NSW PHYSICS MODULES 1 TO 4. Brian Shadwick

Transcription

1 NSW PHYSICS MODULES 1 TO 4 Brian Shadwick

2 2018 First published 2018 Private Bag 7023 Marrickville NSW 1475 Australia Tel: Fax: sales@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. ABN

3 Contents Words to Watch Introduction iv v Dot Points Module 1 Kinematics Module 2 Dynamics Module 3 Waves and Thermodynamics Module 4 Electricity and Magnetism vi vii ix xii Questions Module 1 Kinematics 1 Module 2 Dynamics 65 Module 3 Waves and Thermodynamics 143 Module 4 Electricity and Magnetism 263 Answers Module 1 Kinematics 332 Module 2 Dynamics 349 Module 3 Waves and Thermodynamics 367 Module 4 Electricity and Magnetism 391 Appendix Data Sheet 406 Formulae Sheet 407 Periodic Table 408 Index 409 iii Contents

4 Words to Watch account, account for State reasons for, report on, give an account of, narrate a series of events or transactions. analyse Interpret data to reach conclusions. annotate Add brief notes to a diagram or graph. apply Put to use in a particular situation. assess Make a judgement about the value of something. calculate Find a numerical answer. clarify Make clear or plain. classify Arrange into classes, groups or categories. comment Give a judgement based on a given statement or result of a calculation. compare Estimate, measure or note how things are similar or different. construct Represent or develop in graphical form. contrast Show how things are different or opposite. create Originate or bring into existence. deduce Reach a conclusion from given information. define Give the precise meaning of a word, phrase or physical quantity. demonstrate Show by example. derive Manipulate a mathematical relationship(s) to give a new equation or relationship. describe Give a detailed account. design Produce a plan, simulation or model. determine Find the only possible answer. discuss Talk or write about a topic, taking into account different issues or ideas. distinguish Give differences between two or more different items. draw Represent by means of pencil lines. estimate Find an approximate value for an unknown quantity. evaluate Assess the implications and limitations. examine Inquire into. explain Make something clear or easy to understand. extract Choose relevant and/or appropriate details. extrapolate Infer from what is known. hypothesise Suggest an explanation for a group of facts or phenomena. identify Recognise and name. interpret Draw meaning from. investigate Plan, inquire into and draw conclusions about. justify Support an argument or conclusion. label Add labels to a diagram. list Give a sequence of names or other brief answers. measure Find a value for a quantity. outline Give a brief account or summary. plan Use strategies to develop a series of steps or processes. predict Give an expected result. propose Put forward a plan or suggestion for consideration or action. recall Present remembered ideas, facts or experiences. relate Tell or report about happenings, events or circumstances. represent Use words, images or symbols to convey meaning. select Choose in preference to another or others. sequence Arrange in order. show Give the steps in a calculation or derivation. sketch Make a quick, rough drawing of something. solve Work out the answer to a problem. state Give a specific name, value or other brief answer. suggest Put forward an idea for consideration. summarise Give a brief statement of the main points. synthesise Combine various elements to make a whole. Words to Watch iv

5 Introduction What the book includes This book provides questions and answers for each dot point in the NSW Physics Stage 6 Syllabus for each module in the Year 11 Physics course: Module 1 Kinematics Module 2 Dynamics Module 3 Waves and Thermodynamics Module 4 Electricity and Magnetism Format of the book The book has been formatted in the following way: 1.1 Subtopic from syllabus Assessment statement from syllabus First question for this assessment statement Second question for this assessment statement. The number of lines provided for each answer gives an indication of how many marks the question might be worth in an examination. As a rough rule, every two lines of answer might be worth 1 mark. How to use the book Completing all questions will provide you with a summary of all the work you need to know from the syllabus. 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. When working through the questions, write the answers you have to look up in a different colour to those you know without having to research the work. This will provide you with a quick reference for work needing further revision. v Introduction

