dot point physics preliminary

Brian Shadwick

PRELIMINARY PHYSICS

© Science Press 2007First published 2007 Reprinted 2007, 2008, 2011

Science PressPrivate Bag 7023 Marrickville NSW 1475 AustraliaTel: (02) 9516 1122 Fax: (02) 9550 [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 vVerbs to Watch vi

Dot Points

Moving About viiThe World Communicates ixElectrical Energy in the Home xiThe Cosmic Engine xiii

Questions

Moving About 1The World Communicates 45Electrical Energy in the Home 77The Cosmic Engine 113

Answers

Moving About 147The World Communicates 157Electrical Energy in the Home 167The Cosmic Engine 179

Appendix

Data Sheet 187Formula Sheet 188Periodic Table 189

Dot Point Preliminary Physics iii Contents

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Notes

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Contents iv Dot Point Preliminary Physics

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Introduction

What the book includes

syllabus for each topic in the Year 11 Physics course:

Also included are typical experimental results for students to analyse if the third column of the syllabus indicates

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.

1.1.1

1.1.2

worth in an examination. As a rough rule, every two lines of answer might be worth one mark. Note that in any

involved is worth only one mark.

How to use the book

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.

spend more time revising later, and allow you to spend your study time more productively.

Dot Point Preliminary Physics v Introduction

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account/account for State reasons for, report on, give an account of, narrate a series of events or transactions.

analyse Identify components and the relationships among them, draw out and relate implications.

apply Use, utilise, employ in a particular situation.

appreciate Make a judgement about the value of something.

assess

results or size.

calculate

clarify Make clear or plain.

classify Arrange into classes, groups or categories.

compare Show how things are similar and different.

construct Make, build, put together items or arguments.

contrast Show how things are different or opposite.

critically (analyse/evaluate) Add a degree or level of accuracy, depth, knowledge

deduce Draw conclusions.

demonstrate Show by example.

describe Provide characteristics and features.

discuss Identify issues and provide points for and against.

distinguish Recognise or note/indicate as being distinct or different from, note difference between things.

evaluate Make a judgement based on criteria.

examine

explain Relate cause and effect, make the relationship between things evident, provide why and/or how.

extract Choose relevant and/or appropriate details.

extrapolate Infer from what is known.

identify Recognise and name.

interpret Draw meaning from.

investigate

justify Support an argument or conclusion.

outline Sketch in general terms; indicate the main features.

predict Suggest what may happen based on available data.

propose Put forward (a point of view, idea, argument, suggestion etc) for consideration or action.

recall Present remembered ideas, facts or experiences.

recommend Provide reasons in favour.

recount Retell a series of events.

summarise Express concisely the relevant details.

synthesise Put together various elements to make a whole.

Verbs to Watch

Verbs to Watch vi Dot Point Preliminary Physics

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1. Speed changes 21.1 Identify that a typical journey involves speed changes. 21.2 Distinguish between average and instantaneous speed. 21.3 Distinguish between scalar and

vav r t 41.5 Compare instantaneous and average speed and velocity. 41.6 Solve problems and analyse information using: vav r t 5

measure average speed of an object. 61.8 Graph displacement vs. time data for objects with uniform linear velocity. 81.9 Graph displacement vs. time data

1.10 Present graphically velocity vs. time data for objects with uniform linear velocity. 111.11 Present graphically velocity vs. time

linear velocity. 122. Forces, acceleration and deceleration 132.1 Describe the motion of one body relative to another. 132.2 Identify the usefulness of using vector diagrams. 132.3 Explain the need for a net external force to act to change velocity. 142.4 Describe the actions that must be taken for a vehicle to change direction, speed up and slow down. 142.5 Describe effects of external forces on bodies including friction and air resistance. 152.6 Analyse the effects of external forces on vehicles. 15

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aav v t = (v – u)/t 152.8 Gather information about different situations where acceleration is positive and negative. 16

with reference to effects of gravity. 162.10 Outline forces involved in causing a change in the velocity of a vehicle. 17

F = ma 18

2.12 Solve problems and analyse F = ma 19

2.13 Identify the net force in a wide variety of transport situations and

2.14 Solve problems and analyse information involving: F = mv2/r for vehicles travelling around curves. 24

show the relationship between force, mass and acceleration. 262.16 Solve problems using vector

acceleration and force. 28

to demonstrate vector addition and subtraction. 293. Motion and energy changes 303.1 Identify that a moving object has kinetic energy and that work done on it can increase that energy. 303.2 Solve problems involving the kinetic energy of vehicles and the work done using: Ek = ½mv2 and W = Fs 303.3 Describe the energy transformations that occur in collisions. 31

Moving About

Dot Point Preliminary Physics vii Moving About

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3.4 Analyse information to trace the energy transfers and transformations in collisions leading to irreversible distortions. 32

4. Momentum 33p = mv 33

I = Ft 334.3 Explain conservation of momentum

4.4 Solve problems and analyse data using: p = mv and I = Ft 334.5 Perform investigations to analyse data for the change in momentum in collisions. 364.6 Solve problems to apply the law of conservation of momentum to describe the collision between a moving and a stationary vehicle. 374.7 Solve problems to apply the law of conservation of momentum to describe the collision of a moving vehicle with an immovable object. 374.8 Solve problems to apply the law of conservation of momentum to the collision between objects moving in opposite directions. 38

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4.9 Solve problems to apply the law of conservation of momentum to the collision between objects moving in the same direction. 385. Safety devices 40

tendency to remain in uniform motion or at rest. 40

about the potential danger presented by loose objects in a vehicle. 40

in many real world situations. 415.4 Assess reasons for low speed zones

airbags and crumple zones to vehicles with respect to impulse and momentum. 415.5 Evaluate the effectiveness of some safety features of motor vehicles. 42

avoiding or reducing the effect of a collision. 43 Answers to Moving About 147

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1. The wave model and information transfer 461.1 Describe the energy transformations in one of: mobile telephone, fax or modem, radio, TV (see 3.9). 461.2 Describe waves as a transfer of energy that may occur in 1, 2, or 3 dimensions. 461.3 Identify that mechanical waves need a medium while electromagnetic

displacement, amplitude, period, compression, rarefaction, crest, trough, transverse, longitudinal,

velocity to the wave model. 471.5 Describe the relationship between particle motion and direction of energy transfer in waves. 481.6 Draw diagrams for transverse and longitudinal waves, directions of particle movement and propagation. 481.7 Quantify the relationship between

491.8 Perform an experiment to gather

and amplitude of waves. 501.9 Solve problems and analyse data by applying: to a range of situations. 501.10 Present and analyse information

transverse wave motion. 511.11 Perform an experiment to identify the relationship between the

sound wave at constant velocity. 531.12 Perform an experiment to observe the transfer of waves in slinky springs, water and ropes. 53

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2. Sound waves 542.1 Identify that sound waves are vibrations of particles in a medium. 542.2 Relate compressions and rarefactions of sound waves to crests and troughs of transverse waves. 54

amplitude of sound waves. 54

sound wave. 542.5 Describe the principle of superposition and compare the resulting waves to the original waves in sound. 552.6 Present graphs, solve problems and analyse data for superposition of waves. 55

observe the superposition of two waves using a CRO or computer. 56

analyse sound waves. 573. Using the electromagnetic spectrum 583.1 Describe emr in terms of their speed in space and their lack of need of a medium for propagation. 583.2 Identify electromagnetic wavebands

