calculate the total resistance of the cables.A = πr2 = π(.005)2

= RA/l R = l/A R = (5.0 × 10-8)(15000)/ π(.005)2 R = 9.6 (v) Calculate the current flowing in the cables.

W = VI I = W/V I =2 × 106/ 10 × 103 = 200 A(vi)Calculate the rate at which energy is “lost” in the cables.

P = I2R = (2002)(9.6) = 3.8 × 105 W(vii) Suggest a method of reducing the energy “lost” in the cables.

Higher voltage which means lower current, thicker cable for lower resistance

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Semiconductors

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2009 Question 12 (c) [Ordinary Level]A p-n junction (diode) is formed by doping adjacent layers of a semiconductor.A depletion layer is formed at their junction.(i) Explain the underlined terms. (ii) How is a depletion layer formed? (iii) The diagram shows two diodes connected to two bulbs A and B, a 6 V

supply and a switch. What is observed when the switch is closed? (iv)Explain why this happens.

2006 Question 12 (d) [Ordinary Level](i) A semiconductor material can be doped to form a p-n junction.

Explain the underlined terms.(ii) Name a material used as a semiconductor. (iii) The circuit diagram shows 2 semiconductor diodes and 2 bulbs, labelled A

and B,connected to a 6 V d.c. supply.What is observed when the switch is closed?

(iv)Explain why

2003 Question 11 [Ordinary Level]Read the following passage and answer the accompanying questions.The operation of semiconductor devices depends on the effects that occur when p-type and n-type semiconductor material are in close contact. This is achieved by taking a single crystal of silicon and doping separate but adjacent layers of it with suitable impurities. The junction between the p-type and the n-type layers is referred to as the p–n junction and this is the key to some very important aspects of semiconductor theory.Devices such as diodes, transistors, silicon-controlled rectifiers, etc., all contain one or more p–n junctions.(“Physics – a teacher’s handbook”, Dept. of Education and Science.)(a) What is a semiconductor? (b) Name a material used in the manufacture of semiconductors. (c) Name the two types of charge carriers in semiconductors. (d) What is meant by doping? (e) Give one difference between a p-type semiconductor and an n-type semiconductor. (f) What is a p-n junction? (g) What is a diode? (h) Give an example of a device that contains a rectifier.

2009 Question 12 (b) [Higher Level]A semiconductor diode is formed when small quantities of phosphorus and boron are added to adjacent layers of a crystal of silicon to increase its conduction.(i) Explain how the presence of phosphorus and boron makes the silicon a better conductor.(ii) What happens at the boundary of the two adjacent layers? (iii) Describe what happens at the boundary when the semiconductor diode is forward biased(iv)Describe what happens at the boundary when the semiconductor diode is reverse biased. (v) Give a use of a semiconductor diode.

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2004 Question 12 (d) [Higher Level](i) A p-n junction is formed by taking a single crystal of silicon and doping separate but adjacent layers of

it. A depletion layer is formed at the junction.What is doping?

(ii) Explain how a depletion layer is formed at the junction. (iii) The graph shows the variation of current I with potential difference V for a p-n

junction in forward bias. Explain, using the graph, how the current varies with the potential difference.

(iv)Why does the p-n junction become a good conductor as the potential difference exceeds 0.6 Volts?

Solutions2009 12 (b) (i) Explain how the presence of phosphorus and boron makes the silicon a better conductor.

When phosphorus is added more electrons become available as charge carriers. When boron is added more positive holes become available as charge carriers.

(ii) What happens at the boundary of the two adjacent layers? Electrons and holes cross the junction cancelling each other out and recombine and as a result there are no free charge carriers.A depletion layer is therefore formed between the n-type and p-type regions and as a result a junction voltage is created.

(iii) Describe what happens at the boundary when the semiconductor diode is forward biased.The depletion layer breaks down and the diode conducts.

(iv)Describe what happens at the boundary when the semiconductor diode is reverse biased. The width of depletion layer gets increased and the region acts as an insulator.

(v) Give a use of a semiconductor diode. Rectifier

2004 12 (d) (i) What is doping?

Doping is the addition of a small amount of atoms of another element to a pure semiconductor to increase its conductivity.

(ii) Explain how a depletion layer is formed at the junction. Electrons from n-type and holes from p-type cross the common junction and cancel out with charge carriers on the other side. As a result a narrow insulating region is formed which now acts as a ‘barrier’ or depletion layer.

(iii) Explain, using the graph, how the current varies with the potential difference.Very little current flows between 0 V and 0.6 VIf the potential difference is greater than 0.6 V a large current flows.

(iv)Why does the p-n junction become a good conductor as the potential difference exceeds 0.6 Volts?The depletion layer is overcome and as a result a large current flows.

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Magnetism and Electric Fields

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2006 Question 10 (b) [Ordinary Level](i) What is a magnetic field?(ii) Describe an experiment to show the magnetic field due to a current in a solenoid. (iii) A solenoid carrying a current and containing an iron core is known as an

electromagnet.Give one use of an electromagnet.

(iv)State one advantage of an electromagnet over an ordinary magnet.

2003 Question 9 [Ordinary Level](i) What is a magnetic field?(ii) The earth has a magnetic field. Give one use of the earth’s magnetic field.(iii) Hans Oersted discovered the magnetic effect of an electric current in 1820 while demonstrating

electricity to his students. Describe how you would demonstrate the magnetic effect of an electric current.

(iv)Draw a sketch of the magnetic field around a straight wire carrying a current. Your diagram should show the direction of the current and the direction of the magnetic field.

(v) In an experiment, a thin light conductor is placed between the poles of a U-shaped magnet as shown in the diagram.Describe what happens when a current flows through the conductor.

(vi)Name two devices that are based on the effect demonstrated in this experiment.(vii) What would happen if (i) a larger current flowed in the conductor, (ii) the current flowed in the

opposite direction through the conductor?

2002 Question 12 (d) [Ordinary Level](i) The diagram shows a U-shaped magnet. Copy the diagram and show on it the magnetic field

lines due to the magnet. (ii) Describe an experiment to demonstrate that a current-carrying conductor in a magnetic field

experiences a force.(iii) List two factors that affect the size of the force on the conductor.(iv)Name one device that is based on the principle that a current-carrying conductor in a magnetic

field experiences a force.

2006 Question 10 (a) [Ordinary Level]The diagram shows an experiment to demonstrate that a current-carrying conductor experiences a force in a magnetic field. A strip of aluminium foil is placed at right angles to a U-shaped magnet. The foil is connected in series with a battery and a switch.When the switch is closed the aluminium foil experiences an upward force.

(i) Name a device based on this effect. (ii) Describe what will happen if the current flows in the

opposite direction.(iii) Describe what will happen if a larger current flows

through the aluminium foil.(iv)Describe what will happen if the aluminium foil is

placed parallel to the magnetic field. (v) Calculate the force on the aluminium foil if its length is

10 cm and a current of 1.5 A flows through it when it is placed in a magnetic field of flux density 3.0 T. 2010 Question 11 [Ordinary Level]Read this passage and answer the questions below.In 1819 the Danish physicist Hans Christian Oersted discovered that an electric current flowing through a wire deflected a compass needle.A year later the Frenchman François Arago found that a wire carrying an electric current acted as a magnet and could attract iron filings. Soon his compatriot André-Marie Ampère demonstrated that two parallel

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wires were attracted towards one another if each had a current flowing through it in the same direction. However, the wires repelled each other if the currents flowed in the opposite directions.Intrigued by the fact that a flow of electricity could create magnetism, the great British experimentalist Michael Faraday decided to see if he could generate electricity using magnetism. He pushed a bar magnet in and out of a coil of wire and found an electric current being generated. The current stopped whenever the magnet was motionless within the coil.(Adapted from ‘Quantum' by Manjit Kumar, Icon Books 2008)

(i) Who discovered that an electric current can deflect a compass needle?(ii) What did Arago discover? (iii) What happens when currents flows in the same direction in two parallel wires?(iv)How could two parallel wires be made to repel each other? (v) Draw a sketch of the apparatus Michael Faraday used to generate electricity.(vi)What name is given to the generation of electricity discovered by Michael Faraday?(vii) What energy conversions that take place in Faraday’s experiment (viii) How does Faraday’s experiment show that a changing magnetic field is required to generate

electricity?

2009 question 9 [Ordinary Level]A magnetic field exists in the vicinity of a magnet. What is a magnetic field? (i) Describe an experiment to show the shape of the magnetic

field around a U-shaped magnet.(ii) The diagram shows a compass placed near a wire connected

to a battery and a switch.Why happens to the compass when the switch is closed?

(iii) What does this tell you about an electric current? (iv)What happens to the compass when the switch is opened? (v) The wire is then placed between the poles of a U-shaped magnet, as shown in the

diagram.Describe what happens to the wire when a current flows through it.

(vi)What would happen if the current flowed in the opposite direction?(vii) Name two devices that are based on this effect.

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Effects of an electric current

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2012 Question 8A plug is used to connect an electrical appliance in the home to the 230 volt mains supply.Modern plugs contain a small fuse which comes with a rating of 1A, 2A, 3A, 5A or 13A.The electrical energy supplied to the home is measured in kW h (kilowatt-hour).

(i) What is the colour of the wire that should be connected to the fuse in a plug? (ii) Why is there a fuse in a plug? (iii) Explain how a fuse works.

(iv)A vacuum cleaner has a power rating of 900 W.What is the most suitable fuse to use in the plug of the vacuum cleaner?

(v) Why is a fuse of a lower rating unsuitable? (vi)Name a device found in modern domestic circuits that has the same function as a fuse. (vii) If the vacuum cleaner is used for 90 minutes, calculate the number of units of electricity used.(viii) Calculate the cost of the energy used if the price of each unit of electricity is 22 cent.

2011 Question 12 (c)(i) What is an electric current, and give its unit of measurement?(ii) State the three effects of an electric current.(iii) How would you demonstrate one of the effects?(iv)An electric screwdriver has a power rating of 120 W when connected to its 24 V battery.

Calculate the current supplied by the battery when the screwdriver is turned on.

2010 Question 12 (c)The diagram shows a plug which contains a fuse, an MCB and an RCD, all of which are used in domestic circuits.

(i) Explain how a fuse works (ii) How does the fuse improve safety? (iii) What is an MCB?(iv)What is the function of an RCD? (v) Why should an appliance be earthed?(vi) Give one other precaution that should be taken to improve safety when using electricity in the home.

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2009 Question 8 [Ordinary Level]Plugs are used to connect electrical appliances in the home to the 230 volt ESB supply.Modern plugs contain a small fuse which comes with a rating of 1A, 2A, 3A, 5A or 13A.The electrical energy supplied by ESB to the home is measured in kWh (kilowatt-hour).

(i) What is the colour of the wire that should be connected to the fuse in a plug? (ii) What is the function of a fuse? (iii) Explain how a fuse works. (iv)Name another device with the same function as a fuse. (v) A coffee maker has a power rating of 800 W.

What is the most suitable fuse to use in the plug of the coffee maker? (vi)Why would it be dangerous to use a fuse with too high a rating? (vii) If the coffee maker was in use for 150 minutes:

Calculate the number of units of electricity used by the coffee maker. (viii) Calculate the cost of the electricity used if each unit costs 15 cent.

2006 Question 11 [Ordinary Level]Read this passage and answer the questions below.Electricity is so much part of modern living that we often take it for granted. It is a powerful and versatile energy of great use in the home but can be dangerous if not used properly. The electricity connection into your home comes through the ESB main fuse and the ESB meter. Almost all new electrical appliances now come complete with a fitted 13 Amp, 3-pin plug. Remember, a wrongly wired plug can result in a serious or fatal accident. The first thing to know is the colour code for connecting the cables to the appropriate pin/terminal in the plug. The cables consist of a metal conductor covered in coloured plastic.When wiring a plug it is most important that all the screw connections are fully tightened. You should leave a little extra slack on the earth wire. You must also fit the correct size fuse. When an appliance is double insulated it does not need to be earthed. These appliances will only have two wires, the brown live and the blue neutral, they do not have an earth wire.(Adapted from The Safe Use Of Electricity In The Home by The ESB.)(a) Give one use for electricity in the home. (b) What is the function of the ESB meter?(c) What will happen when a current of 20 A flows through a fuse marked 13 A? (d) Give one safety precaution that should be taken when wiring a plug. (e) What is the colour of the earth wire in an electric cable? (f) Name a common material used to conduct electricity in electric cables.(g) Why is the coating on electric cables made from plastic? (h) Why are some appliances not earthed?

2004 Question 9 [Ordinary Level](i) What is an electric current?(ii) An electric current can cause a heating effect. Name two other effects of an electric current.(iii) Describe an experiment to show the heating effect of an electric current.(iv)State two factors on which the heating effect of an electric current depends. (v) An electric heater has a power rating of 2 kW when connected to the ESB mains supply of 230 V.