6 Module 1 Kinematics Module 1 Kinematics Dot Point Page Dot Point Page Motion In a Straight Line and On a Plane inquiry questions How is the motion of an object moving in a straight line described and predicted? How is the motion of an object that changes its direction of movement on a plane described? 1.1 Describe uniform straight line (rectilinear) 3 motion and uniformly accelerated motion through qualitative descriptions Distance and displacement Working out directions another way Speed and velocity Acceleration SI units and powers of Use mathematical modelling and graphs 12 to analyse and derive relationships between time, distance, displacement, speed, velocity and acceleration in rectilinear motion. 1.3 Describe ways in which the motion of 12 objects changes and describe and analyse these graphically for velocity and displacement Displacement-time graphs Displacement-time graphs Displacement-time graphs Velocity-time graphs Velocity-time graphs Acceleration-time graphs Acceleration-time graphs Some further graph questions Conduct an investigation to gather data 25 to facilitate the analysis of instantaneous and average velocity through quantitative, first-hand measurements and graphical representation and interpretation of data Analysing experimental data Use mathematical modelling to analyse 27 and derive relationships between time, distance, displacement, speed, velocity and acceleration in rectilinear motion including: s = ut + 1 _ 2 at2, v = u + at and v 2 = u 2 + 2as Calculating speed and velocity Calculating acceleration Conduct investigations, selecting from 34 a range of technologies, to record and analyse the motion of objects in a variety of situations in one dimension in order to measure or calculate time, distance, displacement, speed, velocity and acceleration Analysing an experiment Analysing an experiment Describe uniform straight line (rectilinear) 39 motion and uniformly accelerated motion through the use of scalar and vector quantities Vectors and scalars Analyse vectors in one and two 42 dimensions to resolve a two-dimensional vector into two independent, perpendicular components Resolving vectors into components Analyse vectors in one and two dimensions 43 to add two perpendicular vector components to obtain a single vector Finding vector resultants Represent distance and displacement 44 of objects moving on a plane using vector addition and components of vectors Adding vectors in a straight line Subtracting vectors in a straight line Adding and subtracting vectors 46 in a straight line. Dot Points vi

7 Module 1 Kinematics Module 2 Dynamics Dot Point Page Dot Point Page 1.11 Describe ways in which the motion of 47 objects changes and describe and analyse these algebraically and with vector diagrams for velocity and displacement Adding vectors in two dimensions Subtracting vectors in two dimensions Vectors in two dimensions Calculate the relative velocity of two 53 objects moving along the same line using vector analysis Relative velocity Describe and analyse the relative 54 positions and motions of one object relative to another on a plane using vector analysis Relative velocity Analyse the relative motion of objects in 56 two dimensions for the motion of a boat on a flowing river Boats in flowing water Analyse the relative motion of objects in 59 two dimensions for the motion of two moving cars Relative velocities of cars Analyse the relative motion of objects in 61 two dimensions for the motion of an aeroplane in a crosswind Planes in crosswinds. 61 Answers to Kinematics 332 Forces, Acceleration, Momentum and Energy inquiry questions How are forces produced between objects and what effects do forces produce? How can the motion of objects be explained and analysed? How is the motion of objects in a simple system dependent on the interaction between the objects? 2.1 Use Newton s laws of motion and in 67 particular the third law, to describe static and dynamic interactions between two or more objects and the changes that occur resulting from a contact force Dynamic and static forces Equilibrium and Newton s first law Explore the concept of net force and 69 equilibrium in one-dimensional and two-dimensional contexts using algebraic addition, vector addition, and vector addition by resolution into components. 2.3 Apply the following relationships, solve 69 problems or make quantitative predictions about resultant and component forces using F x = F cos θ and F y = F sin θ Forces in one and two dimensions 69 Vector revision Forces in two dimensions Forces in two dimensions Apply Newton s first two laws of motion 73 to a variety of everyday situations, including both static and dynamic examples, and the role played by friction Newton s first law of motion and inertia The role of friction Coefficient of friction Investigate, describe and analyse the 78 acceleration of a single object subjected to a constant net force and relate the motion of the object to Newton s second law of motion through the use of qualitative descriptions and including F = ma for uniformly accelerated motion Newton s second law Qualitative 78 descriptions Newton s second law: F = ma. 79 vii Dot Points

