Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth describe the trajectory of an object undergoing projectil
Trang 1Stephen Bosi John O’Byrne Peter Fletcher Joe Khachan Jeff Stanger Sandra Woodward
Sydney, Melbourne, Brisbane, Perth, Adelaide
Trang 22.4 Momentum bandits: the slingshot effect 44
Chapter 3 Seeing in a weird light: relativity 58
3.1 Frames of reference and classical relativity 58
3.3 Special relativity, light and time 64
4.1 Review of essential concepts 84
4.2 Forces on charged particles in magnetic fields 89
4.4 Forces between parallel wires 93
Chapter 7 Generators and electricity supply: power
Chapter 8 From cathode rays to television 156
8.2 Charges in electric fields 1608.3 Charges moving in a magnetic field 164
9.4 Applications of the photoelectric effect 184
Trang 310.1 Conduction and energy bands 189
12.7 Limitations of the Rutherford–Bohr model 239
13.6 Further developments of atomic theory
17.1 Overview and history: types of X-ray images 320
17.7 Benefits of CAT scans over conventional
Trang 4Chapter 18 Imaging with light 333
Chapter 19 Imaging with gamma rays 340
19.1 Isotopes and radioactive decay 340
19.3 Radiopharmaceuticals: targeting tissues
19.5 Positron emission tomography 347
Chapter 20 Imaging with radio waves 354
20.2 Hydrogen in a magnetic field 355
20.4 It depends on how and where you look 359
24.3 Stars in the prime of life 425
24.5 The fate of massive stars 430
Trang 5in2 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
snippets of relevant information about
physics or physics applications
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
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
From cathode rays
Television
Cathode ray tube (CRT) television sets used the principles of the cathode ray tube for most of the 20th century These are now being superseded by plasma and liquid crystal display television sets, wh ich use different operating principles and allow a larger display area with a sharpe r image However, the CRT television holds quite a significant historical place in this form of communication
A schematic diagram of a colour CRT televi sion set is shown in Figure 8.5.5
Its basic elements are similar to those of the CRO The main difference is the method of deflecting the electrons Magneti c field coils placed outside the tube produce horizontal and vertical magnetic fie lds inside it The magnitude and direction of the current determine the degree and direction of electron beam deflection Recall your right-hand palm rule for the force on charged particles
in a magnetic field The vertical magnetic field will deflect the electrons horizontally; the horizontal field will deflect them vertically.
The picture on the screen is formed by scanning the beam from left to right and top to bottom The electronics in the te levision switches the beam on and off at the appropriate spots on the screen in order to reproduce the transmitted picture However, to reproduce colour imag es, colour television sets need to control the intensity of red, blue and green phosphors on the screen Three separate electron guns are used, each one aim ed at one particular colour The coloured dots on the screen are clustered in groups of red, blue and green dots that are very close to each other and general ly cannot be distinguished by eye without the aid of a magnifying glass For th is reason a method of guiding the different electron beams to their respective coloured dots was devised A metal
sheet, known as a shadow mask (Figure 8.5.6) and consisting of an array of holes, is placed behind the phosphor screen. Each hole guides the three beams to their respective coloured phosphor as the be ams move horizontally and vertically
Black and white television sets did not need the shadow mask since they had only one beam.
heater cathode (negative)
electrons 'boil' off the heated cathode anode (positive)
electron beam electrons attracted
to the positive anode collimator
Figure 8.5.3 The components of an electron gun used in both cathode ray oscilloscopes and CRT televisions
V Time V Time sawtooth voltage for timebase sinusoidal vertical voltage Figure 8.5.4 A sawtooth voltage waveform on the horizontal deflection plates of a CRO sweeps the electron beam across the screen to display the sinusoidal waveform
on the vertical deflection plates.
electron gun magnetic coils electron beam
fluorescent screen Figure 8.5.5 A television picture tube showing the electron gun, deflection coils and fluorescent screen
electron guns deflecting coils focusing coils glass
fluorescent screen vacuum mask
phosphor dots
on screen
fluorescent screen mask
holes in mask
blue beam red beam
green
R
electron beams Figure 8.5.6 A colour CRT television set has three electron guns that will only strike their respective coloured phosphor dots with the aid of a shadow mask.
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
Can an osCillosCope be used
as a television set?
T he similarity between the cathode ray oscilloscope (CRO) and CRT television suggests that a CRO can be used as a television set In fact, there have been some devices that have made use of the CRO as you would a computer monitor So, in principle, it can be used as a television One is then forced to ask ‘why did they need to deflect the fields as in the CRO?’
In principle all television sets could be made in the same design as
a CRO; however, it is much easier and cheaper to deflect the beam with
a magnetic field on the outside of the tube rather than embed electrodes
in the glass and inside the vacuum—this is a little trickier So now another question arises: ‘why not deflect the beam of the CRO using magnetic fields, wouldn’t it result in cheaper CROs?’ Cathode ray oscilloscopes are precision instruments The horizontal sweep rate must be able to be increased to very high frequencies in order
to detect signals that change very quickly Electric fields can be made to change very quickly without significant extra power requirements However, a magnetically deflected system requires higher and higher voltages with increasing horizontal and vertical deflection frequencies in order to maintain the same current in the coils, and therefore, the same angle of beam deflection – thus having a significantly greater power requirement Cathode ray tube television sets, however , only operate at fixed and relatively low scanning horizontal and vertical frequencies Thus it is simpler and cheaper for the mass market to deflect with a magnetic field.
CheCkpoint 8.5
1 Outline the purpose of a CRO.
2 List the main parts of a CRO.
3 Describe the role of each of these parts in the CRO.
4 State the similarities and differences between th e cathode ray tube CRO and CRT TV.
THE COMPLETE PHYSICS PACKAGE FOR NSW STUDENTS
Trang 6programs, 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
69
Method
1 Set up the equipment as shown in Figure 8.1.1.
2 Observe the patterns and note the pressure in the tube.
3 Replace the tube with the next in the series.
4 Repeat the process of observing the patterns and
noting the pressure for each of the tubes in y our set.
HAZARD
High voltages are produced by induction coils and may produce unwanted X-rays The voltages necessar
y to operate the tubes depend upon the dimensions of the tube and the pr essure of the gas in the tube Generally, the higher the voltage used, the greater the danger of the production of unwanted X-rays.
