Physics Concepts and Connections textbook First Edition Igor

Physics Concepts and Connections textbook First Edition Igor
Physics Concepts and Connections textbook First Edition Igor
Physics Concepts and Connections textbook First Edition Igor

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4. book two
Brian Heimbecker
Igor Nowikow
Christopher T. Howes
Jacques Mantha
Brian P. Smith
Henri M. van Bemmel
Don Bosomworth, Physics Advisor
Toronto/Vancouver, Canada

5. Copyright © 2002 by Irwin Publishing Ltd.
National Library of Canada Cataloguing in Publication Data
Heimbecker, Brian
Physics: concepts and connections two
For use in grade 12
ISBN 0-7725-2938-8
1. Physics. I. Nowikow, Igor. II. Title.
QC23.N683 2002 530 C2002-900508-6
All rights reserved. It is illegal to reproduce any portion of this book in any form or
by any means, electronic or mechanical, including photocopy, recording or any
information storage and retrieval system now known or to be invented, without the
prior written permission of the publisher, except by a reviewer who wishes to quote
brief passages in connection with a review written for inclusion in a magazine,
newspaper, or broadcast.
Any request for photocopying, recording, taping, or for storing of informational
and retrieval systems, of any part of this book should be directed in writing CAN-
COPY (Canadian Reprography Collective), One Yonge Street, Suite 1900, Toronto,
ON M5E 1E5.
Cover and text design: Dave Murphy/ArtPlus Ltd.
Page layout: Leanne O’Brien, Beth Johnston/ArtPlus Ltd.
Illustration: Donna Guilfoyle, Sandy Sled, Joelle Cottle, Nancy Charbonneau/
ArtPlus Ltd., Dave McKay, Sacha Warunkiw, Jane Whitney
ArtPlus Ltd. production co-ordinator: Dana Lloyd
Publisher: Tim Johnston
Project developer: Doug Panasis
Editor: Lina Mockus-O’Brien
Photo research: Imagineering, Martin Tooke
Indexer: May Look
Published by
Irwin Publishing Ltd.
325 Humber College Blvd.
Toronto, ON M9W 7C3
Printed and bound in Canada
2 3 4 05 04 03 02
We acknowledge for their financial support of our publishing program, the Canada
Council, the Ontario Arts Council, and the Government of Canada through the Book
Publishing Industry Development Program (BPIDP).

6. Acknowledgements
The authors and the publisher would like to thank the following reviewers for their
insights and suggestions.
Bob Wevers, Teacher, Toronto, Toronto District School Board
Vince Weeks, Teacher, Burlington, Halton District School Board
Peter Mascher, Department of Engineering Physics, McMaster University
Andy Auch, Teacher, Windsor-Essex District School Board
Peter Stone, Teacher, Simcoe County District School Board
George Munro, Teacher, District School Board of Niagara
Brendan Roberts, Teacher, Windsor-Essex Catholic District School Board
To my wife Laurie and my children Alyssa and Emma for making it possible for me
to do this one more time.
I would like to thank David Badregon and Vanessa Mann for their contributions
to the problems and their solutions.
Brian Heimbecker
I would like to dedicate this book to my family: my wife Jane, my children Melissa
and Cameron, my mom Alla, and my brother Alex, as well as all my students.
Special thanks to the students who worked on various aspects of solutions and
research: Ashley Pitcher, Roman and Eugene Zassoko, Teddy Lazongas, and
Katherine Wetmore.
Igor Nowikow
Dedicated to my wife Marcy and daughter Alison, for their never-ending love and
support. In memory of the late Violet Howes and her passion for teaching.
I would like to thank Devin Smith (Queen’s University), Kristen Koopmans
(McMaster University), Jon Ho (University of Waterloo), and Paul Finlay
(University of Guelph) for their solutions to the problems.
Christopher T. Howes
To my wife Lynda for her support and encouragement, and to all my students who
make physics fun. I would like to thank Tyler Samson, a student at Confederation
Secondary School in Val Caron, for his contribution as a problem solver.
Jacques Mantha
I would like to thank my wife Judy and daughter Erin for their valuable sugges-
tions, and my son Brad for his careful solutions to the problems.
Brian P. Smith
I would like to dedicate my portion of this effort to my wife Nadine for her love and
support and to my parents, Hank and Enes, for showing me how to work.
Furthermore, I would like to acknowledge these wonderful students who assisted
in this effort: Valeri Dessiatnitchenko, Mehmood Ul Hassan, Huma Fatima Shabbir,
and Kunaal Majmudar.
Henri M. van Bemmel
Acknowledgements iii

8. Table of Contents
Table of Contents v
To the Student x
AForces and Motion: Dynamics 1
1 Kinematics and Dynamics
in One Dimension 4
1.1 Introduction 5
1.2 Distance and Displacement 5
Defining Directions 7
1.3 Unit Conversion and Analysis 7
1.4 Speed and Velocity 8
1.5 Acceleration 9
1.6 An Algebraic Description of Uniformly
Accelerated Linear Motion 10
1.7 Bodies in Free Fall 19
The Guinea and Feather Demonstration 19
Acceleration due to Gravity 20
1.8 A Graphical Analysis of Linear Motion 24
Velocity 24
1.9 Dynamics 32
1.10 Free-body Diagrams 33
1.11 Newton’s First Law of Motion:
The Law of Inertia 34
Inertial and Non-inertial Frames
of Reference 35
1.12 Newton’s Second Law of Motion: F
Br
netBma
Br36
1.13 Newton’s Third Law: Action–Reaction 39
1.14 Friction and the Normal Force 44
1.15 Newton’s Law of Universal Gravitation 48
Calculating Gravitational Forces 50
STSE — New Respect for the Humble Tire 52
Summary 54
Exercises 55
Lab 1.1 — Uniform Acceleration: The Relationship
between Displacement and Time 61
Lab 1.2 — Uniform Acceleration: The Relationship
between Angle of Inclination and Acceleration 62
2 Kinematics and Dynamics
in Two Dimensions 63
2.1 Vectors in Two Dimensions 64
Vector Addition 64
2.2 Relative Motion 70
Relative Velocity Problems 71
Problems Involving Non-perpendicular
Vectors 74
2.3 Projectile Motion 78
2.4 Newton’s Laws in Two Dimensions 85
2.5 The Inclined Plane 89
2.6 String-and-pulley Problems 93
2.7 Uniform Circular Motion 98
2.8 Centripetal Force 103
Centripetal Force and Banked Curves 106
Centrifugation 107
Satellites in Orbit 109
STSE — The Tape-measure Home Run 112
Summary 114
Exercises 115
Lab 2.1 — Projectile Motion 122
Lab 2.2 — Centripetal Force and Centripetal
Acceleration 123
Lab 2.3 — Amusement Park Physics 126
3 Extension: Statics — Objects
and Structures in Equilibrium 127
3.1 Keeping Things Still: An Introduction
to Statics 128
3.2 The Centre of Mass — The Gravity Spot 128
3.3 Balancing Forces … Again! 130
3.4 Balancing Torques 134
3.5 Static Equilibrium: Balancing Forces
and Torque 139
3.6 Static Equilibrium and the Human Body 148
3.7 Stability and Equilibrium 155
3.8 Elasticity: Hooke’s Law 159
3.9 Stress and Strain — Cause and Effect 161
Stress: The Cause of Strain 161
Strain: The Effect of Stress 163
3.10 Stress and Strain in Construction 170
STSE — The Ultimate Effect of Stress on
a Structure 172
Summary 174
Exercises 175
Lab 3.1 — Equilibrium in Forces 181
Lab 3.2 — Balancing Torque 183
BEnergy and Momentum 185
4 Linear Momentum 188
4.1 Introduction to Linear Momentum 189
4.2 Linear Momentum 189
4.3 Linear Momentum and Impulse 190
Force-versus-Time Graphs 195
4.4 Conservation of Linear Momentum
in One Dimension 199
4.5 Conservation of Linear Momentum
in Two Dimensions 203

9. 4.6 Linear Momentum and Centre of Mass 211
STSE — Recreational Vehicle Safety and Collisions 214
Summary 216
Exercises 217
Lab 4.1 — Linear Momentum in
One Dimension: Dynamic Laboratory Carts 222
Lab 4.2 — Linear Momentum in
Two Dimensions: Air Pucks (Spark Timers) 224
Lab 4.3 — Linear Momentum in
Two Dimensions: Ramp and Ball 227
5 Energy and Interactions 229
5.1 Introduction to Energy 230
Isolation and Systems 230
5.2 Work 233
Work from an F
Br
-versus-rd
Br
Graph 237
5.3 Kinetic Energy 239
Kinetic Energy and Momentum 241
5.4 Gravitational Potential Energy 243
5.5 Elastic Potential Energy and Hooke’s Law 249
Conservation of Energy 253
5.6 Power 255
5.7 Elastic and Inelastic Collisions 260
Equations for One-dimensional
Elastic Collisions 260
Graphical Representations of Elastic
and Inelastic Collisions 266
STSE — The Physics Equation — The Basis
of Simulation 270
Summary 272
Exercises 273
Lab 5.1 — Conservation of Energy Exhibited
by Projectile Motion 280
Lab 5.2 — Hooke’s Law 281
Lab 5.3 — Inelastic Collisions (Dry Lab) 282
Lab 5.4 — Conservation of Kinetic Energy 283
6 Energy Transfer 284
6.1 Gravity and Energy 285
A Comparison of rE
pBmgrh
and E
pBi
aG
r
Mm
i 289
Kinetic Energy Considerations 290
Escape Energy and Escape Speed 292
Implications of Escape Speed 293
6.2 Orbits 295
Kepler’s Laws of Planetary Motion 298
Kepler’s Third Law for Large Masses 300
Extension: Orbital Parametres 301
6.3 Simple Harmonic Motion —
An Energy Introduction 303
Hooke’s Law 304
6.4 Damped Simple Harmonic Motion 308
Three Types of Damping 308
Applications of Damping 309
Shock Absorbers 309
STSE — The International Space Station 310
Summary 312
Exercises 313
Lab 6.1 — The Pendulum 316
7 Angular Motion 317
7.1 Introduction 318
7.2 A Primer on Radian Measure 318
7.3 Angular Velocity and Acceleration 322
Angular Velocity 322
Relating Angular Variables to Linear Ones 323
More About Centripetal Acceleration 325
7.4 The Five Angular Equations of Motion 327
7.5 Moment of Inertia 332
Extension: The Parallel-axis Theorem 337
7.6 Rotational Energy 339
7.7 Rotational Kinetic Energy 342
7.8 The Conservation of Energy 344
7.9 Angular Momentum 347
7.10 The Conservation of Angular Momentum 348
7.11 The Yo-yo 352
Energy Analysis 352
Force Analysis 352
STSE — Gyroscopic Action — A Case of
Angular Momentum 354
Summary 357
Exercises 358
Lab 7.1 — Rotational Motion: Finding the
Moment of Inertia 365
CElectric, Gravitational,
and Magnetic Fields 367
8 Electrostatics and Electric Fields 370
8.1 Electrostatic Forces and Force Fields 371
8.2 The Basis of Electric Charge — The Atom 371
8.3 Electric Charge Transfer 373
Charging by Friction 374
Charging by Contact and Induction 375
8.4 Coulomb’s Law 377
The Vector Nature of Electric Forces
between Charges 384
8.5 Fields and Field-mapping Point Charges 388
Force at a Distance 388
8.6 Field Strength 394
Coulomb’s Law Revisited 395
Electricity, Gravity, and Magnetism:
Forces at a Distance and Field Theory 398
vi Physics: Concepts and Connections Book Two

10. 8.7 Electric Potential and Electric
Potential Energy 400
8.8 Movement of Charged Particles in
a Field — The Conservation of Energy 404
The Electric Potential around a
Point Charge 409
8.9 The Electric Field Strength of a
Parallel-plate Apparatus 414
Elementary Charge 415
STSE — Electric Double-layer Capacitors 418
Summary 421
Exercises 422
Lab 8.1 — The Millikan Experiment 430
Lab 8.2 — Mapping Electric Fields 433
9 Magnetic Fields and Field Theory 435
9.1 Magnetic Force — Another Force
at a Distance 436
9.2 Magnetic Character — Domain Theory 437
9.3 Mapping Magnetic Fields 438
9.4 Artificial Magnetic Fields —
Electromagnetism 441
Magnetic Character Revisited 442
A Magnetic Field around a Coiled
Conductor (a Solenoid) 443
9.5 Magnetic Forces on Conductors
and Charges — The Motor Principle 447
The Field Strength around a
Current-carrying Conductor 451
The Unit for Electric Current
(for Real this Time) 453
Magnetic Force on Moving Charges 456
9.6 Applying the Motor Principle 460
Magnetohydrodynamics 460
Centripetal Magnetic Force 461
The Mass of an Electron and a Proton 462
The Mass Spectrometer 464
9.7 Electromagnetic Induction —
From Electricity to Magnetism
and Back Again 467
STSE — Magnetic Resonance Imaging (MRI) 472
Summary 474
Exercises 475
Lab 9.1 — The Mass of an Electron 479
DThe Wave Nature of Light 481
10 The Wave Nature of Light 484
10.1 Introduction to Wave Theory 485
Definitions 485
Types of Waves 486
10.2 Fundamental Wave Concepts 488
Terminology 488
Phase Shift 490
Simple Harmonic Motion: A Closer Look 491
Simple Harmonic Motion in
Two Dimensions 492
10.3 Electromagnetic Theory 494
Properties of Electromagnetic Waves 494
The Speed of Electromagnetic Waves 494
The Speed of Light 495
The Production of Electromagnetic
Radiation 497
10.4 Electromagnetic Wave Phenomena:
Refraction 500
The Refractive Index, n— A Quick Review 500
Snell’s Law: A More In-depth Look 502
Refraction in an Optical Medium 504
Dispersion 505
The Spectroscope 506
10.5 Electromagnetic Wave Phenomena:
Polarization 507
Polarization of Light using Polaroids
(Polarizing Filters) 508
Malus’ Law: The Intensity of
Transmitted Light 509
Polarization by Reflection 511
Polarization by Anisotropic Crystals 512
10.6 Applications of Polarization 514
Polarizing Filters in Photography 514
3-D Movies 515
Radar 516
Liquid Crystal Displays (LCDs) 516
Photoelastic Analysis 517
Polarization in the Insect World 518
Polarized Light Microscopy 518
Measuring Concentrations of Materials
in Solution 518
10.7 Electromagnetic Wave Phenomena:
Scattering 519
STSE — Microwave Technology: Too Much
Too Soon? 522
Summary 524
Exercises 525
Lab 10.1 — Investigating Simple Harmonic Motion 529
Lab 10.2 — Polarization 530
Lab 10.3 — Malus’ Law 531
11 The Interaction of Electromagnetic
Waves 532
11.1 Introduction 533
11.2 Interference Theory 534
Path Difference 535
Table of Contents vii