8 Module 2 Dynamics Module 2 Dynamics Dot Point Page Dot Point Page 2.6 Investigate, describe and analyse the 82 acceleration of a single object subjected to a constant net force and relate the motion of the object to Newton s second law of motion through the use of graphs and vectors. 2.7 Derive relationships including F = ma 82 and relationships of uniformly accelerated motion Analysing two motion experiments Conduct an investigation to explain 84 and predict the motion of objects on inclined planes Analysing an experiment Objects on 84 an incline Motion on an inclined plane Apply the following relationship, solve 89 problems or make quantitative predictions about resultant and component forces using F AB = F BA Newton s third law Conduct an investigation to analyse 92 Hooke s law: F = kx Hooke s law Analysing experimental 92 results Hooke s law Analysing experimental 92 results Apply the law of conservation of 94 mechanical energy to the quantitative analysis of motion involving elastic potential energy transferred to an object: U P = 1 _ 2 kx Energy stored in a stretched spring Apply the law of conservation of 97 mechanical energy to the quantitative analysis of motion involving work done and change in kinetic energy of an object undergoing acceleration in one dimension: W = F net s Work done by forces Investigate the relationship and analyse 100 information obtained from graphical representations of force versus distance Force-displacement graphs Conduct investigations over a range of 102 mechanical processes to analyse qualitatively and quantitatively the concept of average power: P = E t, P = F, v including uniformly accelerated motion and work done against air resistance, rolling resistance and friction Power Apply the law of conservation of 105 mechanical energy to the quantitative analysis of motion involving changes in gravitational potential energy of an object in a uniform field: ΔU = mgδh Gravitational potential energy Energy transformations near the surface Use Newton s laws of motion and in 112 particular the third law, to describe static and dynamic interactions between two or more objects and the changes that occur resulting from a force mediated by fields Horizontal blocks in contact Masses connected by strings 114 Horizontal surface Masses connected over pulleys Masses connected by vertical strings Conduct investigations over a range of 119 mechanical processes to analyse qualitatively and quantitatively the concept of average power: P = E t, P = F, v including objects raised against the force of gravity Power Investigate the effects of forces involved 122 in collisions and other interactions and analyse the interactions quantitatively using the concept of impulse: Δp = FΔt Impulse and momentum Momentum and road safety Conduct an investigation to describe 126 and analyse one-dimensional interactions of objects in closed systems Analysing a momentum collision. 126 Dot Points viii

9 Module 2 Dynamics Module 3 Waves and Thermodynamics Dot Point Page Dot Point Page 2.20 Quantitatively analyse and predict, 127 using the laws of conservation of momentum: mv before = mv after the results of interactions in collisions Colliding objects Colliding objects Colliding objects Colliding objects Conduct an investigation to describe 133 and analyse two-dimensional interactions of objects in closed systems Analysing experimental data Two 133 dimensions Analysing another two-dimensional 134 collision Quantitatively analyse and predict, 135 using the laws of conservation of momentum: mv before = mv after (two dimensions) the results of interactions in two dimensions Collisions in two dimensions Investigate the relationship and 137 analyse information obtained from graphical representations of force versus time Force-time graphs Force and time in collisions Analyse and compare the kinetic 141 energy of elastic and inelastic collisions Quantitatively analyse and predict, 141 using the laws of conservation of momentum: mv before = mv after and kinetic energy: 1 _ 2 mv2 = before 1 _ 2 mv2 after the results of interactions in elastic collisions Elastic and inelastic collisions. 141 Answers to Dynamics 349 Wave Characteristics inquiry question What are the properties of all waves and wave motion? 3.1 Conduct an investigation to create 145 mechanical waves in a variety of situations to explain the role of the medium in the propagation of mechanical waves Role of the medium carrying a wave Conduct an investigation to create 146 mechanical waves in a variety of situations to explain the transfer of energy involved in the propagation of mechanical waves Transfer of energy by mechanical waves Conduct investigations to explain 147 and analyse differences between transverse and longitudinal waves Transverse matter waves Longitudinal matter waves Conduct investigations to explain 152 and analyse differences between mechanical and electromagnetic waves Electromagnetic waves Some general wave questions Construct and/or interpret graphs 159 of displacement versus time and displacement versus position of transverse and longitudinal waves and relate the features of these graphs to the wave characteristics of velocity, frequency, period, wavelength, wave number, displacement and amplitude Analysing wave graphs Analysing wave graphs Solve problems and/or make predictions 163 by modelling, deriving and applying the following relationships to a variety of situations: v = fλ and f = 1 T The wave equation. 163 ix Dot Points