Calculate the current that flows through the heater.(vi)What is the kilowatt-hour?(vii) Calculate the cost of using a 2 kW electric heater for 3 hours at 10 cent per kilowatt-hour.

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2003 Question 8 [Ordinary Level](i) What is an electric current? (ii) Give the standard colour of the insulation on the wires connected to each of the

terminals L, N and E on the plug in the diagram. (iii) What is the purpose of the wire connected to the terminal E on the plug?(iv)Explain why a fuse is used in a plug.(v) The fuse in the plug of an electric kettle was replaced with a 5 A fuse. The kettle has a

power rating of 2 kW when connected to the ESB mains voltage of 230 V.Calculate the current that flows when the kettle is first plugged in.

(vi)This current will only flow for a very short time. Explain why. (vii) Bonding is a safety precaution used in domestic electric circuits

How does bonding improve safety in the home?(viii) Name a device that is often used nowadays in domestic electric circuits instead of fuses.

2005 Question 8 (a) [Ordinary Level](x) State Ohm’s Law. (xi)The graphs show how current (I ) varies with potential

difference (V) for (a) a metal, (b) a filament bulb.Which conductor obeys Ohm’s law?

(xii) Explain your answer.

2006 Question 9 Higher Level(i) What is an electric current? (ii) Define the ampere, the SI unit of current. (iii) Describe an experiment to demonstrate the principle on which the definition of the ampere is based. (iv)Sketch a graph to show the relationship between current and time for

a) alternating current;b) direct current.

(v) The peak voltage of the mains electricity is 325 V. Calculate the rms voltage of the mains.(vi)What is the resistance of the filament of a light bulb, rated 40 W, when it is connected to the mains?(vii) Explain why the resistance of the bulb is different when it is not connected to the mains.

2003 Question 8 Higher Level(i) Define the unit of current, i.e. the ampere. (ii) Describe an experiment to demonstrate the principle on which the definition of the ampere is based.(iii) Various materials conduct electricity. Draw a graph to show the relationship between current and

voltage for each of the following conductors:a) a metal at constant temperatureb) an ionic solution with inactive electrodesc) a gas.

(iv)How would the graph for the metal differ if its temperature were increasing? (v) How would the graph for the ionic solution differ if its concentration were reduced?

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Magnets and Magnetic Fields

2006 Question 10 (b)(v) What is a magnetic field?(vi)Describe an experiment to show the magnetic field due to a current in a solenoid. (vii) A solenoid carrying a current and containing an iron core is known as an

electromagnet.Give one use of an electromagnet.

(viii) State one advantage of an electromagnet over an ordinary magnet.

2003 Question 9(viii) What is a magnetic field?(ix)The earth has a magnetic field. Give one use of the earth’s magnetic field.(x) Hans Oersted discovered the magnetic effect of an electric current in 1820 while demonstrating

electricity to his students. Describe how you would demonstrate the magnetic effect of an electric current.

(xi)Draw a sketch of the magnetic field around a straight wire carrying a current. Your diagram should show the direction of the current and the direction of the magnetic field.

(xii) In an experiment, a thin light conductor is placed between the poles of a U-shaped magnet as shown in the diagram.Describe what happens when a current flows through the conductor.

(xiii) Name two devices that are based on the effect demonstrated in this experiment.(xiv) What would happen if (i) a larger current flowed in the conductor, (ii) the current flowed in the

opposite direction through the conductor?

2002 Question 12 (d)(v) The diagram shows a U-shaped magnet. Copy the diagram and show on it the magnetic field

lines due to the magnet. (vi)Describe an experiment to demonstrate that a current-carrying conductor in a magnetic field

experiences a force.(vii) List two factors that affect the size of the force on the conductor.(viii) Name one device that is based on the principle that a current-carrying conductor in a

magnetic field experiences a force.

10 (a)The diagram shows an experiment to demonstrate that a current-carrying conductor experiences a force in a magnetic field. A strip of aluminium foil is placed at right angles to a U-shaped magnet. The foil is connected in series with a battery and a switch.When the switch is closed the aluminium foil experiences an upward force.

(vi)Name a device based on this effect. (vii) Describe what will happen if the current flows in the

opposite direction;(viii) Describe what will happen if a larger current flows

through the aluminium foil;(ix)Describe what will happen if the aluminium foil is

placed parallel to the magnetic field. (x) Calculate the force on the aluminium foil if its length is

10 cm and a current of 1.5 A flows through it when it is placed in a magnetic field of flux density 3.0 T.

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2010 Question 11Read this passage and answer the questions below.In 1819 the Danish physicist Hans Christian Oersted discovered that an electric current flowing through a wire deflected a compass needle.A year later the Frenchman François Arago found that a wire carrying an electric current acted as a magnet and could attract iron filings. Soon his compatriot André-Marie Ampère demonstrated that two parallel wires were attracted towards one another if each had a current flowing through it in the same direction. However, the wires repelled each other if the currents flowed in the opposite directions.Intrigued by the fact that a flow of electricity could create magnetism, the great British experimentalist Michael Faraday decided to see if he could generate electricity using magnetism. He pushed a bar magnet in and out of a coil of wire and found an electric current being generated. The current stopped whenever the magnet was motionless within the coil.(Adapted from ‘Quantum' by Manjit Kumar, Icon Books 2008)

(ix)Who discovered that an electric current can deflect a compass needle?(x) What did Arago discover? (xi)What happens when currents flows in the same direction in two parallel wires?(xii) How could two parallel wires be made to repel each other? (xiii) Draw a sketch of the apparatus Michael Faraday used to generate electricity.(xiv) What name is given to the generation of electricity discovered by Michael Faraday?(xv) What energy conversions that take place in Faraday’s experiment (xvi) How does Faraday’s experiment show that a changing magnetic field is required to generate

electricity?

2009 question 9. A magnetic field exists in the vicinity of a magnet. What is a magnetic field? (viii) Describe an experiment to show the shape of the

magnetic field around a U-shaped magnet.(ix)The diagram shows a compass placed near a wire connected

to a battery and a switch.Why happens to the compass when the switch is closed?

(x) What does this tell you about an electric current? (xi)What happens to the compass when the switch is opened? (xii) The wire is then placed between the poles of a U-shaped magnet, as shown in

the diagram.Describe what happens to the wire when a current flows through it.

(xiii) What would happen if the current flowed in the opposite direction?(xiv) Name two devices that are based on this effect.

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The Electron

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Cathode Ray Tube

2002 Question 6 [Ordinary Level](i) What is thermionic emission?(ii) The diagram shows a simple cathode ray tube. (iii) Name the parts labelled A, B, C and D in

the diagram. (iv)Give the function of any two of these parts. (v) How can the beam of electrons be deflected?(vi)Give a use of a cathode ray tube. (vii) In an X-ray tube, electrons are also produced by thermionic emission. (viii) Draw a sketch of an X-ray tube. (ix)Why is a lead-shield normally put around an X-ray tube?

2005 Question 10 [Ordinary Level](i) The electron is one of the three main subatomic

particles.Give two properties of the electron.

(ii) Name another subatomic particle.(iii) The diagram shows a simple cathode ray tube.

Name the parts labelled A, B and C. (iv)Electrons are emitted from A, accelerated across the

tube and strike the screen.Explain how the electrons are emitted from A.

(v) What causes the electrons to be accelerated across the tube? (vi)What happens when the electrons hit the screen?(vii) How can a beam of electrons be deflected? (viii) Give one use of a cathode ray tube.

2009 Question 12 (d) [Ordinary Level](i) The diagram shows a simple cathode ray tube.

Thermionic emission occurs at plate A.(ii) What is thermionic emission?(iii) What are cathode rays? (iv)Why is there a high voltage between A and B?(v) What happens to the cathode rays when they hit the

screen C? (vi)Give a use for a cathode ray tube.

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2012 Question 10 [Ordinary Level]A cathode ray tube and an X-ray tube are practical applications of thermionic emission. In these tubes thermionic emission releases electrons, which are then accelerated into a beam.An electron is a subatomic particle.(i) Name another subatomic particle and give two of its properties. (ii) The diagram shows a simple cathode ray tube.

Name the parts labelled A, B, C. (iii) Give the function of any two of these labelled parts. (iv)How can the beam of electrons be deflected? (v) What happens at C when the electrons hit it? (vi)Why is a vacuum needed in a cathode ray tube? (vii) In an X-ray tube, a beam of electrons is used to produce X-rays.Draw a sketch of an X-ray tube. (viii) Give one safety precaution taken by a radiographer when using an X-ray machine.

2003 Question 9(i) List two properties of the electron.(ii) Name the Irishman who gave the electron its name in the nineteenth

century. (iii) Give an expression for the force acting on a charge q moving at a

velocity v at right angles to a magnetic field of flux density B. (iv)An electron is emitted from the cathode and accelerated through a

potential difference of 4kV in a cathode ray tube (CRT) as shown in the diagram.How much energy does the electron gain?

(v) What is the speed of the electron at the anode? (Assume that the speed of the electron leaving the cathode is negligible.)

(vi)After leaving the anode, the electron travels at a constant speed and enters a magnetic field at right angles, where it is deflected. The flux density of the magnetic field is 5 × 10–2 T.Calculate the force acting on the electron.

(vii) Calculate the radius of the circular path followed by the electron, in the magnetic field.(viii) What happens to the energy of the electron when it hits the screen of the CRT?

mass of electron = 9.1 × 10–31 kg; charge on electron = 1.6 × 10–19 CThe Photoelectric Effect / The Photocell

201l Question 11 [Ordinary Level]Read this passage and answer the questions below.Einstein explained the photoelectric effect by using Planck’s quantum theory (E=hf).The German physicist Heinrich Hertz in 1887 was the first to discover that when light shines on certain metals, they emit electrons.

Metals have the property that some of their electrons are only loosely bound within atoms, which is why they are such good conductors of electricity. When light strikes a metallic surface it transfers its energy to the metal, in the same way as when light shines on your skin, causing you to feel warmer. This transfer of energy from the light can agitate electrons in the metal, and some of the loosely bound electrons can be knocked off the surface of the metal.

But the strange features of the photoelectric effect become apparent when one studies the more detailed properties of the released electrons. As the intensity of the light – its brightness – is increased the number of released electrons will also increase, but their speed stays the same. On the other hand, the speed of the released electrons will increase if the frequency of the light shining on the metal is increased.(Adapted from ‘Elegant Universe' by Brian Greene, Vintage 2000)

a) Who discovered the photoelectric effect?

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b) Who explained the photoelectric effect?c) What happens when light shines on certain metals?d) Why is a metal a good conductor of electricity?e) Why does your skin feel warm when light shines on it?f) In the photoelectric effect, what happens when the intensity of the light is increased?g) How can the speed of electrons emitted in the photoelectric effect be controlled?h) Give one application of the photoelectric effect.

2006 Question 12 (c) [Ordinary Level] (i) In an experiment to demonstrate the photoelectric effect, a piece of zinc is placed on a gold leaf

electroscope, as shown. The zinc is given a negative charge causing the gold leaf to deflect.Explain why the gold leaf deflects when the zinc is given a negative charge.

(ii) Ultraviolet radiation is then shone on the charged zinc and the gold leaf falls.Explain why.

(iii) What is observed when the experiment is repeated using infrared radiation? (iv)Give one application of the photoelectric effect.

2005 Question 12 (d) [Higher Level](i) One hundred years ago, Albert Einstein explained the photoelectric effect.

What is the photoelectric effect? (ii) Write down an expression for Einstein’s photoelectric law. (iii) Summarise Einstein’s explanation of the photoelectric effect.(iv)Give one application of the photoelectric effect.

2004 Question 9 [Higher Level](i) Distinguish between photoelectric emission and thermionic emission. (ii) A freshly cleaned piece of zinc metal is placed on the cap of a negatively charged gold leaf electroscope

and illuminated with ultraviolet radiation. Explain why the leaves of the electroscope collapse.

(iii) Explain why the leaves do not collapse when the zinc is covered by a piece of ordinary glass.(iv)Explain why the leaves do not collapse when the zinc is illuminated with green light.(v) Explain why the leaves do not collapse when the electroscope is charged positively. (vi)The zinc metal is illuminated with ultraviolet light of wavelength 240 nm. The work function of zinc is

4.3 eV.Calculate the threshold frequency of zinc.

(vii) Calculate the maximum kinetic energy of an emitted electron.

