chapter 1 general physics

7/26/2019 Chapter 1 General Physics

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Endorsed by

University

of Cambridge InternationalExaminations

Physics

RevisionGuide

Sarah Lloyd


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O X F O R D

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Tipsfor effective revision 4

1 Generalphysics

1.1 Length, volu me and t ime 7

1.2

Speed, veloci ty and accele ration 8

1.3 Mass and we ig ht 15

1.4 Densi ty 16

1.5 Forces 18

1.6 Energy, wo rk and po we r 33

1.7 Pressure 41

2 Thermalphysics2. 1 Kinetic the ory 50

2. 2 Ther mal propert ies 56

2. 3 Transfer of the rma l energ y 67

3 Properties ofwaves3.1 General wav e properti es 80

3. 2 Light 85

3. 3 Soun d 96

4 Electricity and magnetism4. 1 Magn et ism 105

4. 2 Electrical quan tit ies 110

4. 3 Electric circuit s 118

4.4 Dangers of electricity 129

4. 5 Electro magnet ic effects 131

4. 6 Cat hod e ray oscil loscope 139

5 Atomicphysics

5.1 Radioactivity 150

5. 2 The nuclear at om 158

Howto use this revision guide

This book is designed to be used with Complete Physics for IGCSE. It offers brief notes and

simplif ied explanations, along with practice questions, to help you understand the physics

principles required for the Cambridge IGCSE

syllabus. The notes, examples, summary

questions and examination questions are divided into sections that relate to the syllabus areas.

Th e examinat io n quest ions that acco mpany each subsect ion (e.g. t ransfer of the rmal

energy, which is part of the thermal physics section) wil l al low you to test yourself at regular

intervals. There are also questions at the end of each section so that you can test your

k nowledge and understanding of the whole topic. In this way you can revise topic by topic

unt i l you have covered the entire syllabus.


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KEY IDEAS

J Begin you r revision we ll in adva nce of th e examin ati on


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Writing your own test

Wri te do wn questi ons as you go thr oug h this Revision Guide. When y ou reach the end of

the topic you can use the questions to test your k now led ge and und erstan ding an d check

your progress.

Getting someone else to test you

You could give one of your classmates your revision notes and ask them to test you. Or you

could get th em to ask you abo ut parts of the syllabus they do n' t unde rstan d. This is a go od

test of your understanding of that topic!

Using your syllabus

You can dow nl oa d a copy of the syllabus fr om th e CIE web sit e. Ma ke check lists fo r r evision

using the syllabus to indi cate wh en you have made revision notes, practised exam quest ions

etc. Don't forget to include a column to tick when you feel you have understood a topic.

Doing past exam questions

There are lots of examination questions throughout this book for you to try. Try revising a

small part of a topic , say for ab out 3 0 minute s and then test yourself on the exami natio n

style questions provided here. When you feel ready, full past papers are available on the

H E website

Making revision posters

If you make your revision notes into posters and put them in places where you will see them

often, you will read them without even realising! This will help to keep topics fresh in your

mind . Your family and friends will see what you have been revising and might talk to you

abo ut it, whi ch will help the in for mati on in stick your m ind .

Essential quantities and units

Time t second (s)

Force F newton(N)

Weight W )


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Formulae and magic triangles

These magic tr iangles are a useful way of remembering how to use an equation, but are no

subst i tute for remember ing the equat ion i tsel f.

To use a magic tr iangle, cover the quantity you are trying to f i n d . The relationship left

beh ind shows you how to calculate it. For example, cover up speed, u in the first tr iangle

and you are lef t wi th j .

/ d \ / \ / f \

X


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1 General physics

. / I

U > f K j i ; f l ,

yrj| i jrr>f-'

. ;] fK. I i i r r K

/ Len gth is measu red wi th a ruler, tap e measu re, verni er call ipers or mic rom ete r

screw gauge

S Volu me may be measured wi th a measur ing cyl inder

/ Tim e is measu red wi th a stop clock or sto p wa tc h

Length measurements can be made more precise by using an instrument with a vernier

scale such as vernier call ipers or a micrometer screw gauge. A ruler measures to the nearest

mil l imetre, vernier call ipers to 1/10 mm and a micrometer 1/100 mm . Length measurements

can be made more accura te by measu ring mu ltiple s, such as the thicknes s of 500 sheets o f

paper, then divide by 500 to get the thickness of one sheet. Check the rel iabi l i ty of your

measurements by repeating them. If the repeated results are similar, they are reliable. When

measuring the length, / of a pendulum as in the figure (right), you need to measure to the

centre of gravity. One way of doin g this is to take tw o mea sure ment s and average th em :

f r o m the f ixed end of the str ing to the beginning of the bob, /, and from the fixed end of

the str ing to the far end of the bob /

gap beingmeasured fixed fixed scaleonscale revolvingbarrel

mm0 10_ u _ L

p-trr

J_L

Readthehighestscaledivisionbefore

f

:

I

Add: 7.4 mmA Reading a vernier

Seewheredivisions coincide.Readthisonslidingscale,puttingadecimalpointinfront:

I

0.4I

Readthehighestscaledivisionthatcanbeseen:

5.5L_

Readthescaleonthebarrel,puttingadecimalpoint infront:

I

0.32I

Add: 5.82mmA Reading a micrometer

The volume of a regular solid can be found by measuring its dimensions. For example,

recording the length, width and height of a cuboid (box) and multiplying these

measurements together. The volume of an irregularly shaped object can also be measured

using a measuring cylinder with a eureka can. Place the object in the eureka can and use the

measuring cylinder to measure h ow m uc h wate r is displaced . The vol ume of wate r displa ced

isequal to the volu me of the obj ect.

A digital stop watch measures time to a precision of 0.0 1 s. This is far m or e precise t ha n

human error wil l al low, which is about 0.2 s. If possible, t ime over as long a period as

possible. Wh en t i ming t he t ime per iod for a simple pen du lum , for example, i t is more

accura te to t ime 10 0 swings wi th a stop watch and then divide by the number of swings.

