Table Of ContentEDEXCEL INTERNATIONAL GCSE (9-1)
Brian Arnold
Penny Johnson
Steve Woolley
iii l
CONTENTS
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resources. GLOSSARY 285
INDEX 289
COURSE STRUCTURE COURSE STRUCTURE
UNIT 1 UNIT 5
FORCES AND MOTION SOLIDS, LIQUIDS AND GASES
1 MOVEMENT AND POSITION 03 18 DENSITY AND PRESSURE 173
2 FORCES AND SHAPE 18 19 SOLIDS, LIQUIDS AND GASES 181
3 FORCES AND MOVEMENT 28
UNIT 6
4 MOMENTUM 1;11111+1,wm 40
MAGNETISM AND ELECTROMAGNETISM
5 THE TURNING EFFECT OF FORCES lwll111H•lllrl 48
20 MAGNETISM AND ELECTROMAGNETISM 197
21 ELECTRIC MOTORS AND ELECTROMAGNETIC INDUCTION 206
UNIT2
UNIT 7
ELE TRll.;ITY
MAINS ELECTRICITY 59 RADIOACTIVITY AND PARTICLES
CURRENT AND VOLTAGE IN CIRCUITS 67 22 ATOMS AND RADIOACTIVITY 221
ELECTRICAL RESISTANCE 75 23 RADIATION AND HALF-LIFE 233
9 ELECTRIC CHARGE INNlfi'Wrl 84 24 APPLICATIONS OF RADIOACTIVITY 241
25 FISSION AND FUSION 250
UNIT 3
UNIT 8
WAVES
ASTROPHYSICS
10 PROPERTIES OF WAVES 97
26 MOTION IN THE UNIVERSE 259
11 THE ELECTROMAGNETIC SPECTRUM 106
27 STELLAR EVOLUTION 265
12 LIGHT WAVES 113
28 COSMOLOGY lwh1Mfi'i!lrl 271
13 SOUND 123
UNIT 4
ENERGY RESOURCES AND ENERGY TRANSFER
14 ENERGY TRANSFERS 133
15 THERMAL ENERGY 139
16 WORK AND POWER 150
17 ENERGY RESOURCES AND ELECTRICITY GENERATION lwli111H•lllrl 158
vii i
ABOUT THIS BOOK . ABOUT THIS BOOK
ABOUT THIS BOOK
Looking Mead tells you
Key Point boxes a.a~"-'·----··- what you would learn
summarise the ::.;::~::"I'-:;:=..--·-· if you continued your
essentials. ;..._; ...-....- ~--:--r»--::--·:-. . -.. . --,,.:,o~--.. ~·-- study of Physics to a
This book is written for students following the Edexcel International GCSE (9-1) Physics specification and ._--,..c.-.,.,_Uf'Cl Ihnigtehrenra lteiovneal,l sAu cLhe vaesl.
___
the Edexcel International GCSE (9-1) Science Double Award specification. You will need to study all of :"_:-_:..-:.:.::::,::: ~-....-..,-.--_._---~. ,_ .. -_·_. .- , _.-.,..,e--.t1n.L1s1"uC1..a-1
the content in this book for your Physics examination. However, you will only need to study some of it if _-•._..-. ._,..l,'l.o._t.'C,. ...._. __ .,,. ···-
yeoxaum arinea ttaioknin agn tdh en oDto iunb tlhee A Dwoaurdb les pAewcaifricda stipoenc. iTfichaet iboono. kT oc lceoamrlyp ilnedteic tahtee sD wouhbicleh Acownatredn ct oisu rins eth yeo uP hwyislli casls o --=.. c-.-.".-' °..°:~.._'-C-o -_l--•-_TlX.l-'C, ..U.-_•ll. i.'..C.. _. -_... .-.
