tài liệu vật lý in2physics của tác giả stephen bosi

S
C
I
S
PHY @ HSC

Stephen Bosi
John O’Byrne
Peter Fletcher
Joe Khachan
Jeff Stanger
Sydney, Melbourne, Brisbane, Perth, Adelaide
and associated companies around the world

Sandra Woodward


Contents
Series features
How to use this book
Stage 6 Physics syllabus grid

vi
viii
x

Module 1 Space
Module 1 Introduction
Chapter 1 Cannonballs, apples, planets and gravity
1.1 Projectile motion
1.2 Gravity

1.3 Gravitational potential energy
Practical experiences
Chapter summary
Review questions

2
4
4
10
16
20
22
22

Chapter 2 Explaining and exploring the solar system 26
2.1 Launching spacecraft
26
2.2 Orbits and gravity
35
2.3 Beyond Kepler’s orbits
41
2.4 Momentum bandits: the slingshot effect
44
2.5 I’m back! Re-entry
46
Practical experiences
52
Chapter summary
53
Review questions

54
Chapter 3 Seeing in a weird light: relativity
3.1 Frames of reference and classical relativity
3.2 Light in the Victorian era
3.3 Special relativity, light and time
3.4 Length, mass and energy
Practical experiences
Chapter summary
Review questions

58
58
61
64
69
75
76
76

Module 1 Review

80

Module 2 Motors and Generators
Module 2 Introduction

82

Chapter 4 Electrodynamics: moving charges and
magnetic fields

84
4.1 Review of essential concepts
84
4.2 Forces on charged particles in magnetic fields 89
4.3 The motor effect
90
4.4 Forces between parallel wires
93
Practical experiences
97
Chapter summary
98
Review questions
98

Chapter 5 Induction: the influence of changing
magnetism
5.1 Michael Faraday discovers electromagnetic
induction
5.2 Lenz’s law
5.3 Eddy currents
Practical experiences
Chapter summary
Review questions

100
100
104
106
109

110
110

Chapter 6 Motors: magnetic fields make the world
go around
6.1 Direct current electric motors
6.2 Back emf and DC electric motors
6.3 Alternating current electric motors
Practical experiences
Chapter summary
Review questions

114
114
120
121
126
127
127

Chapter 7 Generators and electricity supply: power
for the people
7.1 AC and DC generators
7.2 Transformers
7.3 Electricity generation and transmission
Practical experiences
Chapter summary
Review questions

130

130
136
141
148
149
149

Module 2 Review

152

Module 3 From Ideas to Implementation
Module 3 Introduction

154

Chapter 8 From cathode rays to television
8.1 Cathode ray tubes
8.2 Charges in electric fields
8.3 Charges moving in a magnetic field
8.4 Thomson’s experiment
8.5 Applications of cathode rays
Practical experiences
Chapter summary
Review questions

156
156
160
164

165
167
170
171
171

Chapter 9 Electromagnetic radiation: particles
or waves?
9.1 Hertz’s experiments on radio waves
9.2 Black body radiation and Planck’s hypothesis
9.3 The photoelectric effect
9.4 Applications of the photoelectric effect
Practical experiences
Chapter summary
Review questions

174
174
178
182
184
185
186
187
iii


Contents

Chapter 10 Semiconductors and the electronic

revolution
10.1 Conduction and energy bands
10.2 Semiconductors
10.3 Semiconductor devices
10.4 The control of electrical current
Practical experiences
Chapter summary
Review questions

188
189
190
193
197
201
202
202

Chapter 11 Superconductivity
11.1 The crystal structure of matter
11.2 Wave interference
11.3 X-ray diffraction
11.4 Crystal structure
11.5 Electrical conductivity and the crystal
structure of metals
11.6 The discovery of superconductors
11.7 The Meissner effect
11.8 Type-I and type-II superconductors
11.9 Why is a levitated magnet stable?
11.10 BCS theory and Cooper pairs

11.11 Applications of superconductors
Practical experiences
Chapter summary
Review questions

204
204
205
207
208

Module 3 Review

224

209
211
212
212
213
215
217
220
221
221

Module 4 Quanta to Quarks
Module 4 Introduction

226

Chapter 12 From Rutherford to Bohr
228
12.1 Atomic timeline
228
12.2 Rutherford’s model of the atom
229
12.3 Planck’s quantised energy
231
12.4 Spectral analysis
232
12.5 Bohr’s model of the atom
235
12.6 Bohr’s explanation of the Balmer series
236
12.7 Limitations of the Rutherford–Bohr model 239
Practical experiences
241
Chapter summary
242
Review questions
243
Chapter 13 Birth of quantum mechanics
13.1 The birth
13.2 Louis de Broglie’s proposal
13.3 Diffraction
13.4 Confirming de Broglie’s hypothesis
13.5 Electron orbits revisited
13.6 Further developments of atomic theory
1924–1930

Practical experiences
Chapter summary
Review questions
iv

247
247
248
250
251
252
253
256
256
257

Chapter 14 20th century alchemists
14.1 Discovery of the neutron
14.2 The need for the strong force
14.3 Atoms and isotopes
14.4 Transmutation
14.5 The neutrino
14.6 Was Einstein right?
14.7 Binding energy
14.8 Nuclear fission
14.9 Chain reactions
14.10 Neutron scattering
Practical experiences
Chapter summary
Review questions

260
260
261
262
263
265
266
268
269
270
272
273
274
275

Chapter 15 The particle zoo
15.1 The Manhattan Project
15.2 Nuclear fission reactors
15.3 Radioisotopes
15.4 Particle accelerators
15.5 The Standard Model
Practical experiences
Chapter summary
Review questions

279
279
280
282

286
292
295
296
297

Module 4 Review

300

Module 5 Medical Physics
Module 5 Introduction

302

Chapter 16 Imaging with ultrasound
16.1 What is ultrasound?
16.2 Principles of ultrasound imaging
16.3 Piezoelectric transducers
16.4 Acoustic impedance
16.5 Types of scans
16.6 Ultrasound at work
Practical experiences
Chapter summary
Review questions

304
304
305
308

310
312
315
317
318
318

Chapter 17 Imaging with X-rays
17.1 Overview and history: types of X-ray images
17.2 The X-ray tube
17.3 Types of X-rays
17.4 Production of X-ray images
17.5 X-ray detector technology
17.6 Production of CAT X-ray images
17.7 Benefits of CAT scans over conventional
radiographs and ultrasound
Practical experiences
Chapter summary
Review questions

320
320
321
322
324
326
326
329
330
331

331


Contents

Chapter 18 Imaging with light
18.1 Endoscopy
18.2 Medical uses of endoscopes
Practical experiences
Chapter summary
Review questions

333
333
336
338
339
339

Chapter 19 Imaging with gamma rays
19.1 Isotopes and radioactive decay
19.2 Half-life
19.3 Radiopharmaceuticals: targeting tissues
and organs
19.4 The gamma camera
19.5 Positron emission tomography
Practical experiences
Chapter summary
Review questions

340
340
343

Chapter 20 Imaging with radio waves
20.1 Spin and magnetism
20.2 Hydrogen in a magnetic field
20.3 Tuning in to hydrogen
20.4 It depends on how and where you look
20.5 The MRI scanner
20.6 Applications of MRI
Practical experiences
Chapter summary
Review questions

354
354
355
357
359
360
362
363
364
364

Module 5 Review

366

344
346
347
350
351
351

Module 6 Astrophysics
Module 6 Introduction

368

Chapter 21 Eyes on the sky
21.1 The first telescopes
21.2 Looking up
21.3 The telescopic view
21.4 Sharpening the image
21.5 Interferometry
21.6 Future telescopes
Practical experiences
Chapter summary
Review questions

370
370
373
374
377
380
382

383
384
384

Chapter 22 Measuring the stars
22.1 How far?
22.2 Light is the key
22.3 The stellar alphabet
22.4 Measuring magnitudes
22.5 Colour matters
Practical experiences
Chapter summary
Review questions

388
388
389
394
397
400
403
405
405

Chapter 23 Stellar companions and variables
23.1 Binary stars
23.2 Doubly different
23.3 Variable stars
23.4 Cepheid variables
Practical experiences

Chapter summary
Review questions

407
407
411
413
415
418
418
419

Chapter 24 Birth, life and death
24.1 The ISM
24.2 Star birth
24.3 Stars in the prime of life
24.4 Where to for the Sun?
24.5 The fate of massive stars
24.6 How do we know?
Practical experiences
Chapter summary
Review questions

422
422
423
425
428
430
433

435
436
436

Module 6 Review

438

Module 7 Skills
Module 7 Introduction

440

Chapter 25 Skills stage 2
25.1 Metric prefixes
25.2 Numerical calculations
25.3 Sourcing experimental errors
25.4 Presenting research for an exam
25.5 Australian scientist
25.6 Linearising a formula

442
442
443
445
446
447
447

Chapter 26 Revisiting the BOS key terms

26.1 Steps to answering questions

448
449

Numerical answers
Glossary
Index
Acknowledgements
Formulae and data sheets
Periodic table

452
454
465
471
473
474

v


S
C
I
S
Y
PH
@ HSC
AGE FOR NSW STUDENTS

CK
PA
S
IC
YS
PH
E
ET
PL
M
CO
THE
in2 Physics is the most up-to-date physics package written for the NSW Stage 6 Physics syllabus. The
materials comprehensively address the syllabus outcomes and thoroughly prepare students for the HSC exam.
Physics is presented as an exciting, relevant and fascinating discipline. The student materials provide
clear and easy access to the content and theory, regular review questions, a full range of exam-style
questions and features to develop an interest in the subject.

in2 Physics @ HSC student book
• The student book closely follows the NSW Stage 6 Physics
syllabus and its modular structure.
• It clearly addresses both the contexts and the prescribed focus
areas (PFAs).
• Modules consist of chapters that are broken up into
manageable sections.
• Checkpoint questions review key content at
8
regular intervals throughout each chapter.
• Physics Philes present short, interesting
snippets of relevant information about

physics or physics applications.
• Physics Features highlight important real-life
examples of physics.
• Physics For Fun—Try This! provide hands-on
activities that are easy to do.
• Physics Focus brings together physics concepts
in the context of one or more PFAs and provides
students with a graded set of questions to
develop their skills in this vital area.