10 Module 3 Waves and Thermodynamics Module 3 Waves and Thermodynamics Dot Point Page Dot Point Page Wave Behaviour and the Ray Model Of Light inquiry questions How do waves behave? What properties can be demonstrated when using the ray model of light? 3.7 Explain the behaviour of waves in a variety 164 of situations by investigating reflection Reflection Reflection Analysing an experiment Reflection from curved surfaces Explain the behaviour of waves in a variety 171 of situations by investigating refraction Refraction Quantitatively predict, using Snell s law 173 and the concept of refractive index, the refraction and total internal reflection of light in a variety of situations including the use of n 1 sin i = n 2 sin r and sin i c = 1 n for the critical angle x ic of medium x Refraction Refraction Total internal reflection Analysing a total internal reflection 179 experiment Conduct investigations to analyse 180 qualitatively and quantitatively the refraction and total internal reflection of light including the use of n x = c for the refractive index of medium x, where v x is the speed of light in the medium Refraction Analysing a refraction experiment Another refraction analysis Some more refraction problems Explain the behaviour of waves in a 187 variety of situations by investigating diffraction Diffraction. 187 v x 3.12 Conduct an investigation to 189 distinguish between progressive and stationary waves Progressive and stationary waves Explain the behaviour of waves in a 191 variety of situations by investigating wave superposition Superposition of waves Superimposing waves Conduct an investigation to explore 194 resonance in mechanical systems and the relationships between the driving frequency, the natural frequency of the oscillating system, the amplitude of motion and the transfer or transformation of energy within the system Mechanical resonance Conduct an investigation to explain 196 the formation of images in mirrors and lenses via reflection using the ray model of light Forming images with concave mirrors Forming images with convex mirrors Forming images with concave lenses Forming images with convex lenses Conduct an investigation to 208 demonstrate and explain the phenomenon of the dispersion of light Dispersion of light Conduct an investigation to 209 demonstrate and relate the inverse square law, the intensity of light and the transfer of energy including the use of l 1 r 2 1 = l 2 r 2 2 to compare the intensity of light at two points, r 1 and r Investigate the relationship between 209 distance and intensity of sound The inverse square law The inverse square law 2 Analysing 210 a graph. Dot Points x

11 Module 3 Waves and Thermodynamics Module 3 Waves and Thermodynamics Dot Point Page Dot Point Page Soundwaves inquiry question What evidence suggests that sound is a mechanical wave? 3.19 Conduct an investigation to relate 212 the pitch and loudness of a sound to its wave characteristics Model the behaviour of sound in air 212 as a longitudinal wave Relate the displacement of air 212 molecules to variations in pressure More about soundwaves Conduct investigations to analyse 215 the reflection of soundwaves Applications of reflection of sound Conduct investigations to analyse 217 the diffraction of soundwaves Diffraction of soundwaves Conduct investigations to analyse 219 the resonance of soundwaves Acoustic resonance Investigate and model the behaviour 220 of standing waves in strings to quantitatively relate the fundamental and harmonic frequencies of the waves produced to the physical properties (e.g. length, mass, tension, wave speed) of the medium Standing waves in strings Investigate and model the behaviour 222 of standing waves in pipes to quantitatively relate the fundamental and harmonic frequencies of the waves produced to the physical properties (e.g. length, mass, tension, wave speed) of the medium Standing waves in pipes Conduct investigations to analyse the 224 superposition of soundwaves Analyse qualitatively and quantitatively, 224 the relationships for the wave nature of sound to explain beats including f beat = f 2 f Superposition of soundwaves. 224 ± 3.29 Analyse qualitatively and quantitatively, 227 the relationships for the wave nature of sound to explain the Doppler effect: f [ = f v ± v wave observer v wave v source ] The Doppler effect Mathematics and the Doppler effect. 229 Thermodynamics inquiry question How are temperature, thermal energy and particle motion related? 3.30 Explain the relationship between the 232 temperature of an object and the kinetic energy of the particles within it The kinetic theory of matter Kinetic theory and properties of matter Temperature and the kinetic theory Changes of state and the kinetic theory Explain the concept of thermal 239 equilibrium Thermal equilibrium Analyse the relationship between the 240 change in temperature of an object, its change in heat energy and its specific heat capacity through the equation ΔQ = mcδt Transferring heat energy xi Dot Points

12 Module 3 Waves and Thermodynamics Module 4 Electricity and Magnetism Dot Point Page Dot Point Page 3.33 Apply the following relationship to 242 solve problems or make quantitative predictions in a variety of situations using ΔQ = mcδt where c is the specific heat capacity of a substance Transferring heat energy Investigate how energy transfer 244 occurs via conduction, convection and radiation Heat conduction Heat convection Heat radiation Conduct an investigation to analyse, 249 qualitatively and quantitatively, the latent heat involved in a change of state Changes of state and latent energy Analysing an experiment Changes of state and latent energy Analysing another experiment Transferring heat energy Quantitatively model and predict 261 energy transfer from hot objects using the concept of thermal conductivity Apply the following relationship 261 to solve problems or make quantitative predictions in a variety of situations: Q t = kaδt where k d is the thermal conductivity of a material Thermal conductivity. 261 Answers to Waves and Thermodynamics 367 Electrostatics inquiry question How do charged objects interact with other charged objects and with neutral objects? 4.1 Conduct investigations to describe 265 and analyse qualitatively and quantitatively the processes by which objects become electrically charged Electrostatic charges The electrostatic charge Conduct investigations to describe 267 and analyse qualitatively and quantitatively the forces produced by objects as a result of their interactions with charged particles Electrostatics research assignment Conduct investigations to describe 268 and analyse qualitatively and quantitatively the variables that affect electrostatic forces between objects. 4.4 Apply the electric field model to 268 account for and quantitatively analyse interactions between charged objects using F = 1 q q πε 0 r Variables affecting electrostatic forces Use electric field lines to model 271 qualitatively the direction and strength of electric fields produced by simple point charges, pairs of charges, dipoles and parallel charged plates Electric fields Apply the electric field model to 275 account for and quantitatively analyse interactions between charged objects using E = F q = kq d Electric field strength Force on a charge in an electric field. 276 Dot Points xii