need to study the Biology and Chemistry parts of the course. __60_•._,• .C.• M .. ____
Examples provide a
In each unit of this book, there are concise explanations and worked examples, plus numerous exercises ___ _____ _ .:,0-Ulooil•"'°°J.lot'C·•'C cfrlaemare, winosrtkru. ctional
trheqaut wireildl hperlapc ytiocua lsb.u ild up confidence. The book also describes the methods for carrying out all of the Einnoxcttle uondnse iot hcnoe Wn stpeoernkct i tfbhicoaaxtte iiossn --__-.,.-.,.-..-- ..-_.-..,-.-,· _,_- -_-. ..-. . --...· ... . 60•t011COJ
The language throughout this textbook is graded for speakers of English as an additional language (EAL), and which you do -...... --.---··---...
not have to learn for ·-.=,._=.,.=_ ._....._....._. _c __lWf_l'C<_ 9_'1'
with advanced Physics specific terminology highlighted and defined in the glossary at the back of the book. your examination. ·--
A list of command words, also at the back of the book, will help you to learn the language you will need in However, the content ·=c-,=.~6:1 :...~-....... ___
will help to extend your I
your examination. understanding of the Practicals describe the
topic. ·::---=..-=.:.:.:=....-:.· .... _,_ methods for carrying out
You will also find that questions in this book have Progression icons and Skills tags. The Progression icons all of the practicals you
refer to Pearson's Progression scale. This scale - from 1 to 12 - tells you what level you have reached ~.:::-E:-::::-'.:::11.~ . =- ywoilul nr eexeadm toin kantioown. for
in your learning and will help you to see what you need to do to progress to the next level. Furthermore,
Edexcel have developed a Skills grid showing the skills you will practise throughout your time on the
course. The skills in the grid have been matched to questions in this book to help you see which skills Hint boxes give you tips on
important points to remember
you are developing. You can find Pearson's Progression scale and Edexcel's Skills grid at in your examination.
www.pearsonschoolsandfecolleges.co.uk along with guidelines on how to use them. ___ ___
____
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iLsnhe eoaawmc ihwn ghC aOhta bypjoeteucrt .wi viells l earn .._ --.__ ._ -.... ...- _....-..... . .._- ._. _-_-_.,_. _.__._._._ .._ .- .-_ ._ .... -._..-_ _··_..-_ "_'_* _- Cl>- ~':._.:.-_:....._=.:.-...-_.. . ,_, -"....,:.....-..-- _..,,.·.-·-.:.-:..::-..--.,.:._. ..-,.-- ,..-_:-_.=,..-_..-.. ,.-. ·.-,-.- .-.... -) D -=COHM..1O.0 - -... -.---,.. .......
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and seconds - you will specification. All other
need to know and use content in this book Chapter Questions test your Skills tags tell you which skills Progression icons show the level of Unit Questions test your knowledge
for the study of a topic. applies to Double Award knowledge of the topic in that you are practising in each difficulty according to the Pearson of the whole unit and provide
students. chapter. question. International GCSE Science quick, effective feedback on your
Progression Scale. progress.
I
- viii ASSESSMENT OVERVIEW ASSESSMENT OVERVIEW ix
ASSESSMENT OVERVIEW EXPERIMENTAL SKILLS
In the assessment of experimental skills, students may be tested on their ability to:
• solve problems set in a practical context
The following tables give an overview of the assessment for this course.
• apply scientific knowledge and understanding in questions with a practical context
We recommend that you study this information closely to help ensure that you are fully prepared for this course and • devise and plan investigations, using scientific knowledge and understanding when selecting appropriate techniques
know exactly what to expect in the assessment.
• demonstrate or describe appropriate experimental and investigative methods, including safe and skilful practical
111Hii1Mil·liiii!@!iiMIMMiiil- techniques
PAPER 1 AVAILABILITY
• make observations and measurements with appropriate precision, record these methodically and present them in
Written examination paper Physics 61.1% 110 2 hours January and June appropriate ways
Paper code 4PH1/1 P and Double Award examination series
• identify independent, dependent and control variables
4SD0/1P First assessment June 2019
Externally set and assessed • use scientific knowledge and understanding to analyse and interpret data to draw conclusions from experimental
by Edexcel activities that are consistent with the evidence
iiijBiiWiiMiiiij!@MfMIMMlill-
PAPER 2 AVAILABILITY • communicate the findings from experimental activities, using appropriate technical language, relevant calculations
and graphs
Written examination paper Physics 38.9% 70 1 hour 15 mins January and June
Paper code 4PH1/2P examination series • assess the reliability of an experimental activity
Externally set and assessed First assessment June 2019 • evaluate data and methods taking into account factors that affect accuracy and validity.