Planck’s constant = 6.6 × 10–34 J s; speed of light = 3.0 × 108 m s–1; 1 eV = 1.6 × 10–19 J

2003 Question 12 (d) [Ordinary Level](i) What is a photon?(ii) The diagram shows a photocell connected in series with a sensitive

galvanometer and a battery. Name the parts labelled A and B.(iii) What happens at A when light falls on it?(iv)What happens in the circuit when the light falling on A gets brighter?(v) Give an application of a photocell.

2008 Question 12 (c) [Ordinary Level](i) What is the photoelectric effect? (ii) A photocell is connected to a sensitive galvanometer as shown in the diagram.

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(iii) When light from the torch falls on the photocell, a current is detected by the galvanometer.(iv)Name the parts of the photocell labelled A and B. (v) How can you vary the brightness of the light falling on the photocell?(vi)How does the brightness of the light effect the current? (vii) Give a use for a photocell.

2012 Question 12 (d) [Higher Level](i) Draw a diagram to show the structure of a photocell. (ii) Describe an experiment to demonstrate how the current through a photocell can be increased. (iii) Give an application of the photoelectric effect.

2009 Question 8 [Higher Level](i) An investigation was carried out to establish the relationship between the current

flowing in a photocell and the frequency of the light incident on it. The graph illustrates the relationship.Draw a labelled diagram of the structure of a photocell.

(ii) Using the graph, calculate the work function of the metal.(iii) What is the maximum speed of an emitted electron when light of wavelength

550 nm is incident on the photocell?(iv)Explain why a current does not flow in the photocell when the frequency of the

light is less than 5.2 × 1014 Hz.(v) The relationship between the current flowing in a photocell and the intensity of

the light incident on the photocell was then investigated. Readings were taken and a graph was drawn to show the relationship.

(vi)Draw a sketch of the graph obtained. (vii) How was the intensity of the light varied?(viii) What conclusion about the nature of light can be drawn from these investigations?

(Planck constant = 6.6 × 10–34 J s; speed of light = 3.0 × 108 m s–1; charge on electron = 1.6 × 10–19 C; mass of electron = 9.1 × 10–31 kg)X-Rays2004 Question 12 (d) [Ordinary Level](i) The diagram shows an X-ray tube.

What are X-rays?(ii) How are electrons emitted from the cathode C? (iii) What is the function of the high voltage across the X-ray

tube?(iv)Name a suitable material for the target T in the X-ray tube.(v) Give one use of X-rays.

2007 Question 10 [Ordinary Level]X-rays were discovered by Wilhelm Röntgen in 1895.(i) What are X-rays? (ii) Give one use for X-rays. (iii) The diagram shows a simple X-ray tube.

Name the parts labelled A, B and C. (iv)Electrons are emitted from A, accelerated across the tube and

strike B. Explain how the electrons are emitted from A. (v) What is the purpose of the high voltage supply? (vi)What happens when the electrons hit part B? (vii) Name a suitable material to use for part B. (viii) Give one safety precaution when using X-rays.

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2010 Question 10 [Ordinary Level]X-rays are produced when high speed electrons collide with a target in an X-ray tube as shown in the diagram.(i) What process occurs at the filament A?(ii) Name a substance commonly used as the target B (iii) Give three properties of X-rays(iv)Give two uses of X-rays(v) State the function of the part marked C(vi)The photoelectric effect can be regarded as the inverse of

X-ray production.(vii) Describe an experiment to demonstrate the photoelectric effect (viii) Give two applications of the photoelectric effect

2010 Question 9 [Higher Level](i) What is thermionic emission?(ii) X-rays are produced when high-energy electrons collide with a target.

Draw a labelled diagram of an X-ray tube.(iii) What are X-rays? (iv)How do they differ from light rays?(v) Give two uses of X-rays.(vi)When electrons hit the target in an X-ray tube, only a small percentage of their energy is converted into

X-rays. What happens to the rest of their energy.(vii) How does this influence the type of target used?(viii) A potential difference (voltage) of 40 kV is applied across an X-ray tube.

Calculate the maximum energy of an electron as it hits the target.(ix)Calculate the frequency of the most energetic X-ray produced.

2006 Question 12 (d) [Higher Level]The first Nobel Prize in Physics was awarded in 1901 for the discovery of X-rays.(i) What are X-rays? (ii) Who discovered them?(iii) In an X-ray tube electrons are emitted from a metal cathode and accelerated across the tube to hit a

metal anode.How are the electrons emitted from the cathode?

(iv)How are the electrons accelerated? (v) Calculate the kinetic energy gained by an electron when it is accelerated through a potential difference of

50 kV in an X-ray tube.(vi)Calculate the minimum wavelength of an X-ray emitted from the anode.

Planck constant = 6.6 × 10–34 J s; speed of light = 3.0 × 108 m s–1; charge on electron = 1.6 × 10–19 C

2002 Question 9 [Higher Level](ii) Explain with the aid of a labelled diagram how X-rays are produced.(iii) Justify the statement “X-ray production may be considered as the inverse of the photoelectric effect.” (iv)Describe an experiment to demonstrate the photoelectric effect. (v) Outline Einstein’s explanation of the photoelectric effect. (vi)Give two applications of a photocell.

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Solutions to higher level questions

2012 Question 12 (d)(i) Draw a diagram to show the structure of a photocell.

See diagram

(ii) Describe an experiment to demonstrate how the current through a photocell can be increased.

1. Set us as shown in diagram.2. Bring the light source closer to the photocell.3. The current in the circuit increases.

(iii) Give an application of the photoelectric effect.Controlling the flame in central heating boilers / automatic doors / fire alarms / photocells / photocopiers / light meters, etc.

2010 Question 9(i) What is thermionic emission?

It is the emission of electrons from the surface of a hot metal.(ii) X-rays are produced when high-energy electrons collide with a target.

Draw a labelled diagram of an X-ray tube.Vacuum Cathode Target / anode High (accelerating anode) voltage or H.T. / shielding / cooling / low (cathode) voltage or L.T.

(iii) What are X-rays? X-rays are electromagnetic radiation of high frequency / short wavelength

(iv)How do they differ from light rays?X-rays penetrate matter / cause ionization.

(v) Give two uses of X-rays.(Medical) analysis of bone structure/ luggage scanners (at airports) / any specific medical, industrial or security use, etc.

(vi)When electrons hit the target in an X-ray tube, only a small percentage of their energy is converted into X-rays. What happens to the rest of their energy.The energy gets converted to heat.

(vii) How does this influence the type of target used?The target material must have (very) high melting point.

(viii) A potential difference (voltage) of 40 kV is applied across an X-ray tube.Calculate the maximum energy of an electron as it hits the target.W = qVW = (1.6 × 10-19)( 40 × 103)W = 6.4 × 10-15 J

(ix)Calculate the frequency of the most energetic X-ray produced.E = hff = E/hf = (6.4 × 10-15)/(6.6 × 10-34)f = 9.7 × 1018 Hz

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2009 Question 8(i) What is a photon?

A photon consists of a discrete (specific) amount of energy/electromagnetic radiation.

(ii) Draw a labelled diagram of the structure of a photocell. See diagram; A = cathode, B = anodeAlso label glass case and vacuum inside

(iii) Using the graph, calculate the work function of the metal.The graph indicates that current only flows when the frequency of the radiation reached 5.2 × 1014 Hz, so this corresponds to the threshold frequency (f0). = hf0 = (6.6 × 10-34)(5.2 × 1014) = 3.432 × 10-19 J

(iv)What is the maximum speed of an emitted electron when light of wavelength 550 nm is incident on the photocell?h(c/λ) = + ½mv2

(6.6 × 10-34)(3 × 108/550 × 10-9) = 3.432 × 10-19 + ½ (9.1× 10-31)(v)2

v = 1.922 × 105 m s-1

(v) Explain why a current does not flow in the photocell when the frequency of the light is less than 5.2 × 1014 Hz.Because the frequency is less than the threshold frequency so does not contain enough energy to cause an electron to be released from an atom.

(vi)The relationship between the current flowing in a photocell and the intensity of the light incident on the photocell was then investigated. Readings were taken and a graph was drawn to show the relationship.Draw a sketch of the graph obtained. Current is directly proportional to Intensity, so a straight line graph with the line going through the origin is required.

(vii) How was the intensity of the light varied?Vary the distance from the light source to the photocell.

(viii) What conclusion about the nature of light can be drawn from these investigations? Light is made up of discrete amounts of energy called photons.

2006 Question 12 (d)(i) What are X-rays? High frequency electromagnetic radiation.(ii) Who discovered them?Rontgen(iii) In an X-ray tube electrons are emitted from a metal cathode and accelerated across the tube to

hit a metal anode. How are the electrons emitted from the cathode?By thermionic emission.

(iv)How are the electrons accelerated? By the high voltage between the anode and cathode.

(v) Calculate the kinetic energy gained by an electron when it is accelerated through a potential difference of 50 kV in an X-ray tube.Ek (= W) = q V = (1.6 × 10-19)(50 × 103) = 8.0 × 10-15 J

(vi)Calculate the minimum wavelength of an X-ray emitted from the anode. E = h c/λ λ = [6.6 × 10-34 × 3.0 × 108] /(8.0 × 10-15)

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2005 Question 12 (d) (i) One hundred years ago, Albert Einstein explained the photoelectric effect.

What is the photoelectric effect? The photoelectric effect is the emission of electrons from the surface of a metal when light of suitable frequency / energy shines on it.

(ii) Write down an expression for Einstein’s photoelectric law. hf = φ + ½mv2

(iii) Summarise Einstein’s explanation of the photoelectric effect.Light is composed of packets (or bundles) of energy which he called photons. All of energy from one photon is given to one electron.Energy must be greater than the work function of the metal for the photoelectric effect to occur.

(iv)Give one application of the photoelectric effect. Sound track in film, photography, counters, photocell, burglar alarm, automatic doors, etc.

2004 Question 9(i) Distinguish between photoelectric emission and thermionic emission.

Photoelectric Effect: Emission of electrons when light of suitable frequency falls on a metal.Thermionic Emission: Emission of electrons from the surface of a hot metal.

(ii) A freshly cleaned piece of zinc metal is placed on the cap of a negatively charged gold leaf electroscope and illuminated with ultraviolet radiation. Explain why the leaves of the electroscope collapse. Photoelectric emission occurs (electrons get emitted from the surface of the metal). The leaves become uncharged and therefore collapse.

(iii) Explain why the leaves do not collapse when the zinc is covered by a piece of ordinary glass.Ordinary glass does not transmit UV light

(iv)Explain why the leaves do not collapse when the zinc is illuminated with green light.The energy associated with photons of green light is too low for the photoelectric effect does not occur, so no electrons are emitted from the electroscope.

(v) Explain why the leaves do not collapse when the electroscope is charged positively. Any electrons emitted are attracted back to the positive electroscope.

(vi)The zinc metal is illuminated with ultraviolet light of wavelength 240 nm. The work function of zinc is 4.3 eV. Calculate the threshold frequency of zinc. = (4.3) eV = (4.3)( 1.6 × 10–19) JE = hf0 f0 = (4.3)( 1.6 × 10–19)/ 6.6 × 10–34 = 1.04 × 1015 Hz

(vii) Calulate the maximum kinetic energy of an emitted electron. c = fλ f = c/λ = (3.0 × 108)/(240 × 109) = 1.25 × 1015 HzEk = hf - Ek = (6.6 × 10–34)[( 1.25 × 1015) - 1.04 × 1015)] = 1.39 × 10-19

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2003 Question 9(i) List two properties of the electron.

Negative charge, negligible mass , orbits nucleus, deflected by electric / magnetic field etc.(ii) Name the Irishman who gave the electron its name in the nineteenth century.

George Stoney(iii) Give an expression for the force acting on a charge q moving at a velocity v at right angles to a

magnetic field of flux density B. F = Bqv

(iv)An electron is emitted from the cathode and accelerated through a potential difference of 4kV in a cathode ray tube (CRT) as shown in the diagram.How much energy does the electron gain? The final kinetic energy gained by the electron equals the initial (electrical) potential energy = 4 KeV = (4000)(1.6 × 10–19) = 6.4×10−16 J

(v) What is the speed of the electron at the anode? (Assume that the speed of the electron leaving the cathode is negligible.) E = ½ mv2 6.4 ×10-16 = ½ (9.1 × 10-31)(v2) v =3.75 × 107 m s-1

(vi)After leaving the anode, the electron travels at a constant speed and enters a magnetic field at right angles, where it is deflected. The flux density of the magnetic field is 5 × 10–2 T.Calculate the force acting on the electron.F = Bev = (5 × 10–2)(1.6 × 10–19)( 3.75 × 107) = 3.0 ×10−13 N

(vii) Calculate the radius of the circular path followed by the electron, in the magnetic field.F = mv2/r 3.0 ×10−13 = (9.1 × 10–31)( 3.75 × 107)2/r r = 4.3×10−3 m

(viii) What happens to the energy of the electron when it hits the screen of the CRT?It gets converted to light.