From ideas to
on
implementati

From
cathode rays
to television

glass

anode (positive)

electrons
'boil' off
the heated
cathode

collimator

electron

beam

heater

cathode (negative)

Figure 8.5.3

electrons attracted
to the positive anode

The components of an electron gun used in
oscilloscopes and CRT televisions

both cathode ray

Television

electron gun

magnetic
coils

fluorescent screen

Figure 8.5.5

A television picture tube
showing the electron gun,
deflection coils and

fluorescent screen

only one beam.

Each student book includes an interactive student CD containing:
• an electronic version of the student book.
• all of the student materials on the companion website with live
links to the website.
vi

mask
blue
beam

electron
guns

red
beam

R
G
B

green
beam

focusing
coils

V

Time

sawtooth voltage for timebase

Figure 8.5.4

V

Time

mask

fluorescent
screen

fluorescent
screen

electron
beams

holes in
mask

Figure 8.5.6

guns
A colour CRT television set has three electron

that will only strike their respective coloured
phosphor dots with the aid of a shadow mask.

sinusoidal vertical voltage

A sawtooth voltage waveform on the horizontal
beam
deflection plates of a CRO sweeps the electron
waveform
across the screen to display the sinusoidal
on the vertical deflection plates.

used the principles of the cathode ray
Cathode ray tube (CRT) television sets
are now being superseded by plasma
tube for most of the 20th century. These
which use different operating principles
and liquid crystal display television sets,
sharper image. However, the CRT
and allow a larger display area with a
place in this form of
television holds quite a significant historical
communication.
television set is shown in Figure 8.5.5.
A schematic diagram of a colour CRT
of the CRO. The main difference is the
Its basic elements are similar to those
field coils placed outside the tube
method of deflecting the electrons. Magnetic
fields inside it. The magnitude and

produce horizontal and vertical magnetic
degree and direction of electron beam
direction of the current determine the
rule for the force on charged particles
deflection. Recall your right-hand palm
field will deflect the electrons
in a magnetic field. The vertical magnetic
deflect them vertically.
horizontally; the horizontal field will
scanning the beam from left to right
The picture on the screen is formed by
the television switches the beam on and
and top to bottom. The electronics in
in order to reproduce the transmitted
off at the appropriate spots on the screen
images, colour television sets need to
picture. However, to reproduce colour
green phosphors on the screen. Three
and
blue
red,
of
intensity
the
control
one aimed at one particular colour. The
separate electron guns are used, each
in groups of red, blue and green dots
coloured dots on the screen are clustered
cannot be distinguished by eye

that are very close to each other and generally
For this reason a method of guiding the
without the aid of a magnifying glass.
coloured dots was devised. A metal
different electron beams to their respective
8.5.6) and consisting of an array of
sheet, known as a shadow mask (Figure
hole guides the three beams to
Each
screen.
holes, is placed behind the phosphor
the beams move horizontally and vertically.
their respective coloured phosphor as
need the shadow mask since they had
Black and white television sets did not

168

phosphor dots
on screen

vacuum

beam to move up or down in
The vertical deflection plates cause the
For example, a sinusoidal voltage will
synchronisation with an input voltage.
as a trace) on the screen.
display a sinusoidal waveform (known

electron
beam

deflecting
coils

try this!
Do not aDjust your
horizontal!
If you have access to an old
black and white TV set or an old
style monochrome computer
monitor, try holding a bar
magnet near the front of the
screen and watch how the
image distorts. This occurs
because the magnetic field
deflects the electrons that strike
the screen. DO NOT do this with

a colour TV set. This can
magnetise the shadow mask and
cause permanent distortion of
the image and its colour. You
can move a bar magnet near the
back of a colour TV set to
deflect the electrons from the
electron gun and therefore
distort or shift the image
without causing permanent

damage to the TV set.

used
Can an osCillosCope be
as a television set?

ray oscilloscope (CRO) and CRT
he similarity between the cathode
be used as a television set. In
television suggests that a CRO can
that have made use of the CRO as
fact, there have been some devices
in principle, it can be used as a
you would a computer monitor. So,
‘why did they need to deflect the
television. One is then forced to ask
fields rather than with electric
beam in a television set with magnetic

T

fields as in the CRO?’
be made in the same design as
In principle all television sets could
with
and cheaper to deflect the beam
a CRO; however, it is much easier
the tube rather than embed electrodes
a magnetic field on the outside of
is a little trickier. So now

in the glass and inside the vacuum—this
deflect the beam of the CRO using
another question arises: ‘why not
CROs?’.
in cheaper
magnetic fields, wouldn’t it result
instruments. The horizontal
Cathode ray oscilloscopes are precision
to very high frequencies in order
sweep rate must be able to be increased
to
quickly. Electric fields can be made
to detect signals that change very
extra power requirements.
change very quickly without significant
system requires higher and higher
However, a magnetically deflected
in
and vertical deflection frequencies
voltages with increasing horizontal
same
the
in the coils, and therefore,
order to maintain the same current
a significantly greater power
angle of beam deflection – thus having
sets, however, only operate at
requirement. Cathode ray tube television
horizontal and vertical frequencies.
fixed and relatively low scanning

the mass market to deflect with a
Thus it is simpler and cheaper for
magnetic field.

CheCkpoint 8.5
1
2
3
4

Outline the purpose of a CRO.
List the main parts of a CRO.
in the CRO.
Describe the role of each of these parts
the cathode ray tube CRO and CRT TV.
State the similarities and differences between
169


in2 Physics @ HSC Activity Manual
Chapter 8
from cathode rays
to television

MODULE

• A write-in workbook
that provides a
structured approach
to the mandatory

practical experiences,
both first-hand and
secondary-source
investigations.
• Dot point and skills
focused.

3

from ideas to
tion
implementa

Chapter 8

from Cathode rays
to television
aCtivity 8.1
first-hand investigation

Changing pressure of
discharge tubes

the occurrence of different striation
first-hand information to observe
Perorm an investigation and gather
discharge tubes.
patterns for different pressures in

Physics skills

in this activity include:
The skills outcomes to be practised
12.1 perform first-hand investigations
12.2 gather first-hand information
14.1 analyse information
syllabus grid on pages vi–viii.
skills outcomes can be found in the
The complete statement of these

Aim

To observe the striation patterns for different

different patterns that
Because of this development,
could be seen depended on the pressure.
the air molecules. To do this,
but it can be made to conduct by ionising
Normally air is considered to be an insulator,
an electric field). At high pressures these
that are always in air are accelerated (with
to ionise the air
energy
the very small fraction of free electrons
sufficient
gain
not
losing their energy and, as a result, do
electrons collide frequently with the air,

molecules, thereby acquiring enough
travel further before colliding with air
they are
atoms. As pressure is reduced, these electrons
in turn, can ionise other atoms. When
will produce more free electrons that,
energy to ionise the air molecules. This
show (known as a discharge). The lower
to be absorbed by atoms, we see a light
discharge.
a
able to travel far enough to gain the energy
producing
and
can travel before colliding with gas molecules
the pressure, the further the electrons
excited (increasing in energy) and
electrons around the gas atom becoming
will also
The light that is emitted is a result of the
energy they can have in an atom). Light
lowest
(the
state
ground
the
to
return
re-emitting the photon of light as they
ground state, emitting photons. As every

with ions and the electrons return to the
be produced when free electrons recombine
the element with which the electron collides.
the colour of light seen will vary with
element has a distinct set of energy levels,
be passed through air. The
it was found that electric current could

Equipment

The patterns are
can carry out the experiment first hand.
If you have the apparatus at school, you
is very dark.
• discharge tubes at different pressures
• induction coil
• DC power supply
• connecting wires
Alternatively, you can use the simulations

them.

Risk assessment

Method
1
2
3
4

8.1.1.
Set up the equipment as shown in Figure
in the tube.
Observe the patterns and note the pressure
series.
Replace the tube with the next in the
and
Repeat the process of observing the patterns
your set.
in
tubes
the
noting the pressure for each of

DC power supply

tube
Figure 8.1.1 Induction coil and discharge

pressures in discharge tubes.

Hypothesis

in Part B and make observations from

hard to see unless the room

HAZARD

The voltages necessary to operate the

coils and may produce unwanted X-rays.
used,
High voltages are produced by induction
the tube. Generally, the higher the voltage
the tube and the pressure of the gas in
tubes depend upon the dimensions of
of unwanted X-rays.
the greater the danger of the production
a minimum of 1 m away from the equipment.
Use the lowest possible voltage and stand

Theory

which the pressure could be reduced
Plücker collaborated to create a tube in
Ever since Heinrich Geissler and Julius
ray tube have advanced tremendously.
atom and developing uses for the cathode
substantially, our understanding of the

69

68

in2 Physics @ HSC Teacher Resource
• Editable teaching materials, including teaching
programs, so that teachers can tailor lessons to
suit their classroom.
• Answers to student book and activity manual
questions, with fully worked solutions and

extended answers and support notes.
• Risk assessments for all first-hand
investigations.

in2 Physics @ HSC companion website
Visit the companion website
in the student lounge
and teacher lounge
of Pearson Places
• Review questions—
auto-correcting multiple-choice
questions for each chapter.
• Web destinations—a list
of reviewed websites that support
further investigation.

For more information on the in2 Physics series,
visit www.pearsonplaces.com.au
vii


How to use this book
in2 Physics @ HSC is structured to enhance student
learning and their enjoyment of learning. It contains many
outstanding and unique features that will assist students
succeed in Stage 6 Physics. These include:
• Module opening pages introduce a range of contexts for
study, as well as an inquiry activity that provides
immediate activities for exploration and discussion.

