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Walton High

2008-2009

AS Quality of Measurement TaskPhysics in Practice Coursework BookletDr. S. Harding.

Quality of Measurement Task

Contents

What are the aims?...........................................................................................................................3Things for You to do........................................................................................................................3Suggested Tasks...............................................................................................................................3Advancing Physics – Quality of Measurement Project Planning Sheet...........................................3Strands of assessment in the Quality of Measurement task.............................................................3Making sense of data coursework - practice....................................................................................3Why do I want to use Excel, anyway?.............................................................................................3

How do I open Excel?..................................................................................................................3How do I save my work?..............................................................................................................3How do I put data into my sheet?.................................................................................................3How do I get it to calculate stuff for me?.....................................................................................3What is the 'Nifty Short Cut' for copying a formula down a column?.........................................3How do I use Excels built in formulae?.......................................................................................3How do I do graphs?....................................................................................................................3How do I change it so it plots V against I or P against I?............................................................3Hmm. Is there a less fiddly way?................................................................................................3Let's get fancy…...........................................................................................................................3


Introduction

As part of your quality of measurement coursework you will be required to devise an approach to an experiment and then carry it out and perform some careful data analysis of your results.

There are many ways to tackle a problem (some better than others) as the following story illustrates:

The following is a question on a physics exam at the University of Copenhagen:

"Describe how to determine the height of a skyscraper with a barometer." One student replied: "You tie a long piece of string to the neck of the barometer, then lower the barometer from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building."

This highly original answer so incensed the examiner that he failed the student who immediately appealed on the grounds that his answer was indisputably correct.

The university appointed an independent arbiter to decide the case.

The arbiter ruled that the answer was indeed correct, but did not display any noticeable knowledge of physics. It was decided to call the student in and allow him six minutes in which to provide a verbal answer which showed at least a minimal familiarity with the basic principles of physics.

For five minutes the student sat in silence, forehead creased in thought. The arbiter reminded him that time was running out, to which the student replied that he had several extremely relevant answers, but couldn't make up his mind which to use.

On being advised to hurry up the student replied: "First, you could take the barometer up to the roof of the skyscraper, drop it over the edge, and measure the time it takes to reach the ground. The height of the building can then be worked out from this formula I have worked out for you on my text paper here."

Then the student added, "But, Sir, I wouldn't recommend it. Bad luck on the barometer."

"Another alternative", offered the student, "is this: If the sun is shining you could measure the height of the barometer, then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper's shadow, and thereafter it is a simple matter of proportional geometry to work out the height of the skyscraper. On the paper is the formula for that as well."

"But, Sir, if you wanted to be highly scientific about it, you could tie a short piece of string to the barometer and swing it like a pendulum, first at ground level and then on the roof of the skyscraper. The height is worked out by the difference in a gravitational formula, which I have determined here this time on a long sheet of paper with a very long and complicated calculation."

"Or, Sir, here's another way, and not a bad one at all. If the skyscraper has an outside emergency staircase, it would be easier to walk up it and mark off the height of the skyscraper in barometer lengths, then add them up."

"But if you merely wanted to be very boring and very orthodox about the answer you seem to seek, of course, you could use the barometer to measure the air pressure on the roof, and on the ground, and then convert the difference in millibars into feet to give the height of the building."

"But since we are constantly being exhorted to exercise independence of mind and apply scientific methods, undoubtedly the best way would be to knock on the janitor's


door and say to him 'If you would like a nice new barometer, I will give you this one if you tell me the height of this skyscraper'."

The student was Niels Bohr, the only Dane ever to win the Nobel Prize in physics.

Niels Henrik David Bohr (1885-1962)Danish physicist and one of the foremost scientists in modern physics. He was professor of theoretical physics at the University of Copenhagen and was later director of its Institute for Theoretical Physics, which he helped to found. He was awarded the Nobel Prize in 1922 for his work on atomic structure and the hydrogen atom. Classical theory had been unable to explain the stability of the nuclear model of the atom, but Bohr solved the problem by postulating that electrons move in restricted orbits around the atom's nucleus and explaining how the atom emits and absorbs energy. He thus combined the quantum theory with this concept of atomic structure. He was also known for his robust jousts, often humorous with Albert Einstein.