Use the lowest possible voltage and stand a minimum of 1 m away from the equipment.
Chapter 8
from Cathode rays
to television
Changing pressure of discharge tubes
Perorm an investigation and gather first-hand information to observe the occurrence of different striation patterns for different pressures in discharge tubes.
Physics skills
The skills outcomes to be practised in th is activity include:
12.1 perform first-hand investigations 12.2 gather first-hand information 14.1 analyse information
The complete statement of these skills outcomes can be found in the syllabus grid on pages vi–viii.
When they are able to travel far enough to gain the energy to be absorbed by atoms, we see a light show (known as a discharge)
The lower the pressure, the further the electrons can trav el before colliding with gas molecules and producing a discharge.
The light that is emitted is a result of the elec trons around the gas atom becoming excited (increasing in energy) and re-emitting the photon of light as they return to the ground state (the lowest energy they c an have in an atom) Light will also
be produced when free electrons recombine w ith ions and the electrons return to the groun d state, emitting photons As every element has a distinct set of energy levels, the colour of light seen will vary with the elemen t with which the electron collides.
Equipment
If you have the apparatus at school, you can carry out the experiment first hand The patterns ar
e hard to see unless the room
is very dark.
• induction coil • discharge tubes at different pressures
• connecting wires • DC power supply Alternatively, you can use the simulations in P art B and make observations from them.
Risk assessment
aCtivity 8.1
first-hand investigation
DC power supply
Figure 8.1.1 Induction coil and discharge tube
Trang 7in2 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
Generators
83
Figure 4.0.1 A generator produces electricity
in each of these wind turbines.
82
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
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.
Context
InQUIRY ACtIVItY
BUIld YoUR own eleCtRIC motoR
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?
Figure 4.0.2 A simple homopolar motor
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
Surprising discovery
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
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.
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.
11.1 The crystal structure of matter
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
Figure 11.1.1 Crystal structure of sodium chloride The red spheres represent positive
sodium ions, and the green spheres represent negative chlorine ions.
try thiS!
Crystals in the kitChen Look at salt grains through a magnifying lens Each grain is
a single crystal that is made from and chlorine atoms shown in Figure 11.1.1 Although the grains mostly look irregular due
to breaking and chipping during the manufacturing process, untouched cubic or rectangular prism that reflects the underlying crystal lattice structure.
CheCkpoInT 11.1
Explain what is meant by the crystal structure of matter.
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 (seein2 Physics @ Preliminarysections 6.4 and 7.4) The overlapping waves will cancel to produce
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.
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 causes the radiating lines to come closer together (Figure 11.2.2b)
Figure 11.2.1 Two identical waves (red, green) travelling in opposite directions can add (blue) (a) constructively or (b) destructively.
Figure 11.2.2 Interference of water waves for two sources that are (a) close together and (b) further apart
a
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
wave travels is known as its path length 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
a path length difference of λ/2, 3λ/2, 5λ/2 etc.
constructive constructive destructive interference
73
Space
PHYSICS FEATURE
TwISTIng SPACETImE
And YoUR mInd
T 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
agree on the spacetime interval s between events.
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’.
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)
1 The history of physics
Mass, energy and the world’s most famous equation
The kinetic energy formula K = 12mv 2 doesn’t apply at relativistic speeds,
even if you substitute relativistic mass mv into the formula Classically, if you
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.
Solve problems and analyse information using:
E = mc2
v = 0 1
t c
= = −
− Using a well-known approximation formula that you might learn at university,
(1 – x )n ≈ 1 – nx for small x:
1−
− ≈ m c0 v2 1+ ×
equivalent in relativity and c 2 is the conversion factor between the energy unit
(joules) and the mass unit (kg) In other words:
E = mc 2
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
energy due to its rest mass Relativistic kinetic energy therefore:
v 2 2 2 1
−
− 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 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)
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 antiparticle, they mutually annihilate—all their opposing 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.
PRACTICAL EXPERIENCES
350
19 Imaging with gamma rays
351
Chapter summary mEdICAL
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.
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.
Review questions
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.
Activity 19.1: Bone scAns
A bone scan is performed to obtain a functional image of the bones and so can be
cancer or other abnormality Because cancer mostly involves a higher than normal
Perform an investigation to compare a bone scan with
an X-ray image.
Figure 19.6.1 Comparison of an X-ray and bone scan of a hand
Figure 19.6.2 Bones scans of (a) a healthy person and (b) a patient with a tumour in the skeleton
• The number of protons in a nucleus is given by the atomic number, while the total number of nucleons is given by the mass number
• Atoms of the same element with different numbers of neutrons are called isotopes of that element
• Many elements have naturally occurring unstable radioisotopes.
• When a positron and an electron collide, their total mass is converted into energy in the form of two gamma-ray photons.
• In gamma decay a gamma ray (g) is emitted from a radioactive isotope.
• The time it takes for half the mass of a radioactive parent isotope to decay into its daughter nuclei is the half-life of the isotope
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 Radiation Radioisotope Nucleon Neutron Proton Isotope Alpha decay Beta decay Gamma decay Antimatter PET Half-life Bone scan Positron decay Scintillator
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.
Table 19.6.1 Properties of some radioisotopes
Radioactive souRce Radiation emitted Half-life
C-11 β + , 20.30 minutes Tc-99m g 6.02 hours TI-201 g 3.05 days I-131 β, g 8.04 days Cs-137 α 30.17 years U-238 α 4.47 × 10 9 years
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.
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.
a b
• Chapter openings list the key words of each chapter and
introduce the chapter topic in a concise and engaging way
• Key ideas are clearly highlighted with a and Syllabus flags indicate where domain dot points 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
• 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
• 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
Trang 8• Module reviews provide a full range of exam-style
questions, including multiple-choice, short-response
and extended-response questions
from ideas to implementation
3 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.
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
2 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?
I II III
AConductor Insulator Semiconductor
BInsulator Conductor Semiconductor
CInsulator Semiconductor Conductor
DSemiconductor Conductor Insulator
3 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.