11. Two-dimensional Cases 536
11.3 The Interference of Light 537
11.4 Young’s Double-slit Equation 538
11.5 Interferometers 544
Extension: Measuring Thickness using
an Interferometer 545
Holography 546
11.6 Thin-film Interference 548
Path Difference Effect 548
The Refractive Index Effect 549
Combining the Effects 549
11.7 Diffraction 553
Wavelength Dependence 553
11.8 Single-slit Diffraction 554
The Single-slit Equation 555
More Single-slit Equations (but they
should look familiar) 559
Resolution 561
11.9 The Diffraction Grating 563
The Diffraction-grating Equation 564
11.10 Applications of Diffraction 569
A Grating Spectroscope 569
Extension: Resolution — What makes
a good spectrometer? 569
X-ray Diffraction 571
STSE — CD Technology 574
Summary 576
Exercises 578
Lab 11.1 — Analyzing Wave Characteristics
using Ripple Tanks 583
Lab 11.2 — Qualitative Observations of the
Properties of Light 586
Lab 11.3 — Comparison of Light, Sound, and
Mechanical Waves 587
Lab 11.4 — Finding the Wavelength of Light
using Single Slits, Double Slits, and
Diffraction Gratings 588
EMatter–Energy Interface 589
12 Quantum Mechanics 592
12.1 Introduction 593
Problems with the Classical or Wave
Theory of Light 593
12.2 The Quantum Idea 594
Black-body Radiation 595
The Black-body Equation 596
12.3 The Photoelectric Effect 598
The Apparatus 598
12.4 Momentum and Photons 603
12.5 De Broglie and Matter Waves 606
12.6 The Bohr Atom 608
The Conservation of Energy 609
The Conservation of Angular Momentum 610
Electron Energy 612
Photon Wavelength 613
Ionization Energy 614
Bohr’s Model applied to Heavier Atoms 614
The Wave-Particle Duality of Light 614
12.7 Probability Waves 615
12.8 Heisenberg’s Uncertainty Principle 617
A Hypothetical Mechanical Example
of Diffraction 617
Heisenberg’s Uncertainty Principle
and Science Fiction 621
12.9 Extension: Quantum Tunnelling 622
STSE — The Scanning Tunnelling Microscope 624
Summary 626
Exercises 627
Lab 12.1 — Hydrogen Spectra 630
Lab 12.2 — The Photoelectric Effect I 631
Lab 12.3 — The Photoelectric Effect II 632
13 The World of Special Relativity 633
13.1 Inertial Frames of Reference and Einstein’s
First Postulate of Special Relativity 634
13.2 Einstein’s Second Postulate of Special
Relativity 637
13.3 Time Dilation and Length Contraction 640
Moving Clocks Run Slow 640
Moving Objects Appear Shorter 643
13.4 Simultaneity and Spacetime Paradoxes 646
Simultaneity 646
Paradoxes 647
Spacetime Invariance 649
13.5 Mass Dilation 652
Electrons Moving in Magnetic Fields 656
13.6 Velocity Addition at Speeds Close to c 659
13.7 Mass–Energy Equivalence 662
Relativistic Momentum 663
Relativistic Energy 664
13.8 Particle Acceleration 668
STSE — The High Cost of High Speed 674
Summary 676
Exercises 677
Lab 13.1 — A Relativity Thought Experiment 683
14 Nuclear and Elementary Particles 685
14.1 Nuclear Structure and Properties 686
Isotopes 687
Unified Atomic Mass Units 687
Mass Defect and Mass Difference 688
viii Physics: Concepts and Connections Book Two

12. Nuclear Binding Energy and Average
Binding Energy per Nucleon 688
14.2 Natural Transmutations 690
Nuclear Stability 690
Alpha Decay 691
Beta Decay 693
n
a
Decay (Electron Emission) 693
n
H
Decay (Positron Emission) 695
Electron Capture and Gamma Decay 695
14.3 Half-life and Radioactive Dating 697
Half-life 697
Radioactive Dating 698
14.4 Radioactivity 700
Artificial Transmutations 700
Detecting Radiation 703
14.5 Fission and Fusion 706
Fission 707
Fission Reactors 710
The CANDU Reactor 711
Fusion 712
Creating the Heavy Elements 715
Comparing Energy Sources — A Debate 717
14.6 Probing the Nucleus 718
14.7 Elementary Particles 720
What is matter? 720
What is matter composed of? 721
The Standard Model 721
Leptons 721
Quarks 723
Hadrons (Baryons and Mesons) 723
14.8 Fundamental Forces and Interactions —
What holds these particles together? 727
Forces or interactions? 727
Boson Exchange 728
Feynman Diagrams 729
Quantum Chromodynamics (QCD): Colour
Charge and the Strong Nuclear Force 730
The Weak Nuclear Force — Decay and
Annihilations 731
STSE — Positron Emission Tomography (PET) 736
Summary 739
Exercises 741
Lab 14.1 — The Half-life of a Short-lived
Radioactive Nuclide 747
Appendices 749
Appendix A: Experimental Fundamentals 750
Introduction 750
Safety 750
Appendix B: Lab Report 752
Lab Report 752
Statistical Deviation of the Mean 753
Appendix C: Uncertainty Analysis 755
Accuracy versus Precision 755
Working with Uncertainties 755
Making Measurements with Stated
Uncertainties 755
Manipulation of Data with Uncertainties 756
Addition and Subtraction of Data 756
Multiplication and Division of Data 757
Appendix D: Proportionality Techniques 758
Creating an Equation from a Proportionality 758
Finding the Correct Proportionality
Statement 759
Finding the Constant of Proportionality
in a Proportionality Statement 761
Other Methods of Finding Equations
from Data 761
Appendix E: Helpful Mathematical Equations
and Techniques 765
Mathematical Signs and Symbols 765
Significant Figures 765
The Quadratic Formula 766
Substitution Method of Solving Equations 766
Rearranging Equations 766
Exponents 767
Analyzing a Graph 767
Appendix F: Geometry and Trigonometry 768
Trigonometric Identities 768
Appendix G:SI Units 770
Appendix H:Some Physical Properties 773
Appendix I:The Periodic Table 774
Appendix J:Some Elementary Particles
and Their Properties 775
Numerical Answers to Applying the Concepts776
Numerical Answers to End-of-chapter
Problems 780
Glossary 786
Index 790
Photograph Credits 798
Table of Contents ix

13. To the Student
Physics is for everyone. It is more than simply the study of the physical uni-
verse. It is much more interesting, diverse, and far more extreme. In physics,
we observe nature, seek regularities in the data, and attempt to create math-
ematical relationships that we can use as tools to study new situations.
Physics is not just the study of unrelated concepts, but rather how every-
thing we do profoundly affects society and the environment.
Features
Flowcharts
The flowcharts in this book are visual summaries that graphically show you
the interconnections among the concepts presented at the end of each section
and chapter. They help you organize the methods and ideas put forward in
the course. The flowcharts come in three flavors: Connecting the Concepts,
Method of Process, and Putting It All Together. They are introduced as you
need them to help you review and remember what you have learned.
Examples
The examples in this book are loaded with both textual and visual cues, so
you can use them to teach yourself to do various problems. They are the
next-best thing to having the teacher there with you.
Applying the Concepts
At the end of most subsections, we have included a few simple practice ques-
tions that give you a chance to use and manipulate new equations and try out
newly introduced concepts. Many of these sections also include extensions of
new concepts into the areas of society, technology, and the environment to
show you the connection of what you are studying to the real world.
x Physics: Concepts and Connections Book Two
example 1
applylyin
g
theC
o
nce p
t
s
m
etho
d
p
r
oce s
s
of
c
o
nnec
tc
t
i
n
g
theC
o
nce p
t
s
puttin
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T
o
T
o
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eth
e
r
it all

14. End-of-chapter STSE
Every chapter ends with a feature that deals exclusively with how our stud-
ies impact on society and the environment. These articles attempt to intro-
duce many practical applications of the chapter’s physics content by
challenging you to be conscious of your responsibility to society and the envi-
ronment. Each feature presents three challenges. The first and most impor-
tant is to answer and ask more questions about the often-dismissed societal
implications of what we do. These sections also illustrate how the knowledge
and application of physics are involved in various career opportunities in
Canada. Second, you are challenged to evaluate various technologies by per-
forming correlation studies on related topics. Finally, you are challenged to
design or build something that has a direct correlation to the topic at hand.
Exercises
Like a good musician who needs to practise his or her instrument regularly,
you need to practise using the skills and tools of physics in order to become
good at them. Every chapter ends with an extensive number of questions to
give you a chance to practise. Conceptual questions challenge you to think
about the concepts you have learned and apply them to new situations. The
problems involve numeric calculations that give you a chance to apply the
equations and methods you have learned in the chapter. In many cases, the
problems in this textbook require you to connect concepts or ideas from
other sections of the chapter or from other parts of the book.
Labs
“Physics is for everyone” is re-enforced by moving learning into the practi-
cal and tactile world of the laboratory. You will learn by doing labs that
stress verification and review of concepts. By learning the concepts first and
applying them in the lab setting, you will internalize the physics you are
studying. During the labs, you will use common materials as well as more
high-tech devices.
Appendices
The appendices provide brief, concise summaries of mathematical methods
that have been developed throughout the book. They also provide you with
detailed explanations on how to organize a lab report, evaluate data, and
make comparisons and conclusions using results obtained experimentally.
They explain uncertainty analysis techniques, including some discussion
on statistical analysis for experiments involving repetitive measurements.
We hope that using this book will help you gain greater enjoyment in
learning about the world around us.
Toronto, 2002
Table of Contents xi
ST
SE
EXERCISES

16. unit a: Forces and Motion: Dynamics 1
1Kinematics and Dynamics
in One Dimension
2Kinematics and Dynamics
in Two Dimensions
3Extension: Statics —
Objects and Structures
in Equilibrium
Forces and
Motion: Dynamics
A
UNIT

17. 585 BC
430 BC
300 BC
14 0
1513
1543
159 6
330 BC
260 BC
530 BC
1570s
Timeline: The History of Forces
and Motion
:600 :400 :200 200 1500 15500
Early Greek natural
philosophers speculated
about the material that
composes everything.
Water and fire are
popular guesses.
Aristotle codified all of
Greek philosophy and
established concepts
of nature and the
universe that would
last for 2000 years.
Greeks suggested that
all matter is composed of
tiny atoms bumping and
clumping in empty space.
Euclid put together
300 years of Greek
mathematics in 13
books of The Elements,
still in use in the early
20th century.
Ptolemy—mathematician,
astronomer, and geographer.
Books by this epitome of
Greek science informed
students for the next
1400 years.
Copernicus improved
Ptolemy’s astronomy by
proposing that Earth
revolves around the Sun.
Copernicus—published
results of 30 years’ analysis
of the planetary system
with Sun at the centre of
planets’ orbits; Earth has
daily rotation on axis.
Kepler began 30-year
study of the orbits of
the planets.
Italian engineers
published studies of
mechanical devices
following principles
of Archimedes.
Archimedes made
substantial analysis of
the physics of floating
bodies and of levers.
Also conducted great
engineering projects.
Pythagoras established the branch of mathematics called geometry.
With three simple laws, Newton explained all motion around us. Yet, these
laws took thousands of years to formulate. Even though the ancient Greeks
made many valuable contributions to mathematics, philosophy, literature,
and the sciences, they didn’t perform experiments to test all their scientific
ideas, which led to some erroneous conclusions.
The classical physics we study today was mostly developed from the
mid-16th to the late 19th centuries. The scientific method was formally
developed and applied during the Enlightenment (17th and 18th centuries).
As a result, many important advances were made in many scientific fields.
Nicolas Copernicus (1473–1543), a Polish mathematician, explained the
daily motion of the Sun and stars by suggesting that Earth rotates on an
axis. Galileo Galilei (1564–1642), an Italian mathematician, experimented
extensively to test ancient theories of motion. His famous experiment of
dropping two stones, a large one and a small one, from the Tower of Pisa
disproved the ancient idea that mass determined the properties of motion.
The understanding of celestial mechanics grew quickly with Johannes
Kepler (1571–1630), who explained celestial results using Tycho Brahe’s
data (1546–1601). Sir Isaac Newton (1642–1727) developed the concepts of
gravity and laid the foundations of our current concepts of motion in his
published book, Principia Mathematica. With his three laws and the devel-
opment of the mathematical methods now called calculus, Newton is
responsible for our understanding of dynamics and kinematics. Newton
and Galileo created a new approach for scientific analysis — testing and
experimentation — which we still use today.
2 unit a: Forces and Motion: Dynamics