2002 Question 9(i) Explain with the aid of a labelled diagram how X-rays

are produced.A = Hot cathode B = target Also label vacuum, shield, cooling, window

(ii) Justify the statement “X-ray production may be considered as the inverse of the photoelectric effect.” X-ray: Electrons in, electromagnetic radiation is emitted.Photoelectric: electromagnetic radiation in and electrons are emitted.

(iii) Describe an experiment to demonstrate the photoelectric effect. Apparatus: gold leaf electroscope with zinc plate on top, ultraviolet light source Procedure: Charge the electroscope negatively.

Shine ultraviolet light on the zinc plate.Observation: The leaves fall together

(iv)Outline Einstein’s explanation of the photoelectric effect. Electromagnetic radiation consists of packets of energy which he called quanta. The amount of energy in each quantum could be calculated using the formula E = hf The incoming radiation needs to have sufficient energy to release an electron from the surface of a

metal or it won’t be absorbed at all. If the incoming energy has more energy than an electron needs to be released (called its work

function) then the excess energy goes to the kinetic energy of the electron.(v) Give two applications of a photocell.

Burglar alarm, smoke alarms, safety switch. light meters, automatic lights, counters, automatic doors, control of central heating burners, sound track in films, scanner reading bar codes, stopping conveyer belt

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Electromagnetic Induction

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2010 Question 11 [Ordinary Level]Read this passage and answer the questions below.In 1819 the Danish physicist Hans Christian Oersted discovered that an electric current flowing through a wire deflected a compass needle.A year later the Frenchman François Arago found that a wire carrying an electric current acted as a magnet and could attract iron filings. Soon his compatriot André-Marie Ampère demonstrated that two parallel wires were attracted towards one another if each had a current flowing through it in the same direction. However, the wires repelled each other if the currents flowed in the opposite directions.Intrigued by the fact that a flow of electricity could create magnetism, the great British experimentalist Michael Faraday decided to see if he could generate electricity using magnetism. He pushed a bar magnet in and out of a coil of wire and found an electric current being generated. The current stopped whenever the magnet was motionless within the coil.(Adapted from ‘Quantum' by Manjit Kumar, Icon Books 2008)(xvii) Who discovered that an electric current can deflect a compass needle?(xviii) What did Arago discover? (xix) What happens when currents flows in the same direction in two parallel wires?(xx) How could two parallel wires be made to repel each other? (xxi) Draw a sketch of the apparatus Michael Faraday used to generate electricity.(xxii) What name is given to the generation of electricity discovered by Michael Faraday?(xxiii) What energy conversions that take place in Faraday’s experiment (xxiv) How does Faraday’s experiment show that a changing magnetic field is required to generate

electricity?

2011 Question 9 (a) [Ordinary Level] State Faraday’s law of electromagnetic induction. A coil of wire is connected to a sensitive meter, as shown in the diagram.(i) What is observed on the meter when the magnet is moved towards the coil? (ii) What is observed on the meter when the magnet is stationary in the coil? (iii) Explain these observations. (iv)How would changing the speed of the magnet affect the observations?

2005 Question 9 [Ordinary Level](i) What is a magnetic field?(ii) Draw a sketch of the magnetic field around a bar magnet. (iii) Describe an experiment to show that a current carrying conductor in a magnetic field experiences a

force.(iv)List two factors that affect the size of the force on the conductor. (v) A coil of wire is connected to a sensitive galvanometer as shown in the diagram.

What is observed when the magnet is moved towards the coil? (vi)Explain why this occurs.(vii) Describe what happens when the speed of the magnet is increased. (viii) Give one application of this effect.

2008 Question 12 (d) [Ordinary Level](i) What is electromagnetic induction? (ii) A magnet and a coil can be used to produce electricity.(iii) How would you demonstrate this? (iv)The electricity produced is a.c. What is meant by a.c.?

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2006 Question 11 [Higher Level] Read the following passage and answer the accompanying questions.

The growth of rock music in the 1960s was accompanied by a switch from acoustic guitars to electric guitars. The operation of each of these guitars is radically different.The frequency of oscillation of the strings in both guitars can be adjusted by changing their tension. In the acoustic guitar the sound depends on the resonance produced in the hollow body of the instrument by the vibrations of the string. The electric guitar is a solid instrument and resonance does not occur.Small bar magnets are placed under the steel strings of an electric guitar, as shown. Each magnet is placed inside a coil and it magnetises the steel guitar string immediately above it. When the string vibrates the magnetic flux cutting the coil changes, an emf is induced causing a varying current to flow in the coil. The signal is amplified and sent to a set of speakers.Jimi Hendrix refined the electric guitar as an electronic instrument. He showed that further control over the music could be achieved by having coils of different turns.(Adapted from Europhysics News (2001) Vol. 32 No. 4)

(a) How does resonance occur in an acoustic guitar? (b) What is the relationship between frequency and tension for a stretched string? (c) A stretched string of length 80 cm has a fundamental frequency of vibration of 400 Hz.

What is the speed of the sound wave in the stretched string? (d) Why must the strings in the electric guitar be made of steel? (e) Define magnetic flux. (f) Why does the current produced in a coil of the electric guitar vary? (g) What is the effect on the sound produced when the number of turns in a coil is increased? (h) A coil has 5000 turns. What is the emf induced in the coil when the magnetic flux cutting the coil

changes by 8 × 10–4 Wb in 0.1 s?

2005 Question 12 (b) [Higher Level](i) Define magnetic flux. (ii) State Faraday’s law of electromagnetic induction. (iii) A square coil of side 5 cm lies perpendicular to a magnetic field of flux density 4.0 T.

The coil consists of 200 turns of wire.What is the magnetic flux cutting the coil?

(iv)The coil is rotated through an angle of 90o in 0.2 seconds. Calculate the magnitude of the average e.m.f. induced in the coil while it is being rotated.

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2008 Question 8(i) What is electromagnetic induction?(ii) State the laws of electromagnetic induction. (iii) A bar magnet is attached to a string and allowed to swing as shown in the diagram.

A copper sheet is then placed underneath the magnet.Explain why the amplitude of the swings decreases rapidly.

(iv)What is the main energy conversion that takes place as the magnet slows down? (v) A metal loop of wire in the shape of a square of side 5 cm enters a magnetic field of flux

density 8 T.The loop is perpendicular to the field and is travelling at a speed of 5 m s–1.How long does it take the loop to completely enter the field?

(vi)What is the magnetic flux cutting the loop when it is completely in the magnetic field?(vii) What is the average emf induced in the loop as it enters the magnetic field?

2004 Question 12 (c) (i) What is electromagnetic induction?(ii) Describe an experiment to demonstrate electromagnetic induction. (iii) A light aluminium ring is suspended from a long thread as shown in the diagram.

When a strong magnet is moved away from it, the ring follows the magnet. Explain why.

(iv)What would happen if the magnet were moved towards the ring?

2003 Question 12 (d)(i) State the laws of electromagnetic induction. (ii) A small magnet is attached to a spring as shown in the diagram.

The magnet is set oscillating up and down. Describe the current flowing in the circuit.

(iii) If the switch at A is open, the magnet will take longer to come to rest. Explain why.

Self-Induction2007 Question 12 (c) [Higher Level](i) State Faraday’s law of electromagnetic induction. (ii) Describe an experiment to demonstrate Faraday’s law. (iii) A resistor is connected in series with an ammeter and an ac power supply. A current flows in the

circuit. The resistor is then replaced with a coil. The resistance of the circuit does not change.What is the effect on the current flowing in the circuit? Justify your answer.

2002 Question 12 (c) [Higher Level](i) What is meant by electromagnetic induction? (ii) State Lenz’s law of electromagnetic induction. (iii) In an experiment, a coil was connected in series with an ammeter and an

a.c. power supply as shown in the diagram. Explain why the current was reduced when an iron core was inserted in the coil.

(iv)Give an application of the principle shown by this experiment.

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Transformers

2002 Question 9 [Ordinary Level] (i) What is electromagnetic induction? (ii) Describe an experiment to demonstrate electromagnetic induction. (iii) The transformer is a device based on the principle of electromagnetic

induction. Name two devices that use transformers.

(iv)Name the parts of the transformer labelled A, B and C in the diagram. (v) The mains electricity supply (230 V) is connected to A, which has 400 turns. C has 100 turns.

What is the reading on the voltmeter? (vi)How is the part labelled B designed to make the transformer more efficient? (vii) The efficiency of a transformer is 90%. What does this mean?

2004 Question12 (c) [Ordinary Level] (i) A transformer is a device based on the principle of

electromagnetic induction.(ii) What is electromagnetic induction?(iii) Name another device that is based on electromagnetic

induction. (iv)Name the parts of the transformer labelled A, B and C in the

diagram. (v) Part A has 400 turns of wire and part B has 1200 turns. Part A

is connected to a 230 V a.c. supply. What is the voltage across part B?

2007 Question 12 (d) [Ordinary Level]The diagram shows a transformer.(i) What is electromagnetic induction? (ii) Name the parts labelled A and B.(iii) The input voltage is 230 V. Part B has 4600 turns and

part C has 120 turns.Calculate the output voltage.(iv)Name a device that uses a transformer.

2011 Question 9 (b) [Ordinary Level]Transformers are used to step up or step down a.c. voltages.(i) What is meant by a.c.? (ii) Draw a labelled diagram showing the structure of a transformer. (iii) The input coil of a transformer has 200 turns of wire and is connected to a 230 V a.c. supply.

What is the voltage across the output coil, when it has 600 turns?

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Solutions2008 Question 8(i) What is electromagnetic induction?

Electromagnetic Induction occurs when an emf is induced in a coil due to a changing magnetic flux.(ii) State the laws of electromagnetic induction.

Faraday’s Law states that the size of the induced emf is proportional to the rate of change of flux.Lenz’s Law states that the direction of the induced emf is always such as to oppose the change producing it.

(iii) Explain why the amplitude of the swings decreases rapidly.An emf is induced in the copper because is its experiencing a changing magnetic field.This produces a current. This current has a magnetic field associated with it which opposes the motion of the magnet.

(iv)What is the main energy conversion that takes place as the magnet slows down? Kinetic (or potential) to electrical (or heat).

(v) time = dist/velocity = 5 cm / 500 cm s-1 = 0.01 s(vi)What is the magnetic flux cutting the loop when it is completely in the magnetic field?

Φ = BA = (8)(.05 × .05) = 0.02 webers.(vii) What is the average emf induced in the loop as it enters the magnetic field?

Induced emf = (Final Flux –Initial Flux) / Time Taken = (0 - 0.02)/0.01 = 2 Volts

2007 Question 12 (c) (i) State Faraday’s law of electromagnetic induction.

Faraday’s Law states that the size of the induced emf is proportional to the rate of change of flux.(ii) Describe an experiment to demonstrate Faraday’s law.

Move the magnet in and out of the coil slowly and note a slight deflection.Move the magnet quickly and note a greater deflection.

(iii) What is the effect on the current flowing in the circuit? Current is reduced

(iv)Justify your answer An emf induced in coil which induces a current which opposes the initial current.

2006 Question 11(i) How does resonance occur in an acoustic guitar?

Energy is transferred from the strings to the hollow body and both vibrate at the same frequency.(j) What is the relationship between frequency and tension for a stretched string?

Frequency is proportional to the square root of tension.(k) A stretched string of length 80 cm has a fundamental frequency of vibration of 400 Hz.

What is the speed of the sound wave in the stretched string? v = f λ v = 400(1.6) = 640 m s-1

(l) Why must the strings in the electric guitar be made of steel? Because only metal strings can be magnitised.

(m) Define magnetic flux. Magnetic flux is the product of magnetic flux density multiplied by area.

(n) Why does the current produced in a coil of the electric guitar vary? Because the induced emf varies due to the amplitude of the vibrating string.

(o) What is the effect on the sound produced when the number of turns in a coil is increased? A louder sound is produced.

(p) A coil has 5000 turns. What is the emf induced in the coil when the magnetic flux cutting the coil changes by 8 × 10–4 Wb in 0.1 s? E=−N(dφ / dt) E = 5000(8 × 10-4 /0.1) = 40 V

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2005 Question 12 (b) (i) Define magnetic flux.

Magnetic flux is defined as the product of magnetic flux density multiplied by area.(ii) State Faraday’s law of electromagnetic induction.

The size of the induced emf is proportional to the rate of change of flux.(iii) What is the magnetic flux cutting the coil?