I II III
ACritical
temperature Superconductor material Normal material
BSuperconductor
material Critical temperature Normal material
CCritical temperature Normal material Superconductor material
DNormal material Superconductor
material Critical temperature
Figure 11.13.1 An electron in a magnetic field
Figure 11.13.2 Energy bands
Figure 11.13.3 Resistance varies with temperature
4 Experimental data from black body radiation during 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.
5 Figure 11.13.4 shows a cathode ray tube that has been evacuated Which answer correctly names each
of the labelled features?
I II III
AStriations Cathode Anode
BFaraday’s Striations Cathode
CCrooke’s dark space Anode Faraday’s
DCathode Faraday’s Striations
extended response
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
12 a Determine the frequency of red light, which has
a wavelength λ = 660 nm (Speed of light
Risk assessment
Method
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.
Results
1 Record your observations of the motor.
2 How did adding more magnets affect how the motor ran?
3 When the current is increased, what changes occurred?
Motors and torque
Solve problems and analyse information about simple motors using:
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.
alligator clip wires paper clip cage fanned out
power Figure 6.2.2 Equipment set-up 1
Figure 6.2.3 Equipment set-up 2
Other features
• Physics Philes present short, interesting items to support or extend the text
•
Physics for Fun—Try This! activities are short, hands-on activities to be dPhysics for Fun—Try This! activities are short, hands-one 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
• A complete glossary of all the key words is included at the end of the student book
• 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
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
the aim, a list of equipment and
PRACTICAL EXPERIENCES
Activity Manual, Page 94
• the companion website on CD
• 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
The complete in2 Physics @ HSC package
Remember the other components of the complete package:
• in2 Physics @ HSC companion website at Pearson Places
• in2 Physics @ HSC Teacher Resource.
Trang 9Prescribed 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
Focus: pp 25, 246, 299
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 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
Focus: pp 113, 173, 353
5 Current issues, research and
developments in physics H5 identifies possible future directions of physics research Feature: pp 391, 410
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
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 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
Act 1.2
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 1.3define gravitational potential energy as
the work done to move an object from
a very large distance away to a point
2 Many factors have to be taken into account to achieve a successful rocket launch, maintain
a stable orbit and return to Earth
describe the trajectory of an object
undergoing projectile motion within the
Earth’s gravitational field in terms of
horizontal and vertical components
5 solve problems and analyse information to calculate the actual velocity of
a projectile from its horizontal and vertical components using:
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
Act 1.1
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
of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O’Neill or von Braun
29 Act 2.1
Trang 10outline Newton’s concept of escape
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,
34, 37,
54, 55
solve problems and analyse information to calculate the centripetal force acting
on a satellite undergoing uniform circular motion about the Earth using:
F = mv r 2
37, 54,
55 Act 2.2
compare qualitatively low Earth and
geo-stationary orbits 43
define the term orbital velocity and the
quantitative and qualitative relationship
between orbital velocity, the
gravitational constant, mass of the
central body, mass of the satellite and
the radius of the orbit using Kepler’s
Law of Periods
36, 40,
56 solve problems and analyse information using:r
T GM
3
2 = 4 2
π
39, 43, 56
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
3 The solar system is held together by gravity
describe a gravitational field in the
region surrounding a massive object in
terms of its effects on other masses
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
Trang 11STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE
outline the features of the aether model
for the transmission of light 61
describe and evaluate the
Michelson-Morley 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
discuss the role of the
Michelson-Morley 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 66describe 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
discuss the implications of mass
increase, time dilation and length
contraction for space travel
70, 73
Module 2 Motors and Generators
1 Motors use the effect of forces on current-carrying conductors in magnetic fields
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 perform a first-hand investigation to demonstrate the motor effect Act 4.1
Trang 12describe qualitatively and quantitatively
the force between long parallel
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 application of the motor effect in:
– the galvanometer – the loudspeaker
91, 119 Act 6.1
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
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
a magnet in a coil or a coil near a magnet 101 Act 5.1
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
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 5.1compare 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 discuss the energy losses that occur as
energy is fed through transmission lines
from the generator to the consumer
144 gather and analyse information to identify how transmission lines are:
– insulated from supporting structures – protected from lightning strikes
146 Act 7.3 assess the effects of the development
of AC generators on society and the
environment
147
Trang 13describe 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 7.3compare step-up and step-down
transformers 137 solve problems and analyse information about transformers using:V
V
n n
p s p s
=
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
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 and transformations involving the conversion of electrical energy into more useful forms in the home and industry
124,
153 Act 7.3
Module 3 From Ideas to Implementation
1 Increased understandings of cathode rays led to the development of television
explain why the apparent inconsistent
behaviour of cathode rays caused
debate as to whether they were charged
particles or electromagnetic waves
157 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
157 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 analyse the information gathered to determine the sign of the charge on cathode rays
Act 8.2
Act 8.2 identify that moving charged particles
in a magnetic field experience a force 164 solve problem and analyse information using:F = qvB sin θ
identify that charged plates produce an
electric field 161
Trang 14describe quantitatively the force acting
on a charge moving through a magnetic
field:
F = qvB sin θ
164
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
due to oppositely charged parallel plates 161
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
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
outline qualitatively Hertz’s experiments
in measuring the speed of radio waves
and how they relate to light waves
175 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 9.4identify the relationships between
photon energy, frequency, speed of light
Trang 15STuDEnTS 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
nearly full band as holes, and recognise
that both electrons and holes help to
carry current
191 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
outline the methods used by the Braggs
to determine crystal structure 208 process information to identify some of the metals, metal alloys and compounds that have been identified as exhibiting the property of superconductivity and their
critical temperatures
211
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 identify that resistance in metals is
increased by the presence of impurities
and scattering of electrons by lattice
vibrations
209 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
superconductors below their critical
temperature of a population of electron
pairs unaffected by electrical resistance
215 process information to discuss possible applications of superconductivity and the
effects of those applications on computers, generators and motors and transmission of electricity through power grids
219 Act 11.1 discuss the BCS theory 215
discuss the advantages of using
superconductors and identify
limitations to their use
217
Trang 16Module 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