13 Module 4 Electricity and Magnetism Module 4 Electricity and Magnetism Dot Point Page Dot Point Page 4.7 Apply the electric field model to 279 account for and quantitatively analyse interactions between charged objects using E = V d Electric field strength between parallel 279 plates. 4.8 Analyse the effects of a moving charge 282 in an electric field to relate potential energy, work and equipotential lines by applying V = Δu where U is q potential energy and q is the charge Work done by fields. 282 Electric circuits inquiry question How do the processes of the transfer and the transformation of energy occur in electric circuits? 4.9 Investigate the flow of electric 285 current in metals and apply models to represent current including the use of I = q t The charge model for electric current Investigate quantitatively the 287 current-voltage relationships in ohmic and non-ohmic resistors to explore the usefulness and limitations of Ohm s law using V = W q and R = V I Electrical potential difference Electrical potential difference Resistance A practical analysis Electrical resistance Ohmic and non-ohmic conductors Investigate series circuits qualitatively 296 and quantitatively to relate the flow of current through individual components, the potential differences across them and the rate of energy conversion by the components to the laws of conservation of charge and energy by deriving the following relationships: Σ I = 0 (Kirchoff s current law conservation of charge) Σ V = 0 (Kirchoff s voltage law conservation of energy) R Series = R 1 + R R n Symbols, open and closed circuits Conductors in series and parallel Using ammeters Using voltmeters Potential around a series circuit Conductors in series Analysing an 304 experiment Conductors in series Investigate parallel circuits qualitatively 308 and quantitatively to relate the flow of current through individual components, the potential differences across them and the rate of energy conversion by the components to the laws of conservation of charge and energy by deriving the following relationships: Σ I = 0 (Kirchoff s current law conservation of charge) Σ V = 0 (Kirchoff s voltage law conservation of energy) 1 = R Parallel R 1 R 2 R n Potential around a parallel circuit Conductors in parallel Analysing an 309 experiment Conductors in parallel. 310 xiii Dot Points

14 Module 4 Electricity and Magnetism Module 4 Electricity and Magnetism Dot Point Page Dot Point Page 4.13 Investigate series and parallel 314 circuits qualitatively and quantitatively to relate the flow of current through individual components, the potential differences across them and the rate of energy conversion by the components to the laws of conservation of charge and energy Conductors in series and parallel Investigate quantitatively the 316 application of the law of conservation of energy to the heating effects of electric currents, including the application of P = IV and variations of this involving Ohm s law Electrical power Analysing an experiment. 318 Magnetism 4.18 Apply models to qualitatively 325 represent and quantitatively describe the features of magnetic fields Features of magnetic fields Conduct investigations into and 326 describe quantitatively the magnetic fields produced by wires, including B = μ I 0 or B = ki. 2πr d Magnetic fields around straight 326 conductors Conduct investigations into and 328 describe quantitatively the magnetic fields produced by solenoids, including B = μ NI 0 L Magnetic fields and solenoids Answers to Electricity and Magnetism 391 inquiry question How do magnetised and magnetic objects interact? 4.15 Investigate and describe qualitatively 320 the force produced between magnetised and magnetic materials in the context of ferromagnetic materials Investigate and explain the process by 320 which ferromagnetic materials become magnetised Magnetic forces and ferromagnetic 320 materials Use magnetic field lines to model 321 qualitatively the direction and strength of magnetic fields produced by magnets, current carrying wires and solenoids and relate these fields to their effect on magnetic materials that are placed within them Magnets and magnetic fields Magnetic fields around straight 322 conductors Magnetic fields and solenoids Dot Points xiv