A = (0.05)2 = 0.0025 φ (= BA ) = (4)(0.0025) φ = 0.01 Wb

(iv)Calculate the magnitude of the average e.m.f. induced in the coil while it is being rotated. E = N(Δφ/Δt) Δφ /Δt = (0.01 – 0 )/0.2 = 0.05 E= 200(0.05) E = 10 V

2004 Question 12 (c) (i) What is electromagnetic induction?

Electromagnetic Induction occurs when an emf is induced in a coil due to a changing magnetic flux.(ii) Describe an experiment to demonstrate electromagnetic induction.

Set up as shown.Move the magnet in and out of the coil and note the deflection in the galvanometer.

(iii) Explain why.Current flows in the ring in such a direction as to oppose the change which caused it. Therefore the ring follows the magnet.

(iv)What would happen if the magnet were moved towards the ring? The ring would be repelled.

2003 Question 12 (d)(i) State the laws of electromagnetic induction.

Faraday’s Law states that the size of the induced emf is proportional to the rate of change of flux.Lenz’s Law states that the direction of the induced emf is always such as to oppose the change producing it.

(ii) Describe the current flowing in the circuit. Alternating current.

(iii) If the switch at A is open, the magnet will take longer to come to rest. Explain why. There is no longer a full circuit, so even though there is an induced potential difference there is no (induced) current, therefore no induced magnetic field in the coil therefore no opposing force.

2002 Question 12 (c)(i) What is meant by electromagnetic induction?

Electromagnetic Induction occurs when an emf is induced in a coil due to a changing magnetic flux.(ii) State Lenz’s law of electromagnetic induction.

Lenz’s Law states that the direction of the induced emf is always such as to oppose the change producing it.

(iii) Explain why the current was reduced when an iron core was inserted in the coil. There would normally be a back emf in the coil due to the alternating current being supplied.When the core was inserted it increased the magnetic flux which in turn increased the self-induction (back emf) and this reduced the overall voltage and therefore the overall current.

(iv)Give an application of the principle shown by this experiment.Dimmer switch, smooth d.c., tuning radios, braking trains, damping in balances, induction coil

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Nuclear Physics

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The Atom

2008 Question 10 [Ordinary Level] Give two properties of an electron.The diagram shows the arrangement used by Rutherford to investigate the structure of the atom. During the investigation he fired alpha-particles at a thin sheet of gold foil in a vacuum.(i) What are alpha-particles? (ii) Describe what happened to the alpha-particles during the

experiment. (iii) What conclusion did Rutherford make about the

structure of the atom?(iv)How are the electrons arranged in the atom? (v) Name a device used to detect alpha-particles. (vi)Why was it necessary to carry out this experiment in a vacuum?

2011 Question 12 (d) [Ordinary Level]The diagram shows the arrangement used to investigate the structure of the atom. During the investigation, alpha-particles were fired at a thin sheet of gold foil in a vacuum.(i) What are alpha-particles?(ii) What happened to the alpha-particles in the

experiment?(iii) What did the experiment reveal about the structure

of the atom?(iv)Name the scientist who designed the experiment.(v) Name a suitable detector of alpha-particles.

2002 Question 12 (d) [Higher Level](i) The diagram shows a simplified arrangement of an experiment

carried out early in the 20th century to investigate the structure of the atom. Name the scientist who carried out this experiment.

(ii) Describe what was observed in this experiment. (iii) Why was it necessary to carry out this experiment in a

vacuum? (iv)What conclusion did the scientist form about the structure of the atom?

2004 Question 10 [Ordinary Level](i) What is radioactivity?(ii) Name the French physicist who discovered radioactivity in 1896.(iii) The diagram illustrates that three types of radiation are emitted from a

radioactive source.Name the radiations labelled (i) X, (ii) Y, (iii) Z, in the diagram.

(iv)Which one is the most ionising?(v) Name a detector of ionising radiation.(vi)Outline the principle on which the detector works. (vii) Great care has to be taken when dealing with radioactive sources.

Give:(i) two precautions that should be taken when dealing with radioactive sources;(ii) one use of a radioactive source;(iii) one harmful effect of radiation.

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2010 Question 12 (d) [Ordinary Level](i) What is radioactivity? (ii) The diagram shows a shielded radioactive source emitting nuclear

radiation.How do you know that the source is emitting three types of radiation?

(iii) Name the radiation blocked by each material.(iv)Give one danger associated with nuclear radiation.(v) State two precautions that should be taken when handling radioactive substances.(vi)Give two uses for radioactive substances

2002 Question 11 [Ordinary Level]The world’s most devastating nuclear accident happened at Chernobyl in the Ukraine in 1986. In the early hours of the morning of 26 April of that year, there were two loud explosions that blew the roof off and completely destroyed the No. 4 reactor, releasing during the course of the following days, 6 to 7 tonnes of radioactive material, with a total activity of about 1018 becquerels, into the atmosphere. The discharge included over a hundred radioisotopes, but iodine and caesium isotopes were of main relevance from a human health and environmental point of view. Contamination in the surrounding areas was widespread, with the half-life of some of the materials measured in thousands of years. Large numbers of people involved in the initial clean up of the plant received average total body radiation doses of about 100 mSv - about five times the maximum dose permitted for workers in nuclear facilities. Average worldwide total body radiation dose from natural ‘background’ radiation is about 2.4 mSv annually. During, and soon after the accident and the initial clean-up, at least 30 plant personnel and firefighters died from burns and radiation. In the eight years following the accident, a further 300 suffered radiation sickness, and there are possible links between the accident and increased numbers of thyroid cancers in neighbouring regions. (Adapted from “Physics – a teacher’s handbook”, Dept. of Education and Science.)

(i) What is meant by a nuclear accident? (ii) The No. 4 reactor was a fission reactor. What is nuclear fission?(iii) Name two parts of a nuclear fission reactor. (iv)What is measured in becquerels? (v) Give two examples of radioisotopes. (vi)What is meant by the half-life of a substance?(vii) What is meant by background radiation?(viii) Give two effects of radiation on the human body.

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2007 Question 11 [Ordinary Level] Read this passage and answer the questions below. Radon is a naturally occurring radioactive gas. It originates from the decay of uranium, which is present in small quantities in rocks and soils. Radon is colourless, odourless and tasteless and can only be detected using special equipment, like a Geiger-Müller tube, that can measure the radiation it releases. Because it is a gas, radon can move freely through the soil and enter the atmosphere. When radon reaches the open air, it is quickly diluted to harmless concentrations, but when it enters an enclosed space, such as a house, it can sometimes accumulate to unacceptably high concentrations. Radon can enter a building from the ground through small cracks in floors and through gaps around pipes and cables. Radon is drawn from the ground into a building because the indoor air pressure is usually lower than outdoors. Being radioactive, radon decays releasing radiation.When radon is inhaled into the lungs the radiation released can cause damage to the lung tissue. (a) What is radioactivity? (b) What is the source of radon? (c) Name a detector of radiation. (d) How does radon enter a building? (e) How can the build-up of radon in the home be prevented? (f) Why is radon dangerous? (g) Why is radon harmless in the open air? (h) Name a radioactive element other than radon.

2011 Question 10 [Ordinary Level]

Radon is a radioactive gas which emits alpha particles. Radon gas comes into houses through gaps in the floors. Exposure to radon gas can cause lung cancer

(i) What is radioactivity?(ii) Name the other two types of radiation emitted by radioactive sources. (iii) Describe an experiment to distinguish between the three types of radiation.(iv)List three properties of one of these radiations. (v) The most stable isotope of radon has a half-life of 4 days.What are isotopes? (vi)Why is it important to prevent radon gas entering your home? (vii) If no more radon gas entered your home, how long would it be until one eight of the radon gas was

left? (viii) Give two uses of radioisotopes.

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Half-life2005 Question 12 (d) [Ordinary Level]Na−25 is a radioactive isotope of sodium. It has a half life of 1 minute.(i) What is meant by radioactivity? (ii) Name a detector of radioactivity. (iii) Explain the term half life. (iv)What fraction of a sample of Na−25 remains after 3 minutes?(v) Give one use of a radioactive isotope.

2007 Question 12 (d) [Higher Level](i) Explain the term half-life. (ii) A sample of carbon is mainly carbon-12 which is not radioactive, and a small proportion of carbon-14

which is radioactive. When a tree is cut down the carbon-14 present in the wood at that time decays by beta emission.Write a nuclear equation to represent the decay of carbon-14.

(iii) An ancient wooden cup from an archaeological site has an activity of 2.1 Bq.The corresponding activity for newly cut wood is 8.4 Bq.If the half-life of carbon-14 is 5730 years, estimate the age of the cup.

(iv)Name an instrument used to measure the activity of a sample.(v) What is the principle of operation of this instrument?

2003 Question 11 [Higher Level]Read the following passage and answer the accompanying questions.Irish Times: Monday, January 11,1999Radioactive decay helps to determine exact dates.Radioactive decay occurs with such precision that it is often used as a clock. Carbon dating has been invaluable to archaeologists, historians and anthropologists. The method is based on the measurement of 14C, a radioactive isotope of carbon with a half-life of 5730 years. 14C occurs to a small extent in the atmosphere together with the much more common 12C. Living organisms constantly exchange carbon with the atmosphere and the ratio of 14C to 12C in living tissue is the same as it is in the atmosphere. This ratio is assumed to have remained the same since prehistoric times. When an organism dies, it stops exchanging carbon with the atmosphere, and its 14C nuclei keep disintegrating while the 12C in the dead tissue remains undisturbed.(i) What is radioactive decay?(ii) What is an isotope?(iii) Apart from “carbon dating”, give two other uses of radioactive isotopes.(iv)How many neutrons are in a 14C nucleus? (v) 14C decays to 14N. Write an equation to represent this nuclear reaction. (vi)How much of a 14C sample remains after 11460 years? (vii) Calculate the decay constant of 14C. (viii) Why does the 12C in dead tissue remain “undisturbed”? (Refer to the Periodic Table of the Elements in the Mathematics Tables, p.44.)

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2011 Question 12 (d) [Higher Level]In the manufacture of newsprint paper, heavy rollers are used to adjust the thickness of the moving paper. The paper passes between a radioisotope and a detector, and a pair of rollers, as shown.

The radioisotope used is Sr-90 and it emits beta-particles, which are recorded by the detector. The output from the detector adjusts the gap between the rollers, so that the paper is of uniform thickness.(i) Name a suitable detector.(ii) Describe how the reading on the detector may vary as the paper passes by. (iii) Why would the radioisotope Am-241, which emits alpha-particles, not be suitable for this process?(iv)Calculate the number of atoms present in a sample of Sr-90 when its activity is 4250 Bq.

The half-life of Sr-90 is 28.78 years.

2009 Question 12 (d) [Higher Level]Smoke detectors use a very small quantity of the element americium-241. This element does not exist in nature and was discovered during the Manhattan Project in 1944.Alpha particles are produced by the americium-241 in a smoke detector.(i) Give the structure of an alpha particle.(ii) How are the alpha particles produced?(iii) Why do these alpha particles not pose a health risk?(iv)Americium-241 has a decay constant of 5.1 × 10–11 s–1.

Calculate its half life in years.(v) Explain why americium-241 does not exist naturally.

2005 Question 8 [Higher Level]Nuclear disintegrations occur in radioactivity and in fission.(i) Distinguish between radioactivity and fission. (ii) Give an application of radioactivity.(iii) Give an application of fission.(iv)Radioactivity causes ionisation in materials. What is ionisation?(v) Describe an experiment to demonstrate the ionising effect of radioactivity. (vi)Cobalt−60 is a radioactive isotope with a half-life of 5.26 years and emits beta particles.

Write an equation to represent the decay of cobalt−60.(vii) Calculate the decay constant of cobalt−60.(viii) Calculate the rate of decay of a sample of cobalt−60 when it has 2.5 × 1021 atoms.

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Fission and Fusion

Nuclear Reactors2012 Question 11 [Ordinary Level]Read this passage and answer the questions below.The Fukushima nuclear disasterIn March 2011, following a powerful earthquake, the Fukushima nuclear reactor in Japan was shut down automatically. A nuclear reactor generates heat by splitting atoms of uranium in a process known as nuclear fission. The uranium is contained in the reactor’s fuel rods. A chain reaction is set up by the neutrons released during fission and these go on to split more atoms of uranium. The power output of the reactor is adjusted by controlling the number of neutrons that are present. Control rods made of a neutron absorber capture neutrons.

Absorbing more neutrons in a control rod means that there are fewer neutrons available to cause fission. Therefore, pushing the control rods deeper into the reactor will reduce its power output, and extracting the control rods will increase it.

The Fukushima nuclear reactor continued to generate heat even after the chain reaction was stopped because of the radioactive decay of the isotopes created during nuclear fission. This decay cannot be stopped and the resulting heat must be removed by circulating cooling water through the reactor core.