3.3 Identify methods for the detection of various wave bands in the em spectrum. 593.4 Explain the relationship between the intensity of emr and the distance from a source as an example of the

modulation of visible light, microwaves and/or radio waves is used to transmit information. 61

The World Communicates

Dot Point Preliminary Physics ix The World Communicates

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3.7 Analyse data to identify the em spectrum range used in modern communications. 613.8 Discuss problems produced by the limited range of the em spectrum available for communications. 621.1 Describe the energy transformations

fax or modem, radio, TV. 623.9 Analyse data to identify the waves involved in the transfer of energy in one of: mobile telephones, TV or radar. 634. electromagnetic waves 644.1 Describe and apply the law of

4.2 Perform an experiment to observe the path of light rays and draw diagrams to show direction of travel of light rays and wavefronts. 644.3 Present information using ray diagrams to show the path of waves

for various surfaces. 664.5 Describe ways in which applications of light, radio and microwaves have helped information transfer. 674.6 Explain that refraction is related to the velocity of a wave in different media and outline how this may result in the bending of a wavefront. 67

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the changes in velocity of a wave in passing from one medium to another. 68

4.9 Solve problems and analyse

4.10 Perform an investigation to graph the angle of incidence and refraction for light encountering a medium change showing the relationship between these angles. 71

calculate the refractive index of glass or perspex. 724.12 Identify the conditions necessary for

to the critical angle. 73

5. Technology and electromagnetic waves 755.1 Identify types of communication data that are stored or transmitted in digital form. 755.2 Discuss some of the physical principles used in one application of physics related to waves in one of the following: GPS, CD technology, DVD technology, the Internet. 76Answers to The World Communicates 157

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1. History of electricity 781.1 Discuss how the main sources of domestic energy have changed over time. 781.2 Assess some of the impacts of changes in, and increased access to, sources of energy. 781.3 Discuss some of the ways on which electricity can be provided in remote locations. 791.4 Analyse differing views of Volta and Galvani on animal and chemical electricity. 791.5 Discuss whether their (Volta and Galvani) different views contributed to increased understanding of electricity. 812. Electricity and electric circuits 822.1 Describe the behaviour of electrostatic charges. 822.2 Describe the behaviour of

2.3 Present diagrams to describe electric

parallel plates. 832.4 Present diagrams to describe electric

between positive and negative point charges. 84

the coulomb. 84

unit charge at that point, i.e. E = F/Q 852.7 Solve problems and analyse information using: E = F/Q 85

2.9 Identify that current can be either direct or alternating. 872.10 Describe electric potential difference (voltage) between points as the change in potential energy per unit charge moving from one point to the other. 87

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2.11 Discuss how potential difference changes at points around a circuit. 882.12 Perform an experiment to show how potential difference varies between points in a circuit (also 3.3). 892.13 Perform an experiment to show the relationship between voltage across, and current in, a circuit (also 3.3). 902.14 Solve problems and analyse information using: R = V/I 912.15 Identify differences between conductors and insulators. 92

to current for a particular conductor. 92

factors affect the movement of electricity through a conductor. 922.18 Identify materials used as conductors to provide household electricity. 933. Series and parallel circuits 953.1 Identify differences between series and parallel circuits. 953.2 Compare parallel and series circuits in terms of voltage across components and current through them. 963.3 Perform experiments to compare current and voltage in series circuits (see 2.12 and 2.13). 97

compare measurements of current and voltage in parallel circuits. 973.5 Identify uses of ammeters and voltmeters. 983.6 Explain why ammeters and voltmeters are connected differently in a circuit. 983.7 Explain why there are different circuits for lighting, heating and other appliances in a house. 993.8 Construct a model to show household circuits. 100

Electrical Energy in the Home

Dot Point Preliminary Physics xi Electrical Energy in the Home

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4. Electrical power 1014.1 Explain that power is the rate at which energy is transformed from one form to another. 1014.2 Identify the relationship between power, potential difference and current. 101

demonstrate the relationship between current, voltage and power. 1014.4 Explain why the kWh is used to measure electrical energy consumption rather than the joule. 1034.5 Identify that the total amount of energy used depends on the length of time

calculated using: Energy = VIt 1044.6 Solve problems using: P = VI and Energy = VIt 1045. 1065.1 Describe the behaviour of the magnetic poles of bar magnets when they are brought close together. 106

force on a small north magnetic pole when placed at that point. 106

5.3 Use and to show the direction of current and and to show the

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pairs of magnetic poles. 1065.5 Describe the production of a magnetic

conductor and how the right hand

build an electromagnet. 1075.7 Compare the nature and generation

a bar magnet. 1085.8 Perform an experiment to observe

straight conductors and solenoids. 1085.9 Explain one application of magnetic

6. Safety devices 1106.1 Discuss the dangers of electric shock from both 240 volt AC mains supply and various DC voltages, from appliances, on the muscles of the human body. 1106.2 Describe the functions of circuit breakers, fuses, earthing, double insulation and other safety devices in the home. 110Answers to Electrical Energy in the Home 167

Electrical Energy in the Home xii Dot Point Preliminary Physics

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1. Models of the Universe 1141.1 Outline historical models of the Universe from the time of Aristotle to that of Newton. 1141.2 Assess one model of the Universe developed from the time of Aristotle to the time of Newton to identify limitations placed on the development of each by available technology. 1152. Origins of the Universe 1182.1 Describe probable origins of the Universe. 1182.2 Outline the discovery of the expansion of the Universe by Hubble, following its earlier prediction by Friedmann. 1222.3 Describe the transformation of radiation into matter following the Big Bang. 1232.4 Identify that Einstein described the

2.5 Outline how the accretion of galaxies and stars occurred through expansion and cooling of the Universe,

energy, gravitational attraction of particles, and lumpiness of gas clouds that allows gravitational collapse. 1243. Stars and their life cycles 127

temperature of a body and the dominant wavelength of the radiation emitted from that body. 1273.2 Identify that the surface temperature of a star is related to its colour. 1273.3 Relate the brightness of an object to its luminosity and distance. 1283.4 Solve problems to apply the inverse

the brightness of a star to its luminosity and distance from the observer. 131

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luminosity against its colour or surface temperature. 133

to examine the variety of star groups

and white dwarfs. 1343.7 Identify energy sources characteristic of each star group including Main

4. The Sun 1384.1 Identify that energy may be released from the nuclei of atoms. 1384.2 Describe the nature of emissions from the nuclei of atoms as radiation of alpha and beta particles and gamma rays in terms of ionising power, penetrating power, effect of magnetic

compare the penetrating power of alpha, beta and gamma radiation. 1394.4 Identify the nature of emissions reaching Earth from the Sun. 1404.5 Describe the particulate nature of the solar winds. 1414.6 Outline the cyclic nature of sunspot activity and its impact on Earth through solar winds. 1414.7 Describe sunspots as representing regions of strong magnetic activity and lower temperature. 1424.8 Assess the effect of sunspot activity

communications. 143Answers to The Cosmic Engine 179

The Cosmic Engine

Dot Point Preliminary Physics xiii The Cosmic Engine

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Notes

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The Cosmic Engine xiv Dot Point Preliminary Physics

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Dot Point Preliminary Physics 1 Moving About

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DOT POINTMoving About

Moving About 2 Dot Point Preliminary Physics

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1. Vehicles do not typically travel at a constant speed.