15 DOT POINT MODULE 1 Kinematics CONTENT FOCUS In this module you will: ~ ~ Investigate aspects of kinematics by describing, measuring and analysing motion without considering the forces and the masses involved in that motion. ~ ~ Explore uniformly accelerated motion in terms of relationships between measurable scalar and vector quantities, including displacement, speed, velocity, acceleration and time. ~ ~ Describe linear motion and predicted motion both qualitatively and quantitatively using graphs and vectors, and the equations of motion. ~ ~ Understand that scientific knowledge can enable scientists to offer valid explanations and make reliable predictions, particularly in regard to the motion of an object. ~ ~ Engage with all the Working Scientifically skills for practical investigations involving the focus content to examine trends in data and to solve problems related to kinematics. 1 Module 1 Kinematics

16 Motion In a Straight Line and On a Plane 1.1 Describe uniform straight line (rectilinear) motion and uniformly accelerated motion through qualitative descriptions Distance and displacement Compare the distance travelled by an object with its displacement Three objects travel from X to Y by three different roads as shown in the diagram. Y is due east of X. Road 1 = 75 km X Road 2 = 50 km Y Road 3 = 150 km Complete the table to show information about the three trips. Object travelling by Distance travelled (km) Displacement (km) Road 1 Road 2 Road Object X starts from A and travels a total distance of 500 m and has a final displacement of 300 m east. Outline, with the inclusion of diagrams if needed, three different ways that object X could do this. 3 Module 1 Kinematics

17 Person X walks from points A to B to C as shown on the diagram, and then back to A. A 10 km N 10 km C 10 km B (a) (b) (c) (d) (e) (f) What is the distance travelled when X is at B? What is the displacement of X at B? What is the distance travelled when X is at C? What is the displacement of X at C? What is the distance travelled when X is back at A? What is the displacement of X at A? The diagram represents a journey made from A to E. The path of the journey is superimposed on a grid where each grid square is m. Complete the table to show details of the journey. Use compass directions for the displacement, taking right as east. B A Position Distance travelled (m) Displacement from A (m) A B C C D E D E Module 1 Kinematics 4

18 1.1.2 Working out directions another way (a) Clarify the idea of bearings as used for directions. (b) Why are bearings preferred when giving directions rather than compass directions? Expressing the directions as bearings, calculate the displacement represented by each of the vectors in the diagram. Each snail started at the origin. (Don t forget the scale!) A C B North D Scale: 1 cm = 10 m F E Vector Displacement (m) Direction as compass direction Direction as bearing A B C D E F 5 Module 1 Kinematics

19 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. Complete the table to show information about the four wombats trips. Wombat 1 N Wombat 2 Wombat 3 Wombat 4 Wombat Distance travelled (m) Displacement (m) (directions as compass readings) Displacement (m) (directions as bearings) X, Y and Z are three beacon towers on the tops of high hills. X is on a bearing of 045 from Y and is 24 km away. Z is on a bearing of 135 from X and is 18 km away. By drawing an appropriate diagram, determine the bearing of Y from Z and the distance between Y and Z. Module 1 Kinematics 6

20 (a) A fishing boat is somewhere in the sea near points A, B and C. Use the information given to find where it is. Mark the position on the map with an X. An observer at A sees the fishing boat on a bearing of 120. An observer at B sees the boat on a bearing of 030. N A N C N B (b) The distance between points A and B is 15 km. How far away from C is the fishing boat? (c) On what bearing would the fisherman see a lighthouse in the middle of C? (d) On what bearing would the lighthouse keeper see the fishing boat? 7 Module 1 Kinematics

21 1.1.3 Speed and velocity Distinguish between speed and velocity Describe two speed changes which occur during typical journeys in a car and state one reason for each change Compare average and instantaneous speed What do we mean by uniform velocity? Explain, giving an appropriate example how the velocity of an object moving at 30 m s 1 can change and yet still continue to move at 30 m s The ticker timer tapes show the motion of four objects starting from the left and moving to the right. A B C D (a) (b) Which tapes indicate the objects moving with constant speed? Which tapes indicate the objects moving with increasing speed? Justify your answer. (c) Which tapes indicate the objects moving with decreasing speed? Justify your answer. (d) Which tape shows motion which is least uniform? Justify your answer Distinguish between the different velocities below. Constant velocity Average velocity Instantaneous velocity Initial velocity Final velocity Module 1 Kinematics 8

22 1.1.4 Acceleration What is acceleration and what are the SI units used to measure it? Indicate the three different ways an object could accelerate What do we mean by uniform acceleration? An object is travelling at 35 m s 1 towards the east. It accelerates without changing its speed. How does it do this? Justify your answer In physics we sometimes refer to acceleration as being positive or negative. Explain what is meant by this An object has zero acceleration. Describe how it might be moving Imagine that you are in a car and wearing a blindfold so that you cannot see outside. The car starts accelerating forwards. (a) How would you be able to tell that the car was accelerating? (b) What name do we give to the effect you describe in your answer to (a)? Explain what it means. 9 Module 1 Kinematics

