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978-1-107-69769-0 – Cambridge International AS and A Level Physics
David Sang Graham Jones Gurinder Chadha and Richard Woodside
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David Sang, Graham Jones,
Gurinder Chadha and Richard Woodside
Cambridge International AS and A Level
Physics
Coursebook
Second Edition
© in this web service Cambridge University Press
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University Printing House, Cambridge CB2 8BS, United Kingdom
Cambridge University Press is part of the University of Cambridge.
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© Cambridge University Press 2010, 2014
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 2010
Second edition 2014
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ersity Press
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notice to teachers in the uk
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Example answers and all other end-of-chapter questions were written by the authors.
ersity Press
Contents
Introduction
vii
Chapter 5: Work, energy and power
69
How to use this book
viii
Doing work, transferring energy
Gravitational potential energy
Kinetic energy
g.p.e.–k.e. transformations
Down, up, down – energy changes
Energy transfers
Power
71
75
76
76
77
78
80
Chapter 1: Kinematics – describing motion
Speed
Distance and displacement, scalar and vector
Speed and velocity
Displacement–time graphs
Combining displacements
Combining velocities
Chapter 2: Accelerated motion
1
2
4
5
6
8
10
14
The meaning of acceleration
Calculating acceleration
Units of acceleration
Deducing acceleration
Deducing displacement
Measuring velocity and acceleration
Determining velocity and acceleration in
the laboratory
The equations of motion
Deriving the equations of motion
Uniform and non-uniform acceleration
Acceleration caused by gravity
Determining g
Motion in two dimensions – projectiles
Understanding projectiles
18
20
22
24
25
25
28
29
Chapter 3: Dynamics – explaining motion
37
Calculating the acceleration
Understanding SI units
The pull of gravity
Mass and inertia
Top speed
Moving through fluids
Identifying forces
Newton’s third law of motion
Chapter 4: Forces – vectors and moments
Combining forces
Components of vectors
Centre of gravity
The turning effect of a force
The torque of a couple
15
15
16
17
17
18
38
39
41
43
44
45
47
49
53
54
56
59
59
63
Chapter 6: Momentum
The idea of momentum
Modelling collisions
Understanding collisions
Explosions and crash-landings
Collisions in two dimensions
Momentum and Newton’s laws
Understanding motion
Chapter 7: Matter and materials
Density
Pressure
Compressive and tensile forces
Stretching materials
Elastic potential energy
Chapter 8: Electric fields
Attraction and repulsion
www.cambridge.org
The
concept of an electric field
Electric field strength
Force on a charge
Chapter 9: Electric current, potential
difference and resistance
85
86
86
89
91
93
95
96
101
102
102
104
105
108
116
117
118
119
122
127
Circuit symbols and diagrams
Electric current
An equation for current
The meaning of voltage
Electrical resistance
Electrical power
128
129
132
134
135
136
Chapter 10: Kirchhoff’s laws
143
Kirchhoff’s first law
Kirchhoff’s second law
Applying Kirchhoff’s laws
Resistor combinations
144
145
146
148
iii
Cambridge International AS and A Level Physics
Chapter 11: Resistance and resistivity
The I–V characteristic for a metallic conductor
Ohm’s law
Resistance and temperature
Resistivity
Chapter 12: Practical circuits
Internal resistance
Potential dividers
Potentiometer circuits
Chapter 13: Waves
Describing waves
Longitudinal and transverse waves
Wave energy
Wave speed
The Doppler effect
Electromagnetic waves
Electromagnetic radiation
Orders of magnitude
The nature of electromagnetic waves
iv
ersity Press
156
157
158
159
162
168
169
172
172
178
179
181
182
183
184
185
186
187
188
Chapter 14: Superposition of waves
192
The principle of superposition of waves
Diffraction of waves
Interference
The Young double-slit experiment
Diffraction gratings
193
194
196
200
203
Chapter 15: Stationary waves
From moving to stationary
Nodes and antinodes
Formation of stationary waves
Determining the wavelength and speed of sound
Chapter 16: Radioactivity
Looking inside the atom
Alpha-particle scattering and the nucleus
A simple model of the atom
Nucleons and electrons
Forces in the nucleus
Fundamental particles?