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
12.1 define Bohr’s postulates 236 solve problems and analyse information using:
concept of quantised energy 231 analyse secondary information to identify the difficulties with the Rutherford-Bohr 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:
discuss the limitations of the Bohr
model of the hydrogen atom 239
2 The limitations of classical physics gave birth to quantum physics
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:
λ =mv h
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
proposal by Davisson and Germer 251, 257
explain the stability of the electron
orbits in the Bohr atom using
de Broglie’s hypothesis
253, 257
Trang 17STuDEnTS lEARn TO: PAGE STuDEnTS: PAGE
define the components of the nucleus
(protons and neutrons) as nucleons and
contrast their properties
261,
278 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
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
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
as a probe by referring to the properties
of neutrons
272, 298 identify ways by which physicists
continue to develop their understanding
of matter, using accelerators as a probe
to investigate the structure of matter
286, 299
discuss the key features and
components of the standard model of
matter, including quarks and leptons
292, 298
Trang 18Module 5 Medical Physics
1 The properties of ultrasound waves can be used as diagnostic tools
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
the effect of using an alternating
potential difference with a piezoelectric
crystal
308 gather secondary information to observe at least two ultrasound images of
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
I I
r o
310, 311
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
be detected through the use of the
Doppler effect
316
2 The physical properties of electromagnetic radiation can be used as diagnostic tools
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
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
Trang 19outline 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
one healthy body part or organ with a scanned image of its diseased counterpart Act 19.2 identify that during decay of specific
radioactive nuclei positrons are
given off
342
discuss the interaction of electrons and
positrons resulting in the production of
gamma rays
342
describe how the positron emission
tomography (PET) technique is used for
diagnosis
349
4 The magnetic field produced by nuclear particles can be used as a diagnostic tool
identify that the nuclei of certain atoms
and molecules behave as small
magnets
355 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
the nucleus have properties of spin and
describe how net spin is obtained
354 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
electromagnet, radio frequency oscillator, radio receiver and computer in the MRI equipment
Act 20.1
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
given out when precessing nuclei relax
is related to the number of nuclei
present
359
explain that large differences would
occur in the relaxation time between
tissue containing hydrogen bound water
molecules and tissues containing other
molecules
360
Trang 20Module 6 Astrophysics
1 Our understanding of celestial objects depends upon observations made from Earth or from space
near the Earth
discuss Galileo’s use of the telescope to
identify features of the Moon 371 Act
21.1
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 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
outline methods by which the resolution
and/or sensitivity of ground-based
systems can be improved, including:
– adaptive optics
– interferometry
– active optics
378, 380
2 Careful measurement of a celestial object’s position in the sky (astrometry) may be used to determine its distance
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:
d=p1
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
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/wavelength graph Act 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
Trang 21define absolute and apparent
magnitude 398 solve problems and analyse information using:
I
A B
= (mB – mA )/5
to calculate the absolute or apparent magnitude of stars using data and
a reference star
400
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
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
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
explain the importance of binary stars
in determining stellar masses 408 solve problems and analyse information by applying:
m + m
GT
r3 2
4
= π
420
classify variable stars as either intrinsic
or extrinsic and periodic or non-periodic 413
explain the importance of the period–
luminosity relationship for determining
the distance of cepheids
416
Trang 226 Stars evolve and eventually ‘die’
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
the characteristics of a star and its evolutionary stage 437describe the types of nuclear reactions
involved in Main-Sequence and
post-Main 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 437discuss 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
Trang 23Figure 1.0.1 The knowledge of how things
move through space,
influenced by gravity, has
transformed the way we work,
play and think.
1
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.
Trang 24of how projectiles move.
InquIry aCtIvIty
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?
Trang 251 apples, planets
and gravity
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
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
What goes up must come down
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
Figure 1.1.1 Galileo’s laboratory notes on his experiments
showing that projectiles follow parabolic paths
Trang 26Opponents of Copernicus’ heliocentric universe claimed that if
the Earth was rotating and orbiting the Sun, then a person jumping
vertically into the air would have the ground move under their feet,
so that they would land very far away from where they started
Galileo argued that a person jumping from a moving Earth is like
a projectile dropped by a rider on a horse (representing the Earth)
moving with a constant velocity (Figure 1.1.3) From the rider’s point
of view, the projectile would appear to drop vertically, straight to the
ground, accelerating downwards the whole time A bystander who is
stationary relative to the ground would see the rider, horse and
projectile whoosh past and, like any other projectile, the dropped
object would appear to follow a parabolic trajectory
Galileo argued that the parabolic motion of the projectile was
made up of two separable parts: its accelerating vertical motion as
seen by the rider, and its constant horizontal velocity (which is the
same as that of the horse) Recall from your Preliminary physics
course that these two contributions to velocity are called vertical and
horizontal components (see in2 Physics @ Preliminary section 2.2, p 26).
Galileo then argued that the Earth doesn’t zoom away under your feet
because at the moment you jump upwards you already have the same horizontal
component of velocity as the Earth’s surface Relative to the Earth’s surface,
your horizontal velocity is zero and so you land on the same spot
In connecting the two problems of projectile motion and a moving Earth,
Galileo developed two important new concepts The first is the idea that
the parabolic trajectory of a projectile can be divided into vertical and
horizontal components The second is the idea of measuring motion relative
to another moving observer (or ‘frame of reference’) The formula
vB (relative to A) = vB – vA (see in2 Physics @ Preliminary, p 8) is used to transform
velocities relative to different frames of reference This formula is sometimes
called the Galilean transformation.
Components of a trajectory
The ideal parabolic trajectory is an approximation that works under two
conditions:
1 Air resistance is negligible (gravity is the only external force)
2 The height and range (horizontal displacement) of the motion are both
small enough that we can ignore the curvature of the Earth
Describe Galileo’s analysis
of projectile motion.
Describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms
of horizontal and vertical components
Figure 1.1.3 Trajectory of the rider’s projectile as seen by (a) the rider and (b) an observer on the ground
Horizontal displacement
Figure 1.1.2 This graph of a parabolic trajectory shows the
vertical and horizontal components of displacement separately The projectile positions are plotted at equal time intervals.
Trang 27Figure 1.1.4 For a fixed initial speed, maximum range
occurs for a 45° angle of launch and maximum
height occurs for a 90° angle of launch.
is true in almost all human-scale situations, typically at or near the Earth’s surface Let’s analyse an example of ideal projectile motion Recall that the acceleration
due to gravity is g = 9.8 m s–2 (see in2 Physics @ Preliminary section 1.3) Here we
are going to write it as a vector g Clearly its direction is downwards.