When the reactor was shut down due to the earthquake, the pumps to keep the cooling water circulating should have been powered by electricity from the national grid or diesel generators. However, connections to the grid were damaged by the earthquake and the diesel generators were destroyed by the tsunami wave that followed the earthquake. As a result, no cooling was available for the reactor core and this resulted in the explosions and subsequent release of radiation, consisting of radioactive isotopes such as caesium and iodine, into the environment. (Adapted from ‘Wikipedia', June 2011)(a) What is meant by nuclear fission?(b) What is radioactivity?(c) What is a nuclear chain reaction?(d) What is the function of the control rods?(e) What type of material are control rods made of?(f) Why did the reactor still generate heat even though the chain reaction had stopped?(g) Why is it important to remove the heat generated?(h) Give one advantage of nuclear energy.

2006 Question 9 [Ordinary Level]The diagram shows a simple nuclear fission reactor.Energy is released in a fission reactor when a chain reaction occurs in the fuel rods.(i) What is meant by fission? Name a material in which fission occurs. (ii) Describe how a chain reaction occurs in the fuel rods.(iii) Explain how the chain reaction is controlled. (iv)What is the purpose of the shielding? (v) Name a material that is used as shielding. (vi)Describe what happens to the coolant when the reactor is working.(vii) Give one effect of a nuclear fission reactor on the environment. (viii) Give one precaution that should be taken when storing radioactive materials.

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2003 Question 10 [Ordinary Level](i) What is radioactivity?(ii) The diagram shows the basic structure of a nuclear reactor.(iii) A nuclear reactor contains (i) fuel rods, (ii) control

rods, (iii) moderator, (iv) heat exchanger.(iv)Give the function of any two of these.(v) In a nuclear reactor, energy is released by nuclear fission

when a chain reaction occurs.(vi)What is nuclear fission?(vii) What is a chain reaction?(viii) Thick shielding is placed around a nuclear reactor because of the penetrating power of the radiation

emitted. Name three types of radiation that are present in a nuclear reactor.

(ix)Name an instrument used to detect radiation. (x) Plutonium is produced in a nuclear reactor. It is a highly radioactive substance with a very long half-life.

When the fuel in a nuclear reactor is used up, the fuel rods are reprocessed to remove the plutonium.(xi)Give two precautions that are taken when storing the plutonium.

2009 Question 10 [Ordinary Level] Radioactive elements are unstable and decay with the release of radiation.(i) How would you detect radiation?(ii) Name the three types of radiation.(iii) Which radiation is negatively charged?(iv)Which radiation has the shortest range?(v) Which radiation is not affected by electric fields? (vi)Nuclear fission occurs in a nuclear reactor.(vii) What is nuclear fission? (viii) What is the role of neutrons in nuclear fission? (ix)Name a fuel used in a nuclear reactor. (x) In a nuclear reactor, how can the fission be controlled or stopped? (xi)How is the energy produced in a nuclear reactor used to generate electricity?(xii) Give one advantage and one disadvantage of a nuclear reactor as a source of energy.

2008 Question 12 (c) [Higher Level](i) In 1939 Lise Meitner discovered that the uranium isotope U–238 undergoes fission when struck by a

slow neutron. Barium–139 and krypton–97 nuclei are emitted along with three neutrons. Write a nuclear reaction to represent the reaction.

(ii) In a nuclear fission reactor, neutrons are slowed down after being emitted. Why are the neutrons slowed down?

(iii) How are they slowed down? (iv)Fission reactors are being suggested as a partial solution to Ireland’s energy needs.

Give one positive and one negative environmental impact of fission reactors.

2010 Question 12 (b) [Higher Level]The following reaction occurs in a nuclear reactor:

(i) Identify the element X.(ii) Calculate the mass difference between the reactants and the products in the reaction(iii) What is a chain reaction?(iv)Give one condition necessary for a chain reaction to occur.(v) Give one environmental impact associated with a nuclear reactor.2012 Question 8 [Higher Level]

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Energy can be produced in a fusion reaction by combining a deuterium and a tritium nucleus as follows:

(i) Distinguish between nuclear fission and nuclear fusion. (ii) What are the advantages of fusion over fission in terms of fuel

sources and reaction products?(iii) How much energy is produced when a deuterium nucleus

combines with a tritium nucleus?(iv)Calculate the force of repulsion between a deuterium and a tritium

nucleus when they are 2 nm apart in free space.(v) Fusion can only take place at very high temperatures. Explain why.

2006 Question 8 [Higher Level]b) Distinguish between fission and fusion. c) The core of our sun is extremely hot and acts as a fusion reactor.

Why are large temperatures required for fusion to occur? d) In the sun a series of different fusion reactions take place. In one of the reactions, 2 isotopes of helium,

each with a mass number of 3, combine to form another isotope of helium with the release of 2 protons.Write an equation for this nuclear reaction.

e) Controlled nuclear fusion has been achieved on earth using the following reaction:

What condition is necessary for this reaction to take place on earth?

f) Calculate the energy released during this reaction. g) Give one benefit of a terrestrial fusion reactor under each of the following headings:

(a) fuel; (b) energy; (c) pollution.

speed of light = 2.998 × 10–8 m s–1; mass of hydrogen-2 nucleus = 3.342 × 10–27 kg ; mass of hydrogen-3 nucleus = 5.004 × 10–27 kg; mass of helium nucleus = 6.644 × 10–27 kg;mass of neutron = 1.674 × 10–27 kgSolutions to Higher Level questions

2012 Question 8(i) Distinguish between nuclear fission and nuclear fusion.

Fission: large nucleus splits into two smaller nuclei (of similar size) Fusion: two small nuclei join to form a larger nucleus

(ii) What are the advantages of fusion over fission in terms of fuel sources and reaction products?(hydrogen) fuel (from the sea) is plentiful – (uranium for fission is scarce) no radioactive waste with fusion – (fission results in radioactive waste)

(iii) How much energy is produced when a deuterium nucleus combines with a tritium nucleus?Reactants: 2.014102 + 3.016049 = 5.030151Products: 4.002603 + 1.008672 = 5.011275Change in mass = 0.018875 u = 3.1344 × 10-29 kgE = mc2 = 2.82096 × 10-12 J

(iv)Calculate the force of repulsion between a deuterium and a tritium nucleus when they are 2 nm apart in free space.

F = 5.77 × 10-11 N(v) Fusion can only take place at very high temperatures. Explain why.

Nuclei must have very high speeds / energy to overcome force of repulsion between the nuclei if they are to combine

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2011 Question 12 (d) (i) Name a suitable detector.

GM tube (linked with a ratemeter/scaler)/ Solid state detector (ii) Describe how the reading on the detector may vary as the paper passes by.

The count rate would decrease with increasing paper thickness.(iii) Why would the radioisotope Am-241, which emits alpha-particles, not be suitable for this

process?The alpha-particles have poor penetrating power so would be easily blocked by the paper.

(iv)Calculate the number of atoms present in a sample of Sr-90 when its activity is 4250 Bq.The half-life of Sr-90 is 28.78 years. 1 year = 365 days OR 365.25 daysT½ = 0.693 / λ = 0.693/ T1/2 λ = 7.77 × 10-10 s-1 / 7.63 × 10-10 s-1

Activity = dN/dt = (-) λN4250 = 7.77 × 10-10(N) OR 4250 = 7.63 × 10-10(N)N = 5.47 × 1012 (atoms) OR N = 5.57 × 1012 (atoms)

2010 Question 12 (b)(i) Identify the element X.

Krypton(ii) Calculate the mass difference between the reactants and the products in the reaction

E = mc2

m = 3.6 × 10-28 kg(iii) What is a chain reaction?

It is a self-sustaining reaction where fission neutrons go on to produce further fission (giving more neutrons) etc.

(iv)Give one condition necessary for a chain reaction to occur.The mass of fuel present must exceed the critical mass / at least one of the neutrons released must cause fission of another nucleus.

(v) Give one environmental impact associated with a nuclear reactor.Toxic /radioactive waste, exposure to radiation, etc.

2009 Question 12 (d) (i) Give the structure of an alpha particle.

It is composed of 2 protons and 2 neutrons(ii) How are the alpha particles produced?

α-decay is produced when the americium (which is radioactive) undergoes radioactive decay. (iii) Why do these alpha particles not pose a health risk?

They have a very short range so are either contained within the smoke detector itself or just travel a cm or two through the air.

(iv)Americium-241 has a decay constant of 5.1 × 10–11 s–1.Calculate its half life in years.T½ = 0.693 / T½ = 0.693 / 5.1 × 10–11 T½ = 1.36 × 1010 seconds = 430.6 years

(v) Explain why americium-241 does not exist naturally. {I don’t think this was a fair question and shouldn’t have appeared on the paper}

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Its half life is very short (with respect to age of the universe) and because it is not a member of a decay series it is not produced ‘in nature’ (it is created artificially).

2008 Question 12 (c)(i) Write a nuclear reaction to represent the reaction.

(ii) In a nuclear fission reactor, neutrons are slowed down after being emitted. Why are the neutrons slowed down? Only slow neutrons cause fission.

(iii) How are they slowed down? They collide with the molecules in the moderator.

(iv)Fission reactors are being suggested as a partial solution to Ireland’s energy needs. Give one positive and one negative environmental impact of fission reactors. Positive: no CO2 emissions / no greenhouse gases / less dependence on fossil fuels.Negative: radioactive waste / potential for major accidents etc.

2007 Question 12 (d) (i) Explain the term half-life.

Time for half the radioactive nuclei in a sample to decay(ii) Write a nuclear equation to represent the decay of carbon-14.

(iii) If the half-life of carbon-14 is 5730 years, estimate the age of the cup. 8.4 Bq to 2.1 Bq requires two half-lives. Answer =11,460 years

(iv)Name an instrument used to measure the activity of a sample.Geiger Muller tube.

(v) What is the principle of operation of this instrument? The gas is ionised and a pulse of charge/current flows.

2006 Question 8(i) Distinguish between fission and fusion.

Nuclear Fission is the break-up of a large nucleus into two smaller nuclei with the release of energy (and neutrons).Nuclear Fusion is the combining of two small nuclei to form one large nucleus with the release of energy.

(ii) Why are large temperatures required for fusion to occur? Nuclei are positively charged so enormous energy is required to overcome the very large repulsion.

(iii) Write an equation for this nuclear reaction.

(iv)What condition is necessary for this reaction to take place on earth?Very large energy/temperature is necessary .

(v) Calculate the energy released during this reaction. Mass of reactants = 8.346 x 10-27 kg: mass of products = 8.318 × 10-27 kg loss in mass /defect mass = 2.8 × 10-29 kg E = m c2

E = (2.8 × 10-29)( 2.998 × 108)2

E = 2.52 × 10-12 J (vi)Give one benefit of a terrestrial fusion reactor under each of the following headings:

(a) fuel; (b) energy; (c) pollution.Fuel: plentiful / cheap Energy: vast energy released

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Pollution: little (radioactive) waste / few greenhouse gases

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2005 Question 8(i) Distinguish between radioactivity and fission.

Nuclear Fission is the break-up of a large nucleus into two smaller nuclei with the release of energy (and neutrons).Nuclear Fusion is the combining of two small nuclei to form one large nucleus with the release of energy.

(ii) Give an application of radioactivity.Smoke detectors, carbon dating, tracing leaks, cancer treatment, sterilising, etc.

(iii) Give an application of fission.Generating electrical energy, bombs

(iv)Radioactivity causes ionisation in materials. What is ionisation?Ionisation occurs when a neutral atom loses or gains an electron.

(v) Describe an experiment to demonstrate the ionising effect of radioactivity. Apparatus: radioactive source and charged (gold leaf) electroscopeProcedure: bring radioactive source close to the cap Observation: leaves collapse Conclusion: charge leaks away through ionised air / electroscope neutralised by ionised air

(vi)Write an equation to represent the decay of cobalt−60.

(vii) Calculate the decay constant of cobalt−60.Formula: T1/2 = ln 2/λ λ = T1/2/ln 2

T1/2 = 5.26 y = 1.66 × 108 s and ln 2 = 0.693λ = 1.66 × 108 / 0.693 λ = 4.18 × 10-9 s-1

(viii) Calculate the rate of decay of a sample of cobalt−60 when it has 2.5 × 1021 atoms. dN/dt = (-) λN

= (4.18 × 10-9)( 2.5 × 1021) = 1.04 × 1013 Bq2003 Question 11(a) What is radioactive decay?

Radioactivity is the breakup of unstable nuclei with the emission of one or more types of radiation.(b) What is an isotope?

Isotopes are atoms which have the same Atomic Number but different Mass Numbers.(c) Apart from “carbon dating”, give two other uses of radioactive isotopes.