by Edexcel
CALCULATORS
If you are studying Physics then you will take both Papers 1 and 2. If you are studying Science Double Award then you Students are permitted to take a suitable calculator into the examinations. Calculators with QWERTY keyboards or that
will only need to take Paper 1 (along with Paper 1 for each of the Biology and Chemistry courses). can retrieve text or formulae will not be permitted.
ASSESSMENT OBJECTIVES AND WEIGHTINGS
ASSESSMENT OBJECTIVE DESCRIPTION % IN INTERNATIONAL GCSE
A01 Knowledge and understanding of physics 38%-42%
A02 Application of knowledge and 38%-42%
understanding, analysis and evaluation
of physics
A03 Experimental skills, analysis and 19%-21 %
evaluation of data and methods in
physics
MOVEMENT ANO POSITION 03 FORCES ANO SHAPE 18 FORCES ANO MOVEMENT 28 MOMENTUM 40 FORCES ANO MOTION
THE TURNING EFFECT OF FORCES 48
1 MOVEMENT AND POSITION
Forces make things move, like ttiis Atlas V rocket carrying the Cygnus spacecraft UJJ to the
International Space Station. Forces hold the particles of matter together and keep us on the Earth.
Forces can make things slow down. This is useful when we apply the brakes when driving a car!
Forces can change the shape of things, sometimes temporarily and sometimes l)ermanently.
forces make things rotate and change direction.
·~
UNITS
• torque (turning effect): newton metre (Nm)
I
• momentum: kilogram metre per second (kg mis).
KfY POINT
Sometimes average speed is shown In this section you will need to use kilogram (kg) as the unit of mass, metre (m) as
by the symbols v. _o r v but in this the unit of length, and second (s) as the unit of time, You will find measurements
book v will be used. of mass made in subdivisions of the kilogram, like grams (g) and milligrams (mg),
measurements of length in multiples of the metre, like the kilometre (km), and
subdivisions like the centimetre (cm) and millimetre (mm). You will also be familiar
with other units for time: minutes, hours, days and years etc. You will need to take
care to convert units in calculations to the base units of kg, m ands when you meet
these subdivisions and multiples.
Other units come from these base units. In the first chapter you will meet the units for:
• speed and velocity: metre per second (m/s)
• acceleration: metre per second squared (mis').
In later chapters you will meet the units for:
• force: newton (N)
• gravitational field strength: newton per kilogram (N/kg)
4 FORCES AND MOTION FORCES AND MOTION
Speed is a term that is often used in everyday fife. Action films often feature
SPEED TRAP•
high-speed chases. Speed is a cause of fatal accidents on the road. Sprinters Suppose you want to find the speed of cars driving down your road. You may
aim for greater speed in competition with other athletes. Rockets must reach have seen the police using a mobile speed camera to check that drivers are
a high enough speed to put communications satellites in orbit around the keeping to the speed limit. Speed guns use microprocessors (computers on a
Earth. This chapter will explain how speed is defined and measured and 'chip') to produce an instant reading of the speed of a moving vehicle, but you
how distance-time graphs are used to show the movement of an object can conduct a very simple experiment to measure car speed.
as time passes. We shall then look at changing speed - acceleration and Measure the distance between two points along a straight section of road with
deceleration. We shall use velocity-time graphs to find the acceleration of an a tape measure or 'click' wheel. Use a stopwatch to measure the time taken
object. We shall also find how far an object has travelled using its velocity-time for a car to travel the measured distance. Figure 1.4 shows you how to operate
graph. You will find out about the difference between speed and velocity on your 'speed trap'.
page 6.
Measure 50 m from a start point along the side of the road.
AVERAGE SPEED 2 Start a stopwatch when your partner signals that the car is passing the start
point.