Consider the trajectory of a ball We start by separating the horizontal and vertical components of its motion While the ball is in the air, the only external force on it is gravity acting downwards, so there is a constant vertical
acceleration ay = g, illustrated by the changing vertical spacing of projectile
positions plotted at equal time intervals in Figure 1.1.2
The net horizontal force is zero, so, consistent with Newton’s first law,
horizontal velocity is constant (ax = 0), which is clear from the equal horizontal spacing of the projectile positions plotted at equal time intervals in Figure 1.1.2
We can recycle the kinematics (SUVAT) equations from the Preliminary
course (See in2 Physics @ Preliminary section 1.3.)
Here we need to apply them separately to the vertical (y) and horizontal (x)
components of motion Instead of displacement s, we’ll use ∆x = xf – xi for horizontal displacement and ∆y = yf – yi for vertical displacement We’ll put
subscripts on the initial and final vertical velocities (uy and vy for example) We only need to use SUVAT equations 3, 4 and 5 θi is the launch angle (between the initial velocity u and the horizontal axis) Remember to adjust the sign
of g to be consistent with your sign convention In problems involving gravity, up
is normally taken as positive, making the vector g negative (i.e g = –9.8 m s–2)
In the syllabus, v x2 = u x2 is included for completeness; but is unnecessary,
as it can be derived from vx = ux
Some properties of ideal parabolic trajectories are:
• At the maximum height of the parabola, vertical velocity vy = 0
• The trajectory is horizontally symmetrical about the maximum height position
• The projectile takes the same time to rise to the maximum height as it takes to fall back down to its original height
• For horizontal ground, initial speed = final speed
• Maximum possible height occurs for a 90° launch angle The maximum possible range (for horizontal ground) occurs for a 45° launch angle (Figure 1.1.4)
• Independent of their initial velocity, all objects projected horizontally from the
same height have the same time of flight as one dropped from rest
from the same height, because they all have a zero initial vertical velocity (Figure 1.1.5)
activity 1.1
pRacTIcaL eXpeRIeNceS
Activity Manual, Page 1
Table 1.1.1 Equations of projectile motion
Horizontal components Vertical components
Trang 28BaLLISTIcS IS a dRag
Air resistance or ‘drag’ introduces deceleration in both the vertical and horizontal directions, distorting the ballistic trajectory from an ideal parabola As a projectile becomes less compact, air resistance increases relative to weight The range decreases, the trajectory becomes less symmetrical, and the final angle becomes steeper The launch angle for maximum range decreases In extreme cases (for example, a loosely crushed piece of paper), the trajectory seems to approach Aristotle’s prediction: it moves briefly in a nearly straight line and then drops nearly vertically.
no air resistance
increasing air resistance Figure 1.1.6 The effect of increasing air resistance
Figure 1.1.5 Multiflash photo of two falling
objects All horizontally projected objects have the same time of flight as an object dropped from rest from the same height.
100 mm
Target practice
You now have all the equations you need to ‘do
some damage’, so let’s launch some projectiles
Safety warning! The following worked example
may seem dangerously long because it illustrates
several alternative methods of solving projectile
problems rolled into one
Worked example
questIon
You throw a ball into the air (Figure 1.1.7) You release the ball 1.50 m above the ground,
with a speed of 15.0 m s–1, 30.0° above horizontal The ball eventually hits the ground
Answer the following questions, assuming air resistance is negligible
a For how long is the ball in the air before it hits the ground (time of flight)?
b What is the ball’s maximum height?
c What is the ball’s horizontal range?
d With what velocity does the ball hit the ground?
Solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using:
1.50 m
Figure 1.1.7 Throwing a ball into the air
Trang 29Always draw a diagram! Divide the motion into vertical (y) and horizontal (x) components
Choose the origin to be the point of release, so xi = yi = 0
This is not always the most convenient choice of origin.
Use the sign convention + → & +↑
Components of initial velocity u (Figure 1.1.8):
ux = +ucos θi = +15.0cos30.0° = +13.0 m s–1
uy = +usinθi = +15.0sin30.0° = +7.50 m s–1The only external force is gravity so vertical acceleration is g = –9.80 m s–2 There is no horizontal force, therefore ax = 0 m s–2 (constant horizontal velocity)
Figure 1.1.8 Components of initial and final velocities
a The ball hits the ground when vertical displacement ∆y = –1.50 m.
Find final vertical velocity: v y2 = u y 2 + 2g ∆y = 7.502 + 2 × –9.80 × –1.50 = 85.65
Alternative method using the quadratic formula ∆y = uy t + 12gt 2 = –1.50 m
b At maximum height, vertical velocity vy = 0, so use v y 2 = u y 2 + 2g ∆y.
0 = u y + 2g ∆ymax = 7.502 + 2 × (–9.80) × ∆ymax
2 9 80
2
× = +2.87 m above the point of release,
so height above ground = 2.87 m + 1.50 m = 4.37 m above the ground.
Alternative method
Use vy = uy + gt to find the time t when v y = 0, then use ∆y = uy t + 12gt 2 to find vertical displacement
c From part a, we know the time of flight t = 1.71 s
Horizontal displacement in this time is:
∆x = ux t = +13.0 m s–1 × 1.71 s = +22.2 m = 22.2 m (to the right)
Trang 30d x-component of final velocity: v x = +13.0 m s–1
y-component of final velocity: vy = –9.255 m s–1 (down) (from part a)
To find magnitude, use Pythagoras’ theorem (see Figure 1.1.8):
v = v x2+ = 13 9 255v y2 2+ 2 = 15.96 ≈ 16.0 m s–1
Direction: tanθf = v
v
y
x =13 09 25.. , so θf = 35.4° down from horizontal
Alternative magnitude calculation
Negligible air resistance, ∴ mechanical energy = kinetic energy + gravitational
potential energy and is conserved (see in2 Physics @ Preliminary section 4.2) Near
the Earth’s surface, gravitational potential energy U = mgh Using the ground as h = 0:
This is the same as for the previous method within the three-figure precision of the
calculation, but doesn’t tell us the direction
In the previous example, time of flight was determined by the vertical
component—the flight ended when the ball hit the ground However, if the
projectile hits a vertical barrier such as a wall, then the time of flight is determined
by the horizontal component
Worked example
questIon
Suppose you kick a ball at 22.0 m s–1, 20.0° above the horizontal, towards a wall 21.0 m
away (Figure 1.1.9) Ignore air resistance and the ball’s radius
a What is the ball’s time of flight (before hitting the wall)?
b At what height does the ball hit the wall?
c Is that the greatest height reached by the ball?
solutIon
Solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using:
Figure 1.1.9 The ball hits the wall.