1.1 Identify that a typical journey involves speed changes.

1.1.1 Describe two speed changes which occur during typical journeys in a car and state one reason for each change.

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1.2 Distinguish between the average and instantaneous speed of vehicles and other bodies.

1.2.1 Compare average and instantaneous speed.

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1.3 Distinguish between scalar and vector quantities in equations.

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1.3.2

Scalar quantities Vector quantities

1.3.3 Compare the distance travelled by an object with its displacement.

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1.3.4 Three objects travel from X to Y by three different roads as shown in the diagram. Y is due east of X.

X Y

Road 1 = 75 km

Road 3 = 150 km

Road 2 = 50 km

Use the information to complete the table.

Object travelling by Distance travelled (km) Displacement (km)

Road 1

Road 2

Road 3

1.3.5 Clarify the idea of expressing direction of travel as a bearing.

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1.3.6 The diagram shows the paths taken by four wombats as they came out of their burrow to search for food. The diagram is drawn to scale where 1 cm = 10 m.

Wombat 1 Wombat 2

Wombat 3

Wombat 4

N

Use the information to complete the table.

Wombat Distance travelled (m)Displacement (m) (directions

as compass readings)Displacement (m)

(directions as bearing)

1

2

3

4


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av r t

1.4.1 r

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1.4.2

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1.5 Compare instantaneous and average speed with instantaneous and average velocity.

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1.5.3 Identify the essential difference between instantaneous speed and instantaneous velocity.

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1.5.4 Identify the essential difference between average speed and average velocity.

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1.5.5 A car takes 2.5 hours to travel along the 150 km road from X and Y as shown in the diagram at a constant speed of 60 kph. X and Y are 120 km apart.

X P Q

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1.6.1 A swimmer dives from the blocks into the pool and races 50 m to the other end of the pool. This takes her 32.6 s.

(a) Calculate her average speed.

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(b) Calculate her average velocity.

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1.6.2

(a) Calculate her average speed.

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(b) Calculate her average velocity.

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1.6.3 Consider three cars travelling from X to Y along three roads shown. Y is due east of X.

X Y

Road 1 = 120 km

Road 3 = 200 km

Road 2 = 90 km

Use this information to complete the table.

Car travelling

by

Distance travelled (km)

Displacement (km)

Time taken (hr)Average speed of cars (kph)

Average velocity of cars (kph)

Road 1 3.0

Road 2 2.0

Road 3 5.0

1.7.1 In an experiment, a ball was rolled down a ramp from rest, from various starting positions as shown in the diagram. The results of the experiment are shown in the table.

P

Q

R

S

T

Starting position

Distance up the slope

(m)Time to roll down slope (s)

Average time to roll down

slope (s)

Average speed down slope (m s–1)

Average speed

squared (m2 s–2)

P 1.0 0.64 0.65 0.63

Q 1.5 0.76 0.79 0.79

R 2.0 0.92 0.91 0.87

S 2.5 1.03 0.99 1.01

T 3.0 1.14 1.09 1.10

(a) Complete the table by calculating values for the missing data (to 2 decimal places).

(b) If you were to draw a graph to show the relationship between the distance the object started up the slope and its average speed as it rolled down the slope, identify the:

independent variable ..............................................................................................................................................................

dependent variable ..................................................................................................................................................................


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(c) Draw this graph.

(d) What conclusion can be made from this graph?

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(e) Explain your answer.

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(f) Calculate appropriate values and write them in the last column of the results table and then use these to draw another graph which will enable you to make a conclusion for the experiment.

(g) Write your conclusion for the experiment based on this second graph.

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(h) Use your graph to predict the average speed of the ball if it was rolled down the slope from a 1.25 m starting position.

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1.8 Present information graphically of displacement vs. time for objects with uniform linear velocity.

1.8.1 Consider the following graph representing the motion of a car.

(a) How far did the car travel in the

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(b) Determine its change in displacement.

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(c) Calculate the average velocity of the car.

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(d) Determine the velocity of the car at time 8 s.

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(e) Predict the velocity of the car at time 30 s.

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(a) How far did the car travel in the

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(b) Determine its change in displacement.

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(d) Determine the velocity of the car at time 8 s.

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(e) Describe the journey of the car.

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10 s?

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(b) Calculate the average speed of the car.

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(d) Determine its displacement after 16 s.

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(e) Determine the velocity of the car at time 8 s.

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velocity.


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(b) Determine its total displacement.

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(d) Determine the velocity of the car at time 12.5 s.

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(e) Describe the journey of the car.

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(c) Calculate the average speed of the car.

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(d) Calculate the average velocity of the car.

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12 s?

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1.10 Present information graphically of velocity vs. time for objects with uniform linear velocity.


(a) How far did the car travel in 20 s?

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(b) Find its displacement after 10 s.

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(d) Calculate the acceleration of the car.

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1.10.2 Consider the following graphs representing the motion of four cars.

-20

-15

-10

-5

0

5

10

15

20

10 15 20

Time (s)

Ve

loci

ty (

m/s

nor

th)

A

BC

D

5

Use this information to complete the table.

CarAverage speed

(m s–1)Average velocity

(m s–1)Acceleration

(m s–2)Displacement after

10 s

A

B

C

D

-18

-12

-6

0

6

12

18

5 10 15 20

Time (s)

Vel

ocity

(m

/s e

ast)


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(b) Calculate the average velocity of the car.

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(c) Calculate the acceleration of the car at time 12 s.

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(d) Calculate the average acceleration of the car.

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(b) Calculate its displacement at time 20 s.

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(e) Determine the acceleration of the car at times 3, 7 and 16 s.

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0

10

20

30

40

50

60

0 5 10 15 20

Time (s)

Vel

ocity

(m

/s n

orth

)

-10

-5

0

5

10

15

0 5 10 15 20

Time (s)

Vel

ocity

(m

/s s

outh

)


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2. An analysis of the external forces on vehicles helps us understand the effects of acceleration and deceleration.

2.1 Describe the motion of one body relative to another.

2.1.1 Object X is moving east at 30 m s–1. Object Y is moving west at 25 m s–1. Object Z is moving east at 15 m s–1. Calculate the velocity of:

(a) X relative to Y ...........................................................................................................................................................................

(b) X relative to Z ...........................................................................................................................................................................

(c) Y relative to X ...........................................................................................................................................................................

(d) Y relative to Z ............................................................................................................................................................................

(e) Z relative to X ...........................................................................................................................................................................

(f) Z relative to Y ............................................................................................................................................................................

2.1.2 From your answers above, identify the relationship between the velocity of object A relative to object B and the velocity of object B relative to object A.

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2.1.3 A person can row a boat at 1.75 m s–1 0.45 m s–1. Calculate the velocity of the person relative to the banks of the river if he rows:

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Calculate the velocity of the boat relative to the water if he rows:

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2.2 Identify the usefulness of using vector diagrams to assist in solving problems.

2.2.1 Object X is moving east at 24 m s–1. Object Y is moving north at 18 m s–1. With the aid of an appropriate vector diagram, calculate the velocity of:

(a) X relative to Y

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(b) Y relative to X ........................................................................

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2.3 Explain the need for a net external force to act in order to change the velocity of an object.