Families of particles
Discovering radioactivity
Radiation from radioactive substances
Discovering neutrinos
Fundamental families
Fundamental forces
Properties of ionising radiation
210
211
212
212
216
222
223
223
225
226
229
229
230
231
231
232
232
232
233
P1: Practical skills at AS level
Practical work in physics
Using apparatus and following instructions
Gathering evidence
Precision, accuracy, errors and uncertainties
Finding the value of an uncertainty
Percentage uncertainty
Recording results
Analysing results
Testing a relationship
Identifying limitations in procedures and
suggesting improvements
Chapter 17: Circular motion
239
240
240
241
241
243
245
246
246
248
250
258
Describing circular motion
Angles in radians
Steady speed, changing velocity
Angular velocity
Centripetal forces
Calculating acceleration and force
The origins of centripetal forces
259
260
261
261
262
264
265
Chapter 18: Gravitational fields
271
Representing a gravitational field
Gravitational field strength g
Energy in a gravitational field
Gravitational potential
Orbiting under gravity
The orbital period
Orbiting the Earth
Chapterwww.cambridge.org
19: Oscillations
Free and forced oscillations
Observing oscillations
Describing oscillations
Simple harmonic motion
Representing s.h.m. graphically
Frequency and angular frequency
Equations of s.h.m.
Energy changes in s.h.m.
Damped oscillations
Resonance
Chapter 20: Communications systems
Radio waves
Analogue and digital signals
Channels of communication
Comparison of different channels
272
274
276
276
277
278
279
285
286
287
288
289
291
292
293
296
297
299
309
310
314
317
319
ersity Press
Contents
Chapter 21: Thermal physics
Changes of state
Energy changes
Internal energy
The meaning of temperature
Thermometers
Calculating energy changes
Chapter 22: Ideal gases
Particles of a gas
Explaining pressure
Measuring gases
Boyle’s law
Changing temperature
Ideal gas equation
Modelling gases – the kinetic model
Temperature and molecular kinetic energy
Chapter 23: Coulomb’s law
Electric fields
Coulomb’s law
Electric field strength for a radial field
Electric potential
Comparing gravitational and electric fields
Chapter 24: Capacitance
Capacitors in use
Energy stored in a capacitor
Capacitors in parallel
Capacitors in series
Comparing capacitors and resistors
Capacitor networks
Chapter 25: Electronics
Components of an electronic sensing system
The operational amplifier (op-amp)
The inverting amplifier
The non-inverting amplifier
Output devices
Chapter 26: Magnetic fields and
electromagnetism
Producing and representing magnetic fields
Magnetic force
Magnetic flux density
Measuring magnetic flux density
Currents crossing fields
Forces between currents
Relating SI units
Comparing forces in magnetic, electric
and gravitational fields
327
328
329
331
332
334
336
345
346
348
348
349
350
351
352
354
359
360
360
362
363
366
372
373
375
377
378
379
380
386
387
393
397
398
398
406
407
409
411
411
413
415
416
417
Chapter 27: Charged particles
Observing the force
Orbiting charges
Electric and magnetic fields
The Hall effect
Discovering the electron
422
423
423
427
428
429
Chapter 28: Electromagnetic induction
435
Observing induction
Explaining electromagnetic induction
Faraday’s law of electromagnetic induction
Lenz’s law
Using induction: eddy currents, generators
and transformers
436
437
441
443
Chapter 29: Alternating currents
Sinusoidal current
Alternating voltages
Power and a.c.
Why use a.c. for electricity supply?
Transformers
Rectification
Chapter 30: Quantum physics
Modelling with particles and waves
Particulate nature of light
The photoelectric effect
Line spectra
Explaining the origin of line spectra
Photon energies
Electron
energies in solids
www.cambridge.org
The nature of light – waves or particles?