Choose the origin to be the initial position, so xi = yi = 0 Use the sign convention +↑
and + →
ux = 22.0cos20.0° (right) = +20.7 m s–1
uy = 22.0sin20.0° (up) = +7.52 m s–1
Trang 311.2 Gravity
like mechanism to keep it in motion Copernicus and Kepler greatly improved the picture, but Isaac Newton finally showed there was a single mechanism for them all—the force of gravity
In Ptolemy’s universe, the Sun, Moon and planets each had a separate clockwork-The calculations of parabolic trajectories in section 1.1 work well close to the
Earth’s surface where g is constant However, if we’re going to venture out into
space, we can’t use these simple equations We need to look at the force of gravity
on a larger scale
Newton’s law of universal gravitation
Newton assumed several properties of gravity (see in2 Physics @ Preliminary
section 13.5):
• All ‘massive’ objects (that is, objects with mass) attract each other The larger the masses, the larger the force
m
m s = 1.014 s ≈ 1.01 s
b The ball hits the wall at a height (vertical displacement) of ∆y = uy t + 12gt 2
Substitute, solve: ∆y = +7.52 × 1.014 + 0.5 × –9.80 × 1.0142 = +2.587 The ball hits the wall ≈ 2.59 m above ground
c Check if the ball reaches maximum height of the parabola before hitting the wall.
Time of flight = 1.01 s vy = 0 at maximum height of parabola
Find the time taken to reach maximum height
Substitute: vy = 0 = uy + gt = +7.52 + –9.80 × t
Rearrange, solve: t=7 529 80.. = 0.767 s which is less than time of flightThe ball would reach the maximum height of the parabola before hitting the wall, therefore the final height is NOT the maximum height for the trajectory
CheCkPoInt 1.1
negligible air resistance.)
(Assume negligible air resistance.)
5 Describe the two conditions that must apply so that a trajectory is a parabola.
Trang 32• Like light intensity, the magnitude of the force decreases with distance
according to the inverse square law (see in2 Physics @ Preliminary sections
6.1 and 15.1) However, astronomer Ismael Boulliau had suggested this
before him
• The law of gravitation is universal—it applies throughout the universe and is
responsible for the orbits of all the planets and moons
All this is expressed mathematically as the law of universal gravitation:
d
G= 1 2
2
where FG is the magnitude of the force of gravitational attraction between
two masses m1 and m2 and d is the distance between their centres of mass (see
in2 Physics @ Preliminary section 3.6) The universal gravitational constant G
(‘big G ’) is 6.67 × 10–11 N m2 kg–2 in SI units It should not be confused with
surface of the other—gravity would not approach infinity if
you were to burrow towards the centre of the Earth
• The resultant force on a mass due to the presence of other
masses is the vector sum of the individual forces on the first
mass due to each of the other individual masses
Worked example
questIon
Calculate the gravitational force between the Earth and the Moon.
Data: Earth’s mass mE = 5.97 × 1024 kg
Moon’s mass mM = 7.35 × 1022 kg
Average Earth–Moon distance dEM = 3.84 × 108 m
Universal gravitational constant G = 6.67 × 10–11 N m2 kg–2
Define Newton’s Law of Universal Gravitation:
F G m m d
= 1 2 2
TRy ThIS!
sligHtly attractiVe
You can see the feeble force of gravity acting between objects in your garage John Walker’s Fourmilab website describes step by step how you can perform a crude version of the Cavendish experiment in your own garage (see Physics Focus ‘How to weigh the Earth’ at the end of this chapter), using commonly found household items and a video camera
If you’re feeling too lazy to do it yourself, you can just download sped-up videos of the experiment in progress
Figure 1.2.1 Cavendish apparatus at home
Trang 33PhysICs Feature
Don’t unDerestImate the PoWer oF boreDom
boreDom Part 1
Bored? Don’t just write graffiti—try revolutionising physics! In 1665, an
outbreak of bubonic plague around London closed Cambridge University,
so Isaac Newton (aged 23) escaped for 2 years to his mother’s farm He was
not a very good farmer, so he fended off his city-boy boredom by inventing
calculus and using prisms to show that white light is actually a mixture of
colours (the spectrum) To top this off, when he saw an apple fall off his
mother’s tree, he wondered if the force accelerating the apple downwards was
also responsible for keeping the Moon orbiting the Earth
So he began formulating his theory of gravitation His mathematics professor
was so impressed that a couple of years after Newton returned to Cambridge,
he resigned and handed his professorship to Newton
After this initial investigation, it took Newton another 20 years to fully
develop and finally publish his law of universal gravitation
Worked example
questIon
A 1000 kg spacecraft is in the vicinity of the Earth–Moon system The spacecraft is at the
origin, the Moon is on the positive y-axis and the Earth is on the positive x-axis (Figure
1.2.2) Given that the Earth–spacecraft and Moon–spacecraft distances are 3.82 × 108 m and 3.91 × 107 m respectively, calculate the resultant gravitational force on the
Figure 1.2.3 Gravitational force vector
diagram Note; This does not resemble the position vector diagram in Figure 1.2.2.
1 The history of physics
3 Applications and uses of physics
Figure 1.2.4 Graffiti carved on a stone at
the King’s School in Grantham, England, by Isaac Newton, then about 10 years old
Trang 34boreDom Part 2
It is said that, at age 17, Galileo was attending church and, bored,
was watching a lantern swing from the ceiling Using his pulse as a
stopwatch, he observed that the oscillation period of a pendulum barely
changed as its amplitude gradually decreased Back at home he started
experiments confirming that the oscillation period depends on pendulum
length L, but not at all on mass and only slightly on amplitude He
proposed (correctly) that pendulums could be used to create the first
accurate mechanical clocks
We now know that, consistent with Galileo’s observations, for a simple
mass-on-string pendulum the formula for oscillation period T is:
T=2π L g
The formula is an approximation, but if the maximum swing angle is
less than 15° from vertical, the formula is correct within 0.5% With this
formula and a pendulum, you can measure the value of ‘little g’, which
varies slightly between locations around the world Figure 1.2.5 Young Galileo watches a swinging
lantern in Pisa cathedral.