2.3.1

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2.3.2

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2.3.3 Describe a situation where an object is travelling with constant speed and yet its velocity is constantly changing.

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2.3.4 Describe the force acting on the object in 2.3.3 above.

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2.4 Describe the actions that must be taken for a vehicle to change direction, speed up and slow down.

2.4.1 Identify what is needed to change the direction or speed of an object.

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2.4.2 What is an object doing if its speed is changing?

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2.4.3

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2.5 Describe the typical effects of external forces on bodies including friction and air resistance.

2.5.1 A car travels along a straight road at constant speed. Draw a diagram to show all the forces acting on it.

2.5.2 Describe what each of these forces does to the car.

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2.5.3 What is the net force on the car? Explain how you determine this.

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2.6 Analyse the effects of external forces operating on a vehicle.

2.6.1 Identify three changes a force acting on a vehicle can cause to its motion.

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aav = v/ t = (v – u)/t

2.7.1

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2.7.2 A force acts on a car for 4.0 s to increase its velocity from 5 m s–1 to 25 m s–1. Calculate the acceleration of the car.

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2.7.3 A car accelerates at 4.0 m s–2

(a) if its initial velocity was 2.0 m s–1 in the same direction as the force

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(b) if its initial velocity was 3.5 m s–1 in the opposite direction to the force

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negative.

2.8.1

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2.8.2 Identify three different situations where the acceleration of a car would be considered to be positive.

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2.8.3 Identify three different situations where the acceleration of a car would be considered to be negative.

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2.9.1

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2.9.2

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2.9.3 Complete the table by comparing various properties of mass and weight.

Mass Weight

2.10.1 It is coasting on a horizontal surface with no pressure on the accelerator.

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2.10.2 The car is moving on a horizontal surface with the driver pressing on the accelerator.

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2.10.3 The car is moving on a horizontal surface with the driver pressing on the brakes.

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2.10.4 The vehicle is passing over an icy patch on a horizontal road.

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2.10.5 The vehicle is climbing a hill.

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2.10.6 The vehicle is descending a hill.

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2.10.7 The vehicle is following a curve on a horizontal road.

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F = ma

2.11.1

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2.11.2 A car is accelerating uniformly along a road. Sketch graphs on the axes below to show the relationships indicated.

F

t

v

t

r

t

2.11.3 Forces act on several cars of different masses to produce identical accelerations. Sketch graphs on the axes below to show the relationships indicated.

F

m

v

m

r

m

2.11.4 Forces act on several cars of different masses to produce identical velocity changes. Sketch graphs on the axes below to show the relationships indicated.

F

m

a

m

r

m


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F = ma

2.12.1 Calculate the force acting on a 5.0 kg mass which accelerates for 3.0 s. During this time its velocity changes from 2.5 m s–1 east to 17.5 m s–1 west.

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2.12.2 A 12 N force acts on a body and accelerates it from rest to 4.5 m s–1 south. This takes 15 s. Calculate the mass of the body.

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2.12.3 An 80 g object is initially at rest. A 0.16 N force to the north acts on it for 5 s. Calculate:

(a) the acceleration produced by the force

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(c) its displacement after 5 s

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2.13 Identify the net force in a wide variety of situations involving modes of transport and explain the consequences of that net force in terms of Newton’s Second law of Motion.

Note that the syllabus says ‘a wide variety of situations’. If you have not studied the examples given here in class, then you don’t have to do them.

2.13.1 Consider the two blocks shown in the diagram. They are resting on a surface which provides a frictional force of 0.25 N kg–1.

2.5 kg 5.5 kg18 N

X

Y


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(a) Calculate the acceleration of the system.

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(b) Calculate the net force on each block.

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(c) Calculate the force block X puts on block Y.

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(d) Calculate the force block Y puts on block X.

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2.13.2 Consider the two blocks shown in the diagram. They are resting on a smooth surface.

3.0 kg 6.0 kg36 N

X

Y

string

(a) Calculate the acceleration of the system.

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(b) Calculate the net force on each block.

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(c) Calculate the force tension in the string.

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2.13.3 Consider the object shown in the diagram. Several forces act on this object which is at rest on a smooth, horizontal surface.

4 kg26 N

15 N

6 N


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(a) Calculate the net force on the object.

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(b) Calculate the acceleration of the object.

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(c) Calculate its velocity after 5.0 s.

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(d) Calculate its displacement after 5 s.

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2.13.4 Consider the two blocks shown in the diagram. They are connected by a light string over a frictionless pulley.

(b) Calculate the acceleration of the system.

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(c) Calculate the net force on each block.

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(d) Calculate the tension in the string connecting the blocks.

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2 kg

4 kg

X

Y


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2.13.5 Consider the two blocks shown in the diagram. They are connected by a light string over a frictionless pulley. Block X is resting on a smooth surface.

this pulley system.

(b) Calculate the acceleration of the system.

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(c) Calculate the net force on each block.

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(d) Calculate the tension in the string connecting the blocks.

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2.13.6 A 3 kg mass is resting on a Newton balance in an elevator. Complete the table to show the reading on the balance in each of the following situations.

Movement of elevator Reading on Newton balance

(a) Stationary

(b) Moving up at 2.0 m s–1

(c) Moving down at 2.0 m s–1

(d) Moving up at 2.0 m s–2

(e) Moving down at 2.0 m s–2

X

Y

2 kg

5 kg


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2.13.7 Two masses are connected by a string and are hanging from the ceiling of an elevator as shown. Complete the table to show the tensions in each string in the following situations.

Movement of elevatorTension in String 1 (N)

Tension in String 2 (N)

(a) Stationary

(b) Moving up at 3.0 m s–1

(c) Moving down at 3.0 m s–1

(d) Moving up at 3.0 m s–2

(e) Moving down at 3.0 m s–2

2.13.8 A ball is hanging by a string from the ceiling of a bus. Describe the motion of the bus when the string is:

(a) hanging straight down

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(b) hanging down towards the rear of the bus

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(c) hanging down towards the front of the bus

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2.13.9 A 3.0 kg ball is hanging by a string from the ceiling of a bus as shown in the diagram.

(b) Using an appropriate vector diagram, calculate the tension in the string when the ball is in the position shown.

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(c) Calculate the acceleration of the bus.

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(d) See over page.

String 1

4 kg

String 2

6 kg

10°

3 kg ball


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(d) At what angle would the ball and string hang if the bus was braking at 2.5 m s–2?

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F = mv2/r for vehicles travelling around curves.

2.14.1 Two 60 kg boys on 20 kg bikes are riding at 15 m s–1 directly towards a wall which is 30 m from them. X continues towards the wall, but slams on his brakes applying a 400 N force. Y does not put on his brakes, but turns his bike with the same force in a circular path in the hope of not hitting the wall.

Analyse this information to determine whether or not the boys hit the wall.

For X For Y

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2.14.2 A toy racing car of mass 150 g is racing around a circular track of diameter 80 cm. It takes 8.4 s to do one lap of the track. Calculate:

(a) the speed of the car

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(a) the acceleration of the car

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(b) the centripetal force acting on the car

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2.14.3 A 1500 kg racing car goes around a circular track of radius 200 m at a constant speed of 270 kph.

(a) Calculate the speed of the car in m s–1.

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(b) Calculate the acceleration of the car.