Medical imaging, (battery of) heart pacemakers, sterilization, tracers, irradiation of food, killing cancer cells, measuring thickness, smoke detectors, nuclear fuel

(d) How many neutrons are in a 14C nucleus? Eight

(e) 14C decays to 14N. Write an equation to represent this nuclear reaction. 14

6C → 714N + -1

0e(f) How much of a 14C sample remains after 11 460 years?

11,460 corresponds to two half lives, and after two half lives one quarter remains.(g) Calculate the decay constant of 14C.

T1/2 = ln 2 /λ λ = 0.693/5730 = 1.21 × 10−4 y-1 = 3.8×10−12 s-1 (h) Why does the 12C in dead tissue remain “undisturbed”?

It is not radioactive, it is not exchanging with the atmosphere, it is stable

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2002 Question 12 (d)(i) Name the scientist who carried out this experiment.

Ernest Rutherford.(ii) Describe what was observed in this experiment.

Most alpha particles passed straight through, some were deflected slightly and a small percentage bounced back.

(iii) Why was it necessary to carry out this experiment in a vacuum? To prevent the alpha particles colliding with other particles.

(iv)What conclusion did the scientist form about the structure of the atom? It consists of a small, dense, positively charged core with negatively charged electrons in orbit around it.

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Particle Physics

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Particle Accelerators (including Cockcroft and Walton experiment)

2007 Question 10 (a)Read the following passage and answer the accompanying questions.Ernest Walton was one of the legendary pioneers who made 1932 the annus mirabilis of experimental nuclear physics. In that year James Chadwick discovered the neutron; Carl Anderson discovered the positron; Fermi articulated his theory of radioactive decay; and Ernest Walton and John Cockcroft split the nucleus by artificial means. In their pioneering experiment Cockcroft and Walton bombarded lithium nuclei with high-energy protons linearly accelerated across a high potential difference (c. 700 kV). The subsequent disintegration of each lithium nucleus yielded two helium nuclei and energy. Their work gained them the Nobel Prize in 1951.(Adapted from “Ernest Thomas Sinton Walton 1903 –1995 The Irish Scientist” McBrierty; 2003)(i) Draw a labelled diagram to show how Cockcroft and Walton accelerated the protons. (ii) What is the velocity of a proton when it is accelerated from rest through a potential difference of 700

kV? (iii) Write a nuclear equation to represent the disintegration of a lithium nucleus when bombarded with a

proton. (iv)Calculate the energy released in this disintegration. (v) Compare the properties of an electron with that of a positron. (vi)What happens when an electron meets a positron? (vii) In beta decay it appeared that momentum was not conserved. How did Fermi’s theory of radioactive

decay resolve this?charge on electron = 1.6022 × 10–19 C; mass of proton = 1.6726 × 10–27 kg; speed of light = 2.9979 × 108 m s–1

mass of lithium nucleus = 1.1646 × 10–26 kg; mass of helium nucleus = 6.6443 × 10–27 kg;

2002 Question 10 (a)(i) Name the four fundamental forces of nature. (ii) Which force is responsible for binding the nucleus of an atom? (iii) Give two properties of this force.(iv)In 1932, Cockcroft and Walton carried out an experiment in which they used high-energy protons to split

a lithium nucleus. Outline this experiment. (v) When a lithium nucleus (7

3Li) is bombarded with a high-energy proton, two α-particles are produced.Write a nuclear equation to represent this reaction.

(vi)Calculate the energy released in this reaction.

mass of proton = 1.6730 × 10-27 kg; mass of lithium nucleus = 1.1646 × 10-26 kg; mass of α-particle = 6.6443 × 10-27 kg; speed of light, c = 3.00 × 108 m s-1.

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2005 Question 11 (a)Read the following passage and answer the accompanying questions.Ernest Rutherford made the following point:If the particles that come out naturally from radium are no longer adequate for my purposes in the laboratory, then maybe the time had come to look at ways of producing streams of fast particles artificially. High voltages should be employed for the task. A machine producing millions of alpha particles or protons would be required. These projectiles would be released close to a high voltage and would reel away at high speed. It would be an artificial particle accelerator. Potentially such apparatus might allow physicists to break up all atomic nuclei at will.(Adapted from “The Fly in the Cathedral” Brian Cathcart; 2004)

(i) Define electric field strength.(ii) What is the structure of an alpha particle? (iii) Rutherford had bombarded gold foil with alpha particles. What conclusion did he form about the

structure of the atom?(iv)High voltages can be used to accelerate alpha particles and protons but not neutrons. Explain why.(v) Cockcroft and Walton, under the guidance of Rutherford, used a linear particle accelerator to artificially

split a lithium nucleus by bombarding it with high-speed protons. Copy and complete the following nuclear equation for this reaction.

(vi)Circular particle accelerators were later developed. Give an advantage of circular accelerators over linear accelerators.

(vii) In an accelerator, two high-speed protons collide and a series of new particles are produced, in addition to the two original protons.

Explain why new particles are produced.(viii) A huge collection of new particles was produced using circular accelerators. The quark model was

proposed to put order on the new particles. List the six flavours of quark. (ix)Give the quark composition of the proton. (Refer to Mathematics Tables, p. 44.)

2009 Question 10 (a)In 1932 Cockcroft and Walton succeeded in splitting lithium nuclei by bombarding them with artificially accelerated protons using a linear accelerator.Each time a lithium nucleus was split a pair of alpha particles was produced.(i) How were the protons accelerated? (ii) How were the alpha particles detected? (iii) Write a nuclear equation to represent the splitting of a lithium nucleus by a proton.(iv) Calculate the energy released in this reaction. (v) Most of the accelerated protons did not split a lithium nucleus. Explain why.

Cockcroft and Walton’s apparatus is now displayed at CERN in Switzerland, where very high energy protons are used in the Large Hadron Collider.In the Large Hadron Collider, two beams of protons are accelerated to high energies in a circular accelerator. The two beams of protons then collide producing new particles. Each proton in the beams has a kinetic energy of 2.0 GeV.(vi) Explain why new particles are formed.(vii) What is the maximum net mass of the new particles created per collision? (viii) What is the advantage of using circular particle accelerators in particle physics?

(mass of alpha particle = 6.6447 × 10–27 kg; mass of proton = 1.6726 × 10–27 kg; mass of lithium nucleus = 1.1646 × 10–26 kg; speed of light = 2.9979 × 108 m s–1; charge on electron = 1.6022 × 10–19 C)

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2011 Question 10 (a) (i) List three quantities that are conserved in nuclear reactions.(ii) Write an equation for a nucleus undergoing beta-decay.(iii) In initial observations of beta-decay, not all three quantities appear to be conserved.

What was the solution to this contradiction? (iv)List the fundamental forces of nature in increasing order of their strength.(v) Which fundamental force of nature is involved in beta-decay?(vi)In the Large Hadron Collider, two protons with the same energy and travelling in opposite directions

collide. Two protons and two charged pi mesons are produced in the collision.Why are new particles produced in the collision?

(vii) Write an equation to represent the collision.(viii) Show that the kinetic energy of each incident proton must be at least 140 MeV for the collision to

occur.

2008 Question 10 part (a) Baryons and mesons are made up of quarks and experience the four fundamental forces of nature. (i) List the four fundamental forces and state the range of each one.(ii) Name the three positively charged quarks. (iii) What is the difference in the quark composition of a baryon and a meson? (iv)What is the quark composition of the proton? (v) In a circular accelerator, two protons, each with a kinetic energy of 1 GeV, travelling in opposite

directions, collide. After the collision two protons and three pions are emitted. What is the net charge of the three pions? Justify your answer. (vi)Calculate the combined kinetic energy of the particles after the collision; (vii) Calculate the maximum number of pions that could have been created during the collision.

(charge on electron = 1.6022 × 10–19 C; mass of proton = 1.6726 × 10–27 kg;mass of pion = 2.4842 × 10–28 kg; speed of light = 2.9979 × 108 m s–1)Pair Annihilation

2012 Question 10 (a) (i) What is a positron? (ii) When a positron and an electron meet two photons are produced.

Write an equation to represent this interaction. (iii) Why are photons produced in this interaction?(iv)Explain why two photons are produced.(v) Calculate the minimum frequency of the photons produced.(vi)Explain why the photons produced usually have a greater frequency than your calculated minimum

frequency value. (vii) Why must two positrons travel at high speeds so as to collide with each other?(viii) How are charged particles given high speeds? (ix)Explain why two positrons cannot annihilate each other in a collision.

2006 Question 10 (a)During a nuclear interaction an antiproton collides with a proton. Pair annihilation takes place and two gamma ray photons of the same frequency are produced.(i) What is a photon? (ii) Calculate the frequency of a photon produced during the interaction.(iii) Why are two photons produced? (iv)Describe the motion of the photons after the interaction. (v) How is charge conserved during this interaction? (vi)After the annihilation, pairs of negative and positive pions are produced. Explain why. (vii) Pions are mesons that consist of up and down quarks and their antiquarks.

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Give the quark composition of (i) a positive pion, (ii) a negative pion. (viii) List the fundamental forces of nature that pions experience. (ix)A neutral pion is unstable with a decay constant of 2.5 × 1012 s–1. What is the half-life of a neutral pion? (mass of proton= 1.673 × 10–27 kg; Planck constant = 6.626 × 10–34 J s; speed of light = 2.998 × 108 m s–1 )

Pair Production

2010 Question 10 (a)(i) What is anti-matter?(ii) An anti-matter particle was first discovered during the study of cosmic rays in 1932.Name the anti-particle and give its symbol.(iii) What happens when a particle meets its anti-particle?(iv)What is meant by pair production?(v) A photon of frequency 3.6 × 1020 Hz causes pair production.

Calculate the kinetic energy of one of the particles produced, each of which has a rest mass of 9.1 × 10–31

kg.(vi)A member of a meson family consists of two particles. Each particle is composed of up and down quarks

and their anti-particles.Construct the possible combinations. Deduce the charge of each combination and identify each combination.

(vii) What famous Irish writer first thought up the name ‘quark’?

2003 Question 10 (a) (i) Leptons, baryons and mesons belong to the “particle zoo”.

Give (i) an example, (ii) a property, of each of these particles. (ii) The following raction represents pair production.

γ → e+ + e–

Calculate the minimum frequency of the γ-ray photon required for this reaction to occur. (iii) What is the effect on the products of the reaction if the frequency of the γ-ray photon exceeds the

minimum value? (iv)The reverse of the above reaction is known as pair annihilation.

Write a reaction that represents pair annihilation. (v) Explain how the principle of conservation of charge and the principle of conservation of momentum

apply in pair annihilation. mass of electron = 9.1 × 10–31 kg; speed of light, c = 3.0 × 108 m s–1 ; Planck constant, h = 6.6 × 10–34 J s

Neutrinos

2004 Question 10 (a) (i) Beta decay is associated with the weak nuclear force.

List two other fundamental forces of nature and give one property of each force. (ii) In beta decay, a neutron decays into a proton with the emission of an electron.

Write a nuclear equation for this decay. Calculate the energy released during the decay of a neutron. (iii) Momentum and energy do not appear to be conserved in beta decay. Explain how the existence of

the neutrino, which was first named by Enrico Fermi, resolved this.

During the late 1930s, Fermi continued to work on the nucleus.His work led to the creation of the first nuclear fission reactor in Chicago during 1942. The reactor consisted of a ‘pile’ of graphite moderator, uranium fuel with cadmium control rods.

(iv)What is nuclear fission?(v) What is the function of the moderator in the reactor?(vi)How did the cadmium rods control the rate of fission? mass of neutron = 1.6749 × 10–27 kg; mass of proton = 1.6726 × 10–27 kg;mass of electron = 9.1094 × 10–31 kg; speed of light = 2.9979 × 108 m s–1

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Solutions2012 Question 10 (a) (i) What is a positron?

A positron is an electron with a positive charge.(ii) When a positron and an electron meet two photons are produced.

Write an equation to represent this interaction.

(iii) Why are photons produced in this interaction?The mass of the electron and positron gets converted into energy

(iv)Explain why two photons are produced.To conserve momemtum.

(v) Calculate the minimum frequency of the photons produced.Mass of electron = 9.1093826 × 10-31 kgE = mc2

E = (9.1093826 × 10-31)(3 × 108)2

E = 8.198444 × 10-14 J

E = hf

f = 1.237 × 1020 Hz

(vi)Explain why the photons produced usually have a greater frequency than your calculated minimum frequency value. In addition to rest mass the colliding particles have kinetic energy.

(vii) Why must two positrons travel at high speeds so as to collide with each other?To overcome the force of repulsion

(viii) How are charged particles given high speeds? Particle accelerators / linear accelerator / cyclotron /synchrotron/magnetic fields/electric fields

(ix)Explain why two positrons cannot annihilate each other in a collision.This would involve a conflict with conservation of charge.(‘zero charge after interaction’ …. award 4 marks)

2011(i) List three quantities that are conserved in nuclear reactions.