2
Context

• Key ideas are clearly highlighted with a
and
indicate where domain dot points
Syllabus flags
appear in the student book. The flags are placed as
closely as possible to where the relevant content is
covered. Flags may be repeated if the dot point has
multiple parts, is complex or where students are
required to solve problems.
3

Motors and
Generators

l v = l0 1 −
tv =

mv =

Figure 4.0.2

of interference of electromagnetic radiation, and examine how this was applied to
crystals using X-rays. Then we will see how the BCS theory of superconductivity
made use of the crystal structure of matter.

try thiS!

CheCkpoInT 11.1

Crystals in the kitChen

Explain what is meant by the crystal structure of matter.

Look at salt grains through a
magnifying lens. Each grain is
a single crystal that is made from
the basic arrangement of sodium
and chlorine atoms shown in
Figure 11.1.1. Although the
grains mostly look irregular due
to breaking and chipping during
the manufacturing process,
occasionally you will see an
untouched cubic or rectangular
prism that reflects the underlying
crystal lattice structure.

11.2 Wave interference
The wave nature of light can be used to measure the size of very small spaces.
Recall that two identical waves combine to produce a wave of greater amplitude
when their crests overlap, as shown in Figure 11.2.1a (see in2 Physics @
Preliminary sections 6.4 and 7.4). The overlapping waves will cancel to produce
t=0s
a resulting wave of zero amplitude when the crest of one wave coincides with the
trough of the other (Figure 11.2.1b). This addition and subtraction is called
constructive and destructive interference respectively and is a property of all
wave phenomena.

t=1s
As an example, two identical circular water waves in a ripple tank overlap (see
Figure 11.2.2). The regions of constructive and destructive interference radiate
outwards along the lines as shown. Increasing the spacing between the sources
t = 3 s (Figure 11.2.2b).
causes the radiating lines to come closer together
a

Figure 11.2.1 Two identical waves (red, green) travelling in opposite directions can add (blue)
t=1s

(a) constructively or (b) destructively.t = 5 s

The interference of identical waves from two sources can also be represented
by outwardly radiating transverse waves (see Figure 11.2.3). The distance that a
twave
= 3 s travels is known as its path length. t = 6 s Constructive interference occurs
when the difference in the path length of the two waves is equal to 0, λ, 2λ, 3λ,
4λ or any other integer multiple of the wavelength λ. Destructive interference
occurs
when the two waves are half a wavelength out of step. This corresponds to
t=4s
t=7s
a path length difference of λ/2, 3λ/2, 5λ/2 etc.

t=5s

lines of destructive
interference

lines of constructive
interference

t=4s

t=0s

11.1 The crystal structure of matter

a

b

waves
in phase

destructive
interference
constructive
interference

204

t=7s

1
2

evil tWinS

T

he most extreme mass–energy
conversion involves antimatter.
For every kind of matter particle
there is an equivalent antimatter
particle, an ‘evil twin’, bearing
properties (such as charge) of
opposite sign. Particles and their
antiparticles have the same rest
mass. When a particle meets its
antiparticle, they mutually
annihilate—all their opposing
properties cancel, leaving only
their mass‑energy, which is
usually released in the form of
two gamma‑ray photons. Matter–
antimatter annihilation has been
suggested (speculatively) as a
possible propellant for powering
future interstellar spacecraft.


1 v2 
1
≈ m0c  1 + × 2  = m0c 2 + m0v 2
2
2 c 

2

E = mc 2

Figure 3.4.6

One of the four ultra-precise superconducting spherical
gyroscopes on NASA’s Gravity Probe B, which orbited
Earth in 2004/05 to measure two predictions of general
relativity: the bending of spacetime by the Earth’s
mass and the slight twisting of spacetime by the
Earth’s rotation (frame-dragging)

In general relativity, Einstein showed that gravity
occurs because objects with mass or energy cause this
4D spacetime to become distorted. The paths of
objects through this distorted 4D spacetime appear to
our 3D eyes to follow the sort of astronomical
trajectories you learned about in Chapter 2 ‘Explaining
and exploring the solar system’. However, unlike
Newton’s gravitation, general relativity is able to handle
situations of high gravitational fields, such as
Mercury’s precessing orbit around the Sun and black
holes. General relativity also predicts another wave that
doesn’t require a medium: the ripples in spacetime
called ‘gravity waves’.

where m is any kind of mass. In relativity, mass and energy are regarded as the
same thing, apart from the change of units. Sometimes the term mass-energy is
used for both. m0 c 2 is called the rest energy, so even a stationary object contains
energy due to its rest mass. Relativistic kinetic energy therefore:

m0c 2
mv c 2 − m0c 2 =
− m0c 2
v2
1− 2
c
Whenever energy increases, so does mass. Any release of energy is
accompanied by a decrease in mass. A book sitting on the top shelf has a slightly
higher mass than one on the bottom shelf because of the difference in
gravitational potential energy. An object’s mass increases slightly when it is hot
because the kinetic energy of the vibrating atoms is higher.
Because c 2 is such a large number, a very tiny mass is equivalent to a large
amount of energy. In the early days of nuclear physics, E = mc 2 revealed the
enormous energy locked up inside an atom’s nucleus by the strong nuclear force
that holds the protons and neutrons together. It was this that alerted nuclear
physicists just before World War II to the possibility of a nuclear bomb. The
energy released by the nuclear bomb dropped on Hiroshima at the end of that
war (smallish by modern standards) resulted from a reduction in relativistic mass
of about 0.7 g (slightly less than the mass of a standard wire paperclip).

Discuss the implications of
mass increase, time dilation
and length contraction for
space travel.

Worked example
qUESTIon
When free protons and neutrons become bound together to form a nucleus, the reduction in
nuclear potential energy (binding energy) is released, normally in the form of gamma rays.
Relativity says this loss in energy is reflected in a decrease in mass of the resulting atom.

• Each chapter concludes with:
– a chapter summary
– review questions, including literacy-based questions
(Physically Speaking), chapter review questions
(Reviewing) and physics problems (Solving
Problems). Syllabus verbs are clearly highlighted as
and where appropriate
– Physics Focus—a unique feature that places key
chapter concepts in the context of one or more
prescribed focus areas.

b

Figure 11.2.2 Interference of water waves for
two sources that are (a) close
together and (b) further apart

19

Imaging with
gamma rays

PRACTICAL EXPERIENCES

ChAPTER 19

This is a starting point to get you thinking about the mandatory practical
experiences outlined in the syllabus. For detailed instructions and advice, use
in2 Physics @ HSC Activity Manual.

Figure 11.2.3 Constructive and destructive interference between

Activity 19.1: Bone scAns

identical transverse waves from two sources

Perform an investigation to
compare a bone scan with
an X-ray image.

205

• Chapters are divided into short, accessible sections—
the text itself is presented in short, easy-to-understand
chunks of information. Each section concludes with
a Checkpoint—a set of review questions to check
understanding of key content and concepts.

A bone scan is performed to obtain a functional image of the bones and so can be
used to detect abnormal metabolism in the bones, which may be an indication of
cancer or other abnormality. Because cancer mostly involves a higher than normal
rate of cell division (thus producing a tumour), chemicals
involved in metabolic processes in bone tend to accumulate in
higher concentrations in cancerous tissue. This produces areas
of concentration of gamma emission, indicating a tumour.
Compare the data obtained from the image of a bone scan
with that provided by an X-ray image.
Discussion questions
1 Identify the best part of the body for each of these

diagnostic tools to image.
2 Compare and contrast the two images in terms of
the information they provide.

Figure 19.6.1

a

Chapter summary
•

•
•
•
•

•

Thenumberofprotonsinanucleusisgivenbythe
atomic number, while the total number of nucleons is
given by the mass number.
Atomsofthesameelementwithdifferentnumbersof
neutrons are called isotopes of that element.
Manyelementshavenaturallyoccurringunstable
radioisotopes.
Inalphadecayanunstablenucleusdecaysbyemitting
an alpha particle (α-particle).
Inbetadecay,aneutronchangesintoaprotonand
a high-energy electron that is emitted as a beta particle
(β-particle).

Inpositrondecay,apositron—theantiparticleofthe
electron—isemitted.

b

Activity 19.2: HeAltHy or diseAsed?
Typical images of healthy bone and cancerous bone are shown. The tumours show
up as hot-spots. Use the template in the activity manual to research and compare
images of healthy and diseased parts of the body.
Discussion questions
1 Examine Figure 19.4.2. There is a hot-spot that is not cancerous near the
left elbow. Explain.
2 In the normal scan (Figure 19.6.2a), the lower pelvis has a region of high
intensity. Why is this? (Hint: It may be soft tissue, not bone. Looking at
Figure 19.6.2b might help you with this question.)
3 State the differences that can be observed by comparing an image of
a healthy part of the body with that of a diseased part of the body.

PHysicAlly sPeAking
Below is a list of topics that have been discussed throughout
this chapter. Create a visual summary of the concepts in
this chapter by constructing a mind map linking the terms.
Add diagrams where useful.

Radioactive
decay

350

Radiation

Radioisotope

Neutron

Proton

Beta decay

Gamma
decay

Antimatter

Bone scan

Positron
decay

Half-life

Bones scans of (a) a healthy person and
(b) a patient with a tumour in the skeleton

•

mEdICAL
PhySICS

Whenapositronandanelectroncollide,theirtotal

mass is converted into energy in the form of two
gamma-ray photons.
Ingammadecayagammaray (g) is emitted from a
radioactive isotope.
Thetimeittakesforhalfthemassofaradioactive
parent isotope to decay into its daughter nuclei is the
half-life of the isotope.
Artificialradioisotopesareproducedintwomainways:
in a nuclear reactor or in a cyclotron.
Agammacameradetectsgammaraysemittedby
a radiopharmaceutical in the patient’s body.
PETimagingusespositron-emitting
radiopharmaceuticals to obtain images using gamma
rays emitted from electron–positron annihilation.

•
•

•
•
•

Review questions

Comparison of an X-ray and bone scan of a hand

Gather and process secondary
information to compare a
scanned image of at least one
healthy body part or organ with

a scanned image of its
diseased counterpart.

