HSC PHYSICS Brian Shadwick
© Science Press 2007 First published 2007 Reprinted 2007, 2008, 2009, 2010 Science Press Private Bag 7023 Marrickville NSW 1475 Australia Tel: (02) 9516 1122 Fax: (02) 9550 1915
[email protected] www.sciencepress.com.au
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Science Press. ABN 98 000 073 861
Contents Introduction
v
Verbs to Watch
vi
Dot Points Space
vii
Motors and Generators
ix
From Ideas to Implementation
xi
From Quanta to Quarks
xiii
Questions Space
1
Motors and Generators
39
From Ideas to Implementation
81
From Quanta to Quarks
121
Summaries Space
161
Motors and Generators
181
From Ideas to Implementation
201
From Quanta to Quarks
219
Answers Space
237
Motors and Generators
247
From Ideas to Implementation
259
From Quanta to Quarks
271
Appendix Data Sheet
282
Formula Sheet
283
Periodic Table
284
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Contents
Notes ........................................................................................................................................................................................................................................................ ........................................................................................................................................................................................................................................................ ........................................................................................................................................................................................................................................................ 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Contents
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Dot Point HSC Physics
Introduction What the book includes ,QWKLVERRN\RXZLOO¿QGW\SLFDOH[DPLQDWLRQTXHVWLRQVDQGDQVZHUVDVZHOODVVXPPDULHVIRUHDFKGRWSRLQWLQ the Board of Studies syllabus for the following topics in the Year 12 Physics course:
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Also included are typical experimental results for students to analyse if the third column of the syllabus indicates WKDWVWXGHQWVVKRXOGFDUU\RXWµ¿UVWKDQGLQYHVWLJDWLRQV¶ Format of the book The book has been formatted in the following way: 1. Main topic statement (column 1 of syllabus) 1.1etc Syllabus requirement from columns 2 and 3. 1RWHWKDWWKHQXPEHULQJRIWKHVHUHTXLUHPHQWVLVWKHDXWKRU¶VFKRLFHDQGKDVEHHQXVHGWRPDNHUHIHUHQFLQJ TXHVWLRQVDQGDQVZHUVFOHDUHU7KHLQGLYLGXDOUHTXLUHPHQWVDUHQRWQXPEHUHGLQWKHV\OODEXVWKH\DUHVLPSO\ EXOOHWHG±KHQFHRXUXVHRIµGRWSRLQWV¶ZKHQZHUHIHUWRWKHP 1.1.1 )LUVWW\SLFDOTXHVWLRQZKLFKFRXOGEHDVNHGLQDQH[DPLQDWLRQIRUWKLVV\OODEXV UHTXLUHPHQW 1.1.2 6HFRQGW\SLFDOTXHVWLRQZKLFKFRXOGEHDVNHGLQDQH[DPLQDWLRQIRUWKLVV\OODEXV UHTXLUHPHQWHWF 7KHQXPEHURIOLQHVSURYLGHGIRUHDFKDQVZHUJLYHVDQLQGLFDWLRQRIKRZPDQ\PDUNVWKHTXHVWLRQPLJKWEH worth in an examination. As a rough rule, every two lines of answer might be worth one mark. Note that in many DQVZHUVWKUHHOLQHVKDYHEHHQSURYLGHGDVWKHDPRXQWRIZULWLQJUHTXLUHGH[FHHGVWZROLQHVEXWWKHSK\VLFV involved is worth only one mark. How to use the book &RPSOHWLQJDOOTXHVWLRQVZLOOSURYLGH\RXZLWKDVXPPDU\RIDOOWKHZRUN\RXQHHGWRNQRZIURPWKHV\OODEXV You may have done work in addition to this with your teacher as extension work. Obviously this is not covered, but you may need to know this additional work for your school exams. :KHQZRUNLQJWKURXJKWKHTXHVWLRQVZULWHWKHDQVZHUV\RXKDYHWRORRNXSLQDGLIIHUHQWFRORXUWRWKRVH\RX NQRZZLWKRXWKDYLQJWRUHVHDUFKWKHZRUN7KLVZLOOSURYLGH\RXZLWKDTXLFNUHIHUHQFHWRZRUN\RXVKRXOG spend more time revising later, and allow you to spend your study time more productively.
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Dot Point HSC Physics
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Introduction
Verbs to Watch account/account for State reasons for, report on, give an account of, narrate a series of events or transactions.
distinguish Recognise or note/indicate as being distinct or different from, note difference between things.
analyse Identify components and the relationships among them, draw out and relate implications.
evaluate Make a judgement based on criteria. examine ,QTXLUHLQWR
apply Use, utilise, employ in a particular situation.
explain Relate cause and effect, make the relationship between things evident, provide why and/or how.
appreciate Make a judgement about the value of something.
extract Choose relevant and/or appropriate details.
assess 0DNHDMXGJHPHQWRIYDOXHTXDOLW\RXWFRPHV results or size.
extrapolate Infer from what is known.
calculate 'HWHUPLQHIURPJLYHQIDFWV¿JXUHVRULQIRUPDWLRQ
identify Recognise and name.
clarify Make clear or plain.
interpret Draw meaning from.
classify Arrange into classes, groups or categories.
investigate 3ODQLQTXLUHLQWRDQGGUDZFRQFOXVLRQVDERXW
compare Show how things are similar and different.
justify Support an argument or conclusion.
construct Make, build, put together items or arguments.
outline Sketch in general terms; indicate the main features.
contrast Show how things are different or opposite.
predict Suggest what may happen based on available data.
critically (analyse/evaluate) Add a degree or level of accuracy, depth, knowledge DQGXQGHUVWDQGLQJORJLFTXHVWLRQLQJUHÀHFWLRQDQG TXDOLW\WRDQDQDO\VLVRUHYDOXDWLRQ
propose Put forward (a point of view, idea, argument, suggestion etc) for consideration or action.
deduce Draw conclusions.
recall Present remembered ideas, facts or experiences.
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recommend Provide reasons in favour.
demonstrate Show by example.
recount Retell a series of events.
describe Provide characteristics and features.
summarise Express concisely the relevant details.
discuss Identify issues and provide points for and against.
synthesise Put together various elements to make a whole. Science Press
Verbs to Watch
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Space Dot Point
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1.
*UDYLWDWLRQDO¿HOG
2
'H¿QHZHLJKWDVWKHIRUFHDFWLQJRQ DQREMHFWGXHWRDJUDYLWDWLRQDO¿HOG
1.2
Use F = mg to determine the weight force of bodies on Earth and other planets.
1.3. 1.4
1.5
Predict the acceleration due to gravity on other planets.
4
Explain that a change in gravitational potential energy is related to work done.
6
2.
Rocket launches and gravity
9
2.1
Describe the trajectory of a projectile ZLWKLQWKH(DUWK¶VJUDYLWDWLRQDO¿HOG
'HVFULEH*DOLOHR¶VDQDO\VLVRISURMHFWLOH motion.
2.4
9
11
2XWOLQH1HZWRQ¶VFRQFHSWRIHVFDSH velocity.
12
2.7
Perform an experiment to calculate WKHLQLWLDODQG¿QDOYHORFLWLHVUDQJH DQGWLPHRIÀLJKWRIDSURMHFWLOH
2.8
Analyse the changing acceleration of a rocket during launch in terms of the Law of Conservation of Momentum and the forces experienced by astronauts.
Explain escape velocity in terms of the gravitational constant, and the mass and radius of the planet.
,GHQWLI\ZK\WKHWHUPµJIRUFHV¶LV used to explain the forces on an astronaut.
17
17
3
'H¿QHGPE as the work done to move DQREMHFWIURPLQ¿QLW\WRDSRLQWLQD JUDYLWDWLRQDO¿HOG
2.10 Analyse forces involved in uniform circular motion for a range of objects, including satellites orbiting Earth.
2
Perform an experiment to determine the acceleration due to gravity and identify reasons for possible variations from 9.8 m s–2.
Solve projectile motion problems using horizontal and vertical components DQG1HZWRQ¶VHTXDWLRQVRIPRWLRQ
Page
2.11 Solve problems about the centripetal force on a satellite in Earth orbit using:
2.3
Dot Point
&RPSDUHTXDOLWDWLYHO\ORZ(DUWKDQG geostationary orbits.
18
2.13 Outline the contribution to space of one of: Tsiolkovsky, Oberth, Goddard, (VQDXOW3HOWHULH2¶1HLOORUYRQ%UDXQ
'H¿QHRUELWDOYHORFLW\DQGLWV relationship with G, the mass of the planet and satellite, and the radius RIWKHRUELWTXDOLWDWLYHO\DQG TXDQWLWDWLYHO\
6ROYHSUREOHPVXVLQJ.HSOHU¶V/DZ of Periods.
21
2.16 Account for the orbital decay of satellites in LEO.
23
2.17 Discuss issues associated with safe UHHQWU\LQWRWKH(DUWK¶VDWPRVSKHUH and landing on the surface.
23
2.18 Identify that there is an optimum angle IRUUHHQWU\LQWRWKH(DUWK¶VDWPRVSKHUH DQGWKHFRQVHTXHQFHVRIIDLOLQJWR achieve this.
24
3.
The Solar System and gravity
25
'HVFULEHDJUDYLWDWLRQDO¿HOGQHDUD massive object in terms of its effects on other masses.
25
'H¿QH1HZWRQ¶V/DZRI8QLYHUVDO Gravitation.
25
12 3.3
Solve problems and analyse information using: 25
3.4 14
'LVFXVVWKHHIIHFWRIWKH(DUWK¶VRUELWDO and rotational motion on rocket launches. 16
Discuss factors affecting the strength of the gravitational force.
27
'LVFXVVWKHLPSRUWDQFHRI1HZWRQ¶V Law of Universal Gravitation in understanding and calculating the motion of satellites.
28
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Space
Dot Point 3.6
Page
Identify that a slingshot effect can be provided by planets for space probes.
28
4.
Understanding time and space
29
4.1
Outline the features of the aether model for the transmission of light.
29
4.2
Describe and evaluate the 0LFKHOVRQ0RUOH\H[SHULPHQW
4.3
Interpret the results of the 0LFKHOVRQ0RUOH\H[SHULPHQW
4.4
Discuss the role of the 0LFKHOVRQ0RUOH\H[SHULPHQWLQ making determinations about competing theories.
30
Outline the nature of inertial frames of reference.