KEY POINT A car travels 1 00 kilometres in 2 hours so the average speed of the car is .6. tFaigkeunre f o1r.3 th Ae svtoephwiclaet ctoh twrailvl eml ethaes udriest tahnec etim. e 3 Stop the stopwatch when the car passes you at the finish point.
50 km/h. You can work this out by doing a simple calculation using the
Sometimes you may see 'd' used
following definition of speed:
as the symbol for distance travelled,
but in this book 's' will be used to be average speed, v = distance moved, s
consistent with the symbol used in time taken, t
A level maths and physics.
V=~
t
The average speed of the car during the journey is the total distance travelled,
divided by the time taken for the journey. ff you look at the speedometer in
a car you will see that the speed of the car changes from instant to instant
as the accelerator or brake is used. The speedometer therefore shows the
instantaneous speed of the car.
UNITS OF SPEED
Typically the distance moved is measured in metres and time taken in
seconds, so the speed is in metres per second (m/s). Other units can be used
for speed, such as kilometres per hour (km/h), or centimetres per second .6. Figure 1.4 How to measure the speed of cars driving on the road
(cm/s). In physics the units we use are metric, but you can measure speed in
miles per hour (mph). Many cars show speed in both mph and kilometres per Using the measurements made with your speed trap, you can work out the
hour (kph or km/h). Exam questions should be in metric units, so remember No measurements should be taken speed of the car. Use the equation:
that m is the abbreviation for metres (and not miles). on the public road or pavement but it average speed, v = distance moved, s
is possible to do so within the school time taken, t
boundary within sight of the road.
REARRANGING THE SPEED So if the time measured is 3.9 s, the speed of the car in this experiment is:
ff you are given information about speed and time taken, you will be expected
EQUATION to rearrange the speed equation to make the distance moved the subject: KfY POINT average speed, v = 50 m
3.9s
distance moved, s = average speed, v x time, t You can convert a speed in mis into a
speed in km/h. = 12.8 m/s
and to make the time taken the subject if you are given the distance moved If the car travels 12.8 metres in one
and speed: second it will travel DISTANCE-TIME GRAPHS
time taken, t = distance moved, s 12.8 x 60 metres in 60 seconds (that is,
average speed, v one minute) and
12.8 x 60 x 60 metres in 60 minutes
REMINDER (that is, 1 hour). which is
46 080 metres in an hour or 46.1 km/h
To use the triangle method to rearrange an equation, cover up the part of the triangle
(to one decimal place).
that you want to find. For example, in Figure 1.2, if you want to work out how long (I)
it takes to move a distance (s) at a given speed (v), covering I in Figure 1.2 leaves We have multiplied by 3600 (60 x 60) to
f. convert from mis to m/h, then divided
.6. Figure 1.2 You can use the triangle method or distance divided by speed. If an examination question asks you to write out by 1000 to convert from mlh to km/h
for rearranging equations likes = v x t. the equation for calculating speed, distance or time, always give the actual equation (as there are 1000 m in 1 km).
(such ass = v x t). You may not get the mark if you just draw the triangle. Rule: to convert mis to km/h simply
multiply by 3.6. .6. Figure 1.5 A car travelling at constant speed
6 FORCES AND MOTION FORCES AND MOTION
Figure 1.5 shows a car travelling along a road. It shows the car at 0.5 second KEY POINT Displacement is an example of a vector. Vector quantities have magnitude
intervals. The distances that the car has travelled from the start position after (size) and a specific direction.
A vector is a quantity that has both size
each 0.5 s time interval are marked on the picture. The picture provides a
and direction. Displacement is distance Velocity is also a vector. Velocity is speed in a particular direction. If a car
record of how far the car has travelled as time has passed. The table below travelled in a particular direction. travels at 50 km/h around a bend, its speed is constant but its velocity will be
shows the data for this car. You will be expected to plot a graph of the distance Force is another example of a vector changing for as long as the direction that the car is travelling in is changing.
travelled (vertical axis) against time (horizontal axis) as shown in Figure 1.6. that you will meet in Chapter 2. The
increase in displacement
size of a force and the direction in
average velocity = time taken
Time from start/s 0.0 0.5 1.0 1.5 2.0 2.5 which it acts are both important.