Weight and gravitational fields
As far as we know, the universal gravitational constant G is a fundamental
constant, unchanging with position or time But the acceleration due to gravity g
is different on other astronomical bodies, at different heights and even at
different positions on the Earth’s surface
Recall that weight w = mg is defined as the force on an object due to gravity
(see in2 Physics @ Preliminary section 3.2); in other words, FG = w = mg ‘Little g’,
the acceleration due to gravity, can also be thought of as the strength of the
gravitational field However, the word weight is usually reserved for the case
in which the gravitational field is due to a body of astronomical size, such as
a planet
Any massive object can be described as being surrounded by a gravitational
field, a region within which other objects experience an attractive force Just as
for electrical and magnetic fields (see in2 Physics @ Preliminary sections 10.6,
12.3 and 12.4), we can draw diagrams of gravitational field lines (Figure 1.2.6)
The arrows on the field lines around a mass, point in the direction of the force
acting on another (normally much smaller) test mass Gravitational field
is a vector (g) The density of the field lines at any particular point in space
represents g, the magnitude of the field at that point, and the direction of the
field lines represents the direction of this vector Field lines run in radial
directions from point masses or spherical masses
Using a small test mass m, let’s derive g, the magnitude of the gravitational
field due to a planet of mass M The weight w of the test mass is defined as the
force on m due to the planet’s gravity; that is:
activity 1.2
pRacTIcaL eXpeRIeNceS
Activity Manual, Page 5
Describe a gravitational field
in the region surrounding a massive object in terms of its effects on other masses in it Define weight as the force
on an object due to a gravitational field.
Trang 35g F
M d
= G =
2
Newton’s equation for gravitational force is symmetrical—you can choose
either mass as the test mass and calculate the field around the other and still get
the same magnitude of force when you multiply them together because of
Newton’s third law (see in2 Physics @ Preliminary section 3.5)—the two masses
are an action–reaction pair However, if one of the masses is much larger (such as
a planet), it is more convenient to calculate the field around it and use the smaller mass as the test mass
In astronomical situations where one of the bodies (such as a planet or star) is
very much larger, the larger body is sometimes called the central body Because
of its large mass, the central body experiences negligible gravitational accelerations compared with a small test mass
Strictly speaking, the acceleration g is the acceleration of the test mass
towards the common centre of mass of the whole system of two masses
However, if the central body is much larger than the test mass, we can ignore its
acceleration, so g effectively becomes the acceleration of the test mass towards the
central body
Gravitational field is a vector, so when calculating the resultant field due to several bodies, the approach is identical to calculating the resultant gravitational force due to several bodies—calculate the field due to each individual mass and then find the vector sum of the fields
Worked example
questIon
Calculate gE the magnitude of the gravitational field at the Earth’s surface
Data: Earth’s mass mE = 5.97 × 1024 kg
Substitute: gE = 6 67 10 5 97 10
6 37 10
11 24 2
This should be a very familiar result
Variations in gravitational field
Newton’s gravitation equation says that the magnitude of a planet’s gravitational field depends on the mass of the planet and decreases with distance from the
planet’s centre For example, on Earth, the value of g is 0.28% lower at the top
Activity Manual, Page 11
Figure 1.2.6 Gravitational field lines around the
Earth (a) on an astronomical scale
and (b) near the surface
b
Trang 36measurements that gets more severe as one approaches the equator Because of the
Earth’s rotation, the (downward) centripetal acceleration (see
in2 Physics @ Preliminary section 2.3) of the ground appears to be subtracted from
the true value of g In fact this centripetal effect is responsible for the formation
of the equatorial bulge, which was predicted by Newton before it was measured
The Sun and Moon also exert a weak gravitational force on objects at the
Earth’s surface, so the magnitude and direction of g vary slightly, depending on
the positions of the Sun and Moon Variation in g caused by the positions of the
Sun and Moon relative to the oceans is responsible for the pattern of tides
Strictly speaking, Newton’s gravitation equation written in the form
above assumes that the planet is a perfectly uniform sphere Close to the surface
of a planet, local deviations from uniform density can result in small local changes
in the magnitude and direction of g The magnitude will be slightly larger than
average when measured on the ground above rock (such as iron ore) of high
density ρ (mass per unit volume) and lower above rock containing low-density
minerals (such as salt or oil), an effect exploited by geologists in mineral
exploration The Earth’s crust is less dense than the mantle, so variations in
thickness of the crust also affect g Variation in g is measured using a gravimeter,
the simplest kind being an accurately known mass suspended from a sensitive
spring balance
Variations in g on larger distance scales around the Earth can be measured
using satellites orbiting in low Earth orbit Deviations in the orbital speed of
satellites indicate that, in addition to the equatorial bulge, Earth is also slightly
pear-shaped—pointier at the North Pole than the South Pole
hooke’S LaW
Isaac Newton had enemies, and Robert
Hooke (1635–1703) was probably his
greatest They argued bitterly over
(among other things) who first suggested
the inverse square law for gravity Hooke
was an accomplished experimental
physicist, astronomer, microscopist,
biologist, linguist, architect and
inventor He is best remembered for the
discovery of (biological) cells and
the invention of the spring balance (see
in2 Physics @ Preliminary section 3.2),
which exploits Hooke’s law F = ‑k x
The force F exerted by a spring is
proportional to x, the change in spring
length The ‘spring constant’ k is a
measure of the spring’s stiffness A
calibrated spring balance can measure
weight, and, if used with an accurately
calibrated mass, it can be used
as a gravimeter to measure g. Figure 1.2.7 Hooke’s notes on the behaviour of springs
Int eractive
Module
Trang 371.3 Gravitational potential energy
We’ve already mentioned gravitational potential energy (GPE) U = mgh
(see in2 Physics @ Preliminary section 4.1) in part d of the worked example
accompanying Figure 1.1.7 This formula for GPE is an approximation that only
works close to the Earth’s surface, where g is very nearly constant It’s good enough for projectile motion but, as you now know, g decreases with distance, so
we need a more accurate formula to understand energy on an astronomical scale
Work and GPE
For clarity we’ll use the symbol EP instead of U to denote gravitational potential
energy calculated using the more accurate formula, even though the two symbols are really interchangeable Potential energy is energy stored by doing work against any force (such as gravity) that depends only on position; therefore,
gravitational potential energy EP is energy stored by doing work against the force
of gravity It can be shown (using calculus to derive the work done against gravity by changing the separation of two masses) that:
gravity in moving the masses together, starting at ‘infinite’ separation where
EP = 0 and bringing them to a separation of r (with no net change in speed) Equivalently, EP is the work done by gravity while the masses are moved apart, starting at a separation of r to a position of ‘infinite’ separation (with no
net change in speed) The gravitational potential energy does not depend on
the path taken by the masses to get to their final positions; it depends only on
the final separation r.