Figure 19.6.2

viii

−

73

constructive
interference

t=6s

1
2

72

Figure 11.1.1 Crystal structure of sodium chloride. The red spheres represent positive
sodium ions, and the green spheres represent negative chlorine ions.

−

1
Rearrange:
mvc 2 – m0c 2 = (mv – m0)c 2 ≈ m0v 2
2

In other words, at low speeds, the gain in relativistic mass (mv – m0)
multiplied by c 2 equals the kinetic energy—a tantalising hint that at low speed
mass and energy are equivalent. It can also be shown to be true at all speeds,
using more sophisticated mathematics. In general, mass and energy are
equivalent in relativity and c 2 is the conversion factor between the energy unit
(joules) and the mass unit (kg). In other words:

c2

here are two more invariants in special relativity.
Maxwell’s equations (and hence relativity)
requires that electrical charge is invariant in all
frames. Another quantity invariant in all inertial frames
is called the spacetime interval.
You may have heard of spacetime but not know
what it is. One of Einstein’s mathematics lecturers
Hermann Minkowski (1864–1909) showed that the
equations of relativity and Maxwell’s equations become
simplified if you assume that the three dimensions of
space (x, y, z) and time t taken together form a
four‑dimensional coordinate system called spacetime.
Each location in spacetime is not a position, but rather
an event—a position and a time.
Using a 4D version of Pythagoras’ theorem,
Minkowski then defined a kind of 4D ‘distance’
between events called the spacetime interval s given by:
s 2 = (c × time period)2 – path length2
= c 2t 2 – ((∆x)2 + (∆y)2 + (∆z)2)
Observers in different frames don’t agree on the
3D path length between events, or the time period

between events, but all observers in inertial frames
agree on the spacetime interval s between events.

from ideaS to
implementation

A crystal is a three-dimensional regular arrangement of atoms. Figure 11.1.1
shows a sodium chloride crystal (ordinary salt also called rock salt when it comes
as a large crystal). The crystal is made from simple cubes repeated many times,
with sodium and chlorine atoms at the corners of the cubes. Crystals of other
materials may have different regular arrangements of their atoms. There are
14 types of crystal arrangements that solids can have.
The regular arrangement of atoms in crystals was a hypothesis before
Max Von Laue and his colleagues confirmed it by X-ray diffraction experiments.
William and Lawrence Bragg took this method one step further by measuring
the spacing between the atoms in the crystal. Let us first look at the phenomenon

 v2 
m0c 2  1 − 2 
c 


2

T

Surprising discovery
crystal, constructive interference,
destructive interference, path length,
diffraction grating, Bragg law,

phonons, critical temperature,
type-I superconductors,
type-II superconductors,
critical field strength, vortices,
flux pinning, BCS theory, Cooper pair,
coherence length, energy gap, spin

v

 v2 
= m0c 2  1 − 2 
c 


m0c 2

v2
1− 2
c
Using a well-known approximation formula that you might learn at university,
(1 – x )n ≈ 1 – nx for small x:

1. The history of physics

InQUIRY ACtIVItY

• Chapter openings list the key words of each chapter and
introduce the chapter topic in a concise and engaging way.

Just as an improved understanding of the conducting properties of

semiconductors led to the wide variety of electronic devices, research
into the conductivity of metals produced quite a surprising discovery
called superconductivity. This is the total disappearance of electrical
resistance below a certain temperature, which has great potential
applications ranging from energy transmission and storage to public
transport. An understanding of this phenomenon required a detailed
understanding of the crystal structure of conductors and the motion
of electrons through them.

mv c 2 =

m0

TwISTIng SPACETImE ...
And YoUR mInd

A simple homopolar motor

83

Superconductivity

c2

c2

1−

82

11

v2

v2

PHYSICS FEATURE

Many of the devices you use every day have electric motors. They spin your DVDs,
wash your clothes and even help cook your food. Could you live without them,
and how much do you know about how they work?
The essential ingredients for a motor are a power source, a magnetic field
and things to connect these together in the right way. It’s not as hard as you
think. All you need is a battery, a wood screw, a piece of wire and a cylindrical or
spherical magnet. Put these things together as shown in Figure 4.0.2 and see
if you can get your motor to spin. Be patient and keep trying. Then try the
following activities.
1 Test the effects of changing the voltage you use. You could add another
battery in series or try a battery with a higher voltage.
2 Try changing the strength of the magnet by using a different magnet or
adding another. What does this affect?
3 Try changing the length of the screw, how sharp its point is or the material
it is made from. Does it have to be made of iron?

A generator produces electricity
in each of these wind turbines.

The kinetic energy formula K = 1 mv 2 doesn’t apply at relativistic speeds,
2
even if you substitute relativistic mass mv into the formula. Classically, if you

apply a net force to accelerate an object, the work done equals the increase in
kinetic energy. An increase in speed means an increase in kinetic energy. But
in relativity it also means an increase in relativistic mass, so relativistic mass
and energy seem to be associated. Superficially, if you multiply relativistic
mass by c 2 you get mv c 2, which has the same dimensions and units as energy.
But let’s look more closely at it.

t0
1−

The first recorded observations of the relationship between electricity and
magnetism date back more than 400 years. Many unimagined discoveries
followed, but progress never waits. Before we understood their nature, inventions
utilising electricity and magnetism had changed our world forever.
Today our lives revolve around these forms of energy. The lights you use to
read this book rely on them and the CD inside it would be nothing but a shiny
coaster for your cup. We use magnetism to generate the electricity that drives
industry, discovery and invention. Electricity and magnetism are a foundation for
modern technology, deeply seated in the global economy, and our use impacts
heavily on the environment.
The greatest challenge that faces future generations is the supply of energy.
As fossil fuels dry up, electricity and magnetism will become even more
important. New and improved technologies will be needed. Whether it’s a hybrid
car, a wind turbine or a nuclear fusion power plant, they all rely on applications
of electricity and magnetism.

Space
How does this formula behave at low speeds (when v 2/c 2 is small)?

Mass, energy and the world’s most famous equation

Solve problems and analyse
information using:
E = mc2

BUIld YoUR own eleCtRIC motoR

Figure 4.0.1

Seeing in a
weird light:
relativity

Isotope

reviewing
1

Recall how the bone scan produced by a radioisotope
compares with that from a conventional X-ray.

2

Analyse the relationship between the half-life of
a radiopharmaceutical and its potential use in the
human body.

3

Explain how it is possible to emit an electron from the

nucleus when the electron is not a nucleon.

4

Assess the statement that ‘Positrons are radioactive
particles produced when a proton decays’.

5

Discuss the impact that the production and use of
radioisotopes has on society.

6

Describe how isotopes such as Tc-99m and F-18 can
be used to target specific organs to be imaged.

7

Use the data in Table 19.6.1 to answer the questions:
a Which radioactive isotope would most likely be
used in a bone scan? Justify your choice.
b Propose two reasons why cesium-137 would not
be a suitable isotope to use in medical imaging.

Nucleon

Alpha decay

PET

Table 19.6.1
Scintillator

Properties of some radioisotopes

Radioactive souRce

Radiation emitted

Half-life

C-11
Tc-99m
TI-201
I-131
Cs-137
U-238

β+, g
g
g
β, g
α
α

20.30 minutes
6.02 hours
3.05 days
8.04 days

30.17 years
4.47 × 109 years

351


How to use this book

Other features

• Module reviews provide a full range of exam-style
questions, including multiple-choice, short-response
and extended-response questions.

3

from ideas to
implementation
4

The review contains questions in a similar style and proportion
to the HSC Physics examination. Marks are allocated to
each question up to a total of 25 marks. It should take you
approximately 45 minutes to complete this review.
5

Experimental data from black body radiation during
Planck’s time showed that predicted radiation levels
were not achieved in reality. Planck best described
this anomaly by saying that:

A classical physics was wrong.
B radiation that is emitted and absorbed is
quantised.
C he had no explanation for it.
D quantum mechanics needed to be developed.

extended response

Figure 11.13.4 shows a cathode ray tube that has
been evacuated. Which answer correctly names each
of the labelled features?

III

6

Explain, with reference to atomic models, why
cathode rays can travel through metals. (2 marks)

7

Outline how the cathode ray tube in a TV works
in order to produce the viewing picture. (2 marks)

8

Give reasons why CRT TVs use magnetic coils and
CROs use electric plates in order to deflect the
beams, given that both methods work. (2 marks).

9

In your studies you were required to gather
information to describe how the photoelectric effect
is used in photocells.
a Explain how you determined which material was
relevant and reliable.
b Outline how the photoelectric effect is used in
photocells. (3 marks)

II

I

multiple choice
(1 mark each)
1 Predict the direction of the electron in Figure 11.13.1
as it enters the magnetic field.
A Straight up
B Left
C Right
D Down

A
B

Figure 11.13.1

An electron in a magnetic field
C

The diagrams in Figure 11.13.2 represent
semiconductors, conductors and insulators. The
diagrams show the conduction and valence bands,
and the energy gaps. Which answer correctly labels
each of the diagrams?

A
B
C
D

3

Figure 11.13.4 An evacuated cathode ray tube

–

I

II

III

Conductor
Insulator
Insulator
Semiconductor

Insulator

Conductor
Semiconductor
Conductor

Semiconductor
Semiconductor
Conductor
Insulator

D

I

A
B
C
D

I

II

III

Critical
temperature
Superconductor
material
Critical
temperature

Normal material

Superconductor
material
Critical
temperature
Normal material

Normal material

Superconductor
material

II

Figure 11.13.2

The graph in Figure 11.13.3 shows how the
resistance of a material varies with temperature.
Identify each of the parts labelled on the graph.

Superconductor
material
Critical
temperature

II

III

Cathode
Striations

Anode
Cathode

Anode

Faraday’s
dark space
Striations

Faraday’s
dark space

10

Justify the introduction of semiconductors to replace
thermionic devices. (4 marks)

11

Magnetic levitation trains are used in Germany and
Japan. The trains in Germany use conventional
electromagnets, whereas the one in Japan uses
superconductors. Compare and contrast the two
systems. (3 marks)

12

a

b

Determine the frequency of red light, which has
a wavelength λ = 660 nm. (Speed of light
c = 3.00 × 108 m s–1)
Calculate the energy of a photon that is emitted
with this wavelength. (Planck’s constant
h = 6.63 × 10–34 J s) (4 marks)

I

Figure 11.13.3

• Physics for Fun—Try This! activities are short, handson activities to be done quickly, designed to provoke
discussion.
• Physics Features are a key feature as they highlight
contextual material, case studies or prescribed focus
areas of the syllabus.