18. 1604
1602
1638
1610
1666
16 87
1769
1672
1785
1792
1971
16 00 16 5 0 1700 175 0 18 00
Galileo began
experimenting with
pendulums and
rolling balls down
inclined ramps.
Earlier theories of
motion had not
fitted experience.
Kepler published first two
laws of planetary motion.
Galileo published discovery
with telescope of Jupiter’s
moon and roughness of the
Moon’s surface.
Newton (age 24) laid
foundations for
calculus, experimental
optics, and notion of
“gravity extending to
the orb of the moon.”
Newton’s Mathematical
Principles of Natural
Philosophy built on
Kepler and Galileo to
describe forces and
motions on Earth and
on planets and comets.
Patents awarded to
Watt for improved
steam engine; and to
Arkwright for
harnessing water
power to spin cotton.
By 1604, Galileo had
derived a new theory
from analyzing
experiments. He found
objects fall distances
proportional to the
square of the time.
After being condemned
for Earth’s motion in
1633, Galileo published
result of a lifetime of
motion studies in his
Two New Sciences.
Huygens in Holland
published mechanical study
of his new pendulum clock,
accurate to 10 s per day —
a gigantic improvement.
Application of steam
engine to machine
spinning of cotton lead
to great expansion of
textile industry in Britain,
giving it economic and
technological domination
in the world.
The 14th General
Conference on Weights and
Measure picked seven
quantities as base quantities,
forming the basis of the
International System of Units
(SI), also called the metric
Republic of France
established a new system
of weights and measures,
defining the metre for the
first time. It also tried a
10-h day.
In this unit, we will learn various methods for
studying a variety of forces ranging from simple motion,
to motion with friction, to orbital motion. We will also
explain the motion of human beings, the development
of a variety of vehicles, and the reasons behind the
designs of different types of equipment, such as skis and
car tires, in terms of the classical laws of physics. This
unit lays the foundation for later units on momentum,
energy, fields, and modern physics.
unit a: Forces and Motion: Dynamics 3
Mechanics
Statics
Kinematics Motion
Neglect
force
Force
Force
No
motion
Motion Dynamics
F
F
F

19. 4
1
Kinematics and Dynamics
in One Dimension
By the end of this chapter, you will be able to
• analyze the linear motion of objects using graphical and algebraic methods
• solve problems involving forces by applying Newton’s laws of motion
• add and subtract vector quantities in one dimension
• solve problems involving Newton’s law of universal gravitation
Chapter Outline
1.1Introduction
1.2Distance and Displacement
1.3Unit Conversion and Analysis
1.4Speed and Velocity
1.5Acceleration
1.6An Algebraic Description of Uniformly
Accelerated Linear Motion
1.7Bodies in Free Fall
1.8A Graphical Analysis of Linear Motion
1.9Dynamics
1.10Free-body Diagrams
1.11Newton’s First Law of Motion:
The Law of Inertia
1.12Newton’s Second Law of Motion: F
AU
netNma
AU
1.13Newton’s Third Law: Action–Reaction
1.14Friction and the Normal Force
1.15Newton’s Law of Universal Gravitation
New Respect for the Humble Tire
1.1Uniform Acceleration: The Relationship
between Displacement and Time
1.2Uniform Acceleration: The Relationship
between Angle of Inclination and Acceleration
ST
SE

20. 1.1Introduction
Every day, we observe hundreds of moving objects. Cars drive down the
street, you walk your dog through the park, leaves fall to the ground. These
events are all part of our everyday experience. It’s not surprising, then, that
one of the first topics physicists sought to understand was motion.
The study of motion is called mechanics. It is broken down into two
parts, kinematics and dynamics. Kinematicsis the “how” of motion, that
is, the study of howobjects move, without concerning itself with whythey
move the way they do. Dynamicsis the “why” of motion. In dynamics, we
are concerned with the causes of motion, which is the study of forces. In the
next two chapters, we will consider the aspects of kinematics and dynam-
ics in relation to motion around us.
1.2Distance and Displacement
In any field of study, using precise language is important so that people can
understand one another’s work. Every field has certain concepts that are
considered the fundamental building blocks of that discipline. When we
begin the study of physics, our first task is to define some fundamental con-
cepts that we’ll use throughout this text.
Suppose a friend from your home town asks you, “How do you get to
North Bay from here?” You reply, “North Bay is 400 km away.” Is this
answer sufficient? No, because you have only told your friend the distance
to North Bay; you haven’t told her the directionin which she should travel.
chapter 1:Kinematics and Dynamics in One Dimension 5
Fig.1.2Moving objects are part of our daily livesFig.1.1Uniform or non-uniform motion?

21. Your answer is a scalar. A scalaris a quantity that has a magnitude only, in
this case, 400 km. An answer such as “North Bay is 400 km east of here”
would answer the question much more clearly. This answer is a vector
answer. A vectoris a quantity that has both a magnitude and a direction.
“400 km east” is an example of a displacementvector, where the magnitude
of the displacement is 400 km and the direction is east. Displacementis
the change in position of an object. The standard SI(Système International
d’Unités) or metricunit is the metre (m), and the variable representing dis-
placement is rd
:F
. Examples of scalars are: 10 minutes, 30°C, 4.0 L, 10 m.
Examples of vectors are: 100 km [E], 2.0 m [up], 3.5 m [down].
Displacement is commonly confused with distance. Distanceis the length
of the path travelled and has no direction, so it is a scalar.
example 1 Distance and displacement
A cyclist travels around a 500-m circular track 10 times (Figure 1.3). What
is the distance travelled, and what is the cyclist’s final displacement?
Fig.1.3
Solution and Connection to Theory
The cyclist travels a distance of 500 m each time she completes one lap.
Since she completes 10 laps, her total distanceis 5000 m. To find her dis-
placement, we draw a line segment from the starting point to the end
point of her motion. Because she starts and ends at the same point, her
displacement has a magnitude of zero.
In this example, we obtain very different answers for distance and
displacement. It is a good reminder of how important it is to clearly dif-
ferentiate between vector and scalar quantities.
6 unit a: Forces and Motion: Dynamics
Position is a vector quantity that
gives an object’s location relative
to an observer.
Total displacement
is zero after
1 complete loop
Position
is 10 m [W]
from the start
2
1
500 m Total distance is
500 m (1 loop)

22. Defining Directions
In two-dimensional vector problems, directions are often given in terms
of the four cardinal directions: north, south, east, and west. For one-
dimensional or linear problems, we use the directions of the standard
Cartesian coordinate system: vectors to the right and up are positive, and
vectors to the left and down are negative.
1.3Unit Conversion and Analysis
In the past, when the Imperial system of measurement was in common use,
it was often necessary to convert from one set of units to another. Today, by
using the SI or metric system, conversions between units need only be done
occasionally. To convert the speed of a car travelling at 100 km/h to m/s, we
multiply the original value by a series of ratios, each of which is equal to
one. We set up these ratios such that the units we don’t want cancel out,
leaving the units of the correct answer. For example,
100 km/h o
:
c
100
h
km
cF:
c
60
1
m
h
in
cF:
c
1
6
m
0
i
s
n
cF:
c
1
1
00
k
0
m
m
cF
o27.8 m/s
example 2 Unit conversions
How many seconds are there in 18 years?
Solution and Connection to Theory
Let’s assume that one year (or annum) has 365 days.
18 a o18 a
:
c
36
1
5
a
d
cF:
c
2
1
4
d
h
cF:
c
60
1
m
h
in
cF:
c
1
6
m
0
i
s
n
cF
o5.7 e10
8
s
There are 5.7 e10
8
s in 18 years.
1.How many seconds are there in a month that has 30 days?
2.A horse race is 7 furlongs long. How many kilometres do the horses
run? (Hint: 8 furlongs o1 mile, 1 km o0.63 miles.)
3.Milk used to be sold by the quart. An Imperial quart contains
20 fluid ounces (1 oz o27.5 mL). How many millilitres of milk are
in a quart?
chapter 1:Kinematics and Dynamics in One Dimension 7
Table 1.1
Prefixes of the Metric System
Factor Prefix Symbol
10
18
exa E
10
15
peta P
10
12
tera T
10
9
giga G
10
6
mega M
10
3
kilo k
10
2
hecto h
10deka da
10
:1
deci d
10
:2
centi c
10
:3
milli m
10
:6
micro s
10
:9
nano n
10
:12
pico p
10
:15
femto f
10
:18
atto a
applylyin
g
theC
o
nce p
t
s
1 m/s oo 3.6 km/h
3.6 is a useful conversion factor to
remember. To convert m/s to km/h,
multiply by 3.6. To convert km/h to
m/s, divide by 3.6.
0.001 kmcc
c
36
1
00
ch

23. applylyin
g
theC
o
nce p
t
s
1.4Speed and Velocity
If you were to walk east along Main Street for a distance of 1.0 km in a time
of 1 h, you could say that your average velocity is 1.0 km/h [E]. However,
en route, you may have stopped to look into a shop window, or even sat
down for 10 minutes and had a cold drink. So, while it’s true that your aver-
age velocity was 1.0 km/h [E], at any given instant, your instantaneous
velocity was probably a different value. It is important to differentiate
between instantaneous velocity, average velocity, and speed.
Average speedis the total change in distancedivided by the total elapsed
time. Average speed is a scalar quantity and is represented algebraically by
the equation
v
avgoc
r
r
d
t
c(eq. 1)
Average velocityis change in displacementover time. Average velocity is a
vector quantity and is represented algebraically by the equation
v
:F
avgoc
r
r
d
:
t
F
c(eq. 2)
Instantaneous velocityis the velocity of an object at a specific time. Note
that speed is a scalar and velocity is a vector, but both use the same variable,
v, and have the same units, m/s. To distinguish velocity from speed, we
place an arrow over the velocity variable to show that it’s a vector. Similarly,
an arrow is placed over the displacement variable, rd
:F
, to distinguish it from
distance, rd. Later, they will be distinguished in the final statement only.
Average and instantaneous velocities can be calculated algebraically. We
will revisit these two terms in Section 1.8 using graphical methods.
1.What is the velocity of the train if it travels a displacement of 25 km
[N] in 30 minutes?
2.A ship sails 3.0 km [W] in 2.0 h, followed by 5.0 km [E] in 3.0 h.
a)What is the ship’s average speed?
b)What is the ship’s average velocity?
3.The table below shows position–time data for a toy car.
d
:F
(m) [E] 0 2.0 4.0 6.0 8.0 8.0 8.0 9.0 9.0
t(s) 0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
a)What is the average velocity of the toy car’s motion?
b)What is the instantaneous velocity of the car at time to5.0 s?
8 unit a: Forces and Motion: Dynamics
Fig.1.4Why doesn’t the sign say
“Velocity Limit”?
Fig.1.5Motion is everywhere

24. chapter 1:Kinematics and Dynamics in One Dimension 9
1.5Acceleration
The simplest possible type of motion that an object can undergo (short of being
at rest) is uniform motion. Uniform motionis motion at a constant speed in
a straight line. Another name for uniform motion is uniform velocity.
When an object’s motion isn’t uniform, the object’s velocity changes.
Because velocity is a vector, its magnitude as well as its direction can
change. An example of a change of magnitude onlyoccurs when a car speeds
up as it pulls away from a stoplight. A change in the direction onlyof an
object’s velocity occurs when a car turns a corner at a constant speed.
Accelerationis the change in velocity per unit time. Velocity can change
in magnitude or direction or both. A negative acceleration in horizontal
motion is an acceleration to the left. If an object’s initial velocity is to the left,
the negative acceleration will cause it to speed up. If an object’s initial veloc-
ity is to the right, the negative acceleration will cause it to slow down.
Algebraically, we can express acceleration as
a
:Foc
r
r
v
:
t
F
c (eq. 3) or
a
:Foc
v
:F
2
r
:
t
v
:F
1
c(eq. 4)
The SI unit for acceleration is a derived unit; that is, it is a unit created by
dividing a velocity unit (such as m/s) by a time unit (such as s), giving
units oo
:
c
m
s
cF
ec
1
s
cor c
m
s
2
c
Writing acceleration units as m/s
2
doesn’t mean that we have measured a
second squared. It is simply a short form for the unit (m/s)/s, which means
that the velocity is changing so many m/s each second.
example 3 Vector acceleration
When struck by a hockey stick, a hockey puck’s velocity changes from
15 m/s [W] to 10 m/s [E] in 0.30 s. Determine the puck’s acceleration.
Recall that in our standard coordinate system, we can represent west as
negative and east as positive.
Solution and Connection to Theory
Given
v
:F
1o:15 m/sv
:F
2oF10 m/srto0.30 s
This example is a vector problem, so be sure to take the directions into
consideration. We can use the kinematics equation
c
m
s
c
c
s
Fig.1.6Slapshot!