Hil:iiii+
Distance travelled from start/m 0.0 6.0 12.0 18.0 24.0 30.0
Note that this graph slopes down
to the right. We call this a The global positioning system (GPS) in Figure 1.9 shows two points on a
30 The distance-time graph tells us about how the car is travelling in a much NEGATIVE SLOPE or negative gradient. journey. The second point is 3 km north-west of the first.
more convenient fonm than the series of drawings in Figure 1.5. We can see a A walker takes 45 minutes to travel from the first point to the second.
24 that the car is travelling equal distances in equal time intervals - it is moving Calculate the average velocity of the walker.
E at a steady or constant speed. This fact is shown immediately by the fact that b Explain why the average speed of the walker must be greater than this.
QJ 18 the graph is a straight line. The slope or gradient of the line tells us the speed
~ of the car - the steeper the line the greater the speed of the car. So in this a Write down what you know:
"·" 12 example: c increase in displacement is 3 km north-west
6 speed = gradient = ditsitmaen ce = 320.5 ms = 12 mis 1~J time taken is 45 min (45 min= 0.75 h)
~ increase in displacement
00+.0- -~0.5 -1~.0 -1~.5 -2.-0 ~2.5 a 1b b C1 U_ 'o ~----ti-me-/s ----.......... average velocity = time taken
time/s object A
{ .6. Figure 1.8 In this graph displacement is = 4 km/h north-west
.6. Ftriagvuerelli n1g.6 c Dairs itna nFcigeu-rteim 1e.5 g raph for the g decreasing with time. b The walker has to follow the roads, so the distance walked is greater
~ KEY POINl than the straight-line distance between A and B (the displacement). The
'6
Always show your working when walker's average speed (calculated using distance) must be greater than
1r·.. .., ..... . _...." ' . ....... -.'"~,. .. ..
time/s time/s time/s answering questions. You should show his average velocity (calculated using displacement).
KEY POINT your working by putting the values ~
given in the question into the equation.
A curved line on distance-time graphs ~
means that the speed or velocity of the
object is changing. To find the speed
at a particular instant of time we would
draw a tangent to the curve at that
an aid to navigation that uses orbiting satellites to locate its position
instant and find the gradient of the
tangent. on the Earth's surface.
time/s time/s
.6. Figure 1.7 Examples of distance-time graphs
ACTIVITY 1
In Figure 1.7a the distance is not changing with time - the line is horizontal.
Tobhijse cmtse aanres mthoavt inthge. Tspheee rde dis l izneer ois. sInte Feipgeurre th 1a.7n bth tehe b glurea plihn es hboewcasu hsoew o btwjeoc t ~ PRACTICAl: INVESTIGATE iTHE MOTION OF. EVERYDAY OBJECTS SUCH AS TOY CARS OR
TENNIS BALLS
A is moving at a higher speed than object B. In Figure 1.7c the object is
speeding up (accelerating) shown by the graph line getting steeper (gradient
getting bigger). In Figure 1.7d the object is slowing down (decelerating). You can use the following simple apparatus to investigate the motion of a toy car.
You could use this to measure the average speed, v of the car for different values of h. Heavy wooden runways need
THE DIFFERENCE BETWEEN SPEED AND VELOCITY to be stacked and moved
carefully. They are best used
Some displacement-time graphs look like the one shown in Figure 1. 7 e. It is at low level rather than being
a straight line, showing that the object is moving with constant speed, but placed on benches or tables
the line is sloping down to the right rather than up to the right. The gradient of where they may fall off. If
such a line is negative because the distance that the object is from the starting heavy trolleys are used as
point is now decreasing - the object is going back on its path towards the 'vehicles', a 'catch box' filled
with bubble wrap or similar
start. Displacement means 'distance travelled in a particular direction' from a
material should be placed at
specified point. So if the object was originally travelling in a northerly direction,
the end of the runway.