30
4.5 4.6
33
([SODLQTXDOLWDWLYHO\WKHFRQVHTXHQFH of special relativity in relation to the relativity of simultaneity.
34
([SODLQTXDOLWDWLYHO\WKHFRQVHTXHQFH RIVSHFLDOUHODWLYLW\WRWKHHTXLYDOHQFH of mass and energy.
34
4.15 Solve problems using:
34
([SODLQTXDOLWDWLYHO\WKHFRQVHTXHQFH of special relativity in relation to mass.
35
4.17 Solve problems using the relativistic PDVVHTXDWLRQ
([SODLQTXDOLWDWLYHO\WKHFRQVHTXHQFH of special relativity in relation to length contraction.
36
4.19 Solve problems using the relativistic OHQJWKHTXDWLRQ
([SODLQTXDOLWDWLYHO\WKHFRQVHTXHQFH of special relativity in relation to time dilation.
37
32
4.21 Solve problems using the time GLODWLRQHTXDWLRQ
33
4.22 Discuss implications of mass increase, time dilation, length contraction for space travel.
38
31
4.7
Discuss the principle of relativity.
32
'HVFULEHWKHVLJQL¿FDQFHRIWKH DVVXPSWLRQRI(LQVWHLQ¶VDVVXPSWLRQ of the constancy of the speed of light. $QDO\VHDQGLQWHUSUHWVRPHRI(LQVWHLQ¶V thought experiments about mirrors and trains and discuss the relationship between thought and reality.
4.10 Identify that if c is constant, then space and time become relative. 4.11 Discuss the concept that length standards DUHGH¿QHGLQWHUPVRIWLPHLQFRQWUDVW to the original metre standard.
Page
4.12 Discuss the relationship between theory and the evidence supporting LWXVLQJ(LQVWHLQ¶VSUHGLFWLRQVEDVHG on relativity that were made many years before evidence was available to support it.
Perform an investigation to distinguish EHWZHHQQRQLQHUWLDODQGLQHUWLDO frames of reference.
Dot Point
32
Answers to Space
33
237
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Motors and Generators Dot Point
Page
1.
Current-carrying conductors
1.1
Discuss the effect, on the force on a FXUUHQWFDUU\LQJFRQGXFWRURI variations in: WKHPDJQHWLF¿HOGLQZKLFKLWLVORFDWHG WKHFXUUHQWLQWKHFRQGXFWRU WKHOHQJWKRIWKHFRQGXFWRULQWKH¿HOG WKHDQJOHEHWZHHQWKHPDJQHWLF¿HOG and conductor.
1.2
Dot Point
40
,GHQWLI\WKDWWKHPDJQHWLF¿HOGLQ '&PRWRUVFDQEHSURGXFHGE\FXUUHQW carrying coils or permanent magnets.
50
2.
Generating electricity
51
2XWOLQH)DUDGD\¶VGLVFRYHU\RIWKH generation of electricity by a moving magnet.
51
Perform an investigation to model the generation of an electric current by moving a magnet in a coil or a coil near a magnet.
52
Plan and perform an experiment to predict and verify the effect on a generated current of the distance between the coil and the magnet, the strength of the magnet, and the relative motion between the coil and the magnet.
52
'H¿QHPDJQHWLF¿HOGVWUHQJWKB as PDJQHWLFÀX[GHQVLW\
'HVFULEHPDJQHWLFÀX[LQWHUPVRI PDJQHWLFÀX[GHQVLW\DQGVXUIDFHDUHD
2.6
Describe generated potential difference DVWKHUDWHRIFKDQJHRIPDJQHWLFÀX[
$FFRXQWIRU/HQ]¶V/DZLQWHUPVRI conservation of energy.
54
5HODWH/HQ]¶V/DZWRWKHSURGXFWLRQ of back emf in motors and that this opposes the supply emf.
55
Explain production of eddy currents LQWHUPVRI/HQ]¶V/DZ
2.2
40
Solve problems and analyse information about the force on FXUUHQWFDUU\LQJFRQGXFWRUVLQ PDJQHWLF¿HOGVXVLQJ
2.3 40
'HVFULEHTXDOLWDWLYHO\DQGTXDQWLWDWLYHO\ the force between long, parallel current–carrying conductors using: 41
1.4
Solve problems using: 42
1.5 1.6 1.8
Describe the forces experienced by a FXUUHQWFDUU\LQJORRSLQDPDJQHWLF ¿HOGDQGGHVFULEHWKHQHWUHVXOWRI the forces. Perform an experiment to demonstrate the motor effect.
44
'H¿QHWRUTXHDVWKHWXUQLQJPRPHQW of a force using: T
45
2.9
Solve problems and analyse information about simple motors using: T
1.9
43
Identify the motor effect is due to the IRUFHDFWLQJRQDFXUUHQWFDUU\LQJ FRQGXFWRULQDPDJQHWLF¿HOG
1.10 Describe the application of the motor effect in a galvanometer. 1.11 Describe the application of the motor effect in a loudspeaker. 1.12 Describe the main features of a DC electric motor and the role of each feature.
46
47 48
Page
2.10 Explain how induction is used in cooktops.
62
2.11 Explain how eddy currents are used in electromagnetic braking.
62
3.
Generators
63
3.1
Describe the main components of a generator.
63
Describe the differences between DC and AC generators.
63
3.2
49
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Motors and Generators
Dot Point 3.3 3.4
3.5 3.6 3.7 3.8 3.9
Compare the structure and function of a motor and a generator. Discuss advantages and disadvantages of AC and DC generators and relate these to their use. Perform an experiment to demonstrate the production of an alternating current.
Page
4.4
4.5 66 66
Assess the effects of the development of AC generators on society.
67
4.9 67
4.
Transformers
71
4.1
Describe the purpose of transformers in electrical circuits.
71
&RPSDUHVWHSXSDQGVWHSGRZQ transformers.
71
Identify the relationship between the ratio of the number of turns in the primary and secondary coils and the ratio of the primary to secondary voltage.
4.7
67
69
4.3
4.6
4.8
3.10 Identify how transmission lines are insulated from supporting structures and protected from lightning.
Solve problems using: 72
66
Analyse the competition between Edison and Westinghouse to supply electricity to cities.
Page
65
Discuss energy losses that occur in transmission lines.
Assess the effects of the development of AC generators on the environment.
Dot Point
Discuss how the heating effects of eddy currents are minimised in transformers.
74
Perform an experiment to model the structure and working of a transformer.
74
Discuss the need for transformers in electricity transmission from source to point of use.
75
Explain why voltage transformations are related to conservation of energy.
75
Discuss why some electrical appliances in the home use transformers.
76
4.10 Discuss the impact of the development of transformers on society.
76
5.
Motors and energy changes
77
5.1
Describe the main features of an AC electric motor.
77
Perform an investigation to demonstrate the principle of an AC induction motor.
78
Identify some of the energy transformations involving the conversion of electrical energy that occur in homes and industry.
79
5.2 5.3
Answers to Motors and Generators
247
72
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From Ideas to Implementation Dot Point
Page
1.
Cathode rays
82
1.1
Explain that cathode ray tubes allowed the manipulation of charged particles.
82
1.2
1.3
Explain why the apparent behaviour of cathode rays caused debate as to whether they were charged particles or electromagnetic waves.
82
84
1.5
Identify that moving charged particles LQDPDJQHWLF¿HOGH[SHULHQFHDIRUFH
'LVFXVVTXDOLWDWLYHO\WKHHOHFWULF¿HOG strength due to point, positive and negative charges.
85
1.7
Identify that charged plates produce DQHOHFWULF¿HOG
'LVFXVVTXDOLWDWLYHO\WKHHOHFWULF¿HOG strength due to oppositely charged parallel plates.
1.10 Outline the experiment by Thomson to measure the charge/mass ratio of an electron.
2.
The photoelectric effect and black body radiation
93
2XWOLQH+HUW]¶VH[SHULPHQWLQ measuring the speed of radio waves and how they relate to light waves.
93
'HVFULEH+HUW]¶VREVHUYDWLRQRIWKH effect of a radio wave on a receiver and the photoelectric effect he produced but failed to investigate.
94
Perform an experiment to show the production and reception of radio waves.
94
,GHQWLI\3ODQFN¶VK\SRWKHVLVWKDW radiation emitted and absorbed by the ZDOOVRIDEODFNERG\LVTXDQWLVHG
,GHQWLI\(LQVWHLQ¶VFRQWULEXWLRQWR TXDQWXPWKHRU\DQGLWVUHODWLRQWR black body radiation.
96
$VVHVV(LQVWHLQ¶VFRQWULEXWLRQWR TXDQWXPWKHRU\DQGLWVUHODWLRQWR black body radiation.
98
Explain the particle model of light in terms of photons with particular energy DQGIUHTXHQF\
Identify the relationships between SKRWRQHQHUJ\IUHTXHQF\VSHHGRI light and wavelength using: and
99
Solve problems using: and
99
2.7 2.8
87
'HVFULEHTXDQWLWDWLYHO\WKHIRUFHRQ a moving charged particle in a PDJQHWLF¿HOGDQGVROYHSUREOHPV using: F = qE F = qvBsin ș
2.3
Perform an investigation to observe the different patterns of striations in cathode ray tubes at different pressures.
For cathode ray tubes, outline the role of: WKHHOHFWURGHVLQWKHHOHFWURQJXQ WKHGHÀHFWLRQSODWHVRUFRLOV WKHÀXRUHVFHQWVFUHHQ
83
2.9
87
90
Page
1.11
Perform an investigation to identify properties of cathode rays using discharge tubes containing: D0DOWHVHFURVV HOHFWULFSODWHV DÀXRUHVFHQWVFUHHQ DJODVVZKHHO and analyse the information to determine the sign of the charge on cathode rays.
1.4
Dot Point
2.10 Summarise the use of the photoelectric effect in solar cells and photocells.
101
'LVFXVV(LQVWHLQDQG3ODQFN¶V GLIIHULQJYLHZVDERXWZKHWKHUVFLHQWL¿F research is removed from social and political forces.
102
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From Ideas to Implementation
Dot Point 3.
Transistors
3.1 3.2
3.3
3.5 3.6
3.7
3.9
Page
Dot Point
103
Page
4.
Superconductors
115
Identify that some electrons in solids are shared between atoms and move freely. 103
4.1
Outline the methods used by the Braggs to determine crystal structure.
115
Describe, in terms of band structures and relative electrical resistance, the differences in conductors, insulators, semiconductors.