25. a
:Foc
v
:F
2
r
:
t
v
:F
1
c
a
:Fo
a
:Fo83 m/s
2
The puck’s acceleration is 83 m/s
2
[E].
The next example deals with negative acceleration.
example 4 Negative acceleration
A car on a drag strip is travelling at a speed of 50 m/s. A parachute opens
behind it to assist the car’s brakes in bringing the car to rest. Is the accel-
eration of this car positive or negative? How would its motion change if
the acceleration was in the opposite direction?
Solution and Connection to Theory
If we use our standard coordinate system and assume that the initial
motion of the car was in the positive direction, its acceleration is in the
direction opposite to its initial motion. Therefore, the car’s acceleration is
negative. If in our example the acceleration of the car is :4.0 m/s
2
, the car
is losing 4.0 m/s of speed every second. The negative value for accelera-
tion doesn’t mean that the car is going backwards. It means that the car is
changing its speed by 4.0 m/s
2
in the negative direction. Since the car was
travelling in a positive direction, it is slowing down.
For motion in one dimension, we will designate the direction by using Fand
:signs. Thus, 12 km [N] becomes F12 km (written as 12 km) and 12 km [S]
is written as :12 km.
We will also omit vector arrows in the equationsfor displacement, velocity,
and acceleration. Instead, we will convey direction by using Fand :signs.
We will place vector arrows over variables only if the full vector quantity is
referred to (e.g., d
:F
o12 km [N]).
1.6An Algebraic Description of Uniformly
Accelerated Linear Motion
Thus far, we have defined two algebraic equations that apply to objects
undergoing uniform acceleration. These two equations are
v
avgoc
r
r
d
t
c(eq. 2) andao c
v2
r
:
t
v
1
c(eq. 4)
10 m/s :(:15 m/s)
ccc
0.30 s
10 unit a: Forces and Motion: Dynamics
If the initial velocity of the car in
Example 4 had been :15.0
c
m
s
c, an
acceleration of :1.0 m/s
2
would
mean that the car was speeding up
in the negative direction.
Fig.1.7

26. From equation 2, we can isolate rd:
rdov
avgrt
If the acceleration is uniform, v
avgoc
v1F
2
v2
c
and rdo :
c
v1F
2
v2
cF
rt(eq. 5)
Even though the vector arrows have been left off of these equations, they
are still vector equations! For linear motion, we will leave the vector arrows
off, but still indicate direction as positive or negative. In general (i.e., when
solving two-dimensional problems), we leave the vector arrows on, other-
wise we might forget to add and subtract these values vectorially.
Equations 4 and 5 are both very useful for solving problems in which
objects are accelerating uniformly in a straight line. If we look carefully at
these two equations, we will notice that many of the variables are common.
The only variables not common to both equations are changes in displace-
ment, rd, and acceleration, a. We can combine equations 4 and 5 by substi-
tuting the common variables to form other new and useful equations. First,
isolate v
2in equation 4:
v
2oartFv 1(eq. 6)
Now, substitute equation 6 into equation 5:
rdo
:
c
v1Fa
2
rtFv 1
cF
rt
rdov
1rtF c
1
2
cart
2
(eq. 7)
The other two possible equations are
rdov
2rt: c
1
2
cart
2
and
v
2
2ov1
2F2ard
The derivation of these equations is left as an exercise in the Applying the
Concepts section. The five equations for uniform linear acceleration are
listed in Table 1.2.
chapter 1:Kinematics and Dynamics in One Dimension 11

27. Table 1.2
The Five Equations Valid for Uniform Linear Acceleration
# Equation rda v 2 v1 rt
1 v
2ov1Faart ✔✔✔✔
2 rdo
c
1
2
c(v2Fv1)rt ✔✔✔✔
3 ∆dov
1∆tF
c
1
2
ca∆t
2
✔✔ ✔✔
4 ∆dov
2∆t:
c
1
2
ca∆t
2
✔✔ ✔ ✔
5 v
2
2ov1
2F2aa∆d ✔✔ ✔✔
example 5 Choosing the correct equation
A physics teacher accelerates her bass boat from 8.0 m/s to 11 m/s at a rate
of 0.50 m/s
2
. How far does the boat travel? Consider forward to be positive.
Solution and Connection to Theory
Given
v
1o8.0 m/sv 2o11 m/sao0.50 m/s
2
To solve this problem, we must first find an equation from Table 1.2 that
contains only the three known variables and the one unknown variable.
Usually, only one equation meets these requirements. (Occasionally, we
may get lucky and find that more than one equation will work.) For this
example, we require equation 5.
v
2
2ov1
2F2ard(eq. 5)
The problem is asking us for the distance travelled. Therefore, we isolate
rdin equation 5:
rdo
c
v2
2
2
:
a
v
1
2
c
rdo
rdo57 m
Therefore, the boat will travel a distance of 57 m.
(11 m/s)
2
:(8.0 m/s)
2
ccc
2(0.5 m/s
2
)
12 unit a: Forces and Motion: Dynamics

28. Figure 1.8 below summarizes how to choose the correct kinematics equation.
Fig.1.8Choosing Kinematics Equations
example 6
A quadratic solution
Jane Bond runs down the sidewalk, accelerating uniformly at a rate of
0.20 m/s
2
from her initial velocity of 3.0 m/s. How long will it take Jane
to travel a distance of 12 m?
Solution and Connection to Theory
Given
ao0.20 m/s
2
v1o3.0 m/srdo12 m
The required equation is equation 3.
rdov
1rtF c
1
2
cart
2
Equation 3 is a quadratic equation for the variable rt. We will have to
solve this problem either by factoring or by using the quadratic formula.
0o
c
1
2
cart
2
Fv1rt:rd
0o(0.1 m/s
2
)rt
2
F(3.0 m/s)rt :12 m
rto
c
:b o
2
b
a
2
:4racr
c
chapter 1:Kinematics and Dynamics in One Dimension 13
Determine which variables you are given values for, and which variables you
are required to find
Check each of the five kinematics equations in order
Do
you have a
value for each
variable in the
equation except for the
variable that you
are required
to find?
YES
NOChoose another
equation
Use this
equation
Fig.1.9Jane Bond
m
etho
d
p
r
oce s
s
of

29. rto
rto
c
:3.0
0.

2
3.7
c
Therefore, rto3.5 s or rto:33.5 s
We use the positive value because time cannot be negative. Therefore,
rto3.5 s. It takes Jane Bond 3.5 s to run 12 m.
example 7 A multiple-step problem
Bounder of Adventure accelerates his massive SUV from rest at a rate of
4.0 m/s
2
for 10 s. He then travels at a constant velocity for 12 s and finally
comes to rest over a displacement of 100 m. Assuming all accelerations
are uniform, determine Bounder’s total displacement and average velocity.
Assume that all motion is in the positive direction.
Solution and Connection to Theory
The first step is to break the problem down into simpler parts or stages.
This problem asks us to find the total displacement and average velocity. We
can solve the problem by first finding the displacement, time, and velocity
at each stage of Bounder’s trip, then adding the results of each stage together
to obtain the final answer. The table below illustrates the different stages of
Bounder’s trip and the information we are given at each stage.
Stage A Stage B Stage C
v
A
1o0 v B
1ovB
2ovA
2 vC
1ovBo?
v
A
2o? rto12 s v C
2o0
ao4.0 m/s
2
ao0 rd co100 m
rto10 s
Stage A:
Given
v
A
1o0 rt Ao10 sa Ao4.0 m/s
2
To calculate the final velocity, we can use equation 1 from Table 1.2:
v
2ov1Fart
v
A
2oart
v
A
2o(4.0 m/s
2
)(10 s)
v
A
2o40 m/s
:3.0
o(3.0)
2
r:4(0r.1)(:1r2)r
cccc
2(0.1)
14 unit a: Forces and Motion: Dynamics
The Quadratic Equation
If ax
2
FbxFco0, then
xo
:b
ob
2
:4racr
cc
2a
Fig.1.10A sport utility vehicle (SUV)
Checking the Units for r t
c
m
s
c
c:
c
m
s
cF
2
:
e
c
s
m
2
ce
e
m
e
c
s
m
2
c
o
c
m
s
c
c:
c
m
s
cF
2
:
e:
c
m
s
cF
2
e
c
s
m
2
c
oo s
c
m
s
c
c
c
s
m
2
c

30. To calculate the displacement, we use equation 3:
rdov
1rtF c
1
2
cart
2
rdAo0 F c
1
2
c(4.0 m/s
2
)(10 s)
2
rdAo200 m
Stage B:
Given
rto12 s
The velocity is constant during this stage, and equal to the final velocity
during stage A:
v
Bo40 m/s; therefore,
rd
BovBrto(40 m/s)(12 s)
rd
Bo480 m
Stage C:
Given
rd
Co100 mv C
2o0
The initial velocity during stage C is the same as the velocity during stage
B because the SUV hasn’t slowed down yet; therefore,
v
C
1ovB o40 m/s
We can calculate the time using equation 2:
rdo
c
1
2
c(v2Fv1)rt
Isolating rt, we obtain
rt
Coc
vC
2
1
r
F
dC
vC
2
c
rtCoc
2
4
(1
0
0
m
0
/
m
s
)
c
rtCo5.0 s
To find the total displacement, we add the displacements at each stage:
rd
totord AFrd BFrd C
rdtoto200 m F480 m F100 m
rd
toto780 m
chapter 1:Kinematics and Dynamics in One Dimension 15

31. Before we can calculate the average velocity, we need to find the total
time of the trip:
rt
totort AFrt BFrt C
rttoto10 s F12 s F5.0 s
rt
toto27 s
To find the average velocity, we substitute displacement and time into the
velocity equation:
v
avgoc
r
r
d
t
t
t
o
o
t
t
c
vavgoc
7
2
8
7
0
s
m
c
vavgo29 m/s
Therefore, Bounder’s total displacement is 780 m and his average veloc-
ity is 29 m/s.
example 8 A two-body problem
Fred and his friend Barney are at opposite ends of a 1.0-km-long drag
strip in their matching racecars. Fred accelerates from rest toward Barney
at a constant 2.0 m/s
2
. Barney travels toward Fred at a constant speed of
10 m/s. How much time elapses before Fred and Barney collide?
Solution and Connection to Theory
Given
rdo1000 ma
Fo2.0 m/s
2
v1
Fo0v Bo:10 m/s
To solve this problem, we must note two things. First, the distance travelled
by Barney plus the distance travelled by Fred must add up to 1000 m.
Second, Fred is accelerating uniformly, while Barney is undergoing uni-
form motion.
We will assume that Fred is moving in the positive direction. At any time
rt, his distance from his starting point is
rdov
1rtF c
1
2
cart
2
rdo0 F c
1
2
cart
2
rdFo c
1
2
cart
2
rdFo c
1
2
c(2 m/s
2
)rt
2
16 unit a: Forces and Motion: Dynamics

32. Barney’s displacement from the same point is 1000 m plus his displace-
ment at time rt:
rd
Bo1000 m Fv Brt
v
Bo:10 m/s
rd
Bo1000 m :(10 m/s)rt
When Fred and Barney meet, their two displacements are equal:
rd
Ford B
c
1
2
c(2 m/s
2
)rt
2
o1000 m :(10 m/s)rt
(1 m/s
2
)rt
2
F(10 m/s)rt:1000 m o0
Using the quadratic equation to solve for rt,
rto
c
:b o
2
b
a
2
:4racr
c
rto
rto
rto27 s or to:37 s
Since time is positive, we choose the positive answer. Fred and Barney
collide after 27 s.
example 9 Catching a bus
Jack, who is running at 6.0 m/s to catch a bus, sees it start to move when
he is 20 m away from it. If the bus accelerates at 1.0 m/s
2
, will Jack over-
take it? If so, how long will it take him?
Solution and Connection to Theory
Given
v
Jacko6.0 m/sv 1
buso0a buso1.0 m/s
2
aJacko0rdo20 m
We will consider Jack’s initial position as our origin and assume that he
is running in the positive direction. His displacement at any time rtis
given by
rdov
1rtF c
1
2
cart
2
rdJacko(6.0 m/s)rt
:10 m/s 64 m/s
ccc
2 m/s
2
:10 m/s o(10 mr/s)
2
:r4(1 mr/s
2
)(:r1000 mr)r
cccccc
2 m/s
2
chapter 1:Kinematics and Dynamics in One Dimension 17

33. The displacement of the bus from the same originat any time rtis
rd
buso20 m Fv 1rtF c
1
2
cart
2
rdbuso20 m F c
1
2
c(1.0 m/s
2
)rt
2
When Jack overtakes the bus, the two displacements are equal:
(6.0 m/s)rto20 m F(0.5 m/s
2
)rt
2
(0.5 m/s
2
)rt
2
:(6.0 m/s)rtF20 m o0
Using the quadratic equation to solve for rt,
rto
rto
There are no real roots for this equation; therefore, there is no real time
at which Jack and the bus have the same position. Jack will have to walk
or wait for the next bus!
1.A CF-18 fighter jet flying at 350 m/s engages its afterburners and
accelerates at a rate of 12.6 m/s
2
to a velocity of 600 m/s. How far
does the fighter jet travel during acceleration?
2.A butterfly accelerates over a distance of 10 cm in 3.0 s, increasing
its velocity to 5.0 cm/s. What was its initial velocity?
3.During a football game, Igor is 8.0 m behind Brian and is running
at 7.0 m/s when Brian catches the ball and starts to accelerate away
at 2.8 m/s
2
from rest.
a)Will Igor catch Brian? If so, after how long?
b)How far down the field will Brian have run?
4.A bullet is fired into a tree trunk (Figure 1.12), striking it with an ini-
tial velocity of 350 m/s. If the bullet penetrates the tree trunk to a depth
of 8.0 cm and comes to rest, what is the acceleration of the bullet?
Fig.1.12
6.0 m/s o36 m
2
r/s
2
:r40 m
2
r/s
2
r
cccc
1 m/s
2
6.0 m/s o(:6.0rm/s)
2
r:4(0r.5 m/sr
2
)(20 mr)r
cccccc
2(0.5 m/s
2
)
18 unit a: Forces and Motion: Dynamics
Before After
8 cm
applylyin
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Frd
bus
Frd
Jack
Assume
they meet
Fig.1.11