Momentum, charge, mass-energy(ii) Write an equation for a nucleus undergoing beta-decay.

(iii) In initial observations of beta-decay, not all three quantities appear to be conserved. What was the solution to this contradiction? The discovery of the neutrino which accounted for the missing momentum.

(iv)List the fundamental forces of nature in increasing order of their strength.gravitational < weak (nuclear) < electromagnetic < (strong) nuclear

(v) Which fundamental force of nature is involved in beta-decay?The weak force.

(vi)Why are new particles produced in the collision?The kinetic energy of the protons is converted into mass.

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(vii) Write an equation to represent the collision.p + p p + p + + + π-

(viii) Show that the kinetic energy of each incident proton must be at least 140 MeV for the collision to occur.

Mass of π+ = 273 me = 273(9.109×10-31) kgE = 2mec2

E = 2(2.4869×10-28)(3×108)2 = 44.76 ×10-12 J

E = 279.94 ×106 eV 280 MeVThis is the total kinetic energy that must be available to produce the two pions so the energy each proton has must be greater than 140 MeV.

2010(i) What is anti-matter?

Antimatter is material/matter/particles that has same mass as another particle but opposite charge.(ii) An anti-matter particle was first discovered during the study of cosmic rays in 1932.

Name the anti-particle and give its symbol.positron / anti-electron

(iii) What happens when a particle meets its anti-particle?Pair annihilation occurs and the mass gets converted to energy.

(iv)What is meant by pair production? Pair production involves the production of a particle and its antiparticle from a gamma ray photon.

(v) A photon of frequency 3.6 × 1020 Hz causes pair production. Calculate the kinetic energy of one of the particles produced, each of which has a rest mass of 9.1 × 10–31 kg.Energy associated with the photon = hf; E = (6.6 × 10-34)( 3.6 × 1020) = 2.376 × 10-13 JEnergy required to produce the two particles = 2[mc2]E = 2(9.1 × 10-31)(3.0 × 108)2 = 1.638 × 10-13 JExtra energy available for kinetic energy = (2.376 × 10-13) – (1.638 × 10-13) = 7.38 × 10-14

Kinetic energy per particle is half of this = 3.69 × 10-14 J

(vi)Construct the possible combinations. Deduce the charge of each combination and identify each combination.

composition charge nameu + 0 Pi-neutrinou + +1 Pi-plusd + -1 Pi-minusd + 0 Pi-neutrino

(vii) What famous Irish writer first thought up the name ‘quark’?(James) Joyce

2009(i) How were the protons accelerated?

They were accelerated by the very large potential difference which existed between the top and the bottom

(ii) How were the alpha particles detected?

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They collide with a zinc sulphide screen, where they cause a flash and get detected by microscopes.(iii) Write a nuclear equation to represent the splitting of a lithium nucleus by a proton.

+ + K.E.(iv)Calculate the energy released in this reaction.

Loss in mass:Mass before = mass of proton (1.6726 × 10–27) + mass of lithium nucleus (1.1646 × 10–26) = 1.33186 × 10-26 kgMass after = mass of two alpha particles = 2 × (6.6447 × 10–27) = 1.32894 × 10-26 kgLoss in mass = 1.33186 × 10-26 - 1.32894 × 10-26 = 2.92 × 10-29 kgE = mc2 = (2.92 × 10-29) (2.9979 × 108)2 = 2.6 × 10-12 J

(v) Most of the accelerated protons did not split a lithium nucleus. Explain why.The atom is mostly empty space so the protons passed straight through.

(vi)Explain why new particles are formed.When the protons collide into each other they lose their kinetic energy and it is this energy which gets converted into mass to form the new particles.

(vii) What is the maximum net mass of the new particles created per collision? Total energy = 4 GeV E = mc2 m = E/ c2 m = (4 × 109) (1.6 × 10-19)/(2.9979 × 108)2

m = 7.121 × 10-27 kg(viii) What is the advantage of using circular particle accelerators in particle physics?

They take up less space / you can achieve greater (particle) speeds with a circular accelerator2008 (i) List the four fundamental forces and state the range of each one.

Strong (short range), Weak (short range), Gravitational (infinite range), Electromagnetic (infinite range).(ii) Name the three positively charged quarks.

Up, top, charm.(iii) What is the difference in the quark composition of a baryon and a meson?

Baryon: three quarks Meson: one quark and one antiquark

(iv)What is the quark composition of the proton? Up, up, down

(v) What is the net charge of the three pions? Justify your answer. Zero, because electric charge must be conserved.

(vi)Calculate the combined kinetic energy of the particles after the collision.Energy equivalent of a pion:) E = mc2

E = (2.4842 )( 2.9979 × 108)2

E = 2.2327 × 10–11 JE = 1.3935 × 108 eVFor 3 pions E = 6.6980 × 10–11 J / 1.58195 × 109 eVEnergy after collision = (2 × 109) - (4.18047 × 108) = 1.58195 × 109 eV = 2.535 × 10–10 J

(vii) Calculate the maximum number of pions that could have been created during the collision.Number of pions = (1.58195 × 109) / 1.3935 × 108 = 11.3524 = 11 pions.Maximum number of pions = 3 + 11 = 14 pions.

2007(i) Draw a labelled diagram to show how Cockcroft and Walton accelerated

the protons. See diagram.

(ii) What is the velocity of a proton when it is accelerated from rest through a potential difference of 700 kV?

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(iii) Write a nuclear equation to represent the disintegration of a lithium nucleus when bombarded with a proton.

(iv)Calculate the energy released in this disintegration. Mass of reactants = 1.1646 × 10-26 + 1.6726 × 10-27 = 1.33186 × 10-26 kgMass of products = 2(6.6443 × 10-27) = 1.32886 × 10-26 kg)Δm = 3.00 × 10-29 kg E = m c2 or E = (3.00 × 10-29)(9 × 1016) = E = 2.7 × 10-12 J

(v) Compare the properties of an electron with that of a positron. Both have equal mass / charges equal / charges opposite (in sign) / matter and anti-matter

(vi)What happens when an electron meets a positron? Pair annihilation occurs.

(vii) In beta decay it appeared that momentum was not conserved. How did Fermi’s theory of radioactive decay resolve this?Fermi (and Pauli) realised that another particle must be responsible for the missing momentum , which they called the neutrino.

2006(i) What is a photon?

A photon is a discrete amount of electromagnetic radiation.(ii) Calculate the frequency of a photon produced during the interaction.

m [= mass of proton + mass of antiproton ] = 2(1.673 × 10-27) = 3.346 × 10-27 kg E = mc2 = (3.346 × 10-27 )(2.998 × 108)2 = 3.0074 × 10-10

Energy for one photon = 1.5037 × 10-10 JE = hf f = E/h / = 1.5037 × 10-10 / 6.626 × 10-34 = 2.2694 × 1023 Hz

(iii) Why are two photons produced? So that momentum is conserved.

(iv)Describe the motion of the photons after the interaction. They move in opposite directions.

(v) How is charge conserved during this interaction? Total charge before = +1-1 = 0 Total charge after = 0 since photons have zero charge

(vi)After the annihilation, pairs of negative and positive pions are produced. Explain why. The energy of the photons is converted into matter .

(vii) Pions are mesons that consist of up and down quarks and their antiquarks. Give the quark composition of (i) a positive pion, (ii) a negative pion. π+ = up and anti-down π- = down and anti-up

(viii) List the fundamental forces of nature that pions experience. Electromagnetic, strong, weak , gravitational

(ix)A neutral pion is unstable with a decay constant of 2.5 × 1012 s–1. What is the half-life of a neutral pion? λ T1/2 = ln 2 (= 0.693) T1/2 = 0.693 / 2.5 × 1012

T1/2 = 2.8 ×10-13 s

2005(i) What is the structure of an alpha particle?

An alpha particle is identical to a helium nucleus (2 protons and 2 neutrons). (ii) Rutherford had bombarded gold foil with alpha particles.

What conclusion did he form about the structure of the atom?

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The atom was mostly empty space with a dense positively-charged core and with negatively-charged electrons in orbit at discrete levels around it.

(iii) High voltages can be used to accelerate alpha particles and protons but not neutrons. Explain why.Alpha particles and protons are charged, neutrons are not.

(iv)Copy and complete the following nuclear equation for this reaction.

+ + K.E.(v) Circular particle accelerators were later developed. Give an advantage of circular accelerators

over linear accelerators. Circular accelerators result in progressively increasing levels of energy and occupy much less space than an equivalent linear accelerator.

(vi)In an accelerator, two high-speed protons collide and a series of new particles are produced, in addition to the two original protons. Explain why new particles are produced.The kinetic energy of the two protons gets converted into mass.

(vii) A huge collection of new particles was produced using circular accelerators. The quark model was proposed to put order on the new particles. List the six flavours of quark. Up, down, strange, charm, top and bottom.

(viii) Give the quark composition of the proton. Up, up, down.

2004 (i) Beta decay is associated with the weak nuclear force.

List two other fundamental forces of nature and give one property of each force. Strong: acts on nucleus/protons + neutrons/hadrons/baryons/mesons, short rangeGravitational: attractive force, inverse square law/infinite range, all particlesElectromagnetic: acts on charged particles, inverse square law/infinite range

(ii) In beta decay, a neutron decays into a proton with the emission of an electron. Write a nuclear equation for this decay.

(iii) Calculate the energy released during the decay of a neutron.Mass lost = mass before – mass after = (mass of neutron) – [(mass of proton + electron)]

= (1.6749 × 10–27) – [(1.6726 × 10–27 + 9.1094 × 10–31)] = 1.3891 × 10-30 kg

E = mc2 = (1.3891 × 10-30)(2.9979 × 108)2 = 1.25 × 1013 J(iv)Momentum and energy do not appear to be conserved in beta decay.

Explain how the existence of the neutrino, which was first named by Enrico Fermi, resolved this. Momentum and energy are conserved when the momentum and energy of the (associated) neutrino are taken into account.

(v) What is nuclear fission?Fission is the splitting of a large nucleus into two smaller nuclei with the release of energy.

(vi)What is the function of the moderator in the reactor?It slows down fast neutrons.

(vii) How did the cadmium rods control the rate of fission? They absorbed neutrons which would otherwise cause fission.

2003 (i) Leptons, baryons and mesons belong to the “particle zoo”.

Give (i) an example, (ii) a property, of each of these particles. LEPTONS; electron, positron, muon , tau, neutrinoNot subject to strong force BARYONS; proton, neutronSubject to all forces, three quarksMESONS pi(on), kaon

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Subject to all forces, mass between electron and proton, quark and antiquark

(ii) The following reaction represents pair production.γ → e+ + e–

Calculate the minimum frequency of the γ-ray photon required for this reaction to occur. E = (2)mc2 = hf2(9.1 × 10–31)( 3.0 × 108)2 = (6.6 × 10–34)f f = 2.5×1020 Hz

(iii) What is the effect on the products of the reaction if the frequency of the γ-ray photon exceeds the minimum value?The electrons which were created would move off with greater speed.There may also be more particles produced.

(iv)The reverse of the above reaction is known as pair annihilation. Write a reaction that represents pair annihilation. e+ + e- → 2γ

(v) Explain how the principle of conservation of charge and the principle of conservation of momentum apply in pair annihilation. Total charge on both sides is zero Momentum of positron + electron = momentum of photons

2002(i) Name the four fundamental forces of nature.

Gravitational, Electromagnetic, Strong (nuclear), Weak (nuclear) (ii) Which force is responsible for binding the nucleus of an atom?

Strong(iii) Give two properties of this force.

Short range, strong(est), act on nucleons, binds nucleus(iv)In 1932, Cockcroft and Walton carried out an experiment in which they used high-energy protons

to split a lithium nucleus. Outline this experiment. Protons are produced and released at the top of the accelerator.The protons get accelerated across a potential difference of 800 kVolt. The protons collide with a lithium nucleus at the bottom, and as a result two alpha particles are produced. The alpha particles move off in opposite directions at high speed. They then collide with a zinc sulphide screen, where they cause a flash and get detected by microscopes.

(v) When a lithium nucleus (7 3Li) is bombarded with a high-energy proton, two α-particles are

produced.Write a nuclear equation to represent this reaction.

(vi)Calculate the energy released in this reaction.

Mass defect = mass before – mass after= [(1.6730 × 10-27) + (1.1646 × 10-26)] – [2(6.6443 × 10-27)] = 3.0 x 10-29 kgUsing E = mc2 E = (3.0 x 10-29)( 3.00 × 108)2 E = 2.7 × 10-12 J

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