The formula isn’t affected by the choice of which mass to move, although normally we treat a large mass such as the Sun or a planet as an immoveable central body and the smaller mass as a moveable test mass The formula seems to
imply that EP approaches negative infinity as the test mass approaches the centre
of a planet However, this formula no longer applies in this form once one mass penetrates the surface of the other
Explain that a change in
gravitational potential energy
is related to work done
Define gravitational potential
energy as the work done to
move an object from a very
large distance away to a point
6 Outline the differences between G and g.
Trang 38Worked example
questIon
A piece of space junk of mass mJ drops from rest from a position of 30 000 km from the
Earth’s centre Calculate the final speed vf it attains when it reaches a height of 1000 km
above the Earth’s surface Assume that above 1000 km, air resistance is negligible
Data: Earth’s mass mE = 5.97 × 1024 kg
Earth’s radius rE = 6.37 × 106 m
Universal gravitational constant G = 6.67 × 10–11 N m2 kg–2
solutIon
Air resistance is negligible, so total mechanical energy (kinetic + potential energy) is
conserved Assume that because of the enormous mass of the Earth, its change in velocity
is negligible Use the Earth as the frame of reference Don’t forget to convert to SI units
5 97 10
6 37 1 00 10
24 6
.( )Rearrange, solve: vf= ×6.67 10× –11× × × −
Note that this result doesn’t depend on m J
Figure 1.3.1 Plots of gravitational force (FG) and gravitational potential energy (EP) versus separation
between a test mass mt and the Earth mE, starting at one Earth radius rE The vertical FGand EP axes are not drawn to the same scale.
Trang 39Isaac Newton showed that what goes up doesn’t necessarily come down Normally,
if one fires a projectile straight up, the object will decelerate until its velocity changes sign and it falls back down However, if a projectile’s initial velocity is
high enough, the 1/d 2 term in the gravity equation will cause the acceleration g to
decrease with height too rapidly to bring the projectile to a stop so it will never turn back—it can ‘escape’ the planet’s gravitational field The minimum velocity
that allows this is called the escape velocity Strictly speaking, it’s really a speed,
because the initial direction of the projectile isn’t critical
Newton treated the projectile as a cannonball (with no thrust) so that, other than the initial impulse from the cannon, the only force acting on it is gravity
He conceived escape velocity using his force equation, and the escape velocity formula can be derived from it However, a more modern derivation using energy
is easier and similar to the previous worked example
Let m be the mass of a projectile, M the mass of a planet, ve the initial speed
and r the initial position (the planet’s radius if you are on the surface) Assume air
resistance is negligible, so total mechanical energy (KE + GPE) is conserved (see
in2 Physics @ Preliminary section 4.2).
The escape velocity represents the minimum limiting case where the projectile
‘just reaches infinite displacement’ with zero speed; in other words, Kf = EPf = 0
depends only on the planet’s mass and the projectile’s starting position r but not
on the projectile’s mass
You may be puzzled that in the above derivation, the total mechanical energy (sum of KE and GPE) was exactly zero This means that the escaping projectile has just enough (positive) KE to overcome its negative potential energy When the mechanical energy is less than zero, there is not enough KE to overcome the
GPE and the two masses are said to be gravitationally bound When the total
mechanical energy ME > 0, the KE can overcome the GPE and the two bodies are no longer bound together This concept of binding also applies to the other three fundamental forces (including electromagnetism, which binds electrons to the nucleus of an atom)
The escape velocity from the Earth’s surface is:
2 6.67 10
m s–11
Explain the concept of escape
velocity in terms of the:
– gravitational constant
– mass and radius of the planet.
Trang 40This idealised escape velocity needs to be modified when applied to real
spacecraft First, the derivation ignores air resistance in the atmosphere
(hundreds of kilometres thick), which would increase the escape velocity
Second, in a real rocket, engines produce an extra force—thrust—that can
accelerate a craft to a higher altitude where the escape velocity is lower It also
ignores other sources of gravitational fields such as the Sun, Moon and planets
The escape velocity for a projectile under the gravitational influence of more
than one body is given by:
vetotal = ve12+ ve22+
where vetotal is the escape velocity for the total system and ve1, ve2 … are the
escape velocities from the individual bodies within the system, calculated for the
projectile using the same starting position in space
ULTImaTe fRISBee
Was the first artificial object to leave the solar system a giant steel
frisbee? In the 1950s, the US started testing nuclear bombs
underground, to minimise atmospheric nuclear fallout In 1957, during
Operation Plumbbob in the Pascal-B test, a nuclear bomb was detonated at
the bottom of a 150 m shaft sealed with concrete and a 900 kg, 10 cm thick
steel cap The steel cap fired upwards at enormous speed and was never
seen again Before the test, it was estimated that an extreme upper limit for
the speed of the steel cap would be 67 km s–1 This is well above the
escape velocity for the whole solar system (43.6 km s –1 from Earth), starting
an urban myth that it beat the Voyager probes (launched in 1977) out of the
solar system A later, more realistic, estimate suggested that, at most, the
cap had a speed of 1.4 km s–1, reaching an altitude of less than 95 km.
CheCkPoInt 1.3
1 Define under what circumstances it is suitable to use the simplified formula U = mgh for gravitational potential
energy (GPE)