Electron waves
Chapter 31: Nuclear physics
Balanced equations
Mass and energy
Energy released in radioactive decay
Binding energy and stability
Randomness and decay
The mathematics of radioactive decay
Decay graphs and equations
Decay constant and half-life
445
451
452
453
455
457
458
460
466
467
468
471
475
476
477
478
480
480
489
490
491
494
494
496
497
499
501
v
Cambridge International AS and A Level Physics
Chapter 32: Medical imaging
The nature and production of X-rays
X-ray attenuation
Improving X-ray images
Computerised axial tomography
Using ultrasound in medicine
Echo sounding
Ultrasound scanning
Magnetic resonance imaging
507
509
511
513
516
518
520
522
P2: Planning, analysis and evaluation
529
Planning
Analysis of the data
Treatment of uncertainties
Conclusions and evaluation of results
Appendix 1: Physical quantities and units
Prefixes
Estimation
vi
ersity Press
506
530
532
536
538
542
542
542
Appendix 2: Data, formulae and
relationships
543
Data
Conversion factors
Mathematical equations
Formulae and relationships
543
543
544
544
Appendix 3: The Periodic Table
545
Glossary
546
Index
555
Acknowledgements
564
Terms and conditions of use for
the CD-ROM
566
www.cambridge.org
ersity Press
Introduction
This book covers the entire syllabus of Cambridge
International Examinations AS and A Level Physics. It is
designed to work with the syllabus that will be examined
from 2016. It is in three parts:
■■
■■
■■
Chapters 1–16 and P1: the AS level content, covered in the
first year of the course, including a chapter (P1) dedicated to
the development of your practical skills
Chapters 17–32 and P2: the remaining A level content,
including a chapter (P2) dedicated to developing your ability
to plan, analyse and evaluate practical investigations
Appendices of useful formulae, a Glossary and an Index.
The main tasks of a textbook like this are to explain the
various concepts of physics that you need to understand
and to provide you with questions that will help you to test
your understanding and prepare for your examinations.
You will find a visual guide to the structure of each chapter
and the features of this book on the next two pages.
When tackling questions, it is a good idea to make
a first attempt without referring to the explanations in
this Coursebook or to your notes. This will help to reveal
any gaps in your understanding. By working out which
concepts you find most challenging, and by spending more
time to understand these concepts at an early stage, you
will progress faster as the course continues.
The CD-ROM that accompanies this Coursebook
includes answers with workings for all the questions in
the book, as well as suggestions for revising and preparing
for any examinations you take. There are also lists of
recommended further reading, which in many cases will
take you beyond the requirements of the syllabus, but
which will help you deepen your knowledge and explain
more of the background to the physics concepts covered in
this Coursebook.
In your studies, you will find that certain key concepts
come up again and again, and that these concepts form
‘themes’ that link the different areas of physics together. It
will help you to progress and gain confidence in tackling
problems if you take note of these themes. For this
Coursebook, these key concepts include:
■■
■■
■■
■■
■■
Models of physical systems
Testing predictions against evidence
Mathematics as a language and problem-solving tool
Matter, energy and waves
Forces and fields
In this Coursebook, the mathematics has been kept to
the minimum required by the Cambridge International
Examinations AS and A Level Physics syllabus. If you
are also studying mathematics, you may find that more
advanced techniques such as calculus will help you with
many aspects of physics.
Studying physics can be a stimulating and worthwhile
experience. It is an international subject; no single
country has a monopoly on the development of the ideas.
It can be a rewarding exercise to discover how men and
women from many countries have contributed to our
knowledge and well-being, through their research into
and application of the concepts of physics. We hope not
only that this book will help you to succeed in your future
studies and career, but also that it will stimulate your
www.cambridge.org
curiosity
and fire your imagination. Today’s students
become the next generation of physicists and engineers,
and we hope that you will learn from the past to take
physics to ever-greater heights.
vii
Cambridge International AS and A Level Physics
How to use this book
Each chapter begins with a short list of the
facts and concepts that are explained in it.
AS Level Physics
Describing movement
1
Our eyes are good at detecting movement. We notice
even quite small movements out of the corners of
our eyes. It’s important for us to be able to judge
movement – think about crossing the road, cycling or
driving, or catching a ball.
Figure 1.1 shows a way in which movement can
be recorded on a photograph. This is a stroboscopic
photograph of a boy juggling three balls. As he juggles,
a bright lamp flashes several times a second so that
the camera records the positions of the balls at equal
intervals of time.
If we knew the time between flashes, we could
measure the photograph and calculate the speed of a
ball as it moves through the air.