4.2
Identify that metals possess a crystal lattice structure.
115
Describe conduction in metals as a movement of free electrons unimpeded by the lattice.
115
Identify that resistance in metals is increased by the presence of impurities and scattering of electrons by lattice vibrations.
115
Identify absences of electrons in nearly full bands as positive holes, and recognise that electrons and holes help to carry current.
4.3 103 4.4 105
&RPSDUHTXDOLWDWLYHO\WKHUHODWLYH number of free electrons in conductors, semiconductors and insulators.
107
Perform an experiment to model the behaviour of semiconductors.
107
Identify that the use of germanium in early transistors was related to the inability to produce other materials of suitable purity. Describe how doping a semiconductor can change its electrical properties. ,GHQWLI\GLIIHUHQFHVLQSDQGQW\SH semiconductors in terms of their relative numbers of negative charge carriers and positive holes. Describe differences between solid state and thermionic devices and why solid state replaced thermionic devices.
3.12 Identify data sources, gather, process and present information to summarise the effect of light on semiconductors in solar cells.
Describe the occurrence in superconductors below their critical temperature of a population of electron pairs unaffected by electrical resistance. 116
4.6
Identify some of the metals, alloys DQGFRPSRXQGVLGHQWL¿HGDVH[KLELWLQJ superconductivity and their critical temperatures.
116
4.7
Discuss the BCS theory.
116
4.8
Discuss the advantages of using superconductors and identify limitations to their use.
117
Explain why a magnet is able to hover above a superconducting material below its critical temperature.
118
108 108
4.9 109
109
3.10 Discuss how shortcomings in communications technology led to an increased knowledge of the properties of materials with reference to the invention of transistors. 110 3.11 Assess the impact of transistors on society with particular reference to their use in microchips and microprocessors.
4.5
4.10 Perform an investigation to demonstrate magnetic levitation.
119
4.11 Describe how superconductors and WKHHIIHFWVRIPDJQHWLF¿HOGVKDYH been applied to develop a maglev train.
119
4.12 Discuss possible applications of superconductivity and the effects of those applications on computers, generators, motors and the transmission of electricity through transmission grids. 120
110
Answers to From Ideas to Implementation
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From Quanta to Quarks Dot Point
Page
1.
Models of the atom
122
1.1
Discuss the Rutherford model of the atom.
122
$QDO\VHWKHVLJQL¿FDQFHRIWKH hydrogen spectrum in the development of the Bohr model.
1.3
2.5
Assess the contribution made by Heisenberg and Pauli to atomic theory.
134
3.
Development of nuclear physics
135
'H¿QHWKHFRPSRQHQWVRIWKHQXFOHXV and contrast their properties.
135
Discuss the importance of the FRQVHUYDWLRQODZVWR&KDGZLFN¶V discovery of the neutron.
135
'H¿QHWKHWHUPQXFOHDUWUDQVPXWDWLRQ
3.4
Describe nuclear transmutations due to natural radioactivity.
137
'HVFULEH)HUPL¶VLQLWLDOH[SHULPHQWDO REVHUYDWLRQRIQXFOHDU¿VVLRQ
3.6
Perform an experiment to observe radiation emitted from a nucleus using a Wilson cloud chamber or similar device.
139
122
123
'LVFXVV3ODQFN¶VFRQWULEXWLRQWRWKH FRQFHSWRITXDQWLVHGHQHUJ\
'H¿QH%RKU¶VSRVWXODWHV
'HVFULEHKRZ%RKU¶VSRVWXODWHVOHG to a mathematical model to account for the hydrogen spectrum.
3.2
125
Solve problems and analyse information using:
125 1.8
Process and present diagrams to show %RKU¶VH[SODQDWLRQRIWKH%DOPHUVHULHV
1.9
Discuss the limitations of the Bohr model of the hydrogen atom.
130
,GHQWLI\GLI¿FXOWLHVZLWKWKH%RKU model, including its inability to explain spectra of larger atoms, LQWHQVLW\RIDQGK\SHU¿QHVSHFWUDO lines and the Zeeman effect.
130
2.
Development of quantum physics
131
'HVFULEHWKHLPSDFWRIGH%URJOLH¶V proposal that any kind of particle has both wave and particle properties.
131
2.2
3.8
3.9
Solve problems and analyse information using: 131
'H¿QHGLIIUDFWLRQDQGLGHQWLI\WKDW interference occurs between waves that have been diffracted.
132
'HVFULEHWKHFRQ¿UPDWLRQRIGH%URJOLH¶V proposal by Davisson and Germer.
133
Page
Explain the stability of the electron orbits in the Bohr atom using GH%URJOLH¶VK\SRWKHVLV
2.6
Perform an experiment to observe the visible components of the hydrogen spectrum.
1.7
Dot Point
'LVFXVV3DXOL¶VLGHDRIWKHWKH neutrino and the need to account for WKHHQHUJ\HOHFWURQVHPLWWHGLQȕGHFD\ Evaluate the relative contribution of electrostatic and gravitational forces between nucleons.
141
Account for the need for the strong nuclear force and describe its properties. 141
3.10 Explain the concept of mass defect XVLQJ(LQVWHLQ¶VHTXLYDOHQFHEHWZHHQ mass and energy.
142
3.11 Solve problems to calculate the mass defect and energy released in natural WUDQVPXWDWLRQDQG¿VVLRQUHDFWLRQV
'HVFULEH)HUPL¶VGHPRQVWUDWLRQVRI a nuclear chain reaction in 1942.
146
&RPSDUHUHTXLUHPHQWVIRUFRQWUROOHG and uncontrolled chain reactions.
147
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From Quanta to Quarks
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4.
Applications of nuclear physics
151
4.1
Explain the basic principles of a ¿VVLRQUHDFWRU
$VVHVVWKHVLJQL¿FDQFHRIWKH Manhattan Project to society.
153
4.3 4.4
4.5
Describe some medical and industrial applications of radioisotopes.
Dot Point 4.6
4.7 153
Describe the use of a named isotope in medicine, agriculture, and engineering.
154
Describe how neutron scattering is used as a probe by referring to the properties of neutrons.
155
Page
Identify ways by which physicists continue to develop their understanding of matter using accelerators as a probe to investigate the structure of matter.
155
Discuss the key features and components of the standard model RIPDWWHULQFOXGLQJTXDUNVDQGOHSWRQV
Answers to From Quanta to Quarks
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Dot Point HSC Physics
DOT POINT Space
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1
Space
1. The Earth has a gravitational field that exerts a force on objects both on it and around it.
'H¿QHZHLJKWDVWKHIRUFHDFWLQJRQDQREMHFWGXHWRDJUDYLWDWLRQDO¿HOG 1.1.1
Predict the weight of a 5 kg object on Earth compared to its weight on Jupiter, and explain the reasoning behind your prediction. The gravitational acceleration on Jupiter is about 24.8 m s–2.
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1.1.2
Complete the table to compare mass and weight. Mass
1.2
Weight
Use F = mg to determine the weight force of bodies on Earth and other planets. 1.2.1
Determine the weight of an object of mass 3.0 kg on Earth and on Mars which has a JUDYLWDWLRQDODFFHOHUDWLRQHTXDOWRWKDWRI(DUWK
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1.2.2
An object has a mass of 12 kg on Earth and a weight of 135.24 N on Saturn. Calculate the YDOXHRIWKHDFFHOHUDWLRQGXHWRJUDYLW\RQ6DWXUQDQGWKHREMHFW¶VZHLJKWRQ(DUWK
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1.2.3
A mass is placed on a set of bathroom scales on Earth and the scales read 10 kg. The same scales and the mass are taken to the Moon to show that the mass of an object is constant regardless of where it is in the Universe. When placed on the scales on the Moon however, the scales read 1.67 kg. Account for this reading.
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1.3
Predict the acceleration due to gravity on other planets. 1.3.1
The table shows masses and diameters of the Sun, our Moon and the planets in the Solar System.
(a)
Complete the fourth column of the table by ranking the gravitational force on each object from smallest (1) to largest (11) given the values for the Sun, the Earth and Pluto.
E
RPSOHWHWKH¿IWKFROXPQRIWKHWDEOHE\SUHGLFWLQJWKHUHODWLYHVL]HRIWKHJUDYLWDWLRQDOIRUFH & on each object given the three values for the Moon, Earth and the Sun. Object
Mass of object (kg)
Diameter of object (km)
Gravitational force (smallest (1) to largest (12))
Gravitational acceleration (m s–2 )
The Sun
1.99 × 1030
1 392 530
11
275.4
Mercury
23
4878
24
12 104
24
12 756
7
9.8
The Moon
7.35 × 1022
3467
Mars
6.43 × 1023
6794
27
142 984
26
120 000
Uranus
25
8.68 × 10
51 800
Neptune
1.03 × 1026
49 250
22
2320
Venus Earth
Jupiter Saturn
Pluto
3.58 × 10
4.90× 10
5.974 × 10
1.90 × 10 5.69 × 10
1.27 × 10
1.6
1
1.3.2
An object has a mass of 60 kg on Mars where the gravitational acceleration is 0.38 that of Earth.
(a)
What will be the mass of the object on Mars?
...............................................................................................................................................................................................................................
(b)
What will be the weight of the object on Earth?
...............................................................................................................................................................................................................................
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Space
(c)
What will be the weight of the object on Mars?
...............................................................................................................................................................................................................................
(d)
What will be the mass of the object on a planet where the acceleration due to gravity is 2.5 times larger than that on Earth?
...............................................................................................................................................................................................................................
(e)
What will be the weight of the object on this planet?
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1.4
Perform an experiment to determine the value of the acceleration due to gravity and identify reasons for possible variations from 9.8 m s–2. 1.4.1
Outline an experiment you have done to determine the acceleration due to gravity.
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1.4.2
(a)
A group of students set up a pendulum and recorded the measurements shown in the table.
Length of pendulum string (m)
Time for 20 swings (s)
0.25 0.50 0.75 1.00 1.25 1.50 2.00
20.0 28.2 38.6 40.0 44.9 49.9 56.5
Period of swing (s)
(Period of swing)2 (s2)
Identify two factors which would have been kept constant if this experiment had been done correctly.
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(b)
Complete the results table.
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(c)
What are these results telling us?
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(d)
Draw a graph of the period of swing (T) against the length of the pendulum (l).
(e)
What conclusion can we draw from this graph? Explain your answer.