This reduces the error due to human reaction time. Repeat t ime measurements to check for

rel iabi l i ty of data.

A Eureka can and measuring

cylinder


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KEY IDEAS

y Speed = d | t aneM

t ime

, change in velocity/ Accelerat ion = ^

/ Velocity and acceler ation can have bo th posit ive and negat ive values

. . . . d istance (m)Spe ed (m/ s) - ,

\

K

t ime

(s)

dt

Workedexamples

1 A car travels at a speed of 20 m/s for 30 s. How far does it travel in this time?

2. A cyclist travels 1000 m in 3 m i n u t e s . What is his speed?

3. A gir l wal ks 3 km at 1.5 m/s. How lo ng does her jou rne y take ?

Answers

1. d= u x t= 2 0 X 30

= 600 m

2. u=d/f= 1000 T ( 3 X 60)

= 1000 + 180

= 5.56 m/s

3. t = dlu= (3 X 1000) - 1.5

= 3 0 0 0 1.5

= 20 00 s (33 min 20 s)

Note: in example 2, t ime in minutes must be converted to seconds. In example 3, distance

in ki lometres must be converted to metres.


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Distance-t ime graphs

A journey can be represented on a graph by plott ing the distance travelled on they-ax is and

t he t ime taken on the x-axis. The shape of the graph describes the journey.

distance/m

ystep

Thegradient of the graph_ y step

~ x step

= speed

xstep

time/s

A Distance-time graph

Examplesof distance-time graphs

1

In a crash test, a car travels at steady speed and then stops suddenly as it hits a wall

Thereis a constant gradient

becausethe object travels

atsteady speed.

distance/m

time/s

Thegradient suddenly

changesto zero (horizontal

line),which means the speed

iszero and the object has

stopped.

2. A ru nner sets off in a race, increasing her speed unti l she reaches her ma xi mu m speed .

Initially, the gradient is low,

whichmeans the speed is low.

distance/m

Thegradient gradually

increasesbecause the

speedis increasing.

time/s


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Revis ion guide: Physics

Velocityand acceleration

Vel oc i ty is a v e c t o r quant i t y ; it is eq ua l to s p e e d in a particular direction. Speed is a

measurement of how fast an object is moving.

Acce l era t i on is also a vector quantity. It is equal to the change in veloci ty per second.

W h e n a n object is slo win g do wn , if i ts veloci ty isd e c re a s in g , the acceleration is negative.

W e say that it isdece l era t i ng . See section 1.5

(scalars and vectors).

Accelerat ion (m/s 2)

init ial velocity = u, f inal velocity = v,

t i m e taken for the change in veloci ty

change in velocity = v u = Av

Workedexamples

1 A car increases its velocity from 10 m/s to 2 0 m/s in 5 s. Wh at is its acc eler atio n?

2. A runner has an accelerat ion of 10 m/ s 2. H ow l ong does it take h im to reach a speed o f

5 m/s from rest? (Note 'rest' means zero velocity.)

3. A tra in accele rates at 9 m/s 2 for 5 s. If its initial velocity is 5 m/s, what is its final

velocity?

Answers

1 a = Av+t

= (20 - 10) 5

= 2 m/s 2

2. t= Av + a= 5 + 10

= 0.5 s

3. Av= a X f=

9 X 5

= 45 m/s

v = u + Av

= 5 + 45

= 50 m/s

= chang e in veloci ty ( m / s ) ti me (s)

__ v - ua -

r

-

= t,


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Speed-timegraphs

speed

m/s

Thearea under the

graph= distance

travelled.xstep

ystep

Thegradientof the speed-time

. y step

9

r a

P

h =

3FItep

= acceleration

time/s

A Speed-time graph.

Th e area under th e gra ph is a calcul ation involv ing the units on th e tw o axes. It is no t a

physical area.

Examplesof speed-time graphs

1

A car accelerating unti l i t reaches its maximum speed.

Thecar starts with its greatest

acceleration(the gradient is

highest). The acceleration

decreaseswith time as the car

approachesits maximum speed

(thegradient decreases).

Atthe maximum speed the

graphis horizontal (gradient

iszero) indicating the car has

reacheda steady speed.

time/s

2. A runner w ho accelerates wi th constan t accelerat ion to his max imu m speed and

then decelerates steadily to a stop at the end of the race.

Atthe start o f the race

theacceleration of

therunner is greatest

(gradientis maximum).

Thisacceleration is

constantand so the

gradiento fthe graph is

constant(a straight line).

Asthe runner reaches a

steadyspeed, the gradient

becomeszero (horizontal line

ongraph).

time/s

Atthe end of the race, the

runnerdecelerates (negative

gradient) to rest (zero velocity).

Thestraight line shows that the

decelerationis constant.

3. A skydiver f ro m the t ime she jum ps from a hel icopter unt i l the mo me nt she

reaches the groun d.

Initiallythe skydiver

acceleratesbut the

accelerationdecreases

withtime as air resistance

increases(gradient is

positivebut decreasing).

speed

Whenshe opens her parachute, the

accelerationchanges from positive to negative

asshe decelerates (negative gradient).

Finally,the deceleration

decreasesand she reaches a

steadyvelocity (zero gradient).

Thisis the te rmi na l velo cit y.

time/s


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.' . 'Re v is io n guide: Physics

Examination stylequestions

1. r

Th e grap h above is for a 60 minu te car journey.

a. Betw een whi ch times is the car speed at its highest?

b. Calcula te the total t im e fo r wh ic h the car is sto ppe d.

c. State wi th ou t calculat ion how the graph could be used

i) to f in d the distance travelle d in the first 12V2

minutes.

i i) to f in d the average speed for the journ ey.

G r a p h a d a p t e d f r o m CIE 0625 J u n e '0 5

Pap er 2 Q 2

A ston e falls fr om the to p of a bui ldin g and hits the g ro un d at a speed of 32 m/s.

Th e air resistance force o n the sto ne is very small and may be negl ecte d.

a. Calculat e the tim e of fall.

b. Copy and dra w the spe ed-t ime graph for the fal l ing stone.