III

II

Normal material

I
Striations
Faraday’s

dark space
Crooke’s
dark space
Cathode

• A complete glossary of all the key words is included at
the end of the student book.

Energy bands

Resistance (Ω)

2

• Physics Philes present short, interesting items to
support or extend the text.

III

Temperature (K)

Resistance varies with temperature

224

225

Practical experiences
The accompanying activity manual covers all of the
mandatory practical experiences outlined in the syllabus.

in2 Physics @ HSC Activity Manual is a write-in
workbook that outlines a clear, foolproof approach to
success in all the required practical experiences.
Within the student book, there are clear cross-references
to the activity manual: Practical Experiences icons refer to
the activity number and page in the activity manual. In
each chapter, a summary of possible investigations is
provided as a starting point to get
students thinking. These include
PRACTICAL
the aim, a list of equipment and
EXPERIENCES
Activity 10.2
discussion questions.
Activity Man

• The final two chapters provide essential reference
material: ‘Skills stage 2’ and ‘Revisiting the BOS
key terms’.
• In all questions and activities, except module review
questions, the BOS key terms are highlighted.

in2 Physics @ HSC Student CD
This is included with the student book and contains:
• an electronic version of the student book
• interactive modules demonstrating key concepts

MODULE

ual, Page 94

2

Chapter 6
motors: magnetic fields
make the world go around

motors and
generators

aCtIVItY 6.2
First-hand investigation

• the companion website on CD

Risk assessment

Motors and torque

Solve problems and analyse information about simple motors using:
τ = nBIA cos θ

Method

Physics skills

1

Cut a length of cotton-covered wire so that the wire is long enough
to wrap around the exterior of a matchbox three times (as shown in

Figure 6.2.2).

2

Leave a straight piece (approx. 10 cm long) hanging out and then wind
the remainder of the wire around the box 2½ times. Leave another
straight piece the same length as at the start, on the opposite side.

3

Wrap the straight pieces around the loops so that they tie both ends.

4

Fan out the loops so that you get equally spaced loops and that it
looks like a bird cage (see Figure 6.2.3).

5

Push out the middle of the paper clip as shown and Blu-Tack to
the bench.

6

Slip the straight pieces of wire through the paper clip supports.
Unwrap the cotton from these parts.

7

Connect an AC power supply to the paper clips.

8

Place two magnets so that a north pole and a south pole face on
opposing sides of the cage.

9

Turn on. You may need to give the cage a tap to get it spinning.

The skills outcomes to be practised in this activity include:
12.4 process information
14.1 analyse information
The complete statement of these skills outcomes can be found in the syllabus grid on pages vii–viii.

Aim

Hypothesis

Theory
The motor effect means that a current-carrying wire experiences
a force when placed in a magnetic field. This is the basis for
the workings of a motor.
For a motor to work as needed, the motion resulting from
the motor effect needs to be circular and the force needs to be
adjusted so the direction of rotation does not change.

Question
Figure 6.2.1 shows the simplified workings of a motor that you
will be making. Label all the parts of the motor.

48

insulatedwirefromwhichinsulationcanberemovedeasily
magnets
magneticfieldsensoranddatalogger(ifavailable)
paperclips

matchbox
wire
b

loop wire
through

Figure 6.2.2 Equipment set-up 1

cage fanned out

paper clip

alligator clip
wires

power
source

Figure 6.2.3 Equipment set-up 2

Record your observations of the motor.

The complete in2 Physics @ HSC package

2

How did adding more magnets affect how the motor ran?

Remember the other components of the complete package:

3

When the current is increased, what changes occurred?

Results
N

S

C:

D:

Figure 6.2.1 Simplified motor

• Blu-Tack
• connectingwireswithalligatorclips
• powersupply

• a link to the live companion website (Internet access
required) to provide access to the latest information and

web links related to the student book.

1

A:
B:

Equipment
•
•
•
•

a

• in2 Physics @ HSC companion website at Pearson Places
49

• in2 Physics @ HSC Teacher Resource.

ix


Stage 6 Physics syllabus grid
Prescribed focus areas
1. The history of physics

H1.evaluates how major advances in scientific understanding and
technology have changed the direction or nature of scientific thinking

Feature: pp. 12, 29, 72

2. The nature and practice of physics

H2.analyses the ways in which models, theories and laws in physics
have been tested and validated

Focus: p. 79

3. Applications and uses of physics

H3.assesses the impact of particular advances in physics on the
development of technologies

Feature: pp. 12, 29, 307,
334, 346

Focus: pp. 25, 246, 299

Focus: pp. 57, 79, 129,
173, 223, 246, 259, 278
4. Implications for society and the
Environment

H4.assesses the impacts of applications of physics on society and the
environment

Feature: pp. 29, 307, 344

5. Current issues, research and

developments in physics

H5.identifies possible future directions of physics research

Feature: pp. 391, 410

Focus: pp. 113, 173, 353
Focus: pp. 79, 113, 173,
223, 353, 386

Module 1 Space
1. The Earth has a gravitational field that exerts a force on objects both on it and around it
Students learn to:

Page Students:

define weight as the force on an object
due to a gravitational field

13

perform an investigation and gather information to determine a value for
Act. 1.2
acceleration due to gravity using pendulum motion or computer-assisted
technology and identify reason(s) for possible variations from the value 9.8 m s–2

Page

explain that a change in gravitational
potential energy is related to work done

16

gather secondary information to predict the value of acceleration due to gravity
on other planets

Act. 1.3

define gravitational potential energy as
the work done to move an object from
a very large distance away to a point
in a gravitational field:
mm
EP = G 1 2
r

16

analyse information using the expression:

Act. 1.3

F = mg
to determine the weight force for a body on Earth and for the same body
on other planets

2. Many factors have to be taken into account to achieve a successful rocket launch, maintain
a stable orbit and return to Earth
Students learn to:

Page Students:

Page

describe the trajectory of an object
undergoing projectile motion within the
Earth’s gravitational field in terms of
horizontal and vertical components

5

7, 9,
23, 24

solve problems and analyse information to calculate the actual velocity of
a projectile from its horizontal and vertical components using:
vx2 = ux2

v = u + at
vy2 = uy2 + 2ay ∆y
∆x = ux t
∆y = uyt + 12 ay t 2

describe Galileo’s analysis of projectile
motion

5

perform a first-hand investigation, gather information and analyse data to
calculate initial and final velocity, maximum height reached, range and time of

flight of a projectile for a range of situations by using simulations, data loggers
and computer analysis

explain the concept of escape velocity
in terms of the:
– gravitational constant
– mass and radius of the planet

18

identify data sources, gather, analyse and present information on the contribution 29
of one of the following to the development of space exploration: Tsiolkovsky,
Act. 2.1
Oberth, Goddard, Esnault-Pelterie, O’Neill or von Braun

x

Act. 1.1


Stage 6
Physics syllabus grid
outline Newton’s concept of escape
velocity

18

identify why the term ‘g forces’ is used
to explain the forces acting on an
astronaut during launch

31

discuss the effect of the Earth‘s orbital
motion and its rotational motion on the
launch of a rocket

34

analyse the changing acceleration of
a rocket during launch in terms of the:
– Law of Conservation of Momentum
– forces experienced by astronauts

30, 33

analyse the forces involved in uniform
circular motion for a range of objects,
including satellites orbiting the Earth

25, 32, solve problems and analyse information to calculate the centripetal force acting
34, 37, on a satellite undergoing uniform circular motion about the Earth using:
54, 55
mv 2
F = r

compare qualitatively low Earth and
geo-stationary orbits

43

define the term orbital velocity and the 36, 40, solve problems and analyse information using:
quantitative and qualitative relationship 56
r3
GM
=
between orbital velocity, the
2
4
π2
T
gravitational constant, mass of the
central body, mass of the satellite and
the radius of the orbit using Kepler’s
Law of Periods
account for the orbital decay of
satellites in low Earth orbit

46

discuss issues associated with safe
re-entry into the Earth’s atmosphere
and landing on the Earth’s surface

47

identify that there is an optimum angle
for safe re-entry for a manned
spacecraft into the Earth’s atmosphere
and the consequences of failing to

achieve this angle

47

37, 54,
55
Act. 2.2

39, 43,
56

3. The solar system is held together by gravity
Students learn to:

Page Students:

Page

describe a gravitational field in the
region surrounding a massive object in
terms of its effects on other masses
in it

13

present information and use available evidence to discuss the factors affecting
the strength of the gravitational force

Act. 1.3

define Newton’s Law of Universal
Gravitation:
mm
F = G 1 22
d

11

solve problems and analyse information using:
mm
F = G 1 22
d

23, 24,
25, 37,
54, 55

discuss the importance of Newton’s
Law of Universal Gravitation in
understanding and calculating the
motion of satellites

35, 38

identify that a slingshot effect can be
provided by planets for space probes

44

xi

Stage 6
Physics syllabus grid
4. Current and emerging understanding about time and space has been dependent upon earlier models
of the transmission of light
Students learn to:

Page Students:

Page

outline the features of the aether model 61
for the transmission of light
describe and evaluate the MichelsonMorley attempt to measure the relative
velocity of the Earth through the aether

62

gather and process information to interpret the results of the Michelson-Morley
experiment

62
Act. 3.2

discuss the role of the MichelsonMorley experiments in making
determinations about competing
theories

62

outline the nature of inertial frames of
reference

58

perform an investigation to help distinguish between non-inertial and inertial
frames of reference

60
Act. 3.1

discuss the principle of relativity

58

analyse and interpret some of Einstein’s thought experiments involving mirrors
and trains and discuss the relationship between thought and reality