Learning outcomes
You should be able to:
■■
■■
■■
■■
define displacement, speed and velocity
draw and interpret displacement–time graphs
describe laboratory methods for determining speed
use vector addition to add two or more vectors
AS Level Physics
The text and illustrations describe and explain all of the facts and concepts
Speed
that We
you
need to know. The chapters, and often
the content within them as
can calculate the average speed of something moving if
If you look at the speedometer in a car, it doesn’t
well,weare
arranged
a similar
sequence
to your
but
with
AS
and
know
the distance itin
moves
and the time
it takes:
tell yousyllabus,
the car’s average
speed;
rather,
it tells
you its
speed
at the instant
when book.
you look at it. This is the car’s
A Levelaverage
content
clearly
halves
of the
distance separated into the two
speed =
2
Figure 13.3 or a similar graph of displacement against
time illustrates the following important definitions about
waves and wave motion:
■■
viii
■■
■■
■■
ersity Press
■■
180
The distance of a point on the wave from its undisturbed
position or equilibrium position is called the displacement x.
The maximum displacement of any point on the wave
from its undisturbed position is called the amplitude A.
The amplitude of a wave on the sea is measured in units
of distance, e.g. metres. The greater the amplitude of the
wave, the louder the sound or the rougher the sea!
The distance from any point on a wave to the next exactly
similar point (e.g. crest to crest) is called the wavelength λ
(the Greek letter lambda). The wavelength of a wave on the
sea is measured in units of distance, e.g. metres.
The time taken for one complete oscillation of a point in a
wave is called the period T. It is the time taken for a point to
move from one particular position and return to that same
position, moving in the same direction. It is measured in
units of time, e.g. seconds..
The number of oscillations per unit time of a point in a
wave is called its frequency f. For sound waves, the higher
the frequency of a musical note, the higher is its pitch.
Frequency is measured in hertz (Hz), where 1 Hz = one
oscillation per second (1 kHz = 103 Hz and 1 MHz = 106 Hz).
The frequency f of a wave is the reciprocal of the period T:
1
f=
T
Waves are called mechanical waves if they need a
substance (medium) through which to travel. Sound is one
example of such a wave. Other cases are waves on strings,
seismic waves and water waves (Figure 13.4).
Some properties of typical waves are given on page 183
in Table 13.1.
Figure 1.1 This boy is juggling three balls. A stroboscopic
lamp flashes at regular intervals; the camera is moved to one
side at a steady rate to show separate images of the boy.
instantaneous speed.
time
In symbols, this is written as:
Questions
throughout the text
QUESTION
give you a chance to check that
1 Look at Figure 1.2. The runner ran 10 000 m, and
youthehave
understood
the Calculate
topic his
clock shows
the total time taken.
during
the race.
youaverage
havespeed
just
read
about. You
can find the answers to these
questions on the CD-ROM.
Units
d
QUESTION
v=
t
1where
Determine
wavelength
of eachtravelled
v is thethe
average
speed and amplitude
d is the distance
thet.two
shown in
Figure1.2)
13.5.
in of
time
Thewaves
photograph
(Figure
shows Ethiopia’s
Kenenisa
6 Bekele posing next to the scoreboard after
breaking
4 the world record in
a a men’s 10 000 metres race.
2 on the clock in the photograph
b
The time
enables us to
0
work out his average
5 10 speed.
15
20 25 30
35
–2
If the
object
is
moving
at
a
constant
speed,
this
–4
Distance
/
cm
equation
will
give
us
its
speed
during
the
time
taken. If its
–6
speed is changing, then the equation gives us its average
Figure 13.5 Two waves – for Question 1.
speed. Average speed is calculated over a period of time.
Displacement / cm
Chapter 1:
Kinematics –
describing motion
There is a short context at the beginning of each chapter, containing an example of
how the material covered in the chapter relates to the ‘real world’.
In the Système Internationale d’Unités (the SI system),
distance is measured in metres (m) and time in seconds (s).
Therefore, speed is in metres per second. This is written as
m s−1 (or as m/s). Here, s−1 is the same as 1/s, or ‘per second’.