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(c) What force holds the car to the road as it speeds around this corner.

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(d) Calculate the value of this force.

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(e) State the direction this force acts.

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(f) Predict the value of this force if the speed of the car was to halve.

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2.15.1 Experiment 1

In this experiment, a trolley of mass 1.5 kg was placed on the bench accelerated by a force attached to it by a string, which passed over a pulley. The mass of the trolley was kept constant and different forces used to accelerate it from rest across the bench top. The time it took the trolley to travel 1.0 m across the benchtop was measured. The results are shown in the table.

Run Accelerating

Force (N) Time to travel

1.0 m (s)Initial speed of trolley (m s–1)

Average speed of trolley

(m s–1)

Final speed of trolley (m s–1)

Acceleration of trolley

(m s–2)

1 1 F 0.89

2 2 F 0.63

3 3 F 0.52

4 4 F 0.45

5 5 F 0.40

(a) Complete the table by calculating values for all missing data.

(b) Draw a graph to show the relationship between the force and acceleration produced. (Place force on the y

(c) Use your graph to write a conclusion for the experiment.

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Trolley Pulley

Mass


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2.15.2 Experiment 2

The students did another experiment using the same apparatus. This time they kept the accelerating force constant, and changed the mass of the trolley. They measured how long it took the trolley to move 1.0 m across the benchtop.

RunTrolley

mass (kg)

Time to travel

1.0 m (s)

Initial speed of trolley

(m s–1)

Average speed of

trolley (m s–1)

Final speed of trolley

(m s–1)

Acceleration of trolley

(m s–2)(Acceleration)–1

1 1.0 1.83

2 2.0 2.58

3 3.0 3.16

4 4.0 3.65

5 5.0 4.08

(a) Complete the table of results by calculating values for all missing

(b) Graph mass vs. (acceleration)–1.

(c) Use your graph to write a conclusion for the experiment.

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Combining your conclusions for Experiments 1 and 2

relationship between the mass of an object, the force acting on it, and the acceleration the force produces.

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experiments above.

Experiment 1

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Experiment 2

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2.16 Solve problems using vector diagrams to determine resultant velocity, acceleration and force.

2.16.1 A 2.5 kg object moving at 5.0 m s–1 east is acted upon by a force which changes its velocity to 12 m s–1 south over a period of 4 s. By drawing an appropriate vector diagram, calculate:

(a) the change in velocity of the object

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(b) the acceleration of the object

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(c) the force that acted on the object

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2.16.2 The velocity of an object changes from 6.0 m s–1 west to 8.0 m s–1 north when a force of 12 N acts on it for 1.25 s. By drawing an appropriate vector diagram, calculate:

(a) the change in velocity of the object

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(b) the acceleration of the object

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(c) the direction of the force that acted on the object

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(d) the mass of the object

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2.17.1 A group of students set up the following apparatus to investigate the addition of vectors. They hung masses on mass carriers to produce forces F1 and F2 on the ends of a long string, then placed a third mass carrier and masses, F3 on the string between the pulleys. They adjusted

. Their results for three sets of forces are shown in the table.

F1 F2 F3

60 g 90 g 132 g 59°

40 g 70 g 95 g 68°

45 g 55 g 70 g 93°

By drawing appropriate vector diagrams, show that these results are consistent with F3 being the resultant of F1 and F2.

F1

F3

F2


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3. Moving vehicles have kinetic energy and energy transformations are an important aspect in understanding motion.

3.1 Identify that a moving object possesses kinetic energy and that work done on that object can increase that energy.

3.1.1 Explain, in terms of the law of conservation of energy, the relationship between the work done on a falling object and its kinetic energy.

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3.2 Solve problems and analyse information to determine the kinetic energy of vehicles and the

Ek = ½mv2 and W = Fs

3.2.1 A 12 kg car, at rest, is acted upon by a force acting towards the north, for 5 s. This changes its kinetic energy by 2400 J.

(a) Calculate the work done on the object by the force.

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(c) Calculate how far the object moves while the force is acting on it.

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(d) Calculate the acceleration of the object.

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(e) Calculate the magnitude of the force acting on the object.

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3.2.2 If the car in Question 3.2.1 had been moving at 10 m s–1 south initially, and the same force acted on it for the same time, calculate:

(a) the initial kinetic energy of the car

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(d) the displacement of the car during the 5 seconds

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on the car by the force.

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(f) Account for your answer to (e).

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3.3 Describe the energy transformations that occur in collisions.

3.3.1 A car of mass 1000 kg is moving at 15 m s–1 when the driver loses control and it runs off the road, slamming into a tree and stopping.

(a) Calculate the initial kinetic energy of the car.

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(b) Calculate the kinetic energy of the car after it has hit the tree.

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(c) Account for the difference.

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3.4 Analyse information to trace the energy transfers and transformations in collisions leading to irreversible distortions.

3.4.1 Explain the role of each of the following forms of energy in collisions between moving objects.

(a) Potential energy of deformation

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(b) Sound energy

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(c) Thermal energy

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3.5.1 Recall the law of conservation of energy.

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3.5.2 A car has kinetic energy before collision and this is changed to the energy forms above during collision. Identify where all this energy ends up.

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4. Change of momentum relates to the forces acting on the vehicle or the driver.

p = mv

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I = Ft

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4.2.2 Clarify the relationship between impulse and momentum change.

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4.3 Explain conservation of momentum in terms of Newton’s Third Law.

4.3.1conservation of momentum during a collision.

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p = mv and I = Ft

4.4.1 A model of a 60.0 kg man and one of a 25 kg child were placed in an 1000 kg car and secured with seatbelts. The car was moving at 70.0 kph as it crashed into a brick wall.

(a) Predict what would happen to the models during the collision.

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(b) Identify the law of Physics you are using in your answer to (a).

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(c) Explain how and why the effect on the models would differ if the front section of the car was specially designed to concertina on impact.

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(d) If the collision took 0.2 s, calculate the average force exerted on each model by its seatbelt.

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(h) By making appropriate calculations, assess if it would be possible for a mother to nurse a child and protect it from a collision like this.

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4.4.2 The graph shows how the force acting on a 0.6 kg object changes with time.

(a) Calculate the acceleration of the object at t = 5 s.

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(b) Calculate the impulse applied to the object during the 5 s.

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(d) If its initial velocity was 22 m s–1

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4.4.3 A 150 g toy car collides with a padded lounge chair at 0.20 m s–1. The collision takes 0.3 s. The toy car stops after the collision.

(a) Calculate the impulse the car applies to the lounge.

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(b) Calculate the impulse the lounge applies to the car.

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(c) Calculate the average force the car applies to the lounge.

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(d) Calculate the average force the lounge applies to the car.

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(e) What law are you using to answer Questions (b) and (d)?

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4.4.4stopping her, puts an average force of 12 000 N on her for 1.0 x 10–2 s. Calculate:

(a) the impulse of the force

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(b) the impulse of the force if the collision time was 0.1 s.

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(c) the initial speed of the car

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4.5.1 The diagrams show the results of a experiment where trolley X, mass 200 g, collided with trolley Y, 300 g. The results were produced using 10 Hz stroboscopic photography. Analyse the results to determine if momentum was conserved.

X Y

X Y

Before collision

After collision

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4.6 Solve problems that apply the principle of conservation of momentum to qualitatively and quantitatively describe the collision of a moving vehicle with a stationary vehicle.