66

describe the significance of Einstein’s
assumption of the constancy of the
speed of light

65

analyse information to discuss the relationship between theory and the evidence
supporting it, using Einstein’s predictions based on relativity that were made
many years before evidence was available to support it

78

identify that if c is constant then space
and time become relative

65

discuss the concept that length
standards are defined in terms of time
in contrast to the original metre
standard

79

explain qualitatively and quantitatively
the consequence of special relativity in
relation to:
– the relativity of simultaneity
– the equivalence between mass and
energy
– length contraction
– time dilation
– mass dilation

64, 69 solve problems and analyse information using:
E = mc 2
lv = l0 1 −

v2

66, 69,
72, 77,
78

c2

t0
tv = 1 −

v2
c2

m0
mv = 1 −
discuss the implications of mass
increase, time dilation and length
contraction for space travel

v2
c2

70, 73

Module 2 Motors and Generators
1. Motors use the effect of forces on current-carrying conductors in magnetic fields
Students learn to:

Page Students:

Page

discuss the effect on the magnitude of
the force on a current-carrying
conductor of variations in:
– the strength of the magnetic field in
which it is located
– the magnitude of the current in the
conductor
– the length of the conductor in the
external magnetic field
– the angle between the direction
of the external magnetic field and
the direction of the length of the
conductor

92

Act. 4.1

xii

perform a first-hand investigation to demonstrate the motor effect


Stage 6
Physics syllabus grid
describe qualitatively and quantitatively 94
the force between long parallel currentcarrying conductors:
II

F
=k 1 2
l
d

solve problems using:
II
F
=k 1 2
l
d

94

define torque as the turning moment of
a force using:
t = Fd

115

solve problems and analyse information about the force on current-carrying
conductors in magnetic fields using:
F = BIl sin θ

92
Act. 4.1

identify that the motor effect is due to
the force acting on a current-carrying
conductor in a magnetic field

90,
116

solve problems and analyse information about simple motors using:
t = nBIA cos θ

117
Act. 6.2

describe the forces experienced by
a current-carrying loop in a magnetic
field and describe the net result of
the forces

117

identify data sources, gather and process information to qualitatively describe the 91, 119
application of the motor effect in:
Act. 6.1
– the galvanometer
– the loudspeaker

describe the main features of a DC
electric motor and the role of each
feature

115

identify that the required magnetic

fields in DC motors can be produced
either by current-carrying coils or
permanent magnets

115

2. The relative motion between a conductor and magnetic field is used to generate an electrical voltage
Students learn to:

Page Students:

outline Michael Faraday’s discovery of
the generation of an electric current by
a moving magnet

100

perform an investigation to model the generation of an electric current by moving 101
a magnet in a coil or a coil near a magnet
Act. 5.1

Page

define magnetic field strength B as
magnetic flux density

101

plan, choose equipment or resources for, and perform a first-hand investigation
to predict and verify the effect on a generated electric current when:

– the distance between the coil and magnet is varied
– the strength of the magnet is varied
– the relative motion between the coil and the magnet is varied

Act. 5.1

describe the concept of magnetic flux
in terms of magnetic flux density and
surface area

101

gather, analyse and present information to explain how induction is used in
cooktops in electric ranges

108
Act. 5.2

describe generated potential difference
as the rate of change of magnetic flux
through a circuit

103

gather secondary information to identify how eddy currents have been utilised in
electromagnetic braking

Act. 5.2
113

account for Lenz’s Law in terms of
conservation of energy and relate it to
the production of back emf in motors

105,
120

explain that, in electric motors, back
emf opposes the supply emf

120

explain the production of eddy currents
in terms of Lenz’s Law

106

3. Generators are used to provide large scale power production
Students learn to:

Page Students:

Page

describe the main components of a
generator

131

plan, choose equipment or resources for, and perform a first-hand investigation

to demonstrate the production of an alternating current

Act. 5.1

compare the structure and function of
a generator to an electric motor

135

gather secondary information to discuss advantages/disadvantages of AC and DC
generators and relate these to their use

135
Act. 7.1

describe the differences between AC
and DC generators

135

analyse secondary information on the competition between Westinghouse and
Edison to supply electricity to cities

141
Act. 7.2

gather and analyse information to identify how transmission lines are:
– insulated from supporting structures
– protected from lightning strikes

146
Act. 7.3

discuss the energy losses that occur as 144
energy is fed through transmission lines
from the generator to the consumer
assess the effects of the development
of AC generators on society and the
environment

147

xiii


Stage 6
Physics syllabus grid
4. Transformers allow generated voltage to be either increased or decreased before it is used
Students learn to:

Page Students:

Page

describe the purpose of transformers in
electrical circuits

136

perform an investigation to model the structure of a transformer to demonstrate

how secondary voltage is produced

Act. 7.3

compare step-up and step-down
transformers

137

solve problems and analyse information about transformers using:
Vp
np
=
Vs
ns

137
Act. 7.3

identify the relationship between the
ratio of the number of turns in the
primary and secondary coils and the
ratio of primary to secondary voltage

137

gather, analyse and use available evidence to discuss how difficulties of heating
caused by eddy currents in transformers may be overcome

139

Act. 7.3

explain why voltage transformations are
related to conservation of energy

139

gather and analyse secondary information to discuss the need for transformers in
the transfer of electrical energy from a power station to its point of use

145
Act. 7.3

explain the role of transformers in
electricity substations

142

discuss why some electrical appliances
in the home that are connected to the
mains domestic power supply use a
transformer

136,
144

discuss the impact of the development
of transformers on society

147

5. Motors are used in industries and the home usually to convert electrical energy into more useful forms
of energy
Students learn to:

Page

Students:

Page

describe the main features of an AC
electric motor

124

perform an investigation to demonstrate the principle of an AC induction motor

Act. 6.3

gather, process and analyse information to identify some of the energy transfers
124,
and transformations involving the conversion of electrical energy into more useful 153
forms in the home and industry
Act. 7.3

Module 3 From Ideas to Implementation
1. Increased understandings of cathode rays led to the development of television
Students learn to:

Students:

Page

explain why the apparent inconsistent
157
behaviour of cathode rays caused
debate as to whether they were charged
particles or electromagnetic waves

Page

perform an investigation and gather first-hand information to observe the
occurrence of different striation patterns for different pressures in discharge
tubes

Act. 8.1

explain that cathode ray tubes allowed
the manipulation of a stream of
charged particles

perform an investigation to demonstrate and identify properties of cathode rays
using discharge tubes:
– containing a Maltese cross
– containing electric plates
– with a fluorescent display screen
– containing a glass wheel

Act. 8.2

analyse the information gathered to determine the sign of the charge on
cathode rays

Act. 8.2

solve problem and analyse information using:
F = qvB sin θ
F = qE
and
V
E=
d

162,
164

157

identify that moving charged particles
in a magnetic field experience a force

164

identify that charged plates produce an
electric field

161

xiv

Stage 6
Physics syllabus grid
describe quantitatively the force acting 164
on a charge moving through a magnetic
field:
F = qvB sin θ
discuss qualitatively the electric field
strength due to a point charge, positive
and negative charges and oppositely
charged parallel plates

160

describe quantitatively the electric field 161
due to oppositely charged parallel plates
outline Thomson’s experiment to
measure the charge/mass ratio of an
electron

165

outline the role of:
– electrodes in the electron gun
– the deflection plates or coils
– the fluorescent screen
– in the cathode ray tube of
conventional TV displays and
oscilloscopes

167

2. The reconceptualisation of the model of light led to an understanding of the photoelectric effect and
black body radiation
Students learn to:

Page

Students:

Page

describe Hertz’s observation of the
effect of a radio wave on a receiver and
the photoelectric effect he produced
but failed to investigate

182

perform an investigation to demonstrate the production and reception of
radio waves

Act. 9.1

outline qualitatively Hertz’s experiments 175
in measuring the speed of radio waves
and how they relate to light waves

identify data sources, gather, process and analyse information and use available

evidence to assess Einstein’s contribution to quantum theory and its relation to
black body radiation

Act. 9.2

identify Planck’s hypothesis that
radiation emitted and absorbed by the
walls of a black body cavity is
quantised

179

identify data sources, gather, process and present information to summarise the
use of the photoelectric effect in photocells

184
Act. 9.3

identify Einstein’s contribution to
quantum theory and its relation to
black body radiation

179

solve problems and analyse information using:
E = hf
and
c = f λ

181

Act. 9.3

explain the particle model of light in
terms of photons with particular energy
and frequency

179

process information to discuss Einstein and Planck’s differing views about
whether science research is removed from social and political forces

Act. 9.4

identify the relationships between
179
photon energy, frequency, speed of light
and wavelength:
E = hf
and
c = f λ

xv


Stage 6
Physics syllabus grid
3.Limitations of past technologies and increased research into the structure of the atom resulted
in the invention of transistors
Students learn to:

Page

Students:

Page

identify that some electrons in solids
are shared between atoms and move
freely

189

perform an investigation to model the behaviour of semiconductors, including
the creation of a hole or positive charge on the atom that has lost the electron
and the movement of electrons and holes in opposite directions when an
electric field is applied across the semiconductor

Act.
10.1

describe the difference between
conductors, insulators and
semiconductors in terms of band
structures and relative electrical
resistance

189

gather, process and present secondary information to discuss how shortcomings
in available communication technology lead to an increased knowledge of the

properties of materials with particular reference to the invention of the transistor

Act.
10.2

identify absences of electrons in a
191
nearly full band as holes, and recognise
that both electrons and holes help to
carry current

identify data sources, gather, process, analyse information and use available
evidence to assess the impact of the invention of transistors on society with
particular reference to their use in microchips and microprocessors

Act.
10.2

compare qualitatively the relative
number of free electrons that can drift
from atom to atom in conductors,
semiconductors and insulators

190

identify data sources, gather, process and present information to summarise the
effect of light on semiconductors in solar cells

Act.
10.3

identify that the use of germanium in
early transistors is related to lack of
ability to produce other materials of
suitable purity