the negative gradient of the graph means that it is now travelling south. .6. Figure 1. t OI nvestigating how a toy car rolls down a slope
8 FORCES AND MOTION FORCES AND MOTION
You need to measure the height, h, of the raised end of the wooden track. The track must be securely clamped at ACCELERATION
the height under test and h should be measured with a metre rule making sure that the rule is perpendicular to
the bench surface. Make sure that you always measure to the same point or mark on the raised end of the track Figure 1.12 shows some objects whose speed is changing. The plane must
(a fiducial mark). accelerate to reach take-off speed. In ice hockey, the puck (small disc that the
player hits} decelerates only very slowly when it slides across the ice. When
To find the average speed you will use the equation: the egg hits the ground it is forced to decelerate (decrease its speed} very
d distance moved, s rapidly. Rapid deceleration can have destructive results.
average spee ' v = lime taken, t I
so you will need to measure the distance AB with a metre rule and measure the time it takes for the car to travel
this distance with a stop clock. When timing with a stop clock, human reaction time will introduce measurement
errors. To make these smaller the time to travel distance AB should, for a given value of h, be measured at least
three times and an average value found. Always start the car from the same point, A. If one value is quite different
from the others it should be treated as anomalous (the result is not accurate) and ignored or repeated.
The results should be presented in a table like the one belo~ You do not need to include these equations in l
I I your table headings but you may be asked to
Distance/m AB: show how you did the calculations. .& Figure 1.12 Acceleration ... ... constant speed ... .. . and deceleration
-
Time, t/s Average time, t/s Average speed, v/m/s Acceleration is the rate at which objects change their velocity. It is defined as
Height, h/m t1 I t2 I t3 t = (t1 + t2 + t3)+ 3 V =AB+ t follows:
I I acceleration, a= change in velocity or final velocity, v - initial velocity, u
time taken, t time taken, t
In a question you may be given a complete set of results or you may be required to complete the table by (v-u)
doing the necessary calculations. You may be asked to plot a graph (see general notes above) and then draw a a=- t-
conclusion. The conclusion you draw must be explained with reference to the graph, for example, if the best fit line
through the plotted points is a straight line and it passes through the origin (the 0, 0 point) you can conclude that Why u? Simply because it comes before v!
there is a proportional relationship between the quantities you have plotted on the graph.
Acceleration, like velocity, is a vector because the direction in which the
Some alternative methods acceleration occurs is important as well as the size of the acceleration.
You could investigate the motion of moving objects using photographic methods either by:
• carrying out the experiment in a darkened room using a stroboscope to light up the object at regular known
intervals (found from the frequency setting on the stroboscope} with the camera adjusted so that the shutter is UNITS OF ACCELERATION Velocity is measured in mis, so increase in velocity is also measured in mis.
open for the duration of the movement, or Acceleration, the rate of increase in velocity with time, is therefore measured
• using a video camera and noting how far the object has travelled between each frame - the frame rate will allow in mls/s (read as 'metres per second per second'}. We normally write this as
you to calculate the time between each image. mls2 (read as 'metres per second squared'}. Other units may be used - for
example, cmls2.
In either case a clearly marked measuring scale should be visible.
·Fil:iiii-
Or you could use an electronically operated stop clock and electronic timing gates. This will let you measure the
time that it takes for the moving object to travel over a measured distance. This has the advantage of removing
A car is travelling at 20 mis. It accelerates steadily for 5 s, after which time
timing errors produced by human reaction time.
it is travelling at 30 mis. Calculate its acceleration.
You can also use timing gates to measure how the speed of the object changes as it moves.
~ - Write down what you know:
timing gate initial or starting velocity, u = 20 mis
card strip final velocity, v = 30 mis
time taken, t = 5 s
a= (v-u)
t
30 mis -20 mis
.& Figure 1.11 Using a timing gate is a more accurate method for measuring time taken to travel a distance. 5s
In this arrangement the stop clock will time while the card strip attached to the moving car passes through the 10mls
timing gate. Measuring the length of the card strip and the time it takes for the card strip to pass through the timing It is good practice to include units in 5s
gate allows you to calculate the average speed of the car as it passes through the timing gate. equations -this will help you to supply The car is accelerating at 2 mls2.
the answer with the correct unit.