4.6.1 A 3.0 kg block, at rest, is hit by a 4.0 kg block moving at 1.5 m s–1. After collision, the 4 kg block stops. Calculate the velocity of the 3 kg block after the collision.

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4.6.2 A 6.0 × 103 kg train engine, moving at 2.5 m s–1 collides, and couples with a stationary carriage. They move at 1.2 m s–1

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4.6.3 A 1200 kg car moving at 60 kph collides with an 800 kg parked car. As a result of this collision, the parked car is pushed forwards at 40 kph. Determine what happens to the other car.

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4.7 Solve problems that apply the principle of conservation of momentum to qualitatively and quantitatively describe the collision of a moving vehicle with an immovable object.

4.7.1 A two tonne truck moving at 15.0 m s–1 collides with a concrete retaining wall. The wall does not

(a) Recall the law of conservation of momentum.

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(b) Explain how this collision does not contravene the law of conservation of momentum.

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4.7.2 A 12 kg ball moving at 2.5 m s–1 collides with a brick wall and rebounds at 1.75 m s–1.

(a) Calculate the change in momentum of the ball.

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(b) Calculate the impulse the ball applies to the wall.

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(c) If the collision lasts 0.15 s, calculate the force the wall places on the ball.

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4.8 Solve problems that apply the principle of conservation of momentum to describe the collision of a moving vehicle with another vehicle moving in the opposite direction.

4.8.1 A 900 kg car, moving at 6.0 m s–1 east collides with a 150 kg motorbike moving west at 8.0 m s–1. The car slows to 4.0 m s–1. Calculate what happens to the motorbike.

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4.8.2 –1. The 30 kg cart rebounds at 4.0 m s–1 while the 45 kg cart rebounds at 2.0 m s–1. Calculate the

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4.9 Solve problems that apply the principle of conservation of momentum to describe the collision of a moving vehicle with another vehicle moving in the same direction.

4.9.1 A 350 g toy train engine is moving at 12 cm s–1 when it collides, and couples with a 200 g carriage moving at 5 cm s–1 in the same direction. Calculate their combined speed.

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4.9.2 A 400 g toy engine pulls four 150 g carriages. They move at 0.3 m s–1 when they run into, and couple with, two identical carriages moving at 0.15 m s–1 in the same direction. Calculate the speed of the combination.

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5. Safety devices are utilised to reduce the effects of changing momentum.

5.1.1

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vehicle.

5.2.1 Explain, in terms of the principles of Physics involved, why it is potentially dangerous to leave loose objects on the back shelf of a car.

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5.2.2 Explain, in terms of the principles of Physics involved why it is dangerous to drive a car without wearing a seatbelt.

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5.3 Discuss reasons why Newton’s First law of Motion is not apparent in many real world situations.

5.3.1how this affects the person involved.

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5.3.2explain why it is not apparent.

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airbags and crumple zones to vehicles with respect to the concepts of impulse and momentum.

5.4.1 With reference to the concepts of impulse and momentum, assess the reasons for the introduction of:

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(b) the use of airbags in collisions

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(c) the inclusion of crumple zones in vehicles

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5.5 Evaluate the effectiveness of some safety features of motor vehicles.

5.5.1 Evaluate the relative safety of the seatbelt harness worn by racing car drivers and the lap/sash

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5.3.3 A passenger in a car that has a synthetic plastic bumper bar will usually sustain less injury than a passenger in a car with a solid, chromed metal bumper bar. Explain how this is possible.

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collision.

5.6.1

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Dot Point Preliminary Physics 145 Answers

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DOT POINTAnswers

Answers 146 Dot Point Preliminary Physics

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Moving About

General comment: Given that we measure things slightly differently from each other and that our measuring instruments might not be totally accurate, consider all numerical answers derived through measurement as correct if they lie within +1 or –1 of the given answers. For example, if the given answer is 58, then accept 57, 58 and 59 as correct.

1.1.1 Car may slow down (reaches a corner, up a hill, speed bump, pedestrian crossing etc) or speed up (down hill, moving away from stop lights, as it starts etc). In each case the change is caused by the force on the car changing due to some factor like increased friction during braking, gravitational force etc.

1.2.1speed is the actual speed of a vehicle at a particular instant of time.

1.3.1 Scalars have magnitude only while vectors have both magnitude and direction. Vectors can be represented by scale diagrams. Scalars are not represented in this way.

1.3.2 Examples include:

Scalar quantities Vector quantities

Mass Displacement

Time Velocity

Speed Acceleration

Distance Force

Length Momentum

1.3.3 Distance travelled is a measure of the total length of the path an object has travelled. Displacement indicates how far, in a

1.3.4 Object travelling by Distance travelled (km) Displacement (km)

Road 1 75 50 east

Road 2 50 50 east

Road 3 150 50 east

1.3.5

1.3.6 Wombat Distance travelled (m)

Displacement (m) (directions as compass readings)

Displacement (m) (directions as bearing)

1 58 58 N 62° W 55 b298

2 63 63 N 65° E 58 b065

3 32 32 S 46° E 30 b134

4 33 33 S 22° W 32 b202

1.4.1 r = change in displacement of the object.

1.4.2 Displacement indicates how far, in a straight line, an object is from its starting point, and we must also state the direction it

1.5.1 Average speed = total distance covered ÷ total time taken.

1.5.2 Difference is in the use of distance travelled and displacement, hence average speed instead of average velocity.

1.5.3 Instantaneous speed measures the speed of on object at a particular instant of time while instantaneous velocity measures the

1.5.4object while average speed uses total distance travelled.

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1.5.5 (a) They will be the same, 60 kph.

(b) At P instantaneous velocity is 60 kph b160 while at Q it is 60 kph b055.

(c) 72 kph

(d) 48 kph b083

1.6.1 (a) 1.53 m s–1

(b) 1.53 m s–1 towards the end of the pool

1.6.2 (a) 1.47 m s–1

(b) zero (she ends up at her starting position)

1.6.3

Car travelling byDistance travelled

(km)Displacement (km) Time taken (hr)

Average speed of cars (kph)

Average velocity of cars (kph)

Road 1 120 90 east 3.0 40 30 east

Road 2 90 90 east 2.0 45 45 east

Road 3 200 90 east 5.0 40 18 east

1.7.1 (a)

Starting position

Distance up the slope (m)

Time to roll down slope (s)Average time to roll down

slope (s)

Average speed down slope

(m s–1)

Average speed squared (m2 s–2)

P 1.0 0.64 0.65 0.63 0.64 1.56 2.43

Q 1.5 0.76 0.79 0.79 0.78 1.92 3.69

R 2.0 0.92 0.91 0.87 0.90 2.22 4.93

S 2.5 1.03 0.99 1.01 1.01 2.48 6.15

T 3.0 1.14 1.09 1.10 1.11 2.70 7.29

(b) Independent variable: distance up the slope. Dependent variable: average speed.

(c)

(d) Average speed down slope increases as distance up slope increases but at a progressively slower rate.

can conclude that the plotted variables are directly proportional to each other.