23 1.1.5 SI units and powers of What are SI units and why are they used? List the rules we should use when using SI units Units like kilometres per hour, or light years, or hours are not SI units, but we often use them in physics. Explain why On the diagram below draw in a labelled arrow to show the size of a school bus. Size of a typical atom Length of a soccer field Radius of the Earth Metres Radius of hydrogen nucleus Diameter of a wire Height of Mount Everest Module 1 Kinematics 10

24 Complete the table to give the SI units most commonly used in calculations for the quantities listed. You may have to research some quantities. Quantity SI unit (name and symbol) Quantity SI unit (name and symbol) Mass Electric potential difference Length Electrical resistance Time Electric current Displacement Speed Force Velocity Energy Acceleration Power Temperature Momentum Volume Complete the table. Unit prefix Symbol Meaning Unit prefix Symbol Meaning deca 10 1 hecta 10 2 k M m μ 10 9 nano pico femto E a zeta yotta Module 1 Kinematics

25 DOT POINT Answers 331 Answers

26 Module 1 Kinematics Distance travelled is a measure of how far an object has moved from its starting point. Displacement indicates how far, in a straight line, an object is from its starting point, and the direction of its finish position from its starting position Answers may vary, for example: (i) Object can start at displacement 200 m west and move 500 m east. (ii) Object could start at a displacement of 800 m east and move 500 m west. (iii) Object could start at zero displacement, move 400 m east then turn around and move back 100 m west (a) Distance travelled when X is at B = 10 km (b) Displacement of X at B = 10 km S 60 E (c) Distance travelled when X is at C = 20 km (d) Displacement of X at C = S 30 W (e) Distance travelled when X is back at A = 30 km (f) Displacement of X at A = Displacement from Position Distance travelled (m) A (m) A (a) Bearings are angles measured clockwise from north and are always expressed as three numeral figures, e.g. bearing 060 or bearing 279. (b) Bearings are used in all navigational directions (boats, planes) as they are less subject to misinterpretation compared to compass directions Object travelling by Vector Distance travelled (km) Displacement (km) Road east Road east Road east B west C S 18 E D S 33.7 W E south Displacement (m) Direction as compass direction Direction as bearing A 95 N 53 W 307 B 26 N 20 W 340 C 60 N 15 E 015 D 23 E 44 S 134 E 50 S 30 W 210 F 91 W 21 S From the diagram, Y is 30 km from Z on a bearing of 262. Y (a) A N N 30 B 30 Wombat km Distance travelled (m) X Displacement (m) (directions as compass readings) km km Displacement (m) (directions as bearing) N 64º W 55 bearing N 65º E 58 bearing S 46º E 30 bearing S 22º W 32 bearing 202 Position of fishing boat (b) About 12.4 km. (c) Approximately bearing 102 (Note: The lighthouse is in the centre of the island C.) (d) Bearing Speed is a measure of how fast an object is moving and velocity is a measure of both how fast it is moving and in what direction it moves. Alternatively: Speed is a measure of the rate of change of distance travelled, while velocity is a measure of the rate of change of displacement Answers will vary for example: Slowing down for traffic lights, corners, going up hills. Pedestrian crossings. Speeding up after lights go green, coasting downhill, change in speed limits. C N Z Answers 332