10 FORCES AND MOTION FORCES AND MOTION
Galileo also noticed that the distance travelled by the ball increased in a
DECELERATION
Deceleration means slowing down. This means that a decelerating object will predictable way. He showed that the rate of increase of speed was steady or
have a smaller final velocity than its starting velocity. If you use the equation uniform. We call this uniform acceleration. Most acceleration is non-uniform -
for finding the acceleration of an object that is slowing down, the answer will that is, it changes from instant to instant - but we shall only deal with uniformly
have a negative sign. A negative acceleration simply means deceleration. accelerated objects in this chapter.
Ph/Hit
VELOCITY-TIME GRAPHS
An object hits the ground travelling at 40 mis. It is brought to rest in 0.02 s.
What is its acceleration?
The table below shows the distances between the bells in an experiment such
Write down what you know: as Galileo's.
initial velocity, u = 40 mis
Bell 2 3 4 5
final velocity, v = 0 mis
time taken, t = 0.02 s Time/s 0.5 1.0 1.5 2.0 2.5
o,stance of bell from start/cm 12 27 48 75
a= (v-u)
t
We can calculate the average speed of the ball between each bell by working
Omls- 40m/s
out the distance travelled between each bell, and the time it took to travel this
0.02s
distance. For the first bell:
-40mls
• distance moved, s
0.02s ve1 o city, v = time taken, t
=-2000mls2
= 3cm =6cmls
0.5s
In Example 3, we would say that the object is decelerating at 2000 mls2.
This is a very large deceleration. Later, in Chapter 3, we shall discuss the This is the average velocity over the 0.5 second time interval, so if we plot it on
consequences of such a rapid deceleration! a graph we should plot it in the middle of the interval, at 0.25 seconds.
Repeating the above calculation for all the results gives us the following table
of results. We can use these results to draw a graph showing how the velocity
MEASURING ACCELERATION When a ball is rolled down a slope it is clear that its speed increases as it rolls - of the ball is changing with time. The graph, shown in Figure 1.14, is called a
that is, it accelerates. Galileo was interested in how and why objects, like the ball velocity-time graph.
EXTENSION WORK rolling down a slope, speed up, and he created an interesting experiment to learn
Galileo was an Italian scientist who more about acceleration. A version of his experiment is shown in Figure 1.13. Time/s 0.25 0.75 1.25 1.75 2.25
was born in 1564. He developed a Mlffliffd & 6 18 30 42 54
telescope, which he used to study the
movement of the planets and stars. He
also carried out many experiments on KEY POINT The graph in Figure 1.14 is a straight line. This tells us that the velocity of the
rolling ball is increasing by equal amounts in equal time periods. We say that
motion (movement). The equations of motion we have
the acceleration is uniform in this case.
learned work for uniform or constant
acceleration only -therefore for objects
EXTENSION WORK with velocity-time graphs that are 60
Twhaotcuhg h(l eGt aalliolenoe daind enloetc htraovnei ca t icmloecr)k, oher straight lines. 50
used his pulse (the sound of his heart) j
and a type of water clock to achieve 40
timings that were accurate enough for .t. Figure 1.13 Galileo's experiment. A ball rolling down a slope, hitting small bells as it rolls } 30
his experiments. ~
Galileo wanted to discover how the distance travelled by a ball depends on the ~ 20
time it has been rolling. In this version of the experiment, a ball rolling down 10
a slope strikes a series of small bells as it rolls. By adjusting the positions of
the bells carefully it is possible to make the bells ring at equal intervals of time 00 -.0- --0,.5- ---.--1,.5- -,----2,. 5
as the ball passes. Galileo noticed that the distances travelled in equal time time/s
intervals increased, showing that the ball was travelling faster as time passed.
Galileo did not have an accurate way of measuring time (there were no digital .t. Figure 1.14 Velocity-time graph for an experiment in which a ball is rolled down a slope. (Note
stopwatches in seventeenth-century Italy!) but it was possible to judge equal that as we are plotting average velocity, the points are plotted in the middle of each successive
0.5 s time interval.)
time intervals accurately simply by listening.