40

30

speed

m/s20

10

1 2 3 4

time/s

CIE 0625 November 06 Paper 3 Q 1 a


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Genera l physics

3. The f igure bel ow shows the spe ed- t ime gra ph for a journ ey t ravel led by a t ractor.

0 50 100 170 200

time/s J

a. Use th e graph to describe the mo ti on of the tracto r durin g th e sections OP, PQ, QR

and RS.

b. Whi ch two points on the graph sh ow wh en the t ractor is stat ionary?

c. State th e greates t speed reached by the tractor.

d. For ho w long was the trac tor travel l ing at con sta nt speed?

e. State ho w the graph may be used to f ind the tot al distance travelled duri ng th e

200 s journ ey. Do no t at tempt a calculat ion.

CIE 0625 Novem ber '0 6 Paper 2 Q3

4. Palm trees are gr ow in g every 25 m alongside the hi ghw ay in a holid ay resort.

Th e IGCSE schoo l bus drives alo ng the highw ay.

a. It takes 2 s fo r the bus to travel betwe en pa lm tree 1 and palm tree 2.

Calculate the average speed of the bus between tree 1 and tree 2.

b. It takes mor e than 2s for the bus to travel fr om tree 2 to tree 3.

State wha t this infor mat io n indicates abo ut the speed of the bus.

c. The speed of the bus cont inue s to do wha t yo u have said in (b). State ho w th e

t ime taken to go from tree 3 to tree 4 compares with the time in (b).

CIE 0625 Novemb er '0 5 Paper 2 Q2

j y


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5. In a tra in in g session, a raci ng cyclist's jo ur ne y is in thr ee stage s.

Stage 1 He accelerates uni for mly fr om rest to 12 m/s in 20 s.

Stage 2 He cycles at 12 m/s for a distance of 4800 m.

Stage 3 He decelerates uni form ly to rest.

Th e whole journey takes 500 s.

a. Calculate th e tim e tak en for stage 2.

b. Cop y the grid be lo w and draw a sp ee d-t ime gra ph of the cyclist's r ide.

0 100 200 300 400 500

time/s)

c. Sh ow th at th e tota l distance travelle d by th e cyclist is 54 00 m.

d. Calcula te th e average speed of the cyclist.

CIE 0625 J u n e '07 Pap er 2 Q 2


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'1,3 M'ji-r;wk.I y . / r :H g : l t i :

# f E V / D > S

/ Mass is a qua nti ty relate d to the inertia of an obje ct, meas ured in kg

/

We ig ht is the forc e, in N, on a mass due to a grav itatio nal f iel d

/ On Earth, th e grav itati onal f iel d stre ngt h is 10 N/kg

Mass is the amo unt of ma t t e r that makes up an object. It is measured in kilograms (kg). All

masses have a qual i ty cal led " iner t ia" , the tendency to keep moving i f al ready moving and

stay still if already still.

For example, a car in a crash test: when the car hits the wal l , it decelerates to rest in a short

t ime. The crash test dummy has inertia due to its mass and so it keeps moving forwards at

the same speed as befo re the car hit the wall . Al th ou gh it looks as th ou gh th e du mm y has

been thrown forward, there is no net forward force on i t .

* %

fc* , i t T T mmrnrnt

W e i g h t is th e force on a mass due to gravity. It is meas ured in new to ns (N).

we i g h t (N) = mass (kg ) X gravi tat ional f ield stren gth (N/kg)

W = m X g

On Earth, the gravi tat ional f ield strength, g = 10 N/kg. This is also calle d th e acce lera tion

du e to gravity or th e acceleratio n of freefall and has an alternative u nit of m/s 2 .

Examination style question

Some IGCSE students were asked to wr i te statements abou t mass and wei ght .

Their statements are pr inted below. Choose the t w o correct statements.

Mass and weig ht are the same thing.

Mass is mea sur ed in ki lograms.

W e i g h t is a ty pe o f for ce.

W e i g h t is the acceler at ion caused by gravity.

CIE 0625 Novembe r 06 Paper 2 Q2


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KEY IDEAS

/

Density = " ?

a s s , measured in g/ cm 3 or kg/m 33

volume

Densi ty is a qua nti ty rela ted to h ow closely packed the particles in a material are as wel l as

h o w much the part icles weigh.

i ,

. mass (g)density ( g / c m

3

)

=

v o | u m e < g r f )

m >

P - t '

A simple met ho d of meas urin g the density of an obje ct ( if its density is greater tha n t ha t

of water) :

measuring

cylinder

water

r

reading

object


17/49


1 A stud ent is given a sprin g balance wi th a Ne wt on scale. She is to ld tha t t he

acceleration due to gravity is 10 m/ s 2.

Describe h ow she could f in d the mass of a toy car.

Describe how she could go on to f ind the average density of the toy car.

A d a p t e d f rom C IE 0625 Novembe r 05

Paper 3 Q1b

2. A stude nt used a suitabl e measurin g cylinder and a spring balanc e to f ind the density of

a sample of a stone.

i) Describe ho w the measu ring cylinder is used, and state the readings tha t are tak en .

ii) Describe ho w th e sprin g balance is used, and state th e reading th at is ta ke n.

i i i) Writ e do wn an equ ati on fr om wh ic h the density of th e stone is calc ulate d.

iv) The stu den t the n wishe s to f in d the density of cork. Suggest how the ap parat us

an d the method would need to be changed.

CIE 0625 Novemb er '0 6 Paper 3 Q1b

3. Fig. (a) sho ws a meas uring cylinder, con tai nin g some wate r, on a balanc e.

Fig. (b) shows the same arrangement wi th a stone added to the water .

a. Whi ch two reading s sho uld be subt ract ed to give th e vo lum e of th e stone?

b. Whi ch tw o readings sho uld be subt ract ed to give th e mass of the sto ne?

c. In a certain experi men t,

mass of stone = 57. 5 g,

vo lume of stone = 25 cm 3 .

i) Wri te dow n the equat i on l inking density, mass and volume.

ii) Calculate the density of th e stone .