34. 5.A delivery truck accelerates uniformly from rest to a velocity of
8.0 m/s in 3.0 s. It then travels at a constant speed for 6.0 s. Finally,
it accelerates again at a rate of 2.5 m/s
2
, increasing its speed for 10 s.
Determine the truck’s average velocity.
6.While undergoing pilot training, a candidate is put in a rocket sled
that is initially travelling at 100 km/h. When the rocket is ignited,
the sled accelerates at 30 m/s
2
. At this rate, how long will it take the
rocket sled to travel 500 m down the track?
7.A parachutist, descending at a constant speed of 17 m/s, acciden-
tally drops his keys, which accelerate downward at 9.8 m/s
2
.
a)Determine the time it takes for the keys to reach the ground if
they fall 80 m.
b)What is the final velocity of the keys just before they hit the ground?
8.Derive the following equations from first principles:
a)v
2
2ov1
2F2ard
b)rdov
2rt : c
1
2
cart
2
1.7Bodies in Free Fall
Galileo Galilei (1564–1642), an Italian astronomer and physicist, is credited
with being the father of modern experimental science because he combined
experiment and calculation rather than accepting the statements of an
authority, namely Aristotle, regarding the study of nature. His greatest con-
tributions were in the field of mechanics, especially dynamics. His experi-
ments on falling bodies and inclined planes disproved the accepted
Aristotelean idea that a body’s rate of descent is proportional to its weight.
Galileo’s conclusions greatly upset Aristotelean scholars of his day.
The Guinea and Feather Demonstration
Galileo experimented in many different fields. One of his experiments in
mechanics involved rolling spheres down a wooden ramp (Figure 1.13b).
He found that the square of the time a sphere took to reach the bottom of a
ramp was proportional to the length of the ramp. He also observed that the
time a sphere took to reach the bottom of the ramp was independent of its
mass; that is, less massive objects and more massive objects both reach the
bottom of the ramp at the same time when released from the same height.
By using ramps inclined at different angles, Galileo extrapolated his find-
ings to a ball falling straight down. He concluded that if two objects of dif-
ferent masses are released from the same height, they will strike the ground
at the same time (see Figure 1.14).
chapter 1:Kinematics and Dynamics in One Dimension 19
Fig.1.13aGalileo Galilei
Fig.1.13bThe inclined plane used
by Galileo Galilei

35. Today, we can easily confirm Galileo’s findings by performing the guinea
and feather demonstration. A guinea (or any coin) and a feather are placed
in a long glass tube with a hole at one end, which is connected to a vacuum
pump. If the guinea and feather are allowed to fall through the tube full of
air, they will not strike the bottom at the same time. The guinea will land
first and the feather will flutter slowly to the bottom due to air resistance.
If the vacuum pump is used to remove the air from the tube, both objects
will strike the bottom at the same time.
Acceleration due to Gravity
Today we know that when objects are dropped from a height close to
Earth’s surface, they accelerate downward at a rate of 9.8 m/s
2
. This num-
ber is known as the acceleration due to gravity. It doesn’t depend on the
object’s mass. For this value to be valid, we must assume that air resistance
is negligible and that Earth is a sphere of constant density and radius. In
Section 1.15, we will study gravity in greater depth.
example 10 A marble in free fall
A marble is dropped from the top of the CN Tower, 553 m above
the ground.
a)How long does it take the marble to reach the ground?
b)What is the marble’s final speed just before it hits the ground?
c)What is the marble’s speed at the halfway point of its journey?
Solution and Connection to Theory
Given
rdo553 mv
1o0aogo9.8 m/s
2
a)We choose down to be the positive direction. To calculate the time, we
use the equation
rdov
1rt F c
1
2
cart
2
20 unit a: Forces and Motion: Dynamics
Coin and paper
Rubber stopper
Screw clip
Glass or “perspex” tube
Pressure tubing
Fig.1.14A hammer and a feather
are dropped on the Moon. Which
will land first?
Fig.1.15The guinea and feather
demonstration
Fig.1.16The CN Tower in
Toronto, Ontario

36. chapter 1:Kinematics and Dynamics in One Dimension 21
Since v 1o0,
rdo
c
1
2
cart
2
Isolating rt, we obtain the equation
rto
c
c
2r
a
d
ce
rtoc
c
2
9
(
.
5
8
5
m
3
e/
m
s
2
)
ce
rto11 s
Therefore, the marble takes 11 s to reach the ground.
b)To find the final speed, we use the equation
v
2
2ov1
2F2ard
v
2oo2(9.8rm/s
2
)(r553 mr)r
v2o1.0 e10
2
m/s
Therefore, the marble’s final speed is 1.0 e10
2
m/s.
c)At the halfway point, do
c
553
2
m
co276.5 m. Using the algebra from b),
v
2oo2(9.8rm/s
2
)(r276.5rm)r
v2o74 m/s
Therefore, the marble’s speed at the halfway point is 74 m/s.
example 11 Maximum height
A baseball is thrown straight up in the air, leaving the thrower’s hand at
an initial velocity of 8.0 m/s.
a)How high does the ball go?
b)How long will it take the ball to reach maximum height?
c)How long will it take before the ball returns to the thrower’s hand?
Solution and Connection to Theory
There are three important things to note in this example:
1)After the ball is released upward, its acceleration is in the opposite
direction of its motion; that is, the ball is moving upward, but acceler-
ation due to gravity is downward. Using our standard coordinate
system, we will make acceleration negative.
B
AC
Fig.1.17Throwing a
baseball straight up

37. 2)At its maximum height, the ball will come to rest. After that, it will fall
back down into the thrower’s hand. This problem is an example of
symmetry because the amount of time it takes the ball to travel
upward to maximum height equals the amount of time it takes the ball
to fall back down. Also because of symmetry, the velocity with which
the ball strikes the thrower’s hand equals its initial upward velocity.
3)The acceleration is constant in both magnitude and direction for the
entire motion. For this reason, the ball slows down as it goes up and
speeds up as it falls down.
Given
v
1o8.0 m/sao:9.8 m/s
2
v2o0
a)To find the maximum height of the ball, we use the equation
v
2
2ov1
2F2ard
rdo
c
:
2
v
a1
2
c
rdoc
2
:
(:
(8
9
.0
.8
m
m
/
/
s
s
)
2
2
)
c
rdo3.27 m
rdo3.3 m
Therefore, 3.3 m is the maximum height of the ball.
b)v
2ov1Fart
rto
c
v2:
a
v1
c
rtoc
0
:
:
9.
8
8
.0
m
m
/s
/
2
s
c
rto0.82 s
Therefore, the ball reaches maximum height in 0.82 s.
c)Because of symmetry, we know that the time to go up equals the time
to come down. The time for the ball to go up and come back down is
simply twice the answer in b); that is, 1.6 s.
or
For the complete motion (up and down),
rdo0
v
1o8.0 m/s
ao:9.8 m/s
2
rt o?
22 unit a: Forces and Motion: Dynamics
In this problem, we are ignoring
the effects of air resistance.

38. Using equation 3,
rdov
1rtF c
1
2
cart
2
0 o(8.0 m/s)rtF(:4.9 m/s
2
)rt
2
rto0 or rto1.6 s
example 12 Throwing a rock upward
A rock is thrown vertically upward from the edge of a cliff at an initial
velocity of 10.0 m/s. It hits the beach below the cliff 4.0 s later. How far
down from the top of the cliff is the beach? Consider up to be positive.
Solution and Connection to Theory
Given
v
1o10.0 m/srto4.0 sao:9.8 m/s
2
rdov 1rtF c
1
2
cart
2
rdo(10.0 m/s)(4.0 s) F c
1
2
c(:9.8 m/s
2
)(4.0 s)
2
rdo40.0 m :78.4 m
rdo:38.4 m
Therefore, the beach is 38.4 m below the top of the cliff.
1.An arrow is shot straight up in the air at 80.0 m/s. Find
a)its maximum height.
b)how long it will take the arrow to reach maximum height.
c)the length of time the arrow is in the air.
2.Tom is standing on a bridge 30.0 m above the water.
a)If he throws a stone down at 4.0 m/s, how long will it take to
reach the water?
b)How long will the stone take to reach the water if Tom throws it
up at 4.0 m/s?
3.A ball thrown from the edge of a 35-m-high cliff takes 3.5 s to reach
the ground below. What was the ball’s initial velocity?
chapter 1:Kinematics and Dynamics in One Dimension 23
applylyin
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39. 1.8A Graphical Analysis of Linear Motion
So far, the examples we have studied have been algebraic problems. We have
therefore used algebraic solutions. Often in physics, especially while per-
forming experiments, data is presented in graphical form. So, physicists
need to be able to analyze graphical data.
There are three main types of graphs used in kinematics: position–time
graphs, velocity–time graphs, and acceleration–time graphs. The relationships
among these graphs provide us with some of our most powerful analytical tools.
Velocity
Figure 1.18 shows the position–time graph for an air-hockey puck moving
down the table. This simple example provides us with a considerable
amount of information about the motion of the object. Recall that
slopeo
c
r
r
u
is
n
e
c
moc
r
r
d
t
(
(
m
s)
)
c
voc
r
r
d
t
c:
c
m
s
cF
By calculating the slope of the linear graph, we can determine the velocity
of the air-hockey puck in metres per second. From this result, we can con-
clude that:
The slope of a position–time graph gives the velocity of the object.
24 unit a: Forces and Motion: Dynamics
02 156789 34
25
10
15
20
5
t (s)
Position–time graph for an air-hockey puck
Fd (m)
Fig.1.18

40. If the slope of a position–time graph gives velocity, and uniform motion is
constant velocity, then the graph must have a constant slope (i.e., be a
straight line). In other words,
If an object is undergoing uniform motion, its position–time graph must
be a straight line.
Not all position–time graphs are straight lines. Some are curves, and some are
a complex combination of curves and straight lines. Regardless of the graph’s
shape, the slope of the position–time graph gives the velocity of the object.
Figure 1.19 summarizes the information we can obtain from position–
time graphs.
Fig.1.19Summary of d
:F
–tGraph Analysis
chapter 1:Kinematics and Dynamics in One Dimension 25
F :
Fd Fd
Fd Fd
Fd
ttt
tt
At rest
Speeding
up
Accelerating
Positive
acceleration
Is
the graph
a straight
line?
YES
YES
YES
NO
NO
NO
Is the
magnitude
of the slope
increasing?
Is
the slope
of the line
o 0?
Constant velocity
(uniform motion)
Increasing
positive velocity
Decreasing
negative velocity
Fd–t
graphs
Fd
Ft
Fd
t
Negative
acceleration
Decreasing
positive velocity
Increasing
negative velocity
Fd
Ft
Fd
t
Slowing
down
Speeding
up
c
o
nnec
tc
t
i
n
g
theC
o
nce p
t
s

41. Figure 1.20 shows the slope of the tangentat points A and B on an
increasing position–time graph. At point B, the velocity of the object (i.e.,
the slope of the tangent) is greater than at point A. The graph also shows a
line joining points A and B. The slope of this secantgives us the average
velocity between points A and B.
v
avgoc
r
r
d
t
c
Average velocityis the slope of a line connecting two points on a
position–time graph. For position–time graphs representing uniform
acceleration, the instantaneous velocity of an object can be determined
by finding the slope of the tangent to the curve.
example 13 The slope of the tangent on a velocity–time graph
The graph in Figure 1.21 represents the motion of a lime-green AMC
Pacer, which has started to roll downhill after its parking brake has
disengaged. Using this data, determine the slope of the tangent to the
position–time graph at four different points. Then plot the corresponding
velocity–time graph, and find its slope. Consider positive values to be
down the hill.
Solution and Connection to Theory
When we calculate the slope (i.e., the velocity) at four different points
along the curve in Figure 1.22a, we find that these values are increasing.
An increasing slope indicates acceleration. Since the velocity–time graph
is a straight line (Figure 1.22c), we know that the acceleration is uniform.
26 unit a: Forces and Motion: Dynamics
1.0 3.04.05.02.0
Time t (s)
50
40
30
20
10
0
Position
Fd (m)
Fig.1.21
rt
A
B
tangent
#1
tangent
#2
0 Time t (s)
Position (m)
F d
rd
rt
rd
rt
rd
Fig.1.20The slope of the secant
joining A to B is the average velocity
of that portion of the motion. That
slope lies between the values of the
slopes of the tangents at A and B.