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I
, QGUDZLQJ\RXUOLQHRIEHVW¿W\RXVKRXOGKDYHLJQRUHGRQHSORWSRLQW,GHQWLI\ZKLFKSORW point and explain why it should be ignored.
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J
7KHHTXDWLRQFRQQHFWLQJWKHYDULDEOHVIRUWKHVZLQJRIDSHQGXOXPLV
5HDUUDQJHWKLVHTXDWLRQWRPDNHµJ¶WKHVXEMHFW
T = 2π
l g
............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
K
VHWKHLQIRUPDWLRQLQ\RXUUHDUUDQJHGHTXDWLRQDQGWKHGDWDLQWKHUHVXOWVWDEOHWRGUDZD 8 graph which does show the relationship between the period of a pendulum and its length.
(i)
Use your graph to determine a value for the acceleration due to gravity as found by this experiment.
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1.4.3
Recall three reasons why the acceleration due to gravity at different places on the surface of the Earth varies slightly from the 9.8 m s–2 value we usually use.
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1.5
Explain that a change in gravitational potential energy is related to work done. 1.5.1
Explain the relationship between the work done on an object which changes its position in a JUDYLWDWLRQDO¿HOGDQGLWVJUDYLWDWLRQDOSRWHQWLDOHQHUJ\
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1.5.2
Identify the source of the work done when a satellite moves:
(a)
to a higher altitude orbit
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(b)
to a lower altitude orbit
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1.5.3
A satellite has 4000 J of work done on it. Does it move to a higher or lower altitude orbit? Explain your answer.
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1.5.4
+
A comet approaches the Sun and swings around it to travel back into the outer Solar System for years. The graphs show how the gravitational potential and kinetic energies of this comet change as it moves away from the Sun. Explain the shape of the two graphs.
KE
0 ............................................................................................................................................... ...............................................................................................................................................
Ep
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-
............................................................................................................................................... ...............................................................................................................................................................................................................................
H¿QHJUDYLWDWLRQDOSRWHQWLDOHQHUJ\DVWKHZRUNGRQHWRPRYHDQREMHFWIURP ' LQ¿QLW\WRDSRLQWLQDJUDYLWDWLRQDO¿HOG 1.6.1
Calculate the gravitational potential energy of a 2000 kg satellite which orbits the Earth at an altitude of 35 000 km. The radius of Earth is 6378 km.
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1.6.2
A satellite of mass 500 kg is boosted from an orbit of altitude 10 000 km to one of altitude 20 000 km. Given the diameter of Earth as 12 756 km, its mass as 5.97 × 1024 kg, calculate the change in the gravitational potential energy of the satellite.
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1.6.3
Explain, in terms of the principles of physics involved, why gravitational potential energy is a QHJDWLYHTXDQWLW\
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1.6.4
Satellite X has its orbit around Earth changed from an altitude of 10 000 km to an altitude of 20 000 km. Satellite Y has its orbit around Earth changed from an altitude of 20 000 km to an altitude of 30 000 km. Both satellites have a mass of 500 kg.
(a)
Predict the amount of work done on X compared to the amount done on Y and explain your reasoning.
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(b)
Calculate the amount of work done on each satellite to see if your prediction was correct.
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1.6.5 (a)
Three spacecraft having masses m1 > m2 > m3 are in the same stable orbit around planet X. Compare their gravitational potential energies and justify your answer.
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(b)
The three spacecraft are now moved to an orbit with twice the radius relative to the centre of the planet. Compare the work which needs to be done on each. Justify your answer.
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(c)
The three spacecraft each undergo orbital decay and fall to identical lower altitude orbits. Compare the changes in their kinetic energies. Justify your answer.
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2. Many factors have to be taken into account to achieve a successful rocket launch, to maintain a stable orbit and to return to Earth. 2.1
Describe the trajectory of an object undergoing projectile motion within the Earth’s JUDYLWDWLRQDO¿HOG 2.1.1
Outline the characteristics of the motion of a projectile.
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2.1.2
A projectile is launched at 40 m s–1 at 75º to the horizontal. Calculate the components of its launch velocity.
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2.2
Describe Galileo’s analysis of projectile motion. 2.2.1
/LVW*DOLOHR¶VWKUHH¿QGLQJVUHJDUGLQJSURMHFWLOHPRWLRQ
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2.2.2
The table shows the results of an experiment where a ball was rolled along a smooth, horizontal surface at 15 m s–1 and then over the edge of a 150 m drop. The ball left the surface and started to fall at time zero. Time (s)
Speed of ball (m s–1)
1
17.92
2
24.68
3
33.01
4
41.97
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'HPRQVWUDWHWKDWWKHVHUHVXOWVDUHFRQVLVWHQWZLWK*DOLOHR¶VDQDO\VLVRISURMHFWLOHPRWLRQ ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.3
Solve projectile motion problems using horizontal and vertical components and Newton’s equations of motion. 2.3.1
$SURMHFWLOHLV¿UHGKRUL]RQWDOO\DWPV–1 from the top of a 196 m high cliff. Calculate:
D
LWVWLPHRIÀLJKW
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(b)
its range
............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
(c)
its velocity on hitting the ground
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2.3.2
$SURMHFWLOHKDVDWLPHRIÀLJKWRIVDQGDUDQJHRIP&DOFXODWH
(a)
its horizontal velocity
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(b)
its maximum height
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(c)
the velocity with which it is projected
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2.3.3
FDQQRQEDOOLV¿UHGDWPV–1 at an angle of 45° to the horizontal. Calculate the height at $ which the ball hits a vertical cliff 150 m away.
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2.4
Explain the concept of escape velocity in terms of the gravitational constant, and the mass and radius of the planet. 2.4.1
.QRZLQJWKDWWKHZRUNGRQHRQDQREMHFWGLVSODFHGLQDJUDYLWDWLRQDO¿HOGLVHTXDOWRLWV FKDQJHLQJUDYLWDWLRQDOSRWHQWLDOHQHUJ\DQGWKDWWKLVDOVRHTXDOVLWVFKDQJHLQNLQHWLFHQHUJ\ show that escape velocity is independent of the mass of the object being put into orbit.
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2.4.2
The escape velocity of Earth is 11.2 kps. That for Neptune is 23.6 kps. Give possible reasons to account for this difference.
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2.4.3
Mercury has a mass of 3.58 × 1023 kg and a diameter of 4880 km. Venus has a mass of 4.92 × 1024 kg and a diameter of 12 104 km. Predict which has the greater escape velocity and explain your reasoning.
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2.5
Outline Newton’s concept of escape velocity. 2.5.1
2XWOLQH1HZWRQ¶VLGHDRIHVFDSHYHORFLW\
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2.6
Identify why the term ‘g-forces’ is used to explain the forces acting on an astronaut. 2.6.1
([SODLQWKHWZRPDLQUHDVRQVZHXVHDJIRUFHVFDOH
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2.6.2
A rocket is accelerating from the launch pad at 26.95 m s–2.
D
&DOFXODWHWKHJIRUFHRQDNJDVWURQDXW
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3UHGLFWWKHJIRUFHDFWLQJRQDQNJDVWURQDXW .................................................................................................. Science Press
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2.6.3
A rocket is accelerating from between Mars and Jupiter at 26.95 m s–2&DOFXODWHWKHJIRUFH on a 60 kg astronaut.
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HUIRUPD¿UVWKDQGLQYHVWLJDWLRQWRFDOFXODWHWKHLQLWLDODQG¿QDOYHORFLWLHVUDQJHDQGWLPHRI 3 ÀLJKWRIDSURMHFWLOH 2.7.1
The diagram shows a stroboscopic photograph of a projectile which was released from SRLQW3UROOHGGRZQWKHFXUYHGWUDFNDQGZDVSURMHFWHGLQWRWKHDLU7KHIUHTXHQF\RIWKH VWURERVFRSHZDV+]DQGHDFKJULGVTXDUHRQWKHGLDJUDPUHSUHVHQWVFPîFP
(a)
Calculate the horizontal component of the projectile as it left the track.
..................................................................................................................... ..................................................................................................................... 0
(b)
Calculate the vertical component of the projectile as it left the track.
..................................................................................................................... ..................................................................................................................... ..................................................................................................................... ..................................................................................................................... ..................................................................................................................... .....................................................................................................................
(c)
Calculate the velocity of the projectile as it left the track.
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(d)
Determine the maximum height of the projectile above the end of the track.
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H
,IWKHSURMHFWLOHKLWWKHÀRRUPEHORZWKHODVWSRVLWLRQVKRZQGHWHUPLQHLWVWLPHRIÀLJKW
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(f)
Calculate the range of the projectile.
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2.8
Analyse the changing acceleration of a rocket during launch in terms of the Law of Conservation of Momentum and the forces experienced by astronauts. 2.8.1
A rocket has a mass of 400 kg, 75% being fuel. It develops a thrust of 8000 N.
(a)
Calculate its initial acceleration.
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(b)
Calculate its acceleration when half its fuel has been consumed.
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F
DOFXODWHWKHJIRUFHRQDNJDVWURQDXWLQWKHURFNHWZKHQKDOIWKHIXHOKDVEHHQ & FRQVXPHG$VVXPHWKHURFNHWLVVWLOOZLWKLQ(DUWK¶VJUDYLWDWLRQDO¿HOG
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2.8.2
UDZDW\SLFDOJIRUFHJUDSKIRUDWZRVWDJHURFNHWDQGXVHLWWRH[SODLQZK\VWDJHGURFNHWV ' are used to put astronauts into space.
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2.8.3
([SODLQZK\WKHJIRUFHDFWLQJRQDQDVWURQDXWLQFUHDVHVDVDURFNHWWDNHVRII
............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.8.4
A rocket has a mass of 30 000 kg, including 25 000 kg of fuel. It develops 360 000 N of thrust. Calculate:
D
LWVDFFHOHUDWLRQDWOLIWRII
............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
(b)
the theoretical maximum acceleration of the rocket
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F
WKHJIRUFHH[SHULHQFHGE\DQDVWURQDXWXQGHUPD[LPXPDFFHOHUDWLRQFRQGLWLRQV
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2.8.5
Explain, in terms of the Law of Conservation of Momentum, how a rocket takes off.
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2.9
Discuss the effect of the Earth’s orbital and rotational motion on the launch of a rocket. 2.9.1
Recall the optimum position on Earth and orientation of a launch in order to place a satellite in orbit around the Earth.
............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.9.2
Justify your answer to 2.9.1 above.