199

describe how ‘doping’ a semiconductor
can change its electrical properties

193

identify differences in p and n-type
semiconductors in terms of the relative
number of negative charge carriers and
positive holes

193

describe differences between solid
state and thermionic devices and
discuss why solid state devices
replaced thermionic devices

199

4. Investigations into the electrical properties of particular metals at different temperatures led to the
identification of superconductivity and the exploration of possible applications
Students learn to:

Page

Students:

Page

outline the methods used by the Braggs 208
to determine crystal structure

process information to identify some of the metals, metal alloys and compounds 211
that have been identified as exhibiting the property of superconductivity and their
critical temperatures

identify that metals possess a crystal
lattice structure

209

perform an investigation to demonstrate magnetic levitation

Act.
11.1

describe conduction in metals as a free
movement of electrons unimpeded by
the lattice

209

analyse information to explain why a magnet is able to hover above a
superconducting material that has reached the temperature at which it is
superconducting

Act.
11.1

209
identify that resistance in metals is
increased by the presence of impurities
and scattering of electrons by lattice
vibrations

gather and process information to describe how superconductors and the effects
of magnetic fields have been applied to develop a maglev train

Act.
11.1

describe the occurrence in
215
superconductors below their critical
temperature of a population of electron
pairs unaffected by electrical resistance

process information to discuss possible applications of superconductivity and the 219
effects of those applications on computers, generators and motors and
Act.
transmission of electricity through power grids
11.1

discuss the BCS theory

215

discuss the advantages of using
superconductors and identify
limitations to their use

217

xvi


Stage 6
Physics syllabus grid

Module 4 From Quanta to Quarks
1. Problems with the Rutherford model of the atom led to the search for a model that would better explain
the observed phenomena
Students learn to:

Page

Students:

Page

discuss the structure of the Rutherford
model of the atom, the existence of the

nucleus and electron orbits

230,
244

perform a first-hand investigation to observe the visible components of the
hydrogen spectrum

Act.
12.1

analyse the significance of the
hydrogen spectrum in the development
of Bohr’s model of the atom

236

process and present diagrammatic information to illustrate Bohr’s explanation of
the Balmer series

236
Act.
12.1

define Bohr’s postulates

236

solve problems and analyse information using:
1

1 
1
= R 2 − 2 
λ
ni 
 nf

233,
245
Act.
12.1

discuss Planck’s contribution to the
concept of quantised energy

231

analyse secondary information to identify the difficulties with the RutherfordBohr model, including its inability to completely explain:
– the spectra of larger atoms
– the relative intensity of spectral lines
– the existence of hyperfine spectral lines
– the Zeeman effect

Act.
12.2

describe how Bohr’s postulates led to
the development of a mathematical
model to account for the existence of
the hydrogen spectrum:

1
1 
1
= R 2 − 2 
λ
n
n
 f
i 

237,
244

discuss the limitations of the Bohr
model of the hydrogen atom

239

2. The limitations of classical physics gave birth to quantum physics
Students learn to:

Page

Students:

Page

describe the impact of de Broglie’s
proposal that any kind of particle has
both wave and particle properties

250,
259

solve problems and analyse information using:
h
λ=
mv

249,
258

define diffraction and identify that
interference occurs between waves that
have been diffracted

250,
257

gather, process, analyse and present information and use available evidence to
assess the contributions made by Heisenberg and Pauli to the development of
atomic theory

255
Act.
13.1

describe the confirmation of de Broglie’s 251,
proposal by Davisson and Germer
257

explain the stability of the electron
orbits in the Bohr atom using
de Broglie’s hypothesis

253,
257

xvii


Stage 6
Physics syllabus grid
3. The work of Chadwick and Fermi in producing artificial transmutations led to practical applications
of nuclear physics
Students learn to:

Students:

Page

define the components of the nucleus
261,
(protons and neutrons) as nucleons and 278
contrast their properties

Page

perform a first-hand investigation or gather secondary information to observe
radiation emitted from a nucleus using Wilson Cloud Chamber or similar
detection device

Act.
14.1

discuss the importance of conservation
laws to Chadwick’s discovery of the
neutron

261,
275

solve problems and analyse information to calculate the mass defect and energy
released in natural transmutation and fission reactions

267,
277

define the term ‘transmutation’

263

describe nuclear transmutations due to
natural radioactivity

263

describe Fermi’s initial experimental
observation of nuclear fission

269

discuss Pauli’s suggestion of the
existence of neutrino and relate it to
the need to account for the energy
distribution of electrons emitted in
β-decay

266,
276

evaluate the relative contributions of
electrostatic and gravitational forces
between nucleons

261

account for the need for the strong
nuclear force and describe its
properties

262

explain the concept of a mass defect
using Einstein’s equivalence between
mass and energy

267

describe Fermi’s demonstration of
a controlled nuclear chain reaction

in 1942

270,
275

compare requirements for controlled
and uncontrolled nuclear chain
reactions

271,
275

4. An understanding of the nucleus has led to large science projects and many applications
Students learn to:

Page

Students:

Page

explain the basic principles of a fission
reactor

280,
298

gather, process and analyse information to assess the significance of the
Manhattan Project to society

280
Act.
15.1

describe some medical and industrial
applications of radioisotopes

283,
298

identify data sources, and gather, process, and analyse information to describe
the use of:
– a named isotope in medicine
– a named isotope in agriculture
– a named isotope in engineering

284,
Act.
15.2

describe how neutron scattering is used 272,
as a probe by referring to the properties 298
of neutrons
identify ways by which physicists
286,
continue to develop their understanding 299
of matter, using accelerators as a probe
to investigate the structure of matter
discuss the key features and
components of the standard model of

matter, including quarks and leptons

xviii

292,
298


Stage 6
Physics syllabus grid

Module 5 Medical Physics
1. The properties of ultrasound waves can be used as diagnostic tools
Students learn to:

Page

Students:

Page

identify the differences between
ultrasound and sound in normal
hearing range

305

solve problems and analyse information to calculate the acoustic impedance of
a range of materials, including bone, muscle, soft tissue, fat, blood and air and
explain the types of tissues that ultrasound can be used to examine

312

describe the piezoelectric effect and
308
the effect of using an alternating
potential difference with a piezoelectric
crystal

gather secondary information to observe at least two ultrasound images of
body organs

Act.
16.1

define acoustic impedance:
Z = ρυ
and identify that different materials
have different acoustic impedances

310,
311

identify data sources and gather information to observe the flow of blood through
the heart from a Doppler ultrasound video image

Act.
16.2

describe how the principles of acoustic

impedance and reflection and
refraction are applied to ultrasound

311

identify data sources, gather, process and analyse information to describe how
ultrasound is used to measure bone density

315
Act.
16.3

define the ratio of reflected to initial
intensity as:

310

solve problems and analyse information using:
Z = ρυ
and

310,
311

2

I r Z2 − Z 1 
=
Io Z + Z  2
 2

1

2

I r Z2 − Z 1 
=
Io Z + Z  2
 2
1

identify that the greater the difference
in acoustic impedance between two
materials, the greater is the reflected
proportion of the incident pulse

310

describe situations in which A scans, B
scans and sector scans would be used
and the reasons for the use of each

312

describe the Doppler effect in sound
waves and how it is used in ultrasonics
to obtain flow characteristics of blood
moving through the heart

315

outline some cardiac problems that can 316
be detected through the use of the
Doppler effect

2. The physical properties of electromagnetic radiation can be used as diagnostic tools
Students learn to:

Page

Students:

Page

describe how X-rays are currently
produced

321

gather information to observe at least one image of a fracture on an X-ray film
and X-ray images of other body parts

Act.
17.1

compare the differences between ‘soft’
and ‘hard’ X-rays

322

gather secondary information to observe a CAT scan image and compare the

information provided by CAT scans to that provided by an X-ray image for the
same body part

Act.
17.1

explain how a computed axial
tomography (CAT) scan is produced

326

perform a first-hand investigation to demonstrate the transfer of light by
optical fibres

Act.
18.1

describe circumstances where a CAT
scan would be a superior diagnostic
tool compared to either X-rays or
ultrasound

329

gather secondary information to observe internal organs from images produced
by an endoscope

Act.
18.1

explain how an endoscope works in
relation to total internal reflection

334

discuss differences between the role of
coherent and incoherent bundles of
fibres in an endoscope

336

explain how an endoscope is used in:
– observing internal organs
– obtaining tissue samples of internal
organs for further testing

337

xix


Stage 6
Physics syllabus grid
3. Radioactivity can be used as a diagnostic tool
Students learn to:

Page

Students:

Page

outline properties of radioactive
isotopes and their half-lives that are
used to obtain scans of organs

340,
343,
344

perform an investigation to compare an image of bone scan with an X-ray image

Act.
19.1

describe how radioactive isotopes may
be metabolised by the body to bind or
accumulate in the target organ

344

gather and process secondary information to compare a scanned image of at least Act.
one healthy body part or organ with a scanned image of its diseased counterpart 19.2

identify that during decay of specific
radioactive nuclei positrons are
given off

342

discuss the interaction of electrons and 342
positrons resulting in the production of
gamma rays
describe how the positron emission
349
tomography (PET) technique is used for
diagnosis

4. The magnetic field produced by nuclear particles can be used as a diagnostic tool
Students learn to:

Students:

Page

identify that the nuclei of certain atoms 355
and molecules behave as small
magnets

Page

perform an investigation to observe images from magnetic resonance image
(MRI) scans, including a comparison of healthy and damaged tissue

Act.
20.1

identify that protons and neutrons in
354
the nucleus have properties of spin and

describe how net spin is obtained

identify data sources, gather, process and present information using available
evidence to explain why MRI scans can be used to:
– detect cancerous tissues
– identify areas of high blood flow
– distinguish between grey and white matter in the brain

Act.
20.1

explain that the behaviour of nuclei
with a net spin, particularly hydrogen,
is related to the magnetic field they
produce