42. Fig.1.22
(a) (b)
(c)
Now we can find the slope of the
velocity–time graph (Figure 1.22c):
slope N
T
r
r
u
is
n
e
T
slope N T
I
I
v
t
T
slope NT
1
4
8
.5
m
s
/s
T
slope N4.0 m/s
2
Nacceleration
From this example, we have determined that:
The slope of a straight-line velocity–time graph is the constant accelera-
tion of the object.
By analogy,
If the velocity–time graph is a curve (Fig.1.22d), the slope of its tangent
at any given point is the instantaneous acceleration of the object.
What can we learn by finding the area under a velocity–time graph? Let’s
look at the following example:
chapter 1:Kinematics and Dynamics in One Dimension 27
1.0 s
6 m
1.0 s
12 m
1.0 s
18 m
1.0 3.04.05.02.0
Time t (s)
50
40
30
20
10
0
Position (m)
Ud
Time (s) Velocity
(m/s)
0.0 0.0
1.5 6.0
3.012
4.5 18
1.0 3.04.05.02.0
Time t (s)
20
10
0
Velocity (m/s)
Uv
t (s)
Iv
It
Uv (m/s)
Fig.1.22dThe slope of a tangent
drawn to a point on a v
U–tgraph gives
the instantaneous acceleration at
that time

43. example 14 The area under a velocity–time graph
What is the area under the graph in Figure 1.23 for the first 3.5 s? (Be sure
to include the correct units.)
Fig.1.23
Solution and Connection to Theory
Figure 1.23 is a linear, increasing velocity–time graph. The area under
this graph is a triangle, which equals half the base times the height:
Ao
c
1
2
cbh
Ao
c
1
2
c(3.5 s)(14 m/s)
Ao24 m
The unit generated in this example is metres; therefore, we can conclude that:
The area under a velocity–time graph is the displacement of the object, rd
:F
.
Similarily,
The area under an acceleration–time graph is the change in velocity of
the object, rv
:F.
Assuming an object starts from rest at the origin, we can summarize our
graphical analysis of linear motion in one simple diagram:
28 unit a: Forces and Motion: Dynamics
1.0 3.04.05.02.0
3.5 s
14 m/s
Time t (s)
20
10
0
Velocity (m/s)
Fv
t (s)
Fd (m)
t (s)
Fv (m/s)
Area
Slope
t (s)
Fa (m/s
2
)
Area
Slope
Fig.1.24

44. chapter 1:Kinematics and Dynamics in One Dimension 29
example 15 Velocity–time graphs
1.From Figure 1.25, what is the instantaneous velocity of the object at
each of the following times?
to4.0 s
to8.0 s
to12 s
2. a)What is the average acceleration from time to0 to to4.0 s?
b)What is the average acceleration from time to10 to to15 s?
3.What is the instantaneous acceleration at to9.0 s?
4.How far has the object travelled in the first 7.0 s?
Solution and Connection to Theory
1.We can determine the instantaneous velocity by simply reading it off
the velocity–time graph. At time to4.0 s, the velocity is 2.0 m/s. At
to8.0 s, the velocity is 5.0 m/s. At to12 s, the velocity is 1.0 m/s.
2.Since acceleration is determined by taking the slope of a velocity–time
graph, we need to find the slope of the graph at each time interval. For
a)to0 to to4.0 s,
slope oacceleration o
c
r
r
v
t
c
slope oc
2.
4
0
.0
m
s
/s
c
slope o0.50 m/s
2
b)From to10 s to to15 s, the graph is a descending straight line. We
therefore expect to have a negative slope:
ao
c
r
r
v
t
c
aoc
v
t2
2:
:
v
t
1
1
c
ao
ao
c
:1
5
0
.0
m
s
/s
c
ao:2.0 m/s
2
The negative acceleration is interesting for two reasons. Above the hori-
zontal time axis, negative acceleration indicates that the object is decreas-
ing in speed (i.e., it is slowing down). At the time axis, the object has a
velocity of zero and is at rest for an instant. Finally, below the time axis,
(:5.0 m/s):(5.0 m/s)
ccc
15 s :10 s
Fig.1.25
6
4
2
0
:2
:4
:6
Fv (m/s)
t (s)
5 10 15

45. 30 unit a: Forces and Motion: Dynamics
15105
t (s)
0
:6
2
4
6
:4
:2
A
1
A
2
A
3
Fv (m/s)
The areas A
2FA
3in Figure 1.26
form a trapezoid. The area of a
trapezoid is the average of the height
times the base; that is,
Ao (3.0 s)
Ao10.5 m
(5.0 m/s F2.0 m/s)
ccc
2
the object is still accelerating in the negative direction, but its speed is
increasing in the opposite direction of its original motion (i.e., the object
is speeding up backwards). As an example of this type of motion, con-
sider an astronaut who is outside her shuttlecraft and is approaching it
with a velocity of 10 m/s [E]. To prevent herself from colliding with the
shuttlecraft, she fires a retro-rocket from her rocket pack, which shoots a
small amount of hot gas in the easterly direction, causing her to acceler-
ate in the westerly direction. If the rocket pack causes an acceleration of
1.0 m/s
2
[W], the astronaut would continue to slow down until she came
to rest 10 s later. If at that point she shut off the rocket pack, she would
remain at rest. If she inadvertently left the rocket pack on, she would con-
tinue accelerating in the westerly direction immediately after having
come to rest. The astronaut’s velocity would increase by 1.0 m/s [W] for
each second that the retro-rocket was left burning.
3.The instantaneous acceleration at time to9.0 s can be found by
inspection. The slope of the velocity–time graph gives the acceleration.
From to7.0 s to to9.0 s, the slope is horizontal, that is, zero. Zero
slope means that the object is undergoing uniform motion.
4.To determine the object’s displacement, we need to find the area
under the graph. In this case, we can simplify the calculation by break-
ing the area down into a series of triangles and rectangles.
Fig.1.26
AtotoA 1FA 2FA 3
A1and A 2are both triangles and A 3is a rectangle. We substitute the
appropriate equations for each area:
A
toto c
1
2
cbhF c
1
2
cbhFlw
A
1o c
1
2
c(4.0 s)(2.0 m/s) o4.0 m
A
2o c
1
2
c(3.0 s)(3.0 m/s) o4.5 m
A
3o(3.0 s)(2.0 m/s) o6.0 m
A
toto4.0 m F4.5 m F6.0 m
A
toto14.5 m
Therefore, the object’s displacement in the first 7.0 s is 14.5 m.

46. Figure 1.27 summarizes how to obtain information from a velocity–time graph.
Fig.1.27Information Obtained from a v
F–tGraph
1.The v :F:tdata in Figure 1.28 are for Puddles, the dog playing at the park.
Fig.1.28
a)Determine Puddles’ instantaneous acceleration at each of the
following points:
to7.0 s
to12 s
to3.0 s
b)How far did Puddles run from time to5.0 s to to13 s?
2.Figure 1.29 shows v
:F:tdata for Super Dave, Sr. and his son, Super
Dave, Jr., who are racing their motorcycles on a straight 150-m track.
From the graph, determine the following:
a)How long does it take both Super Daves to reach the
50-m mark?
b)Who wins the 50-m race, and by how much time?
c)Who would have won if the race had been 100 m long?
chapter 1:Kinematics and Dynamics in One Dimension 31
Slope
Read
Area
Area
Time
Instantaneous
velocity
Average
velocity
Displacement
Instantaneous
acceleration
Average
acceleration
Acceleration
1 point
2 points
Fv:t
puttin
g
T
o
T
o
g
eth
e
r
it all
1 3 4 5 6 7 8 9 1011 12 13 14 15 162
t (s)
0
70
50
20
60
30
40
10
Fv (m/s)
applylyin
g
theC
o
nce p
t
s

47. 32 unit a: Forces and Motion: Dynamics
Fig.1.29
3.Figure 1.30 shows d
:F
:tdata for The Flash, a local jogging enthusiast.
Fig.1.30
a)Determine the average velocity for each segment of The Flash’s motion.
b)What is his average velocity for the entire trip?
1.9Dynamics
Dynamicsis often called the “why” of motion because it is the study of why
objects move as opposed to howthey move. The following terms are very
important in the study of dynamics:
A forceis commonly referred to as a push or pull in a given direction.
These forces are called contact forces. There are also non-contact forces such
as gravity. Force is a vector quantity, and its standard metric unit is the newton
(N). In the next few sections, we will study how different types of forces can
cause or affect the motion of objects.
2.5
2.0
1.5
1.0
0.5
t (s)
Fd (m)
0.501.01.5 2.02.5 3.0
4681020
20
30
40
10
Super Dave, Sr.
Super Dave, Jr.
t (s)
Fv (m/s)
Fig.1.31Understanding crash
test results in the lab can save
countless lives on our roads

48. Massis the amount of matter in an object. It is a measure of an object’s
inertia. The standard SI unit for mass is the kilogram (kg). Weight, on the
other hand, is the force of gravity acting on an object. The terms massand
weightare commonly thought to be synonymous, but they are not. Mass is a
quantity that doesn’t vary with location, whereas weight depends on your
location in the universe.
Gravityis the mutual force of attraction between any two objects that
contain matter. The magnitude of the force of Earth’s gravity (F
g) on an
object can be calculated using the following equation:
F
gomg
The symbol grepresents Earth’s gravitational field strength of 9.80 N/kg. This
value is also commonly referred to as the acceleration due to gravity, with units
m/s
2
. For this equation to be valid, we must assume that the object is reasonably
close to Earth’s surface and that Earth is a sphere of uniform mass and radius.
1.10Free-body Diagrams
Free-body diagrams (FBDs) are very useful conceptual tools for physics stu-
dents because they help us isolate the object we wish to study from its envi-
ronment so that we can examine the forces acting on it. A free-body diagram
is created by drawing a circle around the object. The forces acting on the object
are represented by arrows pointing away from the circle. For example, if we
were to draw a free-body diagram of this textbook sitting at rest on a lab bench,
we would draw a circle around the textbook, and draw two arrows represent-
ing forces acting on it, as shown in Figure 1.32a. One of the forces is the force
of gravity on the book, pulling it downward. The other force is the force due
to the bench pushing the book upward. Note that the force applied by the book
on the bench downward isn’t shown because this force
is exerted by the book. This force would only be
shown in a free-body diagram of the lab bench.
The forces in Figure 1.32a are equal and oppo-
site; that is, the magnitude of the gravitational force
is equal to the magnitude of the upward force due to
the lab bench. These two forces are an example of
balanced forces. When an object is acted on by bal-
anced forces, the forces cancel each other out and
the object behaves as though no force is acting on it.
Figure 1.32b is a free-body diagram of a textbook in
free fall. Assuming negligible air resistance, the only
force acting on the book is the force of gravity down-
ward; there is no balancing upward force. As a result,
the force due to gravity on the book is unbalanced.
chapter 1:Kinematics and Dynamics in One Dimension 33
1 N o(kg):
c
s
m
2
cF
oc
kg
s
·
2
m
c
PHYSICS
F
g
FF
bench
Fig.1.32a
Note:Free-body diagrams only show
forces acting onan object. They don’t
show forces exerted by the object.
PHYSICS
FF
g
Fig.1.32b
150 N
40 N
150 N
40 N
FF
n
FF
f
FF
f
FF
g
FF
g
FF
n
FREE-BODY DIAGRAMS
In more formal physics, the object in a free-body diagram is
reduced to a dot representing the object’s centre of mass. The
forces are shown pointing away from the dot, as in Figure 1.33a .
Notice that side-by-side forces are drawn slightly offset.
An alternative is to place parallel forces head to tail in a line
(Figure 1.33b).
Fig.1.33
(a) (b)

49. Discovering Diverse Content Through
Random Scribd Documents

50. anti-Tank rifle and gun are most effective. The consideration of these
points is long and exhaustive. Ludendorff further hopes much from
“the active and inventive genius of the lower ranks of the non-
commissioned officers to arrange Tank traps, and demands that
every encouragement should be shown to those who show any
inventive talent.”
These were but peddling remedies. When, as at Amiens, the
understanding between infantry and Tanks is almost perfect, and
when the magnificent élan of an assault by Australians and
Canadians is supported by the weight of 400 Tanks, not even the
troops of what was the best-trained Army in the world can stand the
concerted shock of their attack.
A Special Order was issued on August 16 by General Sir Henry
Rawlinson, the 4th Army Commander:
“Tank Corps.—The success of the operations of August 8
and succeeding days was largely due to the conspicuous part
played by the 3rd, 4th and 5th Brigades of the Tank Corps,
and I desire to place on record my sincere appreciation of the
invaluable services rendered both by the Mark V. and the
Mark V. star and the Whippets.
“The task of secretly assembling so large a number of
Tanks entailed very hard and continuous work by all
concerned for four or five nights previous to the battle.
“The tactical handling of the Tanks in action made calls on
the skill and physical endurance of the detachments which
were met with a gallantry and devotion beyond all praise.
“I desire to place on record my appreciation of the
splendid success that they achieved, and to heartily
congratulate the Tank Corps as a whole on the completeness
of their arrangements and the admirable prowess exhibited
by all ranks actually engaged on this occasion. There are
many vitally important lessons to be learned from their

51. experiences. These will, I trust, be taken to heart by all
concerned and made full use of when next the Tank Corps is
called upon to go into battle.
“The part played by the Tanks and Whippets in the battle
on August 8 was in all respects a very fine performance.
“(Signed) H. Raïlinson , General,
“Commanding 4th Army.
“Headquarters, 4th Army,
“August 16, 1918.”
Nor were the Australians less generous.
The following message is typical of many. It was sent to Brig.-
General Courage (commanding 5th Tank Brigade) by the 4th
Australian Divisional Commander:
“G.O.C. 5th Tank Brigade.
“I wish to express to you and the command associated
with us on August 8 and following days, on behalf of the 4th
Australian Division, our deep appreciation of the most gallant
service rendered during our offensive operations by the Tank
Corps. The consistent skill and gallantry with which the Tanks,
individually and collectively, were handled during the battle,
was the admiration of all ranks of the infantry with whom
they were so intimately associated, and our success was due
in a very large measure to your efforts.
“We hope sincerely, that in future offensive operations in
which we may take part, we shall have the honour to be
associated with the same units of the Tank Corps as during
the operations on August 8 and following days.
“(Signed) E. G. Sinclaiê McLagan,
“Major-General,
“Commanding 4th Australian Division.”