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2.9.3
URFNHWLVWREHODXQFKHGWR0DUV([SODLQZLWKUHIHUHQFHWRWKH(DUWK¶VRUELWDOPRWLRQDURXQG $ WKH6XQDQGZLWKWKHDLGRIDGLDJUDPWKHFRQFHSWRIDµODXQFKZLQGRZ¶IRUWKLVURFNHW
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2.10 Analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting Earth. 2.10.1 Choose an object which undergoes uniform circular motion (do not choose a satellite in orbit). With the aid of a labelled diagram, describe the forces acting on this object. ....................................................................................................... ....................................................................................................... ....................................................................................................... ....................................................................................................... ....................................................................................................... ....................................................................................................... ....................................................................................................... ....................................................................................................... ....................................................................................................... .......................................................................................................
2.10.2 State the forces acting on a satellite in a stable orbit around Earth. ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.10.2 $QDVWURQDXWLQDFLUFXODURUELWDURXQG(DUWKIHHOVµZHLJKWOHVV¶$FFRXQWIRUWKLVIHHOLQJ ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.11 Solve problems to calculate the centripetal force acting on a satellite in orbit about Earth using:
2.11.1 A 3000 kg satellite is orbiting Earth at an altitude of 250 km. Its orbital speed is 27 800 kph. and the diameter of Earth is 12 756 km. Calculate: (a)
the centripetal force acting on it
............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
(b)
its centripetal acceleration
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2.11.2 A 150 kg satellite is orbiting Earth at an altitude of 272 km. Its orbital period is 90 minutes. Given that the diameter of Earth is 12576 km, and its mass is 5.974 × 1024 kg, calculate the centripetal force on the satellite. ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.12 Compare qualitatively, low Earth and geostationary orbits. 2.12.1 Recall a use for low Earth orbit and geostationary satellites. ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.12.2 Explain why each type of satellite is ideal for the use you have given in 2.12.1 above. ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.12.3 Complete the table to compare low Earth and geostationary satellites. Low Earth satellites
Geostationary satellites
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2.13 Outline the contribution of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O’Neill or von Braun. ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
' H¿QHRUELWDOYHORFLW\DQGWKHUHODWLRQVKLSEHWZHHQRUELWDOYHORFLW\WKHJUDYLWDWLRQDOFRQVWDQW the mass of the planet, the mass of the satellite and the radius of the orbit qualitatively and quantitatively. 2.14.1 'H¿QHRUELWDOYHORFLW\ ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.14.2 Imagine satellites orbiting Earth and Jupiter, both at altitudes of 2000 km. Compare their RUELWDOYHORFLWLHV TXDOLWDWLYHO\RQO\ DQGDFFRXQWIRUWKHGLIIHUHQFH ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.14.3 Three moons around planet X have masses M, 9 M and 16 M. D
, IDOOPRRQVDUHWKHVDPHGLVWDQFHIURPWKHSODQHW¶VFHQWUHFDOFXODWHWKHUDWLRRIWKHLURUELWDO speeds.
............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
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E
, IWKHGLVWDQFHVRIWKHVHPRRQVIURPWKHSODQHW¶VFHQWUHDUHR, 9 R and 16 R respectively, calculate the ratio of their orbital speeds.
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2.14.4 Three identical moons are in orbit around planets of masses M, 9 M and 16 M. The planets have the same radii. D
,IWKHPRRQVKDYHWKHVDPHRUELWDOVSHHGV¿QGWKHUDWLRRIWKHLURUELWDOUDGLL
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E
,IWKHRUELWDOUDGLLRIWKHPRRQVDUHWKHVDPH¿QGWKHUDWLRRIWKHLURUELWDOVSHHGV
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2.14.5 Calculate the orbital speed of the Earth around the Sun given the mass of the Sun is 1.99 × 1030 kg, and its diameter is 1 392 530 km. The mass of the Earth is 5.974 × 1024 kg, its diameter is 12 756 km, and the distance between the Sun and Earth is 150 000 000 km. ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
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2.15 Solve problems using Kepler’s Law of Periods:
2.15.1 Calculate the orbital period of Deimos, one of the two moons of Mars. Its average distance from Mars is 23 400 km and its irregular shape averages about 13 km across. The mass of Mars is 6.42 × 1023 kg, and its diameter is 6794 km. ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.15.2 Calculate the altitude of an Earth satellite with a period of 12 hours. The mass of the Earth is 5.974 × 1024 kg. ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.15.3 7 KHWDEOHJLYHVLQIRUPDWLRQDERXWIRXURIWKHPRRQVRIWKHSODQHW8UDQXV8VH.HSOHU¶V/DZ of Periods to calculate the missing data in the following table: Moon
Radius of orbit (km)
Miranda
A
Ariel Titania Oberon
Orbital period (Earth days) 1.41
190 900
B
C
8.71
583 400
13.46
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2.15.4 *HRVWDWLRQDU\VDWHOOLWHVRUELWZLWKDUDGLXVRINP8VHWKLVLQIRUPDWLRQWR¿QG (a)
the period of a satellite which orbits with a radius of 15 000 km
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(b)
the orbital radius of a satellite which has an orbital period of 4.0 hours
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2.15.5 Io, closest to the planet, Europa, Ganymede and Callisto, furthest from the planet, are the four moons of Jupiter discovered by Galileo in 1610. There is an interesting relationship between the orbital period (T RIWKH¿UVWWKUHHPRRQVHDFKEHLQJKDOIWKDWRIWKHQH[WPRRQIXUWKHU from the planet. In other words: TIo
=
0.5 × TEuropa
TEuropa
=
0.5 × TGanymede
Given the mass of Jupiter as 1.90 × 1027 kg and the orbital radius of Ganymede as 1.1 × 106 km, calculate: (a)
the orbital radius of Io
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E
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2.16 Account for the orbital decay of satellites in LEO. 2.16.1 Explain, in terms of the principle of physics involved why satellites in low Earth orbits will eventually fall to Earth. ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.16.2 Two students are discussing orbital decay. Maria says that frictional forces between the spacecraft and the atmosphere are responsible. Edward says that this is incorrect and that WKHUHDOUHDVRQLVWKDWJUDYLWDWLRQDOIRUFHVSXOOWKHVSDFHFUDIWGRZQ(YDOXDWHWKHVWXGHQWV¶ statements. ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.17 Discuss issues associated with safe re-entry into the Earth’s atmosphere and landing on the Earth’s surface. 2.17.1 6XPPDULVHKRZKHDWEXLOGXSZDVLVPLQLPLVHGLQVSDFHFUDIWUHHQWU\ D
LQWKHHDUO\GD\VRIVSDFHÀLJKW
............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
(b)
on the space shuttle
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2.17.2 Explain the concept of VDFUL¿FLDOOD\HUVRQUHHQWU\VSDFHFUDIW ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.17.3 ,GHQWLI\DQGMXVWLI\WKHGLUHFWLRQDVWURQDXWVVKRXOGIDFHGXULQJWDNHRIIDQGUHHQWU\ ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.18 Identify that there is an optimum angle for re-entry of a spacecraft into the Earth’s atmosphere and the consequences of failing to achieve this. 2.18.1 5 HFDOOWKHUDQJHRIWKHVDIHUHHQWU\DQJOHIRUWKH$SROORPLVVLRQUHHQWU\FUDIWUHHQWHULQJ (DUWK¶VDWPRVSKHUH ...............................................................................................................................................................................................................................
2.18.2 ,GHQWLI\WKHFRQVHTXHQFHVRIIDLOLQJWRDFKLHYHDUHHQWU\DQJOHZLWKLQWKLVUDQJH ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
2.18.3 7 KHUHHQWU\DQJOHYDULHVIRUGLIIHUHQWUHHQWU\FUDIW3UHGLFWWKHWZRPDLQSURSHUWLHVRIWKH UHHQWU\FUDIWZKLFKGHWHUPLQHVLW ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ............................................................................................................................................................................................................................... ...............................................................................................................................................................................................................................
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3. The Solar System is held together by gravity.
'HVFULEHDJUDYLWDWLRQDO¿HOGQHDUDPDVVLYHREMHFWLQWHUPVRILWVHIIHFWVRQRWKHUPDVVHV 3.1.1
'H¿QHLQJHQHUDOWKHFRQFHSWRIµD¿HOG¶LQSK\VLFV
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3.1.2
'H¿QHWKHFRQFHSWRIDJUDYLWDWLRQDO¿HOG
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'H¿QH1HZWRQ¶V/DZRI8QLYHUVDO*UDYLWDWLRQ 3.2.1
1HZWRQ¶V/DZRI8QLYHUVDO*UDYLWDWLRQLVPDGHXSRIWKUHHVWDWHPHQWV5HFDOOWKHP
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3.2.2
HWHUPLQHWKHXQLWVRI1HZWRQ¶VXQLYHUVDOJUDYLWDWLRQDOFRQVWDQWDQGXVHNQRZQYDOXHVWR ' calculate its magnitude.
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3.3
Solve problems and analyse information using:
3.3.1
Calculate the gravitational force between the Moon and the Earth. The mass of the Moon is 7.35 × 1022 kg, that of the Earth is 5.974 × 1024 kg, the diameter of the Moon is 3467 km, that of the Earth is 12 756 km and the distance between them is about 406 676 km.
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3.3.2
The mass of Jupiter is 1.9 × 1027 kg. Its diameter is 142 984 km. Calculate:
(a)
the weight of a 10 kg object on its surface
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(b)
the value of its acceleration due to gravity at its surface
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3.3.3
The radius of the Earth is 6378 km and its mass is 5.974 × 1024 kg. Calculate the acceleration at an altitude of 15 000 m.
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3.3.4
Two moons have masses M and 4 M and radii R and 4 R respectively. Compare their accelerations due to gravity.
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3.3.5
The mass of Mercury is 3.58 × 1023 kg. Its diameter is 4880 km. Compare its gravitational acceleration with that of Pluto, mass 1.27 × 1022 kg, diameter 2320 km.
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3.3.6
Calculate the gravitational force between two 60 kg students two metres apart.
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3.4
Discuss factors affecting the strength of the gravitational force. 3.4.1
Predict the effect on the gravitational force between two objects of:
(a)
halving the distance between them ................................................................................................................................
(b)
doubling both masses
(c)
doubling one mass and halving the distance between them
............................................................................................................................................................
...............................................................................................................................................................................................................................