There are many other units used for speed. The choice of
unit depends on the situation. You would probably give the
speed
of abook
snail in different
the speed of a racing
This
does units
notfrom
contain
BOX 13.1: Measuring frequency
car. Table
1.1 includes
some alternative units of speed.
AS Level
Physics
detailed
instructions
for
doing
Note that in many calculations it is necessary
to work
You can measure the frequency of soundwww.cambridge.org
waves
−1). experiments, but you
particular
in
SI
units
(m
s
using a cathode-ray oscilloscope (c.r.o.). Figure 13.6
will find background
metresinformation
per second
QUESTIONS
about
the practical
workper
you
centimetres
second
km
s−1
per second
need
do inhow
these
Boxes.
There
7 to
Calculate
muchkilometres
gravitational
potential
km
h−1 or
km/h
kilometres
hour
energy
is gained
if you
climbP1
aper
flight
of stairs.
are
also
two
chapters,
and
Assume that you have
a mass
of 52 kg and that the
mph
miles
per hour
P2, which
detailed
height provide
you lift yourself
is 2.5 m.
Table 1.1 Units of speed.
information
about
practical
8 A climber of
mass 100the
kg (including
the equipment
she is carrying) ascends from sea level to the top
skills you
need to develop during
of a mountain 5500 m high. Calculate the change
your course.
in her gravitational potential energy.
shows how.
A microphone is connected to the input of the
c.r.o. Sound waves are captured by the microphone
and converted into a varying voltage which has the
same frequency as the sound waves. This voltage is
displayed on the c.r.o. screen.
Figure 1.2 Ethiopia’s Kenenisa Bekele set a new world record
is best
tometres
think ofrace
a c.r.o.
as a voltmeter which
forItthe
10 000
in 2005.
is capable of displaying a rapidly varying voltage. To
do this, its spot moves across the screen at a steady
speed, set by the time-base control. At the same
time, the spot moves up and down according to the
voltage of the input.
Hence the display on the screen is a graph of the
varying voltage, with time on the (horizontal) x-axis.
If we know the horizontal scale, we can determine
the period and hence the frequency of the sound
wave. Worked example 1 shows how to do this. (In
Chapter 15 we will look at one method of measuring
the wavelength of sound waves.)
m s−1
cm s−1
a A toy car works by means of a stretched rubber
band. What form of potential energy does the
car store when the band is stretched?
b A bar magnet is lying with its north pole next
to the south pole of another bar magnet. A
student pulls them apart. Why do we say that
the magnets’ potential energy has increased?
Where has this energy come from?
9
Kinetic energy
As well as lifting an object, a force can make it accelerate.
76
Important
other
Again, work isequations
done by the forceand
and energy
is transferred
to theare
object.
In this case,
say that it hasboxes.
gained kinetic
facts
shown
inwe
highlight
energy, Ek. The faster an object is moving, the greater its
kinetic energy (k.e.).
Figure 13.4 The impact of a droplet on the surface of a liquid
creates a vibration, which in turn gives rise to waves on the
surface.
Figure 13.6 Measuring the frequency of sound waves
from a tuning fork.
For an object of mass m travelling at a speed v, we have:
kinetic energy = 12 × mass × speed2
WORKED EXA
3
Calculate th
mass 800 kg
30 m s−1.
Step 1 Cal
Ek = 12 mv2 =
= 160 kJ
Step 2 Cal
Ek = 12 mv2 =
= 360 kJ
Step 3 Cal
change in k
Hint: Take c
by squaring
change in s
incorrect va
QUESTIONS
10 Which has
travelling
250 kg tra
11 Calculate
mass 200
the groun
it at 12.2 m
Ek = 12 mv2
Deriving the formula for kinetic energy
The equation for k.e., Ek = 12mv2, is related to one of the
equations of motion. We imagine a car being accelerated
from rest (u = 0) to velocity v. To give it acceleration a, it
is pushed by a force F for a distance s. Since u = 0, we can
write the equation v2 = u2 + 2as as:
2
g.p.e.–k.e
A motor drags th
hill. The car runs
as it goes (see Fig
to reach the top o
first. It accelerate
The motor pro
car to the top of t
ersity Press
In the earlier examples, we described how the ‘motion’
of one trolley appeared to be transferred to a second
trolley, or shared with it. It is more correct to say that it
is the trolley’s momentum that is transferred or shared.