What are the aims?Candidates should develop a sense of pride in measuring as well as possible given the tools they have, and to

be clear about how well the job has been done. They should be able to experiment well, to recognise the

limitations of instruments and to discuss the uncertainty of measurements, learning to look for important

sources of uncertainty and attempt to reduce them. They should also consider possible systematic errors and

try to remove them. Candidates should be able to analyse data carefully make intelligent use of graphs and

tables, extract as much information as possible and present a report that explains clearly the procedures they

have used. The written record should communicate the results obtained and have a clear outcome that is

qualified with statements of uncertainty.

Quality of Measurement

Candidates undertake a task of the following kind:

• a careful measurement of a physical quantity;

• a careful quantitative study of the relationship between two or more variables, where there are

some indications from theory of what to expect;

• a careful calibration of a sensor or instrument;

• a careful study of one or more of the properties of a sensor or instrument;

• a comparison of methods of measuring the same thing.

The word ‘careful’ implies both practical skill (‘hands on’) and thoughtful analysis of problems and

data (‘minds on’).

Candidates should demonstrate their ability to:

• recognise the qualities and limitations of measuring instruments, particularly resolution,

sensitivity, calibration, response time, stability and zero error;

• identify and estimate the most important source of uncertainty in a measurement and seek

ways to reduce it;

• consider the possibility of systematic errors and seek to estimate and remove them, including

considering calibration;

• make effective plots to display relationships between measured quantities, with appropriate

indication of uncertainty;

• use simple plots of the distribution of measured values to estimate the median (or mean)

value and the spread (which may be estimated from the range of values), and to identify

and account for outlying values.

A written report of the work done is produced. This task builds on the measurement tasks that candidates will have performed in their experimental work throughout the AS course.


Things for You to do

1. Have a go at the practice task near the end of this booklet

2. Choose a task for your investigation.

3. Check with us that it is possible.

4. It is up to you to work out how you will undertake your task and what equipment you will

need so some research is vital – use the web, books journals etc.

5. Produce a plan using the sheet provided and get it signed off by us

6. Create a detailed equipment list – you must list EVERYTHING that you will need including

quantities so the lab technicians can prepare it. If you don’t list it you wont get it

7. Read the textbook Pages very carefully so you know how to handle uncertainties and

errors – this is essential for high marks. You need to gather enough data to estimate the

uncertainties in your measurements

8. If you have a laptop bring it in for the practical’s – record data as you go and use excel to

plot graphs and check the quality of your results. Or plot by hand. It will be too late to redo

things if you find out later that your data is junk

9. Read the mark scheme in this guide very carefully so you know what you need to do to

access the marks

10. There will be NO chance to redraft – once you hand in that’s it.


Suggested Tasks

1. A careful measurement of a physical quality

• Breaking stress of a wire

• Conductivity of copper

• Emf and/or internal resistance of a cell

• Gravitational field strength near the Earth’s surface

• Power and/or magnification of a lens of a lens

• Speed of light

• Speed of sound in air

• Young modulus of copper

2. A careful quantitative study of the relationship between two or more variables, where there are some indications from theory of what to expect

• Absorption of light with thickness of materials, or concentration of a solution

• Resistance of a metal wire and temperature

• Response of a solar cell to varying light intensity

• Speed of a trolley down a slope and angle

• Speed of falling paper cones and area

3. A careful calibration of a sensor or instrument

• LDR used as a simple light meter

• Linear sprung potentiometer used as simple balance

• Rotary potentiometer as an angle sensor

• Thermistor used as a simple thermometer

4. A careful study of one or more of the properties of a sensor or instrument

• Response time of a thermistor

• Sensitivity of a thermistor

5. A comparison of methods of measuring the same thing

• Airflow from a fan using a hinged flap and rotary potentiometer compared with a hot wire anemometer

• Liquid level based on flotation and a rotary potentiometer compared with an LDR and light source

• Measuring g in more than one way


• Proximity using an ultrasonic sensor


Advancing Physics – Quality of Measurement Project Planning Sheet

Name__________________________________________ Teacher_________________________

Dates of practical work_______________________ Hand in the report by:__________________

Proposed title of my project

What I hope to achieve

Outline of my plan

A circuit diagram to show how I will set out my apparatus (at the start)


Equipment I’d like to use including quantities – LIST EVERYTHING

Chemicals required

Safety Issues I need to think about (Compulsory)

Teacher’s comments

Teacher’s signature Date


Strands of assessment in the Quality of Measurement task 1. Quality of practical work in the laboratory

Was the practical work done systematically and carefully, showing skill in handling and using apparatus? Were sufficient observations and measurements made to deal with the problem? Were results tabulated carefully in a well-thought-out structure, recorded as they were taken? Were measurements made so as to minimise systematic error, and to reduce uncertainty to the limits allowed by the apparatus?