CIE 0625 J u n e '0 6 Paper 2 Q3

Practicalquestion

A n IGCSE student is determining the density of a metal alloy.

Th e studen t is prov ided wi th several metal rods, as sh ow n on the right.

1 Measure with a ruler the length, /, of one of the rods.

2. The stu den t measure d the dia mete r of one of the rods wi th a ruler and fou nd it to b e

0.6 cm. Calculate the cross-sectional area,A, of the rod.

3. Use this value to calculate the volum e, V, of one rod and hence the whole bundle.

Th e stude nt used a balanc e to f ind the mass of the bun dle and fo un d it to be 59.1 g.

Calculate the density of the metal alloy.


18/49

KEY IDEAS

/ Forces are vect or quan tit ie s th at can cha nge th e shap e of an obje ct, accelerate it or

change i ts direction

J Mo me nt of a force ab out a pivot = force x perpendic ular distance f ro m the piv ot

S An obje ct is in equ il ib riu m if the re is zero net forc e on it an d zero net m om en t

S An object wi l l no t fa l l over if the l ine of acti on of its we ig ht acts th ro ug h its base;

this depends on the posit ion of the centre of mass

/ The resul tant of two forces can be found by drawing a scale diagram

Forces can produce a change in size or s h a p e of an object. For example, loading a spring

wi l l increase its length.

An experiment to findhow the extension of a springvarieswith

the force applied

Meas ure th e origina l posit ion of the sprin g using the pointe r and ruler, to th e

nearest mm.

Ad d a 100 g mass han ger and measure th e ne w posi t ion .

Repeat 6 t ime s, add ing a 100 g mass each tim e.

Calculate the extension by subtract ing the or iginal posi t ion f ro m each subseque nt

posit ion reading.

Plot a grap h of extens ion again st forc e, wh er e force = mass x 10 N/kg.

Graphof results

extension/m

force/N

Conclusion

From 0 t o P, extension is directly

propor t iona l to the force appl ied.

Beyond P, the extensions are larger

fo r the same increase in force.

A t E, th e elastic l imit is reache d.

Beyond this point, the spring wil l

not return to its origin al leng th

w h e n the force is removed.


19/49

Hooke'sLaw

If a material obeys Hook e's Law, th e exten sion is directly pro por tio nal to the appl ied for ce,

provided that the elastic l imit is not exceeded,

F=kx

Where F = appl ied force (N), k = force constant for object under test (N/m),

x = extension (m)

Force,massand acceleration

A force can acce l era te an object. The larger the force on the object, the greater the

acceleration i f the mass stays constant. The larger the mass of the object, the smaller the

acceleration i f the force stays constant.

Force (N) = mass (kg) X ac celerat ion (m/ s 2)

F = m x a

Workedexamples

1 A force of 10 N acts on an obje ct of mass 5 kg . Wh at is th e accelerat ion of th e o bject?

2. A force of 15 N causes an object to accelerate at 2 m/s 2 . What is its mass?

3. A mass of 3 kg has a dec ele rat ion of 5 m/s2 . What force acts on it?

Answers

1. a = F + m

= 105

= 2 m/s 2

2. m = F r a= I l

2

= 7.5 kg

3. F = m X a= 3 X - 5

= - 1 5 N

Note: in example 3, the ob jec t is decel eratin g so accelera tion is negative.


20/49

'Rev is ion guide: Physics

Resultant force

Th e resu l tan t force acti ng on an obj ect is the net or overa l l force when the size and

direct ion of all the forces acting are taken into account. Force is a vec tor quant i ty.

Examples

1

2N

Resultant

force = 5 N + 2 N = 7 N

The forces are a d d e d together because they act in the same di rect ion.

Resultant force = 15 N 10 N

= 5 N (to the l eft)

Th e forces are subtrac ted because they act in oppos i te directions.

A force can cause an object to chang e d i rec t i on . The object will move in a circle if the

force acts perpendicular (at a right angle) to the direction that the object is travell ing.

Th e force acts at r ight ang l es to the direction that the object is moving. The force does not

do any work on the object because the object does not move in the direction of the force.

Th e force constant ly changes the direct ion of the object which means i ts ve l oc i ty changes

bu t its speed stays constant . The object accelerates towards the centre of the circle.

Th e force which causes an object to move in a circle is called the

centr ipetal fo rce . The centripetal force increases if:

th e mass of the obj ect increases

th e speed of the obje ct increases

th e radius of th e circle decreases

If the force wh ic h is prov idin g the centr ipetal accelerati on is sudd enly r emo ved ,

t he objec t wil l mo ve on a ta ng en t to th e original circle.


21/49


1.

.3

90

.3

90

ZU

15

ZU

15

length/cm

m

length/cm

m

n

n

() 0 5 1 0 1

Ic

5 2

ad/N

0 2 5 3 0

Th e graph abov e wa s obtai ned by a stu den t wh o load ed a sprin g fr om 0.5 N to 3.0 N

an d measured its length.

a. Find th e length of the spring wh en a load of 2.0 N is appli ed

b. Find th e load require d to stretch th e spring to a leng th of 18 cm

c. Find th e exten sion of the spring whe n it is stretc hed by a load of 1.5

N

A d a p t e d f rom CIE 0625 No ve mb er "05 Paper 2 Q1

2. A mass of 5.0 kg accelerate s at 3 m/s 2 in a straight l ine.

a. State w hy accele ration is describ ed as a vecto r quan tity.

b. Calculat e th e force required to accelerate th e mass.

A d a p t e d f rom C IE 0625 J u n e 05

Paper 3 Q3

3. The length of a spring is measur ed wh en various loads fr om 1.ONt o 6.ON are han gin g

f r om i t . The graph below gives the results.

20

15

length/cm

\

i l1 1 1

) i1 I

_

j 1 j

1 !4

! 1 j 1I

_t_.,

i ;! 1 | i

1 1

!1 i

i i i S

1

i

I I i

i i iI

[ 1

[ i l i1

1 1 I

_

T " i_}.