3.4.2
Calculate how far an astronaut would need to be away above the Earth in order for his weight WREHKLVZHLJKWRQWKH(DUWK¶VVXUIDFH
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3.4.3 (a)
An astronaut is in a satellite orbiting the Earth at an altitude of one Earth radius. What is the gravitational force acting on him compared to his weight on the surface of the Earth? Justify your answer.
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(b)
The satellite is boosted to double this altitude. What is the new gravitational force acting on the astronaut?
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(c)
Calculate the orbital velocity of the astronaut in this higher orbit.
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3.5
Discuss the importance of Newton’s Law of Universal Gravitation in understanding and calculating the motion of satellites. 3.5.1
Given that the gravitational force holding an orbiting satellite in a stable orbit is also the centripetal force acting on it due to its orbital speed, determine the relationship between the orbital speed and the mass of the satellite.
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3.5.2
A satellite has an orbital period of T and an orbital radius of R8VLQJWKHHTXDWLRQ\RX GHULYHGLQWKHODVWTXHVWLRQDQGWKHIRUPXODIRUWKHDYHUDJHYHORFLW\RIDQREMHFWIURP m2 > m3VLQFHIURPWKHHTXDWLRQJUDYLWDWLRQDOSRWHQWLDOHQHUJ\LVGLUHFWO\ proportional to the masses of the objects.
(b)
The work needed to put the three spacecraft into a higher, identical orbit is directly proportional to their masses also (W = Fs = mgs. Note that g is the value of the acceleration due to gravity of planet X at the altitude of the orbit). This makes the work done on m1 > m2 > m3.
(c)
As the objects fall to a lower orbit they lose gravitational potential energy and gain kinetic energy. If they all end up at the same altitude, then the loss of EP and gain in KE for each will be the same, but EP loss will depends on their masses, so KE gain will also. Therefore, KE of m1 > m2 > m3.
2.1.1
Horizontal component of its motion is constant velocity (zero acceleration), while the vertical component is accelerated by gravity.
2.1.2
Horizontal component is 10.35 m s–1, vertical component is 38.64 m s–1.
2.2.1
Horizontal and vertical components of the motion of a projectile are independent of each other. Horizontal component of its motion is constant velocity (zero acceleration). Vertical component is constantly accelerated (by gravity).
2.2.2
Using Pythagoras, at t = 1, so therefore
17.92 = vector sum of vy + 15 vy2 = 17.922 – 152 vy = 9.8 m s–1
at t = 2, so therefore
24.68 = vector sum of vy + 15 vy2 = 24.682 – 152 vy = 19.6 m s–1
at t = 3, so therefore
33.01 = vector sum of vy + 15 vy2 = 33.012 – 152 vy = 29.4 m s–1
at t = 4, so therefore
41.97 = vector sum of vy + 15 vy2 = 41.972 – 152 vy = 39.2 m s–1
So, change in velocity each second = 9.8 m s–1, so acceleration is constant at 9.8 m s–2ZKLFKLVFRQVLVWHQWZLWK*DOLOHR¶VDQDO\VLV 2.3.1
2.3.2
(a)
6.32 s
(b)
948.7 m
(c)
162 m s–1 at 22.5º down from the horizontal
(a)
160 m s–1
(b)
68.9 m
(c)
up at 164.2 m s–1 at 12.9º to the horizontal
2.3.3
115.5 m
2.4.1
Given EP = Gm1m2/r = ½m1v2 (m2 = mass planet, m1 = mass satellite) v2 = 2Gm1m2/m1r i.e. v ¥Gm2/r i.e. escape velocity is independent of the mass of the satellite.
2.4.2
Either the mass of Neptune is larger than the mass of Earth, or its radius is smaller, or the combination mass/radius is larger for Neptune than for Earth.
2.4.3
For Mercury, mass/radius = 1.475 × 1020, for Venus this ratio is 8.13 × 1020, therefore this would indicate escape velocity for 9HQXVLVKLJKHUWKDQHVFDSHYHORFLW\RI0HUFXU\ )URPWKHHTXDWLRQHVFDSHYHORFLWLHVIRU0HUFXU\LVPV–1, for Venus it is 10 393 m s–1.)
2.5.1
1 HZWRQDUJXHGWKDWWKHIDVWHUDSURMHFWLOHZDV¿UHGWKHIXUWKHULWZRXOGJRDQGWKDWWKHUHZRXOGHYHQWXDOO\EHDVSHHGZKLFK ZRXOGFDXVHLWWRRUELWWKH(DUWKUDWKHUWKDQIDOOLQJEDFNWRWKHJURXQG+HIXUWKHUUHDVRQHGWKDWLILWZDV¿UHGIDVWHUWKDQWKLV YDOXHLWZRXOGHVFDSH(DUWK¶VJUDYLWDWLRQDO¿HOG
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2.6.1
It is simpler to use than an absolute force scale, and communicates the same relative forces acting on astronauts of different masses.
2.6.2
(a)
3.75
(b)
3.75
2.6.3
2.75
2.7.1
(a)
0.625 m s–1
(b)
2.352 m s–1
(c)
2.43 m s–1 at 75.1º up from horizontal
(d)
0.28 m
(e)
0.84 s
(f)
0.525 m
(a)
10.2 m s–2
(b)
22.2 m s–2
(c)
3.265
2.8.1
2.8.2
6WDJHGURFNHWVDUHXVHGIRUWZRUHDVRQV±¿UVWO\LWHQDEOHVWKHH[WUDPDVVRIHPSW\IXHOWDQNVDQGKXJHURFNHWHQJLQHVWREH discarded, lessening the mass for the second stage engines and so making their thrust more effective and it also reduces the PD[LPXPJIRUFHH[SHULHQFHGE\DVWURQDXWV 4
3 g-force 2
1
0 0
t
Time after lift-off
2.8.3
As fuel is used the mass of the rocket decreases and because the thrust is constant, the force on the rocket stays the same, so the acceleration (as per F = ma) must increase.
2.8.4
(a)
2.2 m s–2
(b)
62.2 m s–2
(c)
7.35
2.8.5
KHPRPHQWXPRIWKHH[KDXVWJDVHV GRZQZDUGV SURYLGHVDQHTXDOEXWXSZDUGVLPSXOVHRQWKHURFNHW7KLVLVWKHWKUXVW 7 which causes the upwards acceleration of the rocket.
2.9.1
)URPWKHHTXDWRUWRZDUGVWKHHDVW
2.9.2
RZDUGVWKHHDVWVRWKDWWKHURFNHWWDNHVDGYDQWDJHRIWKHGLUHFWLRQRIWKH(DUWK¶VURWDWLRQDOPRWLRQDERXWLWVD[LV NSK 7 DQGVDYHVRQIXHOZKLFKZRXOGRWKHUZLVHEHQHHGHGWRJDLQWKLVLQLWLDOVSHHG$WWKHHTXDWRUEHFDXVHLWLVKHUHWKDWWKH(DUWK¶V rotational speed is greatest.
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2.9.3
If the rocket is launched too early, or in the wrong direction, it will reach its destination before Mars gets to the same position. If launched too late, Mars will have passed the intercept point before the rocket gets there.
0OSITIONOF-ARSATLAUNCH ,AUNCHLATE -ARSGONE 0OSITIONOF%ARTHATLAUNCH
0OSITIONOF-ARSAFTERFLIGHT ,AUNCHEARLY -ARSNOTTHERE
2.10.1
For example: An electron in orbit about a nucleus is moving with uniform circular motion. The centripetal force is provided by the electrostatic force of attraction between the positive charge on the protons in the nucleus and the negative charge on the electrons. .EGATIVEELECTRON #ENTRIPETALFORCE ELECTROSTATICATTRACTION
0OSITIVENUCLEUS
#IRCULARORBIT
2.10.2
Gravitational attraction towards the Earth (= centripetal force).
2.10.2
7 KHDVWURQDXWLVLQµIUHHIDOO¶±WKDWLVKHVKHLVIDOOLQJWRZDUGVWKH(DUWKXQGHUWKHLQÀXHQFHRIJUDYLW\%HFDXVHWKHUHLVQR UHDFWLRQIRUFHRQWKHDVWURQDXWKHVKHIHHOVµZHLJKWOHVV¶±KHVKHGRHVQRWQRWLFHWKHJUDYLWDWLRQDOIRUFH
2.11.1
(a)
26 991.3 N towards the centre of the Earth
(b)
8.98 m s–2 towards the centre of the Earth
2.11.2
1350.8 N towards the centre of the Earth
2.12.1
LEO – spy satellites, geostationary – communications
2.12.2
LEO satellites cover the entire surface of the Earth at least once per day and, being much lower, can see more detail in the things they observe (reading car number plates, identifying faces, seeing a golf ball on a golf green). They are therefore useful for spy activities.
*HRVWDWLRQDU\VDWHOOLWHVFRYHUDPXFKODUJHUSURSRUWLRQRIWKH(DUWK¶VVXUIDFHDQGGRQRWKDYHWREHµWUDFNHG¶VRDUH HFRQRPLFDOIRUERXQFLQJFRPPXQLFDWLRQVVLJQDOVDURXQGWKH(DUWK7KHFDQDOVRµVHH¶ORQJGLVWDQFHZHDWKHUSDWWHUQVDQGDUH therefore able to be used to predict weather in other places.
2.12.3 Low Earth satellites
2.13
Geostationary satellites
Altitude 250 - 1000 km
Altitude 35 800 km
Period 90 minutes to 4 or 5 hours
Period 23 hours 65 min 4 sec
Usually polar orbit
Equatorial orbit
Not fixed relative to Earth’s surface
Stay over same position on Earth’s surface
Used for spying
Used for communications and weather forecasting
Answers will vary according to the scientist chosen – check your text for details.
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Space
2.14.1
UELWDOYHORFLW\LVDPHDVXUHRIWKHVSHHGDWZKLFKDVDWHOOLWHPRYHVDURXQGLWVSULPDU\ $µSULPDU\¶LVWKHKHDYHQO\REMHFWD 2 SODQHWRUELWV±HJ7KH6XQLV(DUWK¶VSULPDU\
2.14.2
The orbital speed of the satellite around Jupiter would have to be greater than that of the satellite around Earth if both are to be in stable orbits because the gravitational pull of Jupiter is greater than that of Earth.