Level 1 Methods and approach have limitations, with shortcomings in the measurements and observations and limited attention to practical detail.

Level 3 Methods and approach are adequate, with relevant measurements and observations and competent attention to practical detail.

Level 5 Methods and approach are well chosen, with sufficient measurements and observations made to deal with the problem and considerable skill used to obtain them, avoiding unnecessary systematic error.

2. Quality of thought about uncertainty and systematic error, and attempts to improve the measurements

Were the relevant properties of sensors or measuring instruments studied and assessed systematically and carefully? Was the calibration of instruments considered, and attempted where possible? Was the largest source of uncertainty identified and estimated? Were possible systematic errors considered, and their sign identified? Did the student suggest and try out possible improvements to the experimental method and apparatus used?

Level 1 Measuring instruments are used directly without consideration of their properties; little understanding of the nature of error or uncertainty is shown, and data is limited to a simple set of measurements.

Level 3 Some efforts are made to use measuring instruments to their best advantage; error and uncertainty are considered, possibly with some flaws in approach, and some improvements to experimental method are considered.

Level 5 The relevant properties of measuring instruments are assessed systematically; errors and uncertainty are identified and, where possible, reduced and improvements to the experiment to reduce error and uncertainty are tried out.


3. Quality of communication of physics in the report

Is the report clear, well-ordered and concise, with enough detail to allow someone else to repeat the experiment and obtain similar measurements? Does the report explain clearly the physics of the experiment? Was available ICT used well? Are graphs and tables well-chosen, and presented so as to communicate the findings as well as possible? Is the use of English effective for the purpose?

Level 1 Recording and presentation of data lacks clarity; graphical plots may be inappropriate or incorrect and the report is poorly structured and presented.

Level 3 Data are presented clearly, with some possible inconsistencies in headings, units or significant figures; graphical plots are clear and the report covers most details needed to repeat the experiment.

Level 5 Data are presented clearly and effectively with correct headings, units, tolerances and significant figures; graphical plots are well chosen to display the data to good effect and the report is clear, concise, well-structured and gives all details needed for someone else to repeat the work.

4. Quality of handling and analysis of data

Was data analysed with care and attention, looking for anomalies or unexpected features, and extracting as much information as possible? Does the analysis demonstrate a clear and correct understanding of the physics involved? Were results cross-checked through alternative ways of looking at the data or going back to the apparatus? Was there a clear claim about the outcome, qualified with statements of uncertainty and possible systematic error?

Level 1 Analysis is limited to direct calculations or plots of measured data with possible major flaws in physics, or no attempt to explain the outcomes in terms of physical ideas, and limited attempt to discuss shortcomings in procedures.

Level 3 Some correct calculations of relevant quantities are made with an attempt to discuss the outcomes in terms of physical explanations (including discussion of errors and uncertainties) with minor errors of physics in the analysis. Obvious anomalies are noted.

Level 5 Data are analysed carefully, extracting as much information as possible, leading to a clear claim about the outcome, well-founded in the data and analysis, demonstrating understanding of the physics and relating uncertainties in the conclusions to limitations of the procedures and the measurements made.


Making sense of data coursework - practice.

Below are the results of an experiment about the time period of a pendulum.

Length (m) Time(s)

0.02 0.284 0.04 0.4010.06 0.4910.08 0.5670.10 0.6340.12 0.6950.14 0.7500.16 0.8020.18 0.8510.20 0.8970.22 0.9400.24 0.9820.26 1.020.28 1.060.30 1.09

1. Type these results into Excel and produce a graph with length along the bottom and time up the side. Use the 'Simple Graphs' section of the Bluffer's Guide. Print.

2. The theory of the simple pendulum is that the time for one oscillation

To see if the experimental results agree with the theory you need to process them to find a straight line graph. If the equation above is correct then a graph of T against l will be a straight line through (0,0).

To do this, make another column on the spreadsheet for length. Use a calculator or an equation in Excel to calculate the square root of each of the lengths. [The equation is =(cell with length in it)^0.5]. Print the sheet.

3. Now plot the graph of time against length. You may need to move the columns about to get it with time up the side. Print.