(Strictly speaking, we should refer to linear momentum,
because there is another quantity called angular
momentum which is possessed by spinning objects.)
As with energy, we find that momentum is also
conserved. We have to consider objects which form a
closed system – that is, no external force acts on them. The
principle of conservation of momentum states that:
Within a closed system, the total momentum in any
direction is constant.
The principle of conservation of momentum can also be
expressed as follows:
A group of colliding objects always has as much
momentum after the collision as it had before the collision.
This principle is illustrated in Worked example 1.
QUESTIONS
2
Calculate the momentum of each of the following
objects:
a a 0.50 kg stone travelling at a velocity of 20 m s−1
b a 25 000 kg bus travelling at 20 m s−1 on a road
c an electron travelling at 2.0 × 107 m s−1.
(The mass of the electron is 9.1 × 10−31 kg.)
3
Two balls, each of mass 0.50 kg, collide as shown in
Figure 6.6. Show that their total momentum before
the collision is equal to their total momentum after
the collision.
before
2.0 m s–1 3.0 m s–1
For a closed system, in any direction:
after
2.0 m s–1
B
A
How to use this book
1.0 m s–1
B
A
Wherever
you
needof to
know
how to use a formula to carry out a calculation,
total
momentum
objects
before collision
total momentum
of objectsto
aftershow
collision you howFigure
6.6 this.
For Question 3.
there are worked= example
boxes
to do
88
WORKED EXAMPLE
1
Step 1 Make a sketch using the information given in the
question. Notice that we need two diagrams to show
the situations, one before and one after the collision.
Similarly, we need two calculations – one for the
momentum of the trolleys before the collision and one
for their momentum after the collision.
In Figure 6.5, trolley A of mass 0.80 kg travelling at a
velocity of 3.0 m s−1 collides head-on with a stationary
trolley B. Trolley B has twice the mass of trolley A. The
trolleys stick together and have a common velocity of
1.0 m s−1 after the collision. Show that momentum is
conserved in this collision.
Step 2 Calculate the momentum before the collision:
before
uA = 3.0 m s–1
A
positive
direction
uB = 0
B
0.80 kg
0.80kg
0.80 kg
momentum of trolleys before collision
after
= mA × uA + mB × uB
= (0.80 × 3.0) + 0
= 2.4 kg m s−1
vA+B = 1.0 m s–1
A
0.80 kg
A Level Physics
Trolley B has no momentum before the collision,
because it is not moving.
B
0.80 kg
0.80kg
Step 3 Calculate the momentum after the collision:
Glossary
momentum of trolleys after collision
AS Level Physics
Key words are highlighted in the text
when they are first introduced.
= (mA + mB) × vA+B
= (0.80 + 1.60) × 1.0
Base units, derived units
The metre, kilogram and second are three of the seven SI
base
units.constant
These areThe
defined
withofgreat
precision
so that
Avogadro
number
particles
in one
every
standards
laboratory
can reproduce
mol−1),
mole of
any substance
approximately
(6.02them
× 1023correctly.
OtherNunits,
such as units of speed (m s−1) and
denoted
A.
) are that
known
as derived
unitsor
because
acceleration
s−2idea
band theory(m
The
electrons
in a solid
liquid
absorption line spectrum A dark line of a unique
are combinations
of certain
base units.
units,
You willthey
also
find
definitions
ofSome
can
have
energies
within
ranges
or derived
bands, between
wavelength seen in a continuous spectrum.
such
as
the
newton
and
the
joule,
have
special
names
which are
forbidden
values.
these words
in
the
Glossary.
acceleration The rate of change of an object’s velocity:
which are more convenient to use than giving them in
bandwidth (communications) A measure of the width of
Δv
terms of base units. The definition of the newton will show
a=
a range of frequencies being transmitted.
Δt
you how this works.
base units Defined units of the SI system from which all
Unit: m s−2 .
other units are
derived.
Defining
the
newton
accuracy An accurate value of a measured quantity is one
Cambridge International AS Level Physics
Isaac
Newton
significant
best fit
line A(1642–1727)
straight lineplayed
drawnaas
closely aspart
possible to
which is close to the true value of the quantity.
in
scientific
of force.