1 1

~

i

I 1 1 i i

1 1

[ 1 1 11

t

I

3 4

load/N

Use the graph to f in d

a. the len gth of th e sprin g wi th no load atta che d,

b. the length of the spr ing wi th 4.5N at tac hed,

c. the extens ion caused by a 4.5 N load.

CIE 0625 Novemb er '0 5 Pap er 2 Q1


22/49

(Revision guide: Physics

4. In an expe rime nt, forces are appl ied to a spring as sh ow n in (a). The results of th is

exper iment are shown in (b).

a. Wh at is the na me given to the poin t marked Q in (b)?

b. For the part OP of th e gr ap h, th e sprin g obeys Hooke's Law.

State wha t this means.

c. The sprin g is stretc hed unti l the forc e and extensio n are sh ow n by th e poin t R on

the gra ph. Comp are h ow the spring stretches, as sh ow n by the part of the grap h

OQ, with that shown by QR.

d. The part OP of th e gra ph shows the spring stretc hing accord ing to the expression

F= kx.

Use values from the graph to calculate the value of k.

CIE 0625 No ve mb er '06 Pape r 3 Q2


23/49

5. The points plot ted on the gr id below were obtai ned f rom a spr ing-stretchin g

experiment.

100

80

60

length/mm

40

*

20

load/N

a. Using a straig ht edg e, dr aw a strai ght l ine th ro ug h th e first 5 poin ts. Extend your

line to the edge of the grid.

b. Suggest a reason wh y th e sixth poi nt does not lie on the l ine you have drawn.

c. Calculate the exten sion caused by th e 3N load.

d. A small obje ct is hu ng on the unlo ade d sprin g, and th e length of the s pring

becomes 62 mm .

Use the graph to f in d the we igh t of the object .

CIE 0625 Novem ber 06 Paper 2 Q9

Practicalquestion

A n IGCSE class is investigating the effect of a load on a metre rule attached to a spring. The

apparatus is sh ow n in th e diagr am belo w.

zeroend of rule

tapedto bench


24/49

fR e v i s i o n guide: Physics

Th e zero end of the me tre rule is tap ed to the b ench to sto p it sl ip ping . The spring is

at tached to the rule at th e 40.0 c m mark an d the masses are atta che d at the 9 0.0 cm mark .

Th e masses are added 10 g at a t ime and the angle, 6, between the bench and the rule

measured wi th a protractor .

One studen t's results are sh ow n be lo w

0

10

20

30

40

50

29

28

26

25

22

19

1

Complete the column headings.

2. One stud ent suggests tha t m and 6sho uld be directly propo rtio nal to each other. Plot a

graph o f 6 (y-axis) against m (x-axis). Using your graph show whether this prediction is

correct. State your reason.

Turning effect and equilibrium

Th e turning ef fect or m o m e n t of a forc e abo ut a pivo t is equa l to th e force mult ipl ied by its

perpendicular distance f rom the pivot .

Momen t ( N m )

= Force (N) x dist anc e (m)

M = F X d

If an object is in equil ibrium there is no resultant turning effect and no resultant force.

Worked example

1

A force of 2.0 N acts at distance of 3.0 m from a pivot. Find the moment of the force.

2. A force of 5.0 N provides a mo me nt of 15 Nm ab ou t a pivot . Wh at is the dista nce of

t he force f rom the pivot?

3. A force provides a mo me nt of 20 Nm ab out a pivot at a distance of 2.0 m. What is the

size of the force?


25/49

Genera l physics

Answers

1. M = F X d= 2. 0 X 3.0

= 6.0 Nm

2. d = f

= 1 5 .5.0

= 3.0 m

3. F = Md

= 20

2.0

= 10 N

Examples of objects in equilibrium

2N

-3m r -6 m-

1N

3N

Clockwisemoment = 2 X 3 = 6 Nm

Anticlockwise moment =1 X 6 = 6 Nm

Netmoment = 6 6 = 0 Nm

20N

r+1 m * ~ -

25

N

- 4 m -

5N


Anticlockwise moment = 5 X 4 = 20 Nm

Netmoment = 20 - 20 = 0 Nm

6N

30N

- 4 m -k-1 ITU

7 \

24N


Anticlockwise moment = 6 X 4 = 24 Nm

Netmoment = 24 - 24 = 0 Nm

Taking moments about the pivot in each case.

An experiment to show that there is no net moment on an object

in equilibrium

I

7

spring

balancehorizontally balanced

metrerule

2

C

O

O 1 o _

O O O

10 20

9N

weight

30 40 50 \

60 70 80

horizontalpivot

90 100

Ant ic lockwise mom en t due to th e 9 N we ig ht = 9 x 0.4 = 3.6 Nm

Reading on th e spr ing balan ce = 12 N

Momen t due to the force of the spring balan ce = 12 X 0.3 = 3.6 Nm

Conclusion: in equi l ib r ium, clockwise mome nt = ant iclockwis e m om en t


26/49



1. a. State the two factors on which the tur nin g ef fect of a force depend s.

b. Forces F, an d F2

are applied vertically downwards at the ends of a beam resting on

a pivo t P. The be am has wei gh t W. The beam is sh ow n in the dia gra m b elow .

Ap . V

w

Comple te the statements about the two requirements for the beam to

be in equi l ibr ium.

1. There mus t be no resultant

2. There mus t be no resultant

ii) The beam is in equil i bri um. F is the for ce exerted on th e bea m by th e pivo t P.

Comple te the fol lowing equat ion about the forces on the beam.

F =

i i i) Which one of the four forces on the beam does no t exert a moment about P?

CIE 0625 Novemb er '06 Paper 2 Q5

2. The diagra m below shows apparatus for invest igat ing moment s of forces.

F 1 spring

r j i j l balance

V

horizontallybalanced

.metre rule

0 0 O O O O O O

10 20

6.0N

weight

30 40 50 \ 60 70 80

horizontalpivot

90 100

Th e uni form metre rule shown is in equi l ibr ium.

a. Wri t e do wn tw o condi t ions for the metre rule to be in equi l i br ium.

b. Sho w th at the value of the reading on th e spring balan ce is 8.0 N.

c. The we ig ht of the unif or m met re rule is 1.5 N. Calculate the force exerted by the

pivot on the metre rule and state its direction.