4. Use the 10 steps sheet to make it look more professional. Print.

5. You should have a trendline that is of the form y=mx. According to the theory

is like y = m x so the gradient of the line m = 2/gso, rearranging, mg = 2

g = 2 m

g = 4 m2

Find m from your trendline equation. Create a bubble from Autoshapes, copy the equation for g into it and work out a value for g.

It should be 9.81N/kg. Comment on the value that you got and write it in the bubble. Print


T=2 π √ lg

T=2 π√g

√l

Why do I want to use Excel, anyway?

You really do want to use Excel when you have data and you want to calculate things or make graphs, which pretty much means whenever we do experiments with even a small amount of data.

Please remember that this program was written for business, not science, and that it has no brain. YOU are the one with the grey matter and 'garbage in, garbage out' applies. Always think 'Does that look reasonable?' first, before trusting it or printing it out.

How do I open Excel?Open Excel using the Start menu, then Programs then Microsoft Excel (or Microsoft Office then Microsoft Excel).You will get this (depending on the version):

How do I save my work? From the File menu, click Save As, type a file name for the workbook. Click Save.

How do I put data into my sheet?You make tables in Excel just like the ones that you would draw for data when doing your experiment. Let's imagine that you have the following data for a resistor - type it into Excel so it looks like this:


This is cell A1 - all cells have a reference

This is sheet 1 - you can have lots of sheet in each workbook

Increase decimal places button (decrease is the next one)

Chart wizard

Formula bar

Voltage (V) Current (A)0.0 0.002.0 0.514.0 0.986.0 1.408.0 2.0710.0 2.5512.0 3.00

You should notice that the numbers change so that 0.00 changes to 0. You can change this back by highlighting the column and then pressing the 'increase decimal place' button.

How do I get it to calculate stuff for me?

Type 'Resistance' in the heading of the next column. [Check out the 'Let's get fancy' section at the end to work out how to put () in as well]

Click on cell C2 (underneath where you have typed resistance) and then press the = sign on the left of the formula bar. Then click on cell A2, then / on the keyboard then on cell B2 so that it looks like this:

Click OK and you will get a nasty looking thing that says: #/DIV/0! That's because it doesn't like dividing by zero, and neither should you. We'll let it ride for now.We want to find out the resistance for the other pairs of values and you have a choice. You can repeat that for the rest of the cells (ok if you like that kind of thing and don't have anywhere else that you should be for a while), or you could do the good old-fashioned copy and paste - it works


the same but slower OR you can do the 'Nifty Short Cut'.

What is the 'Nifty Short Cut' for copying a formula down a column?You should by now have seen that your mouse looks like three things:

The mouse pointer looks like this when used for selecting.

The mouse pointer looks like this when used for copying/filling.

The mouse pointer looks like this when used for moving.

Move the pointer so that it rests on the little black box in the bottom right hand corner of cell C2 and looks like the copying/filling pointer above. Then double click. Hey presto, the formula is copied all the way down your table.

Except that you now have a horrendous number of decimal places in most of the cells. If you are saying 'What is horrendous about that number of decimal places' imagine measuring the circumference of the Earth to the nearest centimetre. Fairly unlikely, huh?If you just click the 'decrease decimal place' button again nothing will happen because of the #/DIV/0! You can get rid of the offending item by just clicking on the cell and pressing delete or highlighting and deleting #/DIV/0! in the formula bar. Now highlight the numbers and reduce the decimal places to a decent number [2 or 3 because that is what was given in the data - probably 2].

How do I use Excels built in formulae?

Right, now we want the to work out the resistance of our resistor. We'll need the average, but Excel has that function, along with many others, built in.

Click on cell B9 and type 'Average'.Click on C9 and hit the = again to the left of the formula bar.Click the button to the right of 'SUM' and select 'AVERAGE'.

Excel looks for the likeliest set of numbers you might be wanting to average and says is that it. If you look at what it has done, it has selected C3:C8.

Click OK. The resistance should be 4.0Well done! That's the tricky bit over.

Formula symbols you will need in the future:plus +minus -multiply *divide /a2 a*a or a^2103 10^3 or 1E310-9 10^-9 or 1E-93 SQRT(3) PISin() SIN(80)


Things for you to try:

Can you work out the power using P = V x I for each of our readings?

There is another formula for power P = I2R. Make another column and check that you get the same results as above.