355

gather and process secondary information to identify the function of the
Act.
electromagnet, radio frequency oscillator, radio receiver and computer in the MRI 20.1
equipment

describe the changes that occur in the
orientation of the magnetic axis of
nuclei before and after the application
of a strong magnetic field

355

identify data sources, gather and process information to compare the advantages
and disadvantages of X-rays, CAT scans, PET scans and MRI scans

Act.
20.2

define precessing and relate the
frequency of the precessing to the
composition of the nuclei and the
strength of the applied external
magnetic field

356

gather, analyse information and use available evidence to assess the impact of
medical applications of physics on society

Act.
20.3

discuss the effect of subjecting
precessing nuclei to pulses of radio
waves

357

explain that the amplitude of the signal 359
given out when precessing nuclei relax
is related to the number of nuclei
present

explain that large differences would
360
occur in the relaxation time between
tissue containing hydrogen bound water
molecules and tissues containing other
molecules

xx


Stage 6
Physics syllabus grid

Module 6 Astrophysics
1. Our understanding of celestial objects depends upon observations made from Earth or from space
near the Earth
Students learn to:

Page

discuss Galileo’s use of the telescope to 371
identify features of the Moon
Act.
21.1
discuss why some wavebands can be
more easily detected from space

373

define the terms ‘resolution’ and

‘sensitivity’ of telescopes

375

discuss the problems associated with
ground-based astronomy in terms of
resolution and absorption of radiation
and atmospheric distortion

373,
378

Students:

Page

identify data sources, plan, choose equipment or resources for, and perform an
investigation to demonstrate why it is desirable for telescopes to have a large
diameter objective lens or mirror in terms of both sensitivity and resolution

377
Act.
21.2

outline methods by which the resolution 378,
and/or sensitivity of ground-based
380
systems can be improved, including:
– adaptive optics
– interferometry

– active optics

2. Careful measurement of a celestial object’s position in the sky (astrometry) may be used to determine
its distance
Students learn to:

Page

Students:

Page

define the terms parallax, parsec,
light-year

388

solve problems and analyse information to calculate the distance to a star given
its trigonometric parallax using:
1
d =
p

Act.
22.1

explain how trigonometric parallax can
be used to determine the distance to
stars

388

gather and process information to determine the relative limits to trigonometric
parallax distance determinations using recent ground-based and space-based
telescopes

Act.
22.2

discuss the limitations of trigonometric
parallax measurements

389

3. Spectroscopy is a vital tool for astronomers and provides a wealth of information
Students learn to:

Page

Students:

Page

account for the production of emission
and absorption spectra and compare
these with a continuous black body
spectrum

390

perform a first-hand investigation to examine a variety of spectra produced by
discharge tubes, reflected sunlight, or incandescent filaments

Act.
22.3

describe the technology needed to
measure astronomical spectra

390

analyse information to predict the surface temperature of a star from its intensity/ Act.
wavelength graph
22.4

identify the general types of spectra
produced by stars, emission nebulae,
galaxies and quasars

393

describe the key features of stellar
spectra and describe how these are
used to classify stars

395

describe how spectra can provide
information on surface temperature,
rotational and translational velocity,

density and chemical composition of
stars

393

xxi


Stage 6
Physics syllabus grid
4. Photometric measurements can be used for determining distance and comparing objects
Students learn to:

Page

Students:

Page

define absolute and apparent
magnitude

398

solve problems and analyse information using:

400

M = m − 5 log
and

IA
= 100 (m
IB

B

d 
10

– mA)/5

to calculate the absolute or apparent magnitude of stars using data and
a reference star
explain how the concept of magnitude
can be used to determine the distance
to a celestial object

399

perform an investigation to demonstrate the use of filters for photometric
measurements

Act.
22.5

outline spectroscopic parallax

401

identify data sources, gather, process and present information to assess the

impact of improvements in measurement technologies on our understanding of
celestial objects

Act.
22.6

explain how two-colour values (i.e.
colour index, B – V) are obtained and
why they are useful

401

describe the advantages of
photoelectric technologies over
photographic methods for photometry

397

5. The study of binary and variable stars reveals vital information about stars
Students learn to:

Page

Students:

Page

describe binary stars in terms of the
means of their detection: visual,
eclipsing, spectroscopic and

astrometric

411

perform an investigation to model the light curves of eclipsing binaries using
computer simulation

Act.
23.1

explain the importance of binary stars
in determining stellar masses

408

solve problems and analyse information by applying:
4 π 2r 3
m 1+ m 2 =
GT 2

420

classify variable stars as either intrinsic 413
or extrinsic and periodic or non-periodic
explain the importance of the period–
luminosity relationship for determining
the distance of cepheids

xxii

416


Stage 6
Physics syllabus grid
6. Stars evolve and eventually ‘die’
Students learn to:

Page

Students:

Page

describe the processes involved in
stellar formation

423

present information by plotting Hertzsprung–Russell diagrams for:
– nearby or brightest stars
– stars in a young open cluster
– stars in a globular cluster

Act.
24.1

outline the key stages in a star’s life
in terms of the physical processes
involved

428

analyse information from an HR diagram and use available evidence to determine 437
the characteristics of a star and its evolutionary stage

describe the types of nuclear reactions
involved in Main-Sequence and postMain Sequence stars

425,
430

present information by plotting on a HR diagram the pathways of stars of 1, 5
and 10 solar masses during their life cycle

discuss the synthesis of elements in
stars by fusion

425,
430

explain how the age of a globular
cluster can be determined from its
zero-age main sequence plot for a
HR diagram

433

explain the concept of star death in
relation to:

– planetary nebula
– supernovae
– white dwarfs
– neutron stars/pulsars
– black holes

429,
431

437

xxiii


1
Context

Figure 1.0.1 The knowledge of how things
move through space,
influenced by gravity, has
transformed the way we work,
play and think.

2

Space

Modern physics was born twice. The first time (arguably) was in the 17th century
when Newton used his three laws of motion and his law of universal gravitation to
connect Galileo’s equations of motion with Kepler’s laws of planetary motion. Then

early in the 20th century, when many thought physics had almost finished the job of
explaining the universe, it was unexpectedly born again. Einstein, in trying to
understand the nature of light, proposed the special and general theories of
relativity (and simultaneously helped launch quantum mechanics).
Space was the common thread—Kepler, Galileo, Newton and Einstein were all
trying to understand the motion of objects (or light) through space.
Newton’s laws of mechanics and his theory of gravitation led to space
exploration and artificial satellites for communication, navigation and monitoring of
the Earth’s land, oceans and atmosphere. Einstein’s theory of relativity showed that
mass and energy are connected, and that length, mass and even space and time
are rubbery. Relativity has come to underlie most new areas of physics developed
since then, including cosmology, astrophysics, radioactivity, particle physics,
quantum electrodynamics, anything involving very precise measurements of time
and the brain-bending ‘string theory’.
So, whenever you use the global positioning system (GPS), consult Google
maps, check the weather report or make an international call on your mobile phone,
remember that the technology involved can be traced directly back to physics that
started 400 years ago.


Figure 1.0.2 The revolution in our

Inquiry activity

understanding of the universe
started with the humble question
of how projectiles move.

Go ballistic!
The path through the air of an object subject only to gravity and air resistance,

is called a ballistic trajectory. If the object is compact and its speed is low, then
air resistance is negligible and its trajectory is a parabola.
Investigate parabolic trajectories using a tennis ball, an A4 piece of paper,
a whiteboard or a blackboard and a digital camera.
1 On a board about 2 m wide, draw an accurate grid of horizontal and vertical lines
10 cm apart.
2 With a firmly mounted camera, take a movie of a tennis ball thrown slowly in
front of the board. Try different angles and speeds to get eight or more frames
with the ball on screen, and get as much of a clear parabolic shape (including
the point of maximum height) as you can.
3 Using video-editing software, view the best movie, frame by frame, on a
computer. If your software allows it, create a single composite image with all
the ball’s positions shown on one image, to show the parabolic trajectory.
4 If you can’t do that, then for each frame, on the board, and using the grid,
estimate the x- and y-coordinates of the ball’s centre to the nearest 5 cm
or better. Some video software allows you to read the x- and y-coordinates
(in pixels) by clicking on the image.
5 Plot a graph of x versus y to produce a graph of the parabolic trajectory. The graph
might be a bit irregular because of random error in reading the blackboard scale.
6 Video the trajectory of a loosely crumpled-up piece of A4 paper. Now air
resistance is NOT negligible. Does the trajectory still look like an ideal parabola?

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Cannonballs,
apples, planets
and gravity

What goes up must come down

projectile, trajectory, parabola,
ballistics, vertical and horizontal
components, Galilean transformation,
range, launch angle, time of flight,
inverse square law, law of universal
gravitation, universal gravitation
constant G, gravitational field g, test
mass, central body, density,
gravimeter, low Earth orbit,
gravitational potential energy, escape
velocity, gravitationally bound

One of the powers of physics is that it enables us to find connections
between seemingly unconnected things and then use those
connections to predict new and unexpected phenomena. What
started as separate questions about the shape of the path of
cannonballs through the air and the speed of the Moon’s orbit around
the Earth eventually led to the law of gravitation. This explained how
the solar system works, but also led to the development of artificial
satellites and spacecraft for the exploration of the
solar system.

1.1 Projectile motion
Up and down, round and round
Before Galileo Galilei (1564–1642), it was a common belief that an object such
as a cannonball projected through open space (a projectile) would follow a path
(trajectory) through the air in a nearly straight line until it ran out of ‘impetus’
and then drop nearly straight down in agreement with the ideas of Aristotle.

However, through experiments (Figure 1.1.1) in which he rolled balls off the
edge of a table at different speeds and then marked the position of collisions with
the ground, Galileo demonstrated that the trajectory of a falling ball is actually
part of a parabola (see Figure 1.1.2). Remember that a parabola is the shape of
the graph of a quadratic equation. The immediate result of Galileo’s discovery
was that the art of firing cannonballs at your enemies became a science (ballistics).
However, there were also more far-reaching, constructive consequences.

Figure 1.1.1 Galileo’s laboratory notes on his experiments
showing that projectiles follow parabolic paths
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