52. Finally, in a congratulatory telegram after the battle, the
Commander-in-Chief paid a high tribute to the skill and bravery
displayed by the Tank Corps in the gaining of this signal victory.

54. CHAPTER XVIII
THE GERMAN ATTITUDE—“MAN-TRAPS AND
GINS”—THE BATTLE OF BAPAUME
I
We had, as we have said, called a halt to the Battle of Amiens.
But the pause was to be only one of a few days.
The new battle was to be fought in the area which lay between
the rivers Somme and Scarpe, and for his selection of this particular
place Sir Douglas Haig in his Despatch gives two reasons.
“The enemy did not seem prepared to meet an attack in
this direction, and, owing to the success of the Fourth Army,
he occupied a salient, the left flank of which was already
threatened from the south. A further reason for my decision
was that the ground north of the Ancre River was not greatly
damaged by shell-fire, and was suitable for the use of Tanks.
A successful attack between Albert and Arras in a south-
easterly direction would turn the line of the Somme south of
Péronne, and gave every promise of producing far-reaching
results. It would be a step forward towards the strategic
objective St. Quentin-Cambrai.”
It is interesting to see how high a place Tanks now held in the
estimation of the General Staff, and how carefully their peculiarities
were considered.

55. But it was not only the British High Command which had begun
to busy itself with the natural history of the Tank.
Since the lesser battles of July and the greater battle of August
8, the attitude of the German G.H.Q. had entirely changed.
When we first began to use Tanks it will be remembered that the
Germans, though perfunctorily alluding to them as “cruel and
detestable,” had in effect sneered at them as makeshifts by which
we hoped to supplement our scanty supply of more legitimate
munitions of war.
Besides, their contempt for all we did being sincere, the Tanks’
British parentage damned them without further investigation.
“Search and see, for out of Galilee cometh no good thing.”
The Germans themselves made their attitude perfectly clear.
“The use of 300 British Tanks at Cambrai (1917) was a
‘battle of material,’ and the German Higher Command decided
from the very outset not to fight a ‘battle of material.’”
Their policy was masses of men rather than mechanism,
quantity rather than quality.
The best men went to machine-gun units and to assault troops.
In many cases the remainder of the infantry were of little fighting
value, though many of the men might have been otherwise usefully
employed in a war which, if not one of material, was at least one in
which economic factors played a large part.
The German Higher Command was able, however, to look at an
order of battle, showing some 250 Divisions on paper.
But the Germans were thus naturally not in a position to find the
labour for the construction of additional material, such as Tanks;
they were, besides, concentrating any labour and any suitable
material they possessed upon the work of submarine making.

56. It seems clear that the whole policy, at least as far as Tanks was
concerned, was regretted before the end of the War.
The following now well known extracts from German documents
indicate the effect of our Tanks on the German Army:
“Staff officers sent from G.H.Q. report that the reasons for the
defeat of the Second Army
81
are as follows:
“1. The fact that the troops were surprised by the massed attack
of Tanks, and lost their heads when the Tanks suddenly appeared
behind them, having broken through under cover of natural and
artificial fog.
“2. Lack of organised defences.
“3. The fact that the artillery allotted to reserve infantry units at
the disposal of the Higher Command was wholly insufficient to
establish fresh resistance with artillery support against the enemy
who had broken through and against his Tanks.
“Ludendorff , 11. 8. 18.”
“Crown Prince’s Group of Armies.
“12. 8. 18.
“G.H.Q. reports that during the recent fighting on the
fronts of the 2nd and 18th Armies, large numbers of Tanks
broke through on narrow fronts and pushing straight forward,
rapidly attacked battery positions and the headquarters of
divisions.
“In many cases no defence could be made in time against
the Tanks, which attacked them from all sides.
“Anti-Tank defence must now be developed to deal with
such situations.”
Signal Communication—

57. “Messages concerning Tanks will have priority over all
other messages or calls whatsoever.”
“Order dated 8. 9. 18.”
II
The first efforts at combating Tanks made by the German High
Command were half contemptuously instituted chiefly to reassure
their infantry, who seemed to them, for no particular reason, liable
to extraordinary fits of nerves and panic upon the approach of their
new assailants.
The measures of defence were ill devised and carelessly used.
In the autumn of 1917, it will be remembered that the Germans
had captured a number of our Mark IV. machines.
These they used for the purposes of propaganda, parading them
in the streets of Berlin and showing them to the Army, as a man
might demonstrate the harmless nature of snakes by the aid of a
tame cobra.
The infantry were lectured to about the miseries endured by the
crews who manned Tanks, as to their mechanical defects, their
vulnerability and general worthlessness. For example, the following
passage appeared in an Order issued to the 7th German Cavalry
Division. It will be gathered from the text that the Order was
illustrated by detailed drawings.
“7th Cavalry ‘Schützen’ Div. Div. H.Q. 26.9.18.
“Subject:—Anti-Tank Defence.
“Divisional Order
“1. General.

58. “The infantry must not let itself be frightened by Tanks.
The fighting capacity of the Tank is small owing to the bad
visibility, and the shooting of the machine-guns and guns is
cramped and inaccurate as the result of the motion.
“It has been proved that the Tank crews are nervous and
are inclined to turn back, or leave the Tank, even in the case
of limited fire effects, such as a light T.M. (Trench Mortar)
barrage at 800–1000 yards. In order to make it more difficult
for the artillery, the Tanks pursue a zigzag course towards
their objective.
“The hostile infantry follows Tanks only half-heartedly.
Experience shows that hostile attacks are soon checked by
aimed machine-gun and artillery fire. Co-operation between
the Tanks and their infantry detachments must be hindered
as much as possible. The arms should be separated and
destroyed in detail. All projectiles which do not hit the
armour-plating at right angles ricochet off instead of
penetrating. Artillery, light trench mortar and anti-Tank rifle
fire is effective against all portions of the Tank, especially
against the broadside and the cab (framed in red in the
illustrations). Machine-gun and rifle fire with A.P. bullets, on
the other hand, should be aimed especially at the observation
and machine-gun loopholes (framed in green and blue in the
illustrations).”
But the enemy was not content with a merely dialectical
defence. Among other practical measures the Germans, with curious
inconsequence, decided to form a small Tank Corps of their own,
partly armed with new Tanks of German manufacture and partly with
captured British machines.
But here a little unexpected awkwardness arose. The infantry
from whom they now wished to recruit their Tank crews, had
unfortunately been completely convinced by the unanswerable

59. arguments which they had just heard, and now thoroughly believed
in the perfect uselessness, the extreme vulnerability, of Tanks.
Thus it came about that the German Tank Corps was made up of
a quite astonishingly reluctant and half-hearted body of men.
Altogether, only fifteen German Tanks were ever manufactured, and
only twenty-five captured British Mark IV. Tanks were repaired, so
that the whole affair amounted to but little.
The German Tanks were, as we have said, much heavier and
larger than the British or French heavy Tanks, though, as we have
noted, they rather resembled the French St. Chamond. They could
not cross large trenches or heavily shelled ground, owing to their
shape, and the lack of clearance between the ground and the body.
On smooth ground, their speed was good—being about eight miles
an hour.
Their armour was thick and tough, capable of withstanding
armour-piercing bullets, and, at a long range, even direct hits from
field guns not firing armour-piercing shells. Only the front of the
Tank was, however, sufficiently strong for this, and the roof was
scarcely armoured at all.
They were very vulnerable to the splash of ordinary small arms
ammunition, owing to the numerous crevices and joints left in the
armour-plate.
The most interesting feature of these otherwise exceedingly bad
machines was the fact that they ran on a spring track. The use of
springs for so heavy a Tank was the one progressive departure in
the German design.
Their crew consisted of an officer and no less than fifteen other
ranks. This huge crew, twice that of a heavy British Tank, actually
went into action in a Tank 24 feet long by 10 feet wide. However, the
close association of the crew was merely physical, for they were
composed of no less than three distinct arms, and appear to have
done little or no training together as a crew.

60. There were the drivers who were mechanics, there were the
gunners who were artillerymen, and the machine-gunners who were
infantrymen. Members of the British Tank Corps were at one time
much puzzled by German Tank prisoners’ statements, that on such
or such an occasion the infantry had spoiled their shooting, or that
the artillery had not backed them up, in circumstances when there
was no particular question of co-operation with other arms. They
came afterwards to understand that the anathema’d representatives
of rival arms were inside the machine, not out.
But in reality rival machines constituted but a small part of the
German anti-Tank measures, for, as we have said, after the victories
of July and early August, these begin to be panic-stricken in their
elaboration, and after the Battle of Amiens, we find Ludendorff
himself pouring out his soul on the subject.
He obviously realised that anti-Tank defences had been
neglected, and he probably saw also that this neglect was going to
be difficult to explain to an Army and a public which, as the result of
failures, were about to become extremely critical of their leaders.
After the Battle of Amiens, therefore, the Germans began
feverishly to set their house in order, and we find special Staff
Officers appointed at the Army, Corps, Divisional and Brigade
Headquarters, whose sole duty it was to organise the anti-Tank
defences within their formation.
A special artillery was told off and divided into two sections. The
first was to provide a few forward silent guns in each divisional
sector. They were to remain hidden till the moment of our attack,
and then to concentrate upon our Tanks. These guns, however,
proved apt to be smothered by our barrage, or not to be able to
distinguish their prey in the half-light of our dawn attacks. Secondly,
there were to be reserve guns whose duty it was to go forward and
take up previously reconnoitred positions after the Tank attack had
been launched. It was generally from these pieces that the Tanks
had most to fear. Finally, all German batteries, including howitzers,
had general instructions to plan their positions in such a way that

61. advancing Tanks would be subject to a direct fire at about 500 or
600 yards range. In the event of a Tank attack, the engagement of
our machines was now to be the first call upon the artillery, to the
exclusion of counter-battery or any other work. As for the infantry,
the chief rôle allotted to them was “to keep their heads,” and “to
keep calm.” Other Orders instructed them to move to a flank in the
event of a Tank attack. “No advice was given, however, as to how
this was to be done when Tanks were attacking on a frontage of
twenty or thirty miles.”
A large armoury of special anti-Tank weapons arose, and of
these the most important was the anti-Tank rifle, of which we have
spoken before.
82
 “The weapon weighed 36 lb. and was 5½ feet long. It
had no magazine and fired single shots, using A.P.
ammunition of .530 calibre. It was obviously too conspicuous
and too slow a weapon to be really effective against Tanks,
though the steel core could penetrate the armour of British
Tanks at several hundred yards range.
“The chief disadvantage of the anti-Tank rifle, however,
was that the German soldier would not use it. He was
untrained in its use, afraid of its kick, and still more afraid of
the Tanks themselves. It is doubtful if one per cent. of the
A.T. rifles captured in our Tank attacks had ever been fired.”
Road obstacles, such as carts full of stones, linked up with wire
cables, concrete stockades and mines, provided a good deal of the
rest of the enemy anti-Tank stock-in-trade. Of mines there was a
considerable variety. They ranged from elaborate specially made
pieces of apparatus to high explosive shells, buried and hastily fitted
with a device by which the weight of the Tank exploded them.
They were sometimes buried in lines across roads, and
sometimes extensive minefields were laid. Their singular

62. ineffectiveness always seemed somewhat mysterious to members of
the Tank Corps, the proportion of effort to result seeming always
many tons of mine to each Tank damaged.
However, we always thought we might some day encounter a
really effective type of mine, and possibly the Germans were
satisfied if their efforts so much as made our monsters walk
delicately, for in an elaborate document, giving every kind of anti-
Tank defence instructions, they somewhat pathetically conclude:
“Every obstacle, even if it only checks the hostile Tank temporarily, is
of value.”
But there was one form of weapon which was, we felt sure,
bound to be evolved by the Germans. It was one which we were not
at all anxious to encounter. We imagined a weapon which should
practically be the machine-gun version of the anti-Tank rifle; that is
to say, a weapon which could pour out a stream of high-velocity,
large-calibre bullets at the rate of two hundred a minute. Actually it
was almost precisely such an engine that the Germans had got in
their “Tuf” machine-gun, of which an interesting account is given in
Weekly Tank Notes.
The name was an abbreviation for “Tank und Flieger” (tank and
aeroplane), for it was against these enemies that this machine-gun
was intended. It was to consist of no less than 250 pieces, which
were made by sixty different factories, of which the Maschinen
Fabrik Augsburg Nürnberg, was the only one entrusted with the
assembling and mounting. The projectile fired was to be 13
millimetres in diameter. From experiments made with captured
Tanks, the Germans ascertained that these bullets could pierce steel
plates of 30 millimetres in thickness. No less than six thousand of
these guns were to be in the field by April 1919, and delivery was to
begin early in the previous December—just a month too late.
However, when the Armistice was signed, the firms were already
in possession of the greater part of the stores and raw material for
the manufacture of the guns, a quantity of which were by then well
on the way to completion. Immediately after the signing of the

63. Armistice, all the factories were instructed by telephone to continue
manufacturing the “Tuf,” and about November 20 they received
confirmation in writing of this order, and were instructed to keep on
their workmen at all costs. Our occupation of the left bank of the
Rhine proved a serious drawback to a continuation of the
manufacture, as it completely interrupted communication between
several of the factories. The Pfaff Works of Kaiserlautern (Palatinate)
and the great Becker steel works of Frefeld, which played an
important part in the manufacture of the guns, had to close down,
both being on the left bank of the Rhine.
The Minister of War throughout the period of its manufacture
asked for daily and minute reports as to the progress of the “Tuf,”
and it was given priority over both submarines and aeroplanes. But
once more, as ever in all that concerned Tanks, the Germans were
several months too late. We were never destined to face this
particular weapon with the Mark V. The modern Tank fears it not at
all.
III
Our chronicle has now reached the three last, and the decisive
months of the war.
It was a period of continuous fighting, in which a battle begun in
any particular sector would spread along the front on either hand,
until at last, by the middle of October, the whole line was in roaring
conflagration; and by the second week in November the blaze had
swept on almost to the borders of Germany, and the forces of the
enemy had withered and shrivelled before it.
At first we made a series of more or less set attacks. Then came
the break through the Hindenburg Line after the Second Battle of
Cambrai, and the hastily-organised running fights of October, which
culminated in the complete overthrow of German arms.