Building
on lie
thedeveloping
points of athe
graph
so thatidea
similar
numbers
of points
acoustic impedance Acoustic impedance Z is the product
Galileo’s
above andearlier
belowthinking,
the line. he explained the relationship
of the density ρ of a substance and the speed c of sound in
between
force, mass
acceleration,
which
we now
write
binding energy
Theand
minimum
external
energy
required
that substance (Z = ρc). Unit: kg m−2 s−1.
as
F = ma. For
thisneutrons
reason, the
unit of of
force
is named
to separate
all the
andSIprotons
a nucleus.
There is a summary of
activity The rate of decay or disintegration of nuclei in a
after him.
bit A basic unit of information storage, the amount of
radioactive sample.
key points at the end
We can use the equation F = ma to define the newton (N).
■ Forces are vector quantities that can be added by
■ The principle of moments states that, for information
any object stored by a device that exists in only two
ampere The SI unit of electric current (abbreviated A).
of each chapter. You
distinct states, usually given as the binary digits 0 and 1.
means of a vector triangle. Their resultant can be
that is in equilibrium, the sum of the clockwise
amplitude
displacement
of point
a particle
from by the
determined using trigonometry or by scale
drawing.The maximum
moments
about any
provided
One newton
is the force
that will give aconstant
1 kg massgiven
an by
might find this helpful
Boltzmann
constant
A fundamental
546
its equilibrium position.forces acting on the object equals the sum ofacceleration
the
of 1 m s−2 in the direction of the force.
R
■ Vectors such as forces can be resolved into
and NA is the
= , where R is−2the ideal gas constant
when you are revising.
40 same kpoint.
−2
amplitude
modulation
A
form
of
modulation
in
which
anticlockwise
moments
about
that
N
or
1
N
=
1
kg
m
s
1
N
=
1
kg
×
1
m
s
A
components. Components at right angles to one
Avogadro constant.
the
signal
causes variations
in the amplitude of a carrier
another can be treated independently of
one
another.
■ A couple is a pair of equal, parallel but opposite forces
wave.the
law The pressure exerted by a fixed mass of gas
For a force F at an angle θ to the x-direction,
whose effect is to produce a turning effectBoyle’s
on a body
The
seven
base units
is inversely
proportional
to its volume, provided the
analogue signal A signal
that isgiving
continuously
variable,
components are:
without
it linear acceleration.
temperature
thestudy
gas remains
constant.
having a continuum of torque
possibleofvalues.
In
mechanicsof(the
of forces
and motion), the units
x-direction: F cos θ
a couple = one of the forces × perpendicular
we
use are
based on X-rays
three base
units: when
the metre,
kilogram
braking
radiation
produced
electrons
are
analogue-to-digital conversion
(ADC) the
Conversion
distance between
forces of a
y-direction: F sin θ
and
second.(also
As wecalled
moveBremsstrahlung
into studying electricity,
decelerated
radiation).we will
continuous analogue■ signal
toobject
discrete
numbers. the resultant
For an
to digital
be in equilibrium,
force
■ The moment of a force = force × perpendicular
need to add another
base
unit, the
ampere.
requires
www.cambridge.org
The ratio
of charge
stored
by aHeat
capacitor
to
angular
The angle
through
anzero
object
on the
object which
must be
and thecapacitance
resultant
distance of the pivot from the line of action
of displacement acting
another
base difference
unit, the kelvin
the potential
across(the
it. unit of temperature).
moves in a circle.
moment must be zero.
the force.
Table 3.2 shows the seven base units of the SI system.
carrier wave A waveform (usually sinusoidal) which is
angular frequency The frequency of a sinusoidal
Remember that all other units can be derived from these
modulated by an input signal to carry information.
oscillation expressed in radians per second:
seven. The equations that relate them are the equations
2π
Chapter 15:
Stationary
waves
centre
gravity
point
the entire
of an
angular frequency ω =
that
youofwill
learnThe
as you
go where
along (just
as F =weight
ma relates
T
object
appears
to act.
the
newton
to the
kilogram, metre and second). The unit
angular velocity The rate of change of the angular
centripetal
Theisresultant
an object
of
luminousforce
intensity
not partforce
of theacting
A/ASon
course.
position of an object as it moves along a curved path.
moving in a circle; it is always directed towards the centre
Questions at the end of each chapter begin with shorter answer
then
move
on to more
antinode Aquestions,
point on a stationary
wave
with maximum
Base unit
Symbol
Base unit
of the circle.