27 Average speed is a calculated value equal to the total distance travelled divided by the total time taken while instantaneous speed is the actual speed of a vehicle at a particular instant of time Uniform used in this context means constant. If the velocity is uniform then its magnitude and direction of travel are constant If a car goes around a corner at constant speed, its speed is uniform, but because its direction is changing, its velocity is also changing (a) Tapes B and C. (b) First half of motion of D. (c) Tape D showing increasing speed initially, constant in the middle, then decreasing at the end. (d) Tape D object is decelerating in second half of the tape dots getting closer together Constant velocity Average velocity Instantaneous velocity Initial velocity Final velocity The velocity an object which travels the same displacement in every period of time. The constant velocity an object would need to travel at so as to travel the same displacement in the same time. The velocity of an object in the instant of time we consider it. This will vary from instant to instant depending on road and traffic conditions etc. The velocity of an object when we first consider it. The object s velocity at the start of its journey. The velocity of an object at the end of its journey or when we finish our consideration of its motion Acceleration is a measure of the rate at which velocity changes, measured in m s 2 (plus direction) (i) Speed up. (ii) Slow down. (iii) Turn a corner Uniform used in this context means constant. If the motion is uniform then the velocity of the object is constant. If the acceleration is uniform, then the object is accelerating at a constant rate and in a constant direction The object must turn a corner without changing its speed. Because the direction of travel changes, this constitutes an acceleration A positive acceleration is in the same direction of the velocity of the object under consideration, i.e. it speeds the object up. A negative acceleration is in the opposite direction to that motion, i.e. it slows the object down The object could be stationary or moving with uniform velocity (a) You would feel as if there was a force pushing you backwards (there isn t this is a fictitious force). (b) Your inertia acts to try to keep you in the same position, but the seat of the car puts a forwards force on you. Your body exerts a reaction force backwards on the seat due to its inertia your brain interprets this as a real force backwards which is it not SI units are units of measurement which form the Standard System of Units. These are units for the measurement of quantities which have been agreed on internationally and used so that communications of quantities between nations is easier. It is the modern form of the metric system (a) No full stops are used after units. (b) All units are lower case unless they are named in honour of a person (e.g. amperes = A). The only exception is L for litre to avoid confusion with some typeface number 1 s or letter i s. (c) If a combination of units is used, e.g. metres per second, there are three acceptable formats: (i) m/s (use a slider between the m and the s) (ii) m.s 1 (a full stop between the m and the s 1 ) (iii) m s 1 (a space between the m and the s 1 ) For large measurements, it is more sensible to use units which better suit that measurement. For example, we would not measure the distance to the next galaxy in metres. Light years, or parsec are much more sensible units. While they are not SI, there is international agreement on their use Size of a typical atom Length of a soccer field Radius of the Earth Metres Radius of hydrogen nucleus Diameter of a wire Bus Height of Mount Everest 333 Answers

28 Quantity SI unit (name and symbol) Quantity Mass kilogram (kg) Electric potential difference Length metre (m) Electrical resistance SI unit (name and symbol) volt (V) ohm (Ω Time second (s) Electric current ampere (A) Displacement metre (m) Speed metres per second (m s 1 ) Force newton (N) Velocity metres per second (m s 1 ) Energy joule (J) Acceleration metres per second per second (m s 2 ) Power watt (W) Temperature kelvin (K) Momentum kilogram metre per second (kg m s 1 or newton second (N s) Volume litre (L) Unit prefix Symbol Meaning Unit prefix Symbol Meaning deca da 10 1 deci d 10 1 hecta h 10 2 centi c 10 2 kilo k 10 3 mille m 10 3 mega M 10 6 micro μ 10 6 giga G 10 9 nano n 10 9 tera T pico p peta P femto f exa E atto a zeta Z zepto z (a) 7 m (b) 20 m south (c) 1.0 m s 1 south (d) 1.33 m s 1 south (a) 15 m (b) 1.5 m s 1 (c) 1.5 m s 1 south (d) 10 m south (e) 1.5 m s 1 south (a) 34 m (b) 56 m north (c) 2.8 m s 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 (a) 30 m (b) 70 m south (c) 3.5 m s 1 (d) 3.5 m s 1 south (e) About 2.25 m s 1 south (a) 40 m (b) 110 m north (c) 5.5 m s 1 (d) 5.5 m s 1 north (e) About 8.9 m s 1 north (a) Time (s) Displacement 4 m E 4 m E 8 m E 12 m E 16 m E 8 m E 0 yotta Y yocto y B C A D B D (a) Object starts at the zero displacement position then travels uniformly at 1.5 m s 1 east for 14 s then stops. After 14 s it is at a displacement of 21 m east. (b) Object starts at the zero displacement position then travels uniformly as 2.5 m s 1 for 8 s until it is at a displacement of 20 m N. It then stops and stays at this displacement for 6 s. (c) Object starts at a displacement of 12 m W then travels uniformly at 1.5 m s 1 east for 18 s at which time it is at a displacement of 15 m east. (d) Object starts at a displacement of 20 m north then travels uniformly at 2.5 m s 1 south for 14 s at which time it is at a displacement of 15 m south (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 (b) (c) (d) (e) (f) (a) From t = 0 to 4 s, 4 to 10 s, and 10 to 14 s (different values) Time interval 2.0 m s m s 1 west Distance travelled (m) Speed during time interval Velocity during time interval t = 0 and t = 2 Zero Zero t = 4 and t = 10 2 m s 1 2 m s 1 east t = 10 and t = 14 4 m s 1 4 m s 1 west Time (s) Time Instantaneous velocity (m s 1 ) m s 1 S 8 3 m s 1 S m s 1 N m s 1 N m s 1 N Answers 334