CIE 0625 November '0 5 Paper 3 Q2


27/49

Practicalquestion

Th e IGCSE class is determining the weight of a metre rule.

Below is a diag ram of the appa ratus

l I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I |I I hf

newton

meter

metre

rule

bench

\ me tre rule is sup por ted at one end by a pivo t th ro ug h the 1.0

cm mark. The other end is

suppor ted at the 91 .0 cm mark by a newton meter hanging f rom a clamp.

1- Describe ho w you wo ul d check th at the metre rule is hori zon tal. You may draw a

d iagram i f you wish.

2. The stud ents record the force Fsho wn on the ne wto n meter and the distance d f rom

t he pivot to the 91 cm mark. They then repeat the experiment several t imes using a

range of values of the distance d. The readings are shown in the table.

0.74 0.900

0.78 0.850

0.81 0.800

0.86 0.750

0.92 0.700

Copy the table. Calculate and record on your table the values of 1/d

3. a. On grap h paper, plo t a gra ph of F/N (y-axis) against l / i (x-axis).

Start the y-axis at 0.7 and the x-axis at 1.0.

b. Draw the l ine of best f i t on your gr aph .

c. Dete rmine the gra dien t G of the l ine.

4. Calculate the we ig ht of the metre rule using the e qua tion

1 / 1 / w h e r e

k = 0 .490 m.


28/49


Centreof mass

Th e centre of mass of an obje ct is th e poi nt on the ob jec t wh er e the mass can be

considered to be concentrated and hence where the weight of the object can be

considered t o ac t .

Th e centre of mass of a very thin obje ct (a lamina) can be fo un d by ex peri ment ;

Push a pin through a point on the edge of the lamina and allow it to swing freely. Use a

p lumb line (a small mass on a piece of string) to mark a vertical line from the pin point

across th e lamina . Repeat fo r a seco nd poi nt on the edg e of the la mina. Wher e the t wo

lines cross is the posit ion o f the ce ntre of mass.

Th e posit ion of the centre of mass affects the stabi l i ty of an object

Forexample:

If objec t 1 is t i l te d thro ug h a small angle, the w e i g h t wi l l act outside the base.

There wil l be a net moment on object 1 that wil l cause it to fall over. If object 2 is t i l ted

t h rough a small angle the weight wil l sti l l act inside the base. There wil l be a net mo me nt

on object 2 that wil l cause it to go back to its original posit ion and it wil l not fall over.


29/49


1

A piece of stiff cardboa rd is stuck to a plan k of wo o d by means of tw o sticky- tape

"hi nge s". This is sho wn below.

a. Init ial ly, th e card board is f lat on the pla nk of wo o d. A box of matche s is placed o n

it. The cardb oard is the n slowl y raised at th e left hand ed ge, as sh ow n be low. State

the condit ion for the box of matches to fall over.

i) Comp lete the sentence below, using ei ther the word s "great er th an " or " t he

same as" or " less than".

In (b), the angle thro ugh wh ich t he cardboard can be l i f ted before the

box of match es falls is th e angle

before the box of matches falls in (a).

ii) Give a reason fo r yo ur ans we r to (i).

A d a p t e d f rom CIE 0625 June 07 Paper 2 Q3


30/49


2. a. A light vertic al tri an gu lar piece of rigid plastic PQR is piv ote d at co rne r P.

A hor izon tal 5N force acts at Q, as sh ow n in b elow .

Describe what, i f anything, wi l l happen to the piece of p las t i c ,

b. On anoth er occasion, tw o horiz onta l 5N forces act on the piece of plastic, as

s hown in below.

i) Describe wh at , if any thi ng , wil l happe n to th e piece of plastic.

ii) Cop y the diagr am above and mark the forc e tha t the pivot exerts on the piece

of plastic. Show the direction of the force by means of an arrow and write the

magn i t ude of the force next to the arrow.

CIE 0625 June '0 5 Paper 2 Q3


31/49

Genera l physics

Scalarsand vectors

A scalar quant i ty h a s s ize only.

A vec tor quant i ty has s ize and d i rect ion.

Mass

Energy

Time

tSBSMSiSSMSISR

Velocity

Acceleration

Force

Resultants

To calculate the resultant (overall) force on a point acted on by two forces, f ,

and F2

you can

d raw a scale diagram.

Chooseascalee.g. a line of 1cm

represents a force of 1N

Drawthe forcesF , andF2

acting

on the point

^ ^ Y P l

^ T ^ ^ ^ ^ ^ p i . n n p

|

; , | ,

p

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

mm

1N = 1 cm

Put the forces"nose to tail" i.e.

sothe arrowsfollowon.

Draw the resultant force linefrom

thetailof one arrow to the head

ofthe secondarrow.

Measurethe length of the

resultant force line in cm and

thenconvert this value back to

newtons.0 10 20 30 40 50 60 70 80 90 100 110 120 130 140

mm

1 cm= 1N


32/49

i Rev is ion guide: Physics


1

A student sets up the apparatus shown below in order to f ind the resultant of the two

tensions 7 ,a nd T2

act ing at P. Wh en t he tensio ns Tv

T

2

and T3

are bala nced , th e angles

be tween 71

and the vertical and T2

and the vertical are as marked on the diagram.

Draw a scale diagram of the forces 7 ,a nd T2

. Use the diagram to f ind the resultant of the

t w o forces.

State:

a. The value of th e resultant

b. The direc tion of th e resultan t

c. The scale used in the d ra win g

CIE 0625 June '0 6 Paper 3 Q2


33/49

KEY IDEAS

S

Energy can be transformed from one type to another but it cannot be created

or destroyed

S Different types of stored energ y can be tran sfor med into electrical energy in powe r

stations

/

Work don e = for ce x dist ance, pow er = energy /time

kinetic energy =

j mass x velocity2

J

cha nge in gravitational potential energ y = mass X gravitational field

X ch ang e in height

Energy

An object may have energy beca use it is moving or b ecau se of its position. Energy can be

t r a n s f e r r e d from one place to another, transformed from one type to another or stored.