64
amplitude.
demanding exam-style questions,
some of which may require
use of knowledge from previous characteristic
length
x, l, s etc.
m (metre)
radiation Very intense X-rays produced in
atomic mass unit A unit of mass (symbol u)
mass
m
kg (kilogram)
chapters. Answers to these questions can be found on theapproximately
CD–ROM.
an
X-ray tube, having specific wavelengths
that
depend on
−27 kg. The mass of an
equal
to
1.661
×
10
1 A ship is pulled at a constant speed by two small boats, A and B, as shown in Figure 4.27. The engine of the the
time
t
s (second)
target metal.
atom of 126 C = 12.000 u exactly.
ship does not produce any force.
electriccarrier
current Any charged particle,
I
(ampere)
charge
such asAan
electron,
1 Figure 15.19 shows a stationary wave
on a string.
attenuation
The gradual loss in strength or intensity of a
thermodynamic
T
K (kelvin)
responsible
for atemperature
current.
signal.
A
amount oflaw
substance
n
(mole)
Charles’s
The volume occupied
by a gas mol
at constant
average speed The total distance travelled by an object
pressure
directly proportional
40°
luminousisintensity
I to its thermodynamic
cd (candela)
divided by the total time taken.
(absolute) temperature.
Figure 6.5 The state of trolleys A and B, before and after
the collision.
= 2.4 kg m s−1 see thermodynamic scale.
absolute scale of temperature;
So, both before and
after the
collision,
the trolleys have
absolute
zero
The temperature
at which a system has
a combined momentum
of 2.4
kg m s−1energy;
. Momentum
has to −273.15 °C.
minimum
internal
equivalent
been conserved.
Summary
End-of-chapter questions
End-of-chapter questions
40°
vibrator
Figure 15.19 For End-of-chapter Question 1.
Figure 4.27 For End-of-chapter Question 1.
Table 3.2 SI base quantities and units. In this course, you will
learn about all of these except the candela.
B
a On a copy of Figure 15.19, label one node (N) and one antinode (A).
b Mark
on your
the
wavelength
ofship
the standing
The tension
in each
cablediagram
between
A and
B and the
is 4000 N.wave and label it λ.
c a The
frequency
of the
vibratorthe
is doubled.
Describe
the changes
inthe
theship.
standing wave pattern.
a Draw
free-body
diagram
showing
three horizontal
forces
acting on
b Draw
a vector
diagram
scale showing
forces and
usea your
to find filled
the value
2 A tuning
fork
whichto
produces
a note these
of 256three
Hz is placed
above
tubediagram
which is nearly
with water.
of the
drag
force
onisthe
ship. until resonance is first heard.
The
water
level
lowered
a Explain what is meant by the term resonance.
b The length of the column of air above the water when resonance is first heard is 31.2 cm.
Calculate the speed of the sound wave.
3 a State two similarities and two differences between progressive waves and stationary waves.
b Figure 15.20 shows an experiment to measure the speed of a sound in a string. The frequency of the
vibrator is adjusted until the standing wave shown in Figure 15.20 is formed.
vibrator
75 cm
[2]
[1]
[1]
[1]
[2]
[1]
[2]
[4]
pulley
slotted masses
Figure 15.20 For End-of-chapter Question 3.
i
On a copy of the diagram, mark a node (label it N) and an antinode (label it A).
[2]
219
QUESTION
4
The pull
weight) i
internati
of force a
reasons
useful de
Other SI un
Using only seve
of quantities ha
would be confu
units were also
were defined as
of water would
unlikely that th
exactly the mas
kilogram, whic
which ix
all mass
All other un
is done using th
speed is define
speed in the SI
Since the de
units for force
Equations t
same base unit
not happen the
When each te
the equation
QUESTIONS
5
Determi
a press
b energ
c densi
6
Use base
equation
a press
=d
b dista
= in