2.14.3
(a)
1 : 1 : 1 (orbital speed is independent of the mass of the satellite)
(b)
12 : 4 : 3
(a)
1 : 9 : 16
(b)
1:3:4
2.14.4
2.14.5
2.968 m s–1 = 106 839 kph
2.15.1
133240.6 s = 37 hours
2.15.2
20 229.2 km
2.15.3
A = 129 643 km B = 2.51 days C = 436 464 km
2.15.4
2.15.5
(a)
5.075 hours
(b)
12 798.6 km
(a)
4.37 × 105 km
(b)
17 009 m s–1 = 4750 kph
2.16.1
Friction between the satellite and the atmosphere reduces the speed of the satellite, so gravitational forces can attract it closer to Earth where the denser atmosphere will provide greater frictional forces which will slow it even more and allow gravity to pull it even closer to Earth, and so on.
2.16.2
Both students are correct in that each factor contributes to orbital decay, but both are incorrect in assuming that their factor is the only one involved. Both frictional forces to slow the craft and gravity are needed before orbital decay can occur. Without the slowing of the craft due to friction, gravity will simply keep it in a stable orbit, and without gravity, the craft would not be pulled to Earth.
2.17.1
(a)
Because air is one of the best heat insulators, the most effective heat protection is the cushion of air that builds up in IURQWRIWKHEOXQWQRVHRUEHOO\RIWKHUHHQWU\FUDIW2WKHUVWUDWHJLHVXVHGWRPLQLPLVHKHDWEXLOGXSLQVLGHUHHQWU\ FDSVXOHVKDYHLQFOXGHGVDFUL¿FLDOVNLQVLQLWLDOO\PHWDODOOR\VWKHQPRUHHI¿FLHQW¿EUHJODVVRUKHDWUHVLVWDQWFHUDPLFV that absorb much of the heat energy as they vaporise.
E
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2.17.2
DFUL¿FLDOOD\HUVDUHOD\HUVRIPHWDODOOR\VDQG¿EUHJODVVDQGKHDWUHVLVWDQWFHUDPLFVWKDWDEVRUEVRPHKHDWDVVRFLDWHGZLWK 6 UHHQWU\IULFWLRQDVWKH\PHOWDQGYDSRULVH,QWKLVZD\WKLVKHDWLVQRWFRQGXFWHGWKURXJKDQGLQWRWKHUHHQWU\FDSVXOH
2.17.3
LYHQWKHVPDOOJIRUFHVLQYROYHGLQPRGHUQVSDFHFUDIWLWUHDOO\GRHVQ¶WPDWWHUEXWWRJLYHPD[LPXPVSLQDOVXSSRUWDQG * VXSSRUWIRUVRIWIDFLDOWLVVXHVHVSHFLDOO\H\HVDVWURQDXWVVKRXOGIDFHIRUZDUGVGXULQJWDNHRII LQHUWLDOIRUFHVSXVKWKHP EDFNZDUGVLQWRWKHLUFRQWRXUHGVHDWV DQGEDFNZDUGVGXULQJUHHQWU\IRUWKHVDPHUHDVRQ
2.18.1
2.18.2
7RRVKDOORZDQGWKHFUDIWZLOOµVNLSRII¶EDFNLQWRVSDFH WRRGHHSDQGWKHIRUFHVDQGKHDWLQYROYHGZLOOEHWRRODUJHIRU survival of the astronauts or the craft.
2.18.3
7KHVSHHGVRIUHHQWU\DQGWKHVKDSHRIWKHFUDIW
3.1.1
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3.1.2
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3.2.1
Every object in the Universe attracts every other object with a gravitational force. The force is directly proportional to the masses of the objects. 7KHIRUFHLVLQYHUVHO\SURSRUWLRQDOWRWKHVTXDUHRIWKHGLVWDQFHEHWZHHQWKHP
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3.2.2
Units for G are N m2 kg–2 or kg–1 m3 s–2. Using weight force = mg = GMm/r2 We get G = gr2/M, and substituting values for the mass of Earth and its radius, and 9.8 for g, we get 6.673 × 10–11.
3.3.1
1.702 × 1020 N
3.3.2
(a)
247.95 N
(b)
24.795 m s–2
3.3.3
9.75 m s–2
3.3.4
gM : g4M = 4 : 1
3.3.5
gM : gP = 4.01 : 0.63 = 6.37 : 1
3.3.6
6 × 10–8 N attraction
3.4.1
(a)
multiplies the force by 4
(b)
multiplies the force by 4
(c)
multiplies the force by 8
3.4.2
1.93 × 105 km
3.4.3
D
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(b)
0.11 times his surface weight force.
(c)
If you do this calculation using weight force = centripetal force, you should get 4564 m s–1 which is 1268 kph.
,I\RXXVHWKHRUELWDOYHORFLW\HTXDWLRQ\RXZLOOJHWPV–1 which is 1215 kph.
The difference can be accounted for in rounding off errors and approximations of values used. 3.5.1 3.5.2
3.6.1
% \HTXDWLQJWKHWZRHTXDWLRQVDQGUHDUUDQJLQJWKHP\RXVKRXOGVKRZWKDWRUELWDOVSHHGLVLQGHSHQGHQWRIWKHPDVVRIWKH satellite. GM 2πR From v = = we get R T GM 4π 2 R 2 = v2 = R T2 R 3 GM Which, on rearranging, gives 2 = 2 4π T $ VDVSDFHFUDIWDSSURDFKHVDQGJRHVFORVHWRDSODQHWDQRQFRQWDFWHODVWLFFROOLVLRQRFFXUVZKLFKUHVXOWVLQWKHWUDQVIHURI rotational kinetic energy from the planet to linear kinetic energy of the spacecraft.
3.6.2
Gravitational forces draw the spacecraft close enough to the planet so that the slingshot collision can occur, but gravitational forces are not responsible for the increase in speed that results. Gravitational forces which increase the speed of the spacecraft as it approaches the planet (and decrease its speed for a shorter time as it recedes from the planet) do contribute to a small amount of speed increase, but this is in addition to the slingshot effect.
4.1.1
List the properties of the aether as predicted by scientists in the 1800s, and justify their perception of the need for each property. Property of the aether
4.2.1
Justification
Fill space
Light travelled everywhere.
Be transparent
We cannot see it.
Permeate all matter
Light travels everywhere.
Have an extremely low density
It cannot be detected.
Have great elasticity
Transfer of energy over long distances requires the medium transmitting the wave to be highly elastic otherwise significant amounts of energy will be ‘lost’ to the particles of the medium.
7 KH\VHWXSWKHLUDSSDUDWXVRQDODUJHKHDY\URFNZKLFKWKH\ÀRDWHGRQPHUFXU\7KHODUJHURFNZDVDQDWWHPSWWRHOLPLQDWH vibrations from external sources as these would blur the light pattern results. Floating the apparatus on mercury enabled them to rotate it to try to detect the expected interference patterns from different directions. The interferometer used by Michelson DQG0RUOH\UHÀHFWHGOLJKWIURPDFRPPRQVRXUFHLQWZRGLUHFWLRQVDQGWKHQEDFNWRDQREVHUYDWLRQSRLQW,IWKHDHWKHU existed, then the light rays travelling with and against the aether should interfere with each other more than the rays travelling DWULJKWDQJOHVWRWKHDHWKHU¶VPRWLRQ
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4.2.2
They were looking for a difference in the speed of light relative to the Earth depending on the direction of its travel through the aether.
4.2.3
If the aether existed, then the light rays travelling with the aether and against the Earth should interfere with each other more WKDQWKHUD\VWUDYHOOLQJDWULJKWDQJOHVWRWKH(DUWK¶VPRWLRQ
4.2.4
, WZDVWKRURXJKZLGHO\DFFHSWHGDQGZKLOHQRWGLVSURYLQJWKHH[LVWHQFHRIWKHDHWKHUFKDQJHGWKHGLUHFWLRQWKDWVFLHQWL¿F WKRXJKWKDGEHHQERJJHGGRZQLQIRU\HDUVDQGVWDUWHGVFLHQWLVWVORRNLQJDWDOWHUQDWHLGHDVIRUWKH¿UVWWLPHLQDJHV
4.3.1
Nothing – only predicted properties.
4.3.2
7KH\DFKLHYHGDQXOOUHVXOW±WKDWLVWKH\GLGQRW¿QGDQ\LQWHUIHUHQFHSDWWHUQV
4.3.3
No conclusion could be drawn as no results were obtained.
4.4.1
Many accepted the experimental null result as evidence that the aether did not exist, others still search for the aether, blaming WKHQXOOUHVXOWRQHTXLSPHQWWKDWZDVQRWDFFXUDWHHQRXJK
4.5.1
A frame of reference that is not accelerating is known as an inertial frame of reference. A spaceship at constant velocity in deep space would be an inertial frame of reference. Motion cannot be detected in an inertial frame of reference. Motion is GHWHFWDEOHLQDQRQLQHUWLDOIUDPHRIUHIHUHQFH±RQHZKLFKLVDFFHOHUDWLQJIRUH[DPSOHDSODQHWDNLQJRII
4.5.2
(a)
Craft was no longer an inertial frame of reference. Craft was accelerating in the opposite direction to the angle of hang.
(b)
Inertial frame of reference. If the craft was accelerating, inertial forces would be noticeable (the mascot would not hang vertically down).
4.5.3
1RQLQHUWLDO±PRWLRQLVREYLRXVEHFDXVHRIWKHLQHUWLDOIRUFHVDFWLQJRQWKHPDVFRWDQGFDXVLQJLWWRKDQJDWDQDQJOH
4.6.1
Answers will vary – check with your teacher if unsure.
4.6.2
7KHUHDUHQRLQHUWLDOIRUFHVDFWLQJLQDQLQHUWLDOIUDPHRIUHIHUHQFH WKHUHFDQEHQRQLQHUWLDOIUDPHVRIUHIHUHQFHwithin the inertial frame of reference, but we are not talking about these here), so there will be no effects by which movement of the frame of reference can be judged.
4.7.1
$OOPRWLRQLVUHODWLYHEXWFRQVWDQWPRWLRQFDQQRWEHGHWHFWHGZLWKRXWUHIHUHQFHWRD¿[HGSRVLWLRQRXWVLGHWKHIUDPHRI reference. Motion may appear different from different frames of reference.
4.8.1
If the aether permeated all matter, then measurements of the speed of light made from an object moving with constant velocity would give different values, depending on which way the object was moving relative to the aether. These measurements would enable the observer to determine that they were in an inertial frame of reference. This would violate the principle of relativity.