(f)

(h) 2.6 m s–1

0

0.5

1

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2

2.5

3

0 0.5 1 1.5 2 2.5 3Distance up slope (m)

Ave

rage

spe

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1.8.1 (a) 8 m (b) 15 m north (c) 0.75 m s–1 north (d) 0.75 m s–1 north (e) 0.75 m s–1 north

1.8.2 (a) 7 m (b) 20 m south (c) 1.0 m s–1 south (d) 1.33 m s–1 south (e) Car is stationary at displacement 20 m north for 5 seconds then moves at 1.33 m s–1 south for 15 s at which time it is

at displacement zero.

1.8.3 (a) 15 m (b) 1.5 m s–1 (c) 1.5 m s–1 south (d) 9 m south (e) 1.5 m s–1 south

1.9.1

–1 north (d) about 3.5 m s–1 north (e) Car starts at displacement zero and travels for 20 s with increasing velocity (accelerating) until it reaches displacement

56 m north.

1.9.2 (b) 70 m south (c) 3.5 m s–1 (d) 3.5 m s–1 south (e) about 2.2 m s–1 south

1.9.3

(c) 5.5 m s–1 (d) 5.5 m s–1 north

–1 north

1.10.1 (a) 150 m (b) 75 m west (c) 0 (d) 1.5 m s–2 east

1.10.2

CarAverage speed

(m s–1)Average velocity

(m s–1)Acceleration (m s–2) Displacement after 10 s

A 12 12 north 0 120 m north

B about 5.1 1.25 north 1.0 north 38 m south

C about 7.5 about 0.1 north 0.5 north about 70 m south

D 5 5 south 0.5 south 25 m south

1.11.1 (a) about 390 m (b) about 19.5 m s–1 north (c) about 3.3 m s–2 north (d) 2.75 m s–2 north

1.11.2 (a) about 152 m (b) about 60 m (c) about 70.8 m s–1 (d) about 2.0 m s–1 south (e) at time 3, a = 0

at time 7, a = 4 m s–2 north at time 16, a = 2.5 m s–2 south

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2.1.1 (a) 55 m s–1 east (b) 15 m s–1 east (c) 55 m s–1 west (d) 40 m s–1 west (e) 15 m s–1 west (f) 40 m s–1 east

2.1.2 Velocity of A relative to B = – velocity of B relative to A (i.e. opposite direction).

2.1.3 (a) 2.2 m s–1 downstream (b) 1.3 m s–1 upstream (c) 1.75 m s–1 downstream (d) 1.75 m s–1 upstream

2.2.1 (a) 30 m s–1 E 37º S (or b127) (b) 30 m s–1 W 37º N (or b307)

2.3.1 An object at rest or moving with constant velocity will remain ar rest or moving with constant velocity while no net (unbalanced) force acts on it.

2.3.2 A car on an icy road will continue with the same speed in the same direction until the wheels stop sliding allowing the road to exert a frictional force on the car through the tyres.

2.3.3 Any object moving with constant speed and turning a corner, for example a geostationary satellite in orbit above Earth.

2.3.4 Force acts towards the centre of curvature of the corner. It is also called a centripetal force.

2.4.1 An unbalanced force from outside the system.

2.4.2 Accelerating.

2.4.3 This idea depends on the convention we choose to make for each situation we deal with. One viewpoint of this is that a positive force acts in the direction of motion of an object causing it to go faster while a negative force acts against the direction of the motion of the object causing it to go more slowly. A positive force could also be considered to be an attractive force (between oppositely charged objects) and a negative force a repulsive force between like charges.

2.5.1 Your diagram should show air resistance acting against the motion, and friction between the tyres and the road acting forwards in the direction of the motion, gravity vertically down and reaction force to gravity perpendicularly up from surface. (Note

2.5.2 Air resistance and friction act against the driving force to reduce its effect. The driving force causes the forward movement.

2.5.3 Zero – car is moving with constant speed – i.e. no acceleration therefore no net force.

2.6.1 Speed it up, slow it down or change its direction of travel.

2.7.1

2.7.2 5.0 m s–2 in the direction of the applied force.

2.7.3 (a) 12.0 m s–1 in the direction of the original motion. (b) 6.5 m s–1 in the direction the force acts.

2.8.1 A positive acceleration is in the direction of motion of an object causing it to go faster while a negative acceleration is opposite the direction of the motion of the object causing it to go more slowly.

2.8.2 Accelerating from rest, accelerating away from a corner, coasting downhill.

2.8.3 Braking as it approaches a corner or stop sign, coasting uphill (i.e. foot not on accelerator).

2.9.1

2.9.2 Weight is a measure of the gravitational force acting on an object. Weight is given by W = mg, is measured in newtons and is


2.9.3 Mass Weight

Measured in kg Measure in newtons

Cannot be zero Can be zero (if no gravitational field)

Does not change with position Changes according to position of object

Measure of amount of matter in an object Measure of force of gravity on an object

Is a scalar quantity Is a vector quantity

2.10.1 Forward force = friction between the tyres and the road Retarding forces = air resistance


2.10.3 Forward force = friction between the tyres and the road Retarding forces = air resistance, friction between brake pads and wheel drums


2.10.5 Forward force = friction between the tyres and the road Retarding forces = air resistance, component of gravity down the slope

2.10.6 Forward force = friction between the tyres and the road, component of gravity down the slope Retarding forces = air resistance

2.10.7 Forward force = friction between the tyres and the road Retarding forces = air resistance Turning force = component of the frictional force between the tyres and the road perpendicular to the direction of travel

produced as the wheels change direction.

2.11.1 The acceleration caused by a net force acting on an object is directly proportional to the force and inversely proportional to the

force acting on it (see Year 12 work).

2.11.2

2.11.3

2.11.4

2.12.1 About 33.3 N against the motion.

2.12.2 40 kg

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2.12.3 (a) 2 m s–2 north (b) 10 m s–1 north (c) 25 m north

2.13.1 (a) 2 m s–2 right (b) Force on X = 5 N right Force on Y = 11 N right (c) 11 N right (d) 11 N left

2.13.2 (a) 4 m s–2 left (b) Force on X = 12 N left Force on Y = 24 N left (c) 24 N both directions

2.13.3 (a) 6.25 m s–2 b307 (b) 6.25 m s–2 b307 (c) About 31 m s–1 b307 (d) About 78 m b307

2.13.4 (a) Show gravity down on each mass, and tension in each side of the string acting both ways. (b) 3.27 m s–2 Y moving down (c) Force on X = about 6.5 N up Force on Y = about 13 N down (d) About 26.1 N acting both ways in string

2.13.5 (a) Show gravity down on each mass, reaction force up on mass X and tension in both bits of the string acting in both directions.

(b) 7 m s–2 Y moving down (c) Force on X = 14 N right Force on Y = 35 N down (d) 14 N acting in both directions

2.13.6 (a) 29.4 N (b) 29.4 N (c) 29.4 N (d) 35.4 N (e) 23.4 N

2.13.7 (a) 98 N, 58.8 N (b) 98 N, 58.8 N (c) 98 N, 58.8 N (d) 127.4 N, 88.2 N (e) 68.6 N, 29.4 N

2.13.8 (a) Stopped or moving with constant velocity. (b) Accelerating forwards. (c) Accelerating backwards or braking.

2.13.9 (a) Weight force vertically down, tension in string (acting both ways) and a third force (= ma) horizontally to the left (pulling the ball aside).