The unit of energ y is the j ou le (J) .

Typesof energy

The energy gained as an object is moved away fromthe Earth

e.g. a book being liftedonto a shelf

The energy an object has due to its movement

e.g.a person running

Stored energythatcan be released in a chemical reaction

e.g. a battery, fuel suchas coal

Theenergy stored when an objectchangesshape

e.g. a stretched rubber band

The energy carried by an electric current

The energycanied by a sound wave

:

- I M

; Thetotalkinetic and potential energies of all of the particles in an

object

The energy released when the temperature of a hot object decreases

dueto a decrease in its internal energy

Stored energythatcan be released in a nuclear reaction

e.g. energy stored in the sun.

;

Energy given off, for example, by very hot objects

Heat energy can be transferred from a hot object to a cooler one.

Kinetic energy can be transferred from one car to another in a collision.

Energy transformations

In an energy transfo rmatio n, energy is convert ed from one type to another. For example:

Light bulb Waterfall

gravitational potential > kinetic

Bowand arrow Cell

chemical

electrical


34/49


Principle of conservation of energy

Energy cann ot be created or destroyed. It is t ran sfor med fr om on e form to another.

Example

Electrical energy

in = 100 J

Heatenergy out = 98 J

Light energy out = 2 J

10 0 J in = (9 8 J + 2 J) ou t


1

A piece of fru it is fall in g fro m a tree.

Th e l ist below contains the names of some di f ferent forms of e n e r g y ,

chemical

electrical

gravi tat ional (PE)

in ternal ( thermal)

kinet ic (KE)

l ight

sound

strain

a. Which f o u r forms of energy are possessed by the fall ing fruit?

b. Wh ic h fo rm of energy increases as the fruit fal ls?

c. Wh ic h fo rm of energ y decreases as th e fru it falls?

d. Wh ic h for m of ene rgy is store d in the bo dy of a perso n as a result of eating the fru it?

CIE 0625 June '06 Pap er 2 Q 4

m


35/49

A child is sitt in g on an oscil lating swi ng , as sh ow n bel ow. At the top o f the oscil lat ion,

t he child and swing are momentari ly at rest.

i) Use the names of appropr iat e types of energy to comp lete the fol low ing wo rd

equat ion.

gravi tat ional

potent ia l energy

at the top of the

oscil lation

energy at the

bo t t om of the

oscil lation

energy at the

bo t t om of the

oscil lation

energy losses

ii) The child contin ues to sit sti l l on the swi ng . The amp lit ud e of th e oscil lations slowly

decreases.

Explain why this happens.

CIE 0625 Novembe r 06 Paper 2 Q4b and c


36/49

R e v i s i o n

guide: Physics

Energy resources

Energy resources are used to produce electrical energy from other forms of energy.

Coal,oil andgasfiredpower stations

11

Geothermalpower stations

Thechem ica l energy in the fuel is released by burning.

The chemical energy is transformed to heat energy

which isused to heat water and increase its internal

energy, turning it intosteam. The steam turns turbines,

transferring its kinetic energy to them. The kinetic

energyis transformed to electrical energy in the

generator.

Water is pumped underground and gains heat energy

fromthe hot rocksdeep underground. The heat energy is

thenconverted to kinetic energy in the turbines, which

turnthe generator to produce electrical energy.

Hydroelectric power stations

Solarcells

Solarpower station

Wavepower

Thegravit ation al pote ntial energy of the falling water

istransformed to kinetic energy as the water passes

throughthe turbines. The turbinesturn the generator to

produceelectrical energy.

Thelightenergyfromthe Sun is transformed to

electrical energy in the solar cell.

The heat energyfromthe Sun is concentrated by a

seriesof curved mirrors, which focus the energyinto

onep lace. Thisheat energy converts water to steam,

whichturns the turbines, givingthemk ine tic energy. The

kinetic energy is transformed to electrical energy in the

generator.

Asthe turbines bob on the surface of the sea,

gravitational po tenti al energy is transformed to

kin eti c energy. The kinetic energy is then transformed

intoelectrical energy in the generators.

Tidal power As thetidecomes in, the water builds up behind the

damand gains grav itat iona l pote ntial energy. When

the water is released the gravitat ional potential energy

is transformed to kinetic energy and then to electrical

energy in the generator.

Nuclear power The nuclear energy stored in uranium-235 is released

whenthe uranium nuclei split in aprocesscalled nuclear

fission.The nuclear energy is transformed to heat energy

i , which isusedto turnwater to steam. The steam turns

; j the turbines and then this kin et ic energy is transformed

j i

to ele ct ric al energy in the generator.


37/49

Nuclear fusion

Th e process of nucle ar fusion is carried ou t in th e Sun. Hydrog en n uclei coll ide at grea t

speed in the Sun and fuse together to form helium nuclei. This releases energy in the form

of heat and l ight.


1 The diagram below represents a hydroelectric system for generating electricity.

Answer the fol lowing quest ions, using words f rom this l ist .

chemical

electrical

gravi tat ional

internal (heat)

:

kinetic

l ight

nuclear

sound

strain

a. Wh at sort of energy, possessed by th e wa te r in the reservoir, is the ma in source of

energy for this system?

b. Wh en the water f lows dow n the pipe, i t is movi ng. Wh at sor t of energy does i t

possess because of this movement?

c. The wa te r makes the turbi nes in the pow er statio n rotate. Wh at sort of energ y do

the turbines possess because of their rotation?

d. Wh at sor t of energy does the power stat ion generate?

e. None of th e ener gy trans fer processes is perfec t. In wh at fo rm is mos t of th e

wasted energy released?