How do I do graphs? Select the cells you wish to use for your graph - here it would be A2 to B8 - highlight them. Select 'Chart Wizard' (if the button isn't there go to Insert then Chart.) 999,999 times out of 1,000,000 we will want an x-y scatter graph because it's scientific. I know 3D doughnut shaped graphs look much sexier but don't be distracted.

Step 1. Select X-Y (scatter). Select the points without the line (top box). Click Next.

Step 2. Click Next.

Step 3. In Chart Title highlight 'Current (A)' and delete it. Type ' Current /Voltage graph for a Resistor' then Enter. In Value (X) axis type 'Voltage (V)' then Enter, in Value (Y) axis type 'Current (A)' then Enter. Click on the Legend tab at the top of this box and click on the box with the tick in it (show legend). It should now not have a tick in it. Click Next.

Step 4. Select top dot - as new sheet. Highlight Chart 1 and delete it. Type 'IV graph'. Click Finish.

You can play with your chart and make it pretty. If you right click anywhere on your chart and select Format Plot area then you can change the background area (none is good!)

Now we can add a line and see what the equation is. Click on any point and all the points should be highlighted. Click Chart on the menu line, then Add Trendline. 'Linear' should be selected already. Click the Options tab at the top of the box. Select 'Set Intercept = 0' and 'Display equation on chart'. Click OK.


The equation should be y = 0.2511x.

How do I change it so it plots V against I or P against I?

1. V against I instead of I against V.Select the cells you wish to use for your graph - here it is A2 to B8 again- highlight them. Select 'Chart Wizard' Step 1. Select X-Y (scatter). Select the points without the line (top box). Click Next.

Step 2. Click on the Series tab at the top of the box then click on the funny looking button the right of 'X values=Sheet1!$A$2:$A$8'. This takes you to this screen:

Highlight the numbers in the Current column not including the title or the word 'Average'. Click the funny looking button again. Click on the funny looking button the right of 'Y =Sheet1!$B$2:$B$8'. This time highlight the numbers in the Voltage column but not the title then click that button again. Click Next.

Step 3. Add titles as before and remove legend. Click Next.

Step 4. Select top dot - as new sheet. Highlight Chart 1 and delete it. Type 'VI graph'. Click Finish.


Oh look. If the resistance is 4 then the conductance is ¼ S = 0.25S.And the conductance is also the gradient of an I vs. V graph. Well done Excel.

Funny looking button

Highlight this column

If you now add a trendline, make sure that it goes through 0, you should find that the gradient is 4, as you would expect.

2. P against I instead of I against V.Select the cells you wish to use for your graph - here it is B1 to D8 because that selection includes just current and power. Highlight them. Select 'Chart Wizard' Step 1. Select X-Y (scatter). Select the points without the line (top box). Click Next.

Step 2. Click on the Series tab at the top of the box then in the 'Series' box make sure that 'Resistance' is highlighted then click on the Remove as below. Click Next.

Step 3. Add titles as before and remove legend. Click Next.

Step 4. Select top dot - as new sheet. Highlight Chart 1 and delete it. Type 'PI graph'. Click Finish.

Hmm. Is there a less fiddly way?

If you like you can highlight the column that contains the numbers that you want on the bottom (x-values) and copy and paste them to a place below your original table. Then copy what you want to be up the side and paste it next to it. The only problem you will have will be if your columns contain formulae. Then it will come up with #REF! To fix it try again but don't paste. From the Edit menu select Paste Special, then Values. Then just do chart wizard and you won't have to mess around with the series bit at all.


Click here

Let's get fancy…

1. and other fancy symbol. These, just like in Word, are Greek letters. Click on your Resistance box, the click in the formula bar. Type (W) - make sure that it is capital W - then highlight the W. Go to Format, Cells, Font and select Symbol. A weird thing will happen. It will still say W in the formula line, but it will say in the column heading.

2. Renaming sheets. Point to where it says 'Sheet 1' then right click and select Rename (or go to Format, Sheet, Rename). Call it what you like.

3. Changing the lines on my chart. Instead of the statutory horizontal lines on your chart you can change it.

Point at anywhere outside of the chart and right click and select Chart Options. On the Gridlines tab select Value X axis Major gridlines.Point at any of the grid lines and right click and select Format Gridlines. On the Scale tab try changing the values.Point at the x axis line and right click and select Format Axis. On the Patterns tab select Minor Tick Mark type Outside. See what happens.


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