4.9.1
Einstein wondered: ‘Suppose I am sitting in a train travelling at the speed of light. If I hold a mirror in front of me, will I see P\UHÀHFWLRQ"¶7KHUHDUHWZRSRVVLELOLWLHV
R,IWKHWUDLQLVWUDYHOOLQJDWWKHVSHHGRIOLJKWOLJKWIURPKLVIDFHZRXOGQRWUHDFKWKHPLUURULQRUGHUWREHUHÀHFWHGEDFN 1 %\QRWEHLQJDEOHWRVHHKLVUHÀHFWLRQKHZRXOGNQRZWKDWWKHWUDLQZDVWUDYHOOLQJDWWKHVSHHGRIOLJKWZLWKRXWKDYLQJWRUHIHU to an outside point. This violates the principle of relativity. Yes. This means that light would travel at its normal speed relative to the train. This does not violate the principle of relativity. However, it also means that, relative to a stationary observer outside the train, light would have to travel at twice its usual speed!
4.9.2
Einstein concluded that, if we accept that the principle of relativity can never be violated, then: 1.
The aether model must be wrong.
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3.
The speed of light is constant regardless of the motion of the observer.
4.10.1
The length of an object and the time taken to do something depends on the motion of the observer. Length and time can no ORQJHUEHUHJDUGHGDVVHSDUDWHFRQFHSWV,QRUGHUWRGH¿QHDQREMHFW¶VSRVLWLRQZHPXVWFRQVLGHUfourFRRUGLQDWHVLQWKHVSDFH time continuum – three dimensions of space and time.
4.11.1
:LWKWKHUHDOLVDWLRQWKDWWKHOHQJWKRIDQREMHFWFKDQJHVDVLWVVSHHGFKDQJHVDQHZXQFKDQJLQJGH¿QLWLRQZDVQHHGHG
4.12.1
LWKWKHWHFKQRORJ\RIDWRPLFFORFNVDEOHWRNHHSWLPHWRDQXQSUHFHGHQWHGDFFXUDF\RQHFORFNÀRZQDURXQGWKHZRUOGZDV : found to record less time passing than an identical clock kept stationary at the airport.
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4.12.2
Answers will vary – you may support the statement as long as you give supporting evidence, or you may disagree, but must RIIHUWKHVDPHHYLGHQFH)RUH[DPSOHGH%URJOLH¶VLGHDDERXWPRYLQJPDWWHUSDUWLFOHVKDYLQJDZDYHOHQJWKKDGQRVXSSRUWLQJ HYLGHQFHEXWLWVWLPXODWHGRWKHUVFLHQWLVWVWRWKLQNDERXWWKHFRQFHSWDQGHYHQWXDOO\ZDVSURYHQWUXHDQGOHGWRVLJQL¿FDQW DGYDQFHVLQLGHDVDERXWWKHVWUXFWXUHRIPDWWHU,QDVLPLODUZD\(LQVWHLQ¶VLGHDVLQLWLDOO\KDGQRVXSSRUWLQJH[SHULPHQWDO evidence, but because of the strength of the mathematics describing them were accepted and eventually proven correct as technology advanced to catch up with them. In addition, the existence of a theory will provide a direction for further VFLHQWL¿FVWXG\DQGIRFXVVFLHQWL¿FZRUN±LWZLOOJLYHGLUHFWLRQWRZKDWVFLHQWLVWVGRDQGWKHUHIRUHZLOOEHYDOXDEOHZKHWKHU experimental evidence for it exists or not.
4.13.1
µ6LPXOWDQHLW\¶UHIHUVWRRXULGHDWKDWGLIIHUHQWWKLQJVKDSSHQDWWKHVDPHWLPH(LQVWHLQ¶VUHODWLYLW\FRPSOLFDWHVWKLVVLPSOH idea. At speeds approaching that of light, events that are simultaneous in one frame of reference, may not be simultaneous in another frame of reference.
4.13.2
An astronomer sees two supernova explosions appear in his telescope at exactly the same time. However, when he checks his VWDUFKDUWVKH¿QGVWKDWRQHVWDUZDVWHQWLPHVWKHGLVWDQFHIURP(DUWKRIWKHRWKHU7KHPRUHGLVWDQWVWDUPXVWKDYHH[SORGHG a long time before the closer one.
4.14
(LQVWHLQ¶V WKHRUHWLFDO H[SODQDWLRQRIWKLVLVWKDWZKHQDQREMHFWLVPRYLQJ DWDQ\VSHHG WKHHQHUJ\XVHGWRDFFHOHUDWHWKH mass also changes its mass. At high speeds, while the energy still changes the mass of the object, not all of it results in an increase in speed. He put forward a new concept for the energy of an object: E = KE + m0c2
4.15.1
Rest mass is the mass of an object when it is at rest.
4.15.2
Because the mass of an object increases as its speed increases.
4.15.3
1.506 × 10–10 J
4.15.4
(a)
The mass changes in normal chemical reactions are so small that they are not detected by any instruments normally used. If we consider mass and energy to be independent substances then both conservation laws would be broken by (LQVWHLQ¶VSURSRVDO E = mc2). Because the amounts of mass involved are so small however, we do not detect any change and therefore do not consider either law broken.
E
*LYHQWKHHTXLYDOHQFHRIPDVVDQGHQHUJ\LWLVRQO\E\FRQVLGHULQJWKHPERWKDWWKHVDPHWLPHWKDWDVHQVLEOH conservation law can be considered.
(c)
In an endothermic process, energy put into the system would be converted into mass. In an exothermic process, mass is converted into energy and this is the source of the energy released.
4.16
7 KHPDVVRIDQREMHFWLVDIIHFWHGLILWLVPRYLQJ$WDOOVSHHGVPDVVLQFUHDVHVDFFRUGLQJWR(LQVWHLQ¶VUHODWLYLVWLFPDVV HTXDWLRQ6RPDVVFDQQRWEHUHJDUGHGDVDIXQGDPHQWDOTXDQWLW\±LWFKDQJHVDFFRUGLQJWRWKHVSHHGRIWKHREMHFW
4.17.1
9.214 × 10–31 kg
4.17.2
2.788 × 10–27 kg
4.18
Moving objects always appear to be shorter when measured from a different frame of reference. To generalise, observers from outside a moving system will always see the system as shorter than its real length. This effect is known as length contraction. 6ROHQJWKFDQQRWEHUHJDUGHGDVDIXQGDPHQWDOTXDQWLW\±LWFKDQJHVDFFRUGLQJWRWKHIUDPHRIUHIHUHQFHRIWKHREVHUYHU
4.19.1
120 m
4.19.2
0.8 c
4.19.3
The spaceship will appear to be 12 m wide but will retain its 20 m height and thickness because there in no relative motion in those two directions.
4.20
Time in a moving frame of reference always passes more slowly than time in any other frame of reference. This effect LVNQRZQDVWLPHGLODWLRQ6RWLPHFDQQRWEHUHJDUGHGDVDIXQGDPHQWDOTXDQWLW\±LWFKDQJHVDFFRUGLQJWRWKHIUDPHRI reference of the observer.
4.21.1
11.5 hours
4.21.2
(a)
5.0 s
(b)
5.0 s
(c)
Because both the pilot and the girlfriend are in inertial frames of reference, special relativity works for the REVHUYDWLRQVWKH\HDFKPDNH%RWKZLOOVHHWLPHUXQQLQJPRUHVORZO\LQWKHRWKHU¶VIUDPHRIUHIHUHQFHVRWKH\ZLOO both think a longer time has passed in their frame of reference.
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4.21.3
0.99 c
4.21.4
Star X is 8.0 ly from Earth. A spaceship travels at 0.5 c to reach the star.
4.22
(a)
16 years
(b)
13.86 years
(c)
6.93 ly
(d)
0.5 c
Note 7KHDQVZHUJLYHQLVLQPXFKPRUHGHWDLOWKDQQHHGHGWRJLYH\RXDEURDGSHUVSHFWLYHRIWKHFRQVHTXHQFHV The nearest galaxy to us, Andromeda galaxy, is about 2 million light years away. If we could travel at the speed of light it would take us 2 million years to get there. The fastest any space probe has gone is about 150 000 kph following a slingshot around the Sun. This would involve temperatures humans could not survive. The fastest space probes following slingshots around Mars, Jupiter and Saturn have travelled at about 100 000 kph. At this speed it would take us about 21 600 000 000 years to get to Andromeda.
EYLRXVO\LIZHFRXOGDFKLHYHIDVWHUVSHHGVWKHWLPHGLODWLRQDQGOHQJWKFRQWUDFWLRQHIIHFWVPHDQWKHUHZRXOGQ¶WEHDVIDUWR 2 travel, and it would take less time to get there than we think – well, less time as far as the astronauts are concerned, but still a long time from an Earth perspective. Unfortunately, while the time and length contractions work in our favour, relativistic mass increases mean that we would need DQLQ¿QLWHDPRXQWRIIXHOWRSURGXFHDQLQ¿QLWHO\ODUJHIRUFHWRDFFHOHUDWHRXUVSDFHFUDIWZKLFKLVDSSURDFKLQJDQLQ¿QLWH mass as it approaches the speed of light. None of this is possible. So, with current technology, space travel outside the Solar System is not feasible. Within the Solar System, where distances are much smaller (say 5900 000 000 km to Pluto – the furthest planet), travelling at 100 000 kph would take us 6.7351598 years. The time dilation effect would make this seem like 6.7351597 years – a saving RIDERXWVHFRQGV6RFRQVHTXHQFHVIRU6RODU6\VWHPWUDYHODWWKHVSHHGVZHFDQUHDFKDUHKDUGO\VLJQL¿FDQW
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4.7.2
Quarks are fundamental particles within the nucleus. They combine to make larger particles such as the proton and neutron. 7KHVL[NQRZQTXDUNVDUHXSGRZQFKDUPVWUDQJHWRSDQGERWWRP
4.7.3
(a)
proton = up, up, down
(b)
neutron = up, down, down
4.7.4
Leptons are fundamental particles which include the electron, and various neutrinos.
4.7.5
(a)
Fundamental particles are those which cannot be broken down into component parts – they exist as an integral whole DQGDUHGH¿QHGLQWKHLURZQULJKW
(b)
Quarks and leptons (including the electron).
F
7ZRRIWKHRULJLQDOIXQGDPHQWDOSDUWLFOHV SURWRQVDQGQHXWURQV ZHUHIRXQGWREHFRPSRVHGRITXDUNVDQGZHUH therefore not fundamental.
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From Quanta to Quarks