CIE 0625 J u n e '0 5 Pap er 2 Q 4


38/49


Workand power

Th e w o r k d o n e in joules by a forc e acti ng on an obje ct = forc e X distance moved by the

object in the direction of the force.

wo r k do ne (J) = f or ce (N) X distance (m)

W = F X d

Th e p o w e r in w a t t s is the wo rk do ne per second or the energy t ran sfor med per second.

power

'

- !Workedexamples

1

A car eng ine prod uces a forc e of 2000 N while accel erating th e car th ro ug h a distance

of 200 m in a t ime of 10 s.

a. Wh at is th e wo rk do ne on the car by the eng ine force ?

b. Wh at is the pow er developed by the engine?

Answers

a. W= Fx d

= 2 0 0 0 X 200

= 400 00 0 J

= 400 kJ

b. P = |

=

400 000

10

= 4 0 00 0 W

= 40 kW

Kineticenergy

Kinetic energy can be calculated f rom the formula:

where m = mass in kg ; v = velocity in m/s

W h e n an object is l i f ted higher above the Earth's surface work must be done.

Since wo rk = force X distance

and force = weight of the object

wo r k done = weight x height l i f ted

where we ig ht = mass x g ravit ation al f ield = mg.

Gravitational potential energy

Itfol l ows tha t the change in g rav i ta t i ona l potent i al ener gy ( the work done in l i f t ing

t he objec t) is given by the f orm ula :

PE= mgh

w h e r e m = mass in kg ;g = accelerat ion due to gravi ty 1 0 m / s 2 ;

h - ch ang e in hei gh t in m

I


39/49

Workedexamples

1

A car of mass 1000 kg is tra vel lin g at a velo city of 20 m/s. Calc ula te its kin etic energy .

2. Calculate the chan ge in pote ntia l energy of a 70 kg parachut ist as she falls th ro ug h a

he igh t of 100 m.

3. A ball of mass 0.5 kg is dro pp ed fr om rest at a hei ght of 5 m above the gr ou nd . Find its

velocity wh en i t hi ts the g rou nd.

Answers

1. KE = mv2

= 1 X 1000 X 20 2

= 20 0 000 J

= 200 kJ

2. PE= mgh= 7 0 X 10 x 10 0

= 70 000 J

= 70 kJ

3. PE = mgh

= 0.5 X 10 X 5

= 25 J

loss o f PE = gain of KE

v = V(2K/m)

= V(2 X 25/0.5)

= 10 m/s


1

An electric pu mp is used to raise wa te r fro m a well , as sh ow n belo w.

pump

ground

a. The pu mp does wo rk in raising the water. State an equ ati on that coul d be used to

calculate the work done in raising the water.


40/49


b. The wa ter is raised th ro ug h a vertical distance of 8.0 m. The we ig ht of wate r raised

in

5. 0

s is 10 0 N.

i) Calculate the wo rk do ne in raising th e wa te r in this t im e.

i i) Calculate the pow er the pum p uses to raise the wa ter.

i ii) The energy transferr ed by the p um p to the wat er is greater tha n yo ur

answer to (i).

Suggest what the addit ional energy is used for.

CIE 0625 J u n e '06 Paper 3 Q3

2. A stude nt wishes to wor k out ho w much po wer she uses to l i f t her body whe n cl imbin g

a f l ight of stairs.

Her bo dy mass is 50 kg an d the vertical hei ght of t he stairs is 4.0 m. She takes 20 s to

wa lk up the stairs.

a. Calculate

i) the wo rk don e in raising her bod y mass as she climbs the stairs,

i i) th e ou tp ut powe r she develops wh en raising her bod y mass.

b. At the to p of th e stairs she has gravi tation al poten tial energy. Describe the energ y

t rans fo rmat ions taking place as she walks back down the stairs and stops at

t he bo t t om.

CIE 0625 J u n e '07 Paper 3 Q3

3. The diagra m below shows water fal l ing over a dam .

a. The vertical heigh t th at the wa te r falls is 7.0 m.

Calculate the potential energy lost by 1.0

kg of water dur ing the fall.

b. Ass umin g all this pote ntia l energy loss is cha nge d to kinetic energy of th e water,

calculate the speed of the water, in the vertical direction, at the end of the fall.

c. The vertical speed of th e wa te r is less tha n th at calculate d in b. Sugge st on e reason

fo r this.

CIE 0625 No ve mb er '06 Pape r 3 Q3


41/49

1 , / FVf^ijr *

KEY IDEAS

^ Pressure = te

J Pressure is me as ur ed in Pascals (Pa) w i t h 1 Pa =

/ Atmo sph er ic pressure can be measured using a barom eter

/ The pressure at a de pt h h under the surface of a l iquid of density p = pgh

/ The pressure of a gas ca n be measured using a manometer

Th e p ressure o n a surface d ue to a forc e is th e force on 1 m2

of the surface.

KU fo rce (N)pressure(Nftrf)

-

he unit of pressure, N/m 2 is also known as the pascal (Pa)

Workedexamples

1 A force of 10 kN acts on the surface of a l iquid, of area 0.08 m2

. Wh at is th e pressure

o n the surface of the l iquid?

2. A person of wei gh t 60 0 N exerts a pressure of 200 kPa on the gr ou nd . Wh at is the area

of their feet?

3. The area of a do g' s pa w is 10 c m2 . The pressure un der th e pa w is 50 kPa w h en it

exerts half of its body weight on the paw. What is its weight?

Answers

1. P =

10 000

0.08

125 000 Pa

125 kPa

2. ^=

600

200 000

0.003 m2

3. F=p XA= 50 000 X (10 + 10 000)

= 50 N

Total we ig ht = 2 x 50 = 10 0 N

No te: In que sti on 1 , 1 kN = 10 00 N

In question 3, area in cm 2 is con vert ed to area in m 2 by dividing by (100 x 1 0 0 ) ie

by 10 000


42/49

R e v i s i o n

guide: Physics

Atmospher ic (air) pressure can be measured with a barometer.

r

Theglass tube is evacuated

andso the mercury can move

upinside.Thegreater the

airpressure, the higher the

mercuryrises up the tube.

The height of the mercury

column is proportional to

theoutside air pressure.

air pressure

_Jv

>

chapter 1 general physics

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