(b) 29.85 N (c) 1.73 m s–2 (d) 14.3° towards the front of the bus

2.14.1 X stops in 22.5 m so does not hit the wall. Y turns a curve with a radius of 45 m, so Y hits the wall.

2.14.2 (a) 0.3 m s–1 (b) 0.225 m s–2 (c) 0.034 N towards centre of curve


2.14.3 (a) 75 m s–1 (b) 28.125 m s–2 (c) Friction between the tyres and the road – the inertia of the car tries to keep it going straight and the friction opposes

this, pulling the car around in the curve. (d) 4.21 × 104 N (e) Towards the centre of the curve. (f) Will be four times smaller = 1.05 × 104 N.

2.15.1 (a)

Run Accelerating force

(N) Time to travel

1.0 m (s)Initial speed of trolley (m s–1)

Average speed of trolley (m s–1)

Final speed of trolley (m s–1)

Acceleration of trolley (m s–2)

1 F 0.89 0 1.12 2.25 2.53

2 2 F 0.63 0 1.59 3.17 5.03

3 3 F 0.52 0 1.92 3.85 7.40

4 4 F 0.45 0 2.22 4.44 9.87

5 5 F 0.40 0 2.50 5.00 12.5

(b)

0

1

2

3

4

5

6

0 5 10 15Acceleration (ms–2)

For

ce (

F u

nits

)

(c) The acceleration produced by forces applied to a constant mass is directly proportional to the force applied.

2.15.2 (a)

RunTrolley mass

(kg)

Time to travel

1.0 m (s)

Initial speed of trolley

(m s–1)

Average speed of

trolley (m s–1)

Final speed of trolley

(m s–1)

Acceleration of trolley (m s–2)

(Acceleration)–1

1 1.0 1.83 0 0.55 1.09 0.60 1.67

2 2.0 2.58 0 0.39 0.78 0.30 3.33

3 3.0 3.16 0 0.32 0.63 0.20 5.00

4 4.0 3.65 0 0.27 0.55 0.15 6.67

5 5.0 4.08 0 0.25 0.49 0.12 8.33

(b)

0

1

2

3

4

5

6

0 2 4 6 8 101/Acceleration (s2 m–1)

Mas

s (k

g)

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(c) The acceleration produced by a constant force acting on various masses is indirectly proportional to the mass. (d) F = ma (e) Experiment 1, force = 3.75 N (use gradient of graph). Experiment 2, force = 0.6 N.

2.16.1 (a) 13 m s–1 b203 (b) 3.25 m s–2 b203 (c) 8.125 N b203

2.16.2 (a) 10 m s–1 b037 (b) 8 m s–1 b037 (c) b037 (d) 1.5 kg

2.17.1 You need to draw vectors to add F1 and F2 3. If all angles are drawn correctly, F3 will be vertical. If you get lost, ask your teacher for help.

3.1.1potential energy the objects loses).

3.2.1 (a) 2400 J (b) 20 m s–1 north (c) 50 m (d) 4 m s–2 (e) 48 N

3.2.2 (a) 600 J (b) 10 m s–1 (c) 600 J (d) 0 (e) 0

KE initial = KE

600 J done to accelerate it in the opposite direction.

3.3.1 (a) 1.125 × 105 J (b) 0 (c) Kinetic energy has been changed into other forms – sound during the collision, deformation of the car, heat involved

of air particles.

3.4.1 (a) The bending of car panels and other metal parts, the breaking of glass and plastic absorbs most of the kinetic energy of the car.

(b) The sound associated with collisions as parts break and bend and move into and across each other absorbs some of the KE.

KE.

3.5.1 In the absence of any external forces, the total energy of a system remains constant.

3.5.2 The energy eventually dissipates as molecular motion of the molecules in the air.

4.1.1

4.2.1

4.2.2

4.3.1 i.e. FA = –FB

impulse on object B, i.e. (Ft)A = –(FT)B or IA = –IB

A B.


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4.4.1 (a) They would continue to move forwards at 70 kph because of their inertia until the force of their seatbelts stopped them.

(c) Crumple sections increase the time of the collision and therefore reduce the forces involved in the collision (I = FT),

so, while the models would still continue to move forwards until their seatbelts stopped them, the decelerating force of the belts would be less (acting over a longer time) so any detrimental effect on the models would be reduced.

(d) Man = 5833.3 N opposing the motion. Child = 2430.6 N opposing the motion. (e) 19.44 m s–1 (70 kph) (f) There is no forward force acting on them, they simply continue forwards because they are moving forwards until a

backward force stops them.

would be strong enough, so for most mums – impossible to hold the child.

4.4.2 (a) 16.6 m s–2 east (b) 25 Ns east (c) 41.67 m s–1 east (d) 19.67 m s–1 east

4.4.3 (a) 0.03 Ns onto the lounge (b) 0.03 Ns onto the car (c) 0.1 N onto the lounge (d) 0.1 N onto the car

4.4.4 (a) 1.2 Ns backwards (b) 12 Ns backwards (c) 2.4 m s–1

4.5.1 Momentum is conserved. If you have problems with this analysis, see your teacher for assistance.

4.6.1 2.0 m s–1 north

4.6.2 6500 kg

4.6.3 The car continues forwards at 33.3 kph.

4.7.1 (a) In the absence of external forces, the total momentum of a system remains the same. (b) When the truck hits the wall it puts an impulse on the wall. This, while not collapsing the wall, will cause it to move

(vibrate, shake) a little. Hence the momentum of the truck transfers to the wall and then into molecular motion of air

4.7.2 (a) 51 kg m s–1 away from the wall (b) 51 kg m s–1 onto the wall (c) 340 N away from the wall

4.8.1 The bike rebounds at 4.0 m s–1

4.8.2 2.67 m s–1

4.9.1 9.45 cm s–1

4.9.2 0.26 m s–1

5.1.1 An object will stay at rest or moving with constant velocity until an unbalanced force acts on it.

5.1.2

5.2.1

5.2.2hit (the net force) the windscreen and go through it, or hit the steering wheel and dash and receive injuries.


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5.3.1 When you walk along and then step off a moving walkway at normal walking speed, the inertia you have due to the motion of

5.3.2actually your forward inertia trying to keep you moving straight ahead.

If you are sitting in a car moving with constant velocity in a straight line, your inertia is not apparent. It only becomes noticeable when the car brakes.

5.4.1 (a) If you are travelling more slowly, then your momentum is less, so in the event of a collision, the impulse on you due to the collision will be less, both because you do not have as much momentum to lose and also because the time of the collision will probably be shorter.

(b) During a collision, as your inertia causes you to continue to move forwards, the airbag ensures that you lose your momentum slowly, by making the time of collision with the bag much longer than it would be if you hit the windscreen. Therefore, while the impulse will be the same, the force involved will be less.

(c) Crumple zones in vehicles are designed to increase the time of the collision and so while the momentum lost (the impulse imparted to the car and you) is the same, the forces involved will be smaller.

5.5.1

5.5.2 One reason is that the impulse of the airbag on the child, whose bones are softer can cause more injury than a similar impulse on an adult.

5.5.3 The plastic bumper bar crumples more easily than a steel bar and so momentum of the collision is absorbed in the crumpling,

possibility.

5.6.1 Crumple bars, airbags, plastic components instead of all steel, seatbelts, engines that move downwards under the driver instead of straight back into the driver.

5.6.2the time of the collision or, in the case of the engine movement, totally avoiding an impact.


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