64. The whole period is at the moment of writing exceedingly
difficult to dissect and to classify into definite battles, it being usually
a matter of opinion when one engagement can be said to have
ended and another to have begun. The nomenclature even is still
fluid. Take, for example, the vast inchoate battle which raged from
August 21 and 23 and culminated on September 2. It was fought by
three separate armies. There were at least three principle “Z” days,
and the battle seems to be indifferently known as the Battle of
Bapaume, the Second Battle of Arras, or even as the Battle of
Amiens. Nor if the historian were to attempt to name it by date
would it be clearly more proper to call it the Battle of August 23 or
21. There is a good deal to be said for the German plan of
christening their battles by some fancy name, or dubbing them
“Kaiserchlact” or “Clarence,” according to one’s taste. A campaign of
nameless battles is apt to defy Clio’s efforts at dissection and tidy
arrangement, and to defeat her longing to see a neat row of actions
dried, classified, and labelled in her Hortus Siccus.
We have indicated the changes which had taken place in the
attitude of our own and the German High Commands toward Tanks.
Much had been learnt by the Tank Corps themselves, and much had
been regularised and systematised in their methods. We find that by
August, Tank Corps preparation for a battle had been so completely
reduced to a routine that to attempt to chronicle the preparation for
any of our set attacks would be to make a mere cento, whose pieces
might be culled from particulars already recorded for Cambrai, for
Hamel and for Amiens. We therefore trust that the reader, without
hearing any enumeration of gallons of petrol, tons of grease, or
acres of maps, will understand that each of these “formal” battles
was preceded by the usual herculean tasks of preparation.
IV
The Battle of Bapaume was, as we have already said, to
constitute a sequel to the Battle of Amiens (August 8). On August 21

65. the 3rd Army was to launch an attack to the north of the Ancre with
the general object of pushing the enemy back towards Bapaume.
Meanwhile the 4th Army was to continue its pressure on the enemy
south of the river. August 22 was to be a “slack” day and was to be
used to get troops and guns into position on the 3rd Army front. The
principal attack was to be delivered on the 23rd by the 3rd Army,
and those divisions of the 4th Army which lay to the north of the
Somme, the rest of the 4th Army fighting a covering action on the
flank of the main operation. Afterwards, if our efforts were
successful, the whole of both Armies were to press forward with
their utmost vigour and exploit any advantage we might have
gained. If our success was such as to force the enemy back from the
high ground he held, thus securing our southern flank, the 1st Army
was further to make another attack immediately to the north. This
gradual extension of the front of assault was intended to mislead the
enemy as to where the main blow would fall and cause him to throw
in his reserves piecemeal.
A large number of Tanks were to be concentrated in the 3rd
Army area. They were to attack between Moyenneville and Bucquoy
with the 4th and 6th Corps. With them the 1st and 2nd Brigades
were to operate.
With the 4th Army the 3rd Corps was to attack on August 23,
between Bray and Albert, and the 4th Tank Brigade was to assist in
this assault. Then, with the portion of the 4th Army which operated
south of the Somme, namely, the Australians, the 5th Tank Brigade
was as usual to co-operate, their action also taking place on the
23rd. In the course of the two days’ operations the 3rd, 6th, 7th,
14th, 15th, 11th, 12th, 10th and 17th Battalions were to be
employed.
The total of 280 machines seems at first sight a curiously small
one, considering the number of battalions involved, but it must be
remembered that most units had been hotly in action at Amiens ten
days before, and that some battalions could not muster more than

66. sixteen fighting Tanks, pending repairs and a fresh issue of
machines.
Supply Tanks and aeroplanes were to co-operate as usual, the
latter in greater strength than before; for just before the battle No.
73 Squadron, armed with Sopwith Camels, was attached to the Tank
Corps, in addition to No. 8 Squadron for counter-gun work.
One of the most prominent features of the whole sector of
attack was the Albert-Arras railway, which lay some distance behind
the enemy’s front line. It proved to have been carefully prepared for
defence by the enemy, being commanded at point-blank range by a
large number of field guns, which had been specially and secretly
withdrawn from more forward positions, and all the sections of the
line where it would be possible for the Tanks to cross—that is to say,
the “neutral” portions where the line was neither embanked nor in a
cutting—were not only carefully registered, but were blocked by
concrete and iron anti-Tank stockades.
The attack was to be opened at 4.55 a.m. on the 21st by the 4th
and 6th Corps and their Tanks.
V
The morning dawned in the inevitable white blanket of mist
which now always seemed to accompany our attacks. Till nearly 11
a.m. it was impossible to see more than a few yards ahead, and it
was with the greatest difficulty that the Tanks kept their direction. If,
however, the mist was confusing to us, it was doubly so to the
enemy. The Germans were completely taken by surprise; we even
found candles still burning in the trenches when we crossed them,
and papers and equipments were scattered broadcast, bearing
witness to a hurried flight.

67. GERMAN ANTI-TANK GUNNERS
(FROM A PHOTOGRAPH FOUND ON A PRISONER)

68. AN ANTI-TANK GUN IN A STEEL CUPOLA (VPRES)

69. A CAPTURED GERMAN TANK

70. A GERMAN ANTI-TANK RIFLE
We carried the front line so easily that we soon realised we must
be up against a system of defence rather like that which the
Germans had adopted at Ypres. He was keeping his reserves well in
rear of a lightly-held outpost line, and, as we have said, unknown to
us, his guns had been withdrawn in such a way as to cover the
railway.
The Armoured Cars and the Whippets both took an active part in
the attack on Bucquoy. At the entrance of the village a large crater
had been blown in the road over which the armoured cars were
hauled, after a smooth path had been beaten down across it by a
Whippet. The cars then sped on through the enemy’s lines, reaching
Achiet-le-Petit ahead of our infantry, and silenced a number of

71. machine-guns. Two of the cars received direct hits, one of them
being burnt and completely destroyed.
During the attack on Courcelles, Captain Richard Annesley West
of the 6th Battalion took charge of some infantry who had lost their
bearings in the dense fog. He gathered up all the scattered men he
could find. He was mounted, and in the course of the morning he
had two horses shot under him; but after the second horse had
been shot he went on with his work on foot. Having rallied the
infantry, he continued his original task of leading forward his Tanks,
and our capture of Courcelles was chiefly due to his individual
initiative and gallantry. He was awarded a bar to his D.S.O.
About eleven o’clock the greater number both of Mark V. Tanks
and Whippets had reached the line of the railway. A few leading
Tanks had even crossed it, when all in a moment the mist lifted with
the suddenness of a withdrawn curtain. A blazing sun appeared, and
each advancing Tank stood out clearly under its bright light. The
German artillery, which was covering the railway, immediately
directed a deadly fire on the Tanks, and each individual machine
became the centre of a zone of bullets and bursting shells. The
infantry as they advanced had to avoid these little whirlwinds of fire.
It was at this time that most of the thirty-seven Tanks which were
hit by shells during the day were accounted for.
It was a good day for the enemy from an anti-Tank point of
view, such a day indeed as they were never to repeat.
Second Lieutenant Hickson of the 3rd Tank Battalion was one of
the few who had got his Tank across the line just before the mist
lifted. As the sun came out he found himself right in front of the
enemy’s batteries at point-blank range. His Whippet was immediately
hit, but he managed to get his two men away in safety. The artillery
and machine-gun fire was extremely heavy, but without any thought
of his own safety, he at once went back on foot to warn a number of
other Tanks which were about to cross the railway at the same
place. In this he was successful and undoubtedly saved a large
number of machines from being knocked out. Later, though the spot

72. was still under heavy fire, he made several ineffectual efforts to
salve his Tank.
The weather could hardly have done us a worse turn. Had the
mist lasted for half an hour longer the Tanks would have been able
to overrun the artillery positions without being seen. However, the
lifting of the fog at least enabled the aeroplanes attached to the
Tanks to go up. The counter-gun machines at once flew out to
attack the hostile batteries, and a good deal of execution was done.
All the rest of the day we fought under a blazing sun.
The German resistance was curiously patchy; here and there we
found every inch of our advance disputed, the machine-gunners and
artillerymen fighting their weapons till the last moment, and the
reserves launching small counter-attacks whenever opportunity
offered.
Here and there large parties, a hundred and more strong, would
surrender before the Tanks had time to open fire.
The Tank crews,—especially of the Mark V.’s and the Whippets,
whose ventilation was less adequate than the old Mark IV.’s—
suffered greatly from the terrific heat.
In one or two instances the whole crew of a Mark V. seems to
have become unconscious through the appalling heat, the fumes
from their own engines, and the gas used by the enemy, the
unconsciousness being followed by temporarily complete loss of
memory and extreme prostration.
Inside the Whippets, though the men fared slightly better, the
lack of ventilation was equally fatal to efficiency.
83
“The heat temporarily put several Whippets out of
action as fighting weapons.
“On a hot summer’s day one hour’s running with door
closed renders a Whippet weaponless except for revolver fire.

73. “The heat generated is so intense that it not only causes
ammunition to swell so that it jams the gun, but actually in
several cases caused rounds to explode inside the Tank.
“Guns became too hot to hold, and in one case the
temperature of the steering wheel became unbearable.”
But evening came at last, and with the darkness the two armies
disengaged.
We had suffered more casualties than we had quite bargained
for—chiefly owing to the accident of the mist—but upon the whole
we were well satisfied with the events of the day.
We had reached the general line of the railway practically along
the whole front of attack. We had captured Achiet-le-Petit and
Longeast Wood, Courcelles and Moyenneville. Most important of all,
the position we needed for the launching of our principal attack had
been successfully gained and we had taken over 2000 prisoners.

75. CHAPTER XIX
BREAKING THE DROCOURT-QUÉANT LINE—THE
BATTLE OF EPEHY
I
WÉ have said that August 22 had, in the original plan, been
devoted to consolidation and to the moving up of guns. Only the 3rd
Corps in the 4th Army area, with its twenty-four Tanks of the 4th
and 5th Battalions, launched an interim attack on the Bray-Albert
front.
We gained all our objectives. The 18th Division crossed the river
Ancre, captured Albert by an enveloping movement from the south-
east, and our line between the Somme and the Ancre was now
advanced well to the east of the Bray-Albert road.
The left of the 4th Army was taken forward in conformity with
the rest of our line.
The way had now been cleared for what was really the main
attack, though it was not the attack in which the greatest number of
Tanks were employed.
The assault opened on August 23 by a series of attacks on the
whole of a thirty-three-mile front, that is to say, from our junction
with the French, north of Lihons, to the spot near Mercatel, where
the Hindenburg Line from Quéant and Bullecourt joined the old
Arras-Vimy defence of 1916.

76. The hundred Tanks which went into action on this day were
nearly all fresh machines which had not fought on the 21st.
They were distributed in groups along the fronts of both the 3rd
and 4th Armies.
South of the Somme, with the Australians near Chuignolles, the
largest group of nearly sixty Tanks went into action. They were
machines belonging to the 2nd, 8th and 13th Battalions.
The enemy had withdrawn their anti-Tank guns to the top of the
ridge, which it was impossible for Tanks to climb except at one spot.
Upon this one crossing-place they had trained their guns, and here
several Tanks suffered direct hits.
We attacked as usual without a preliminary bombardment and
met with a desperate resistance, the German machine-gunners
defending their posts with extraordinary heroism, and often firing
their guns till the very moment when they and their weapons were
crushed to the earth by an attacking Tank.
A particularly interesting account of the action is given in the
13th Battalion History—
“It was soon evident that the enemy were prepared to
make a stout resistance; there was no definite trench system,
but nests of machine-guns were encountered in organised
shell-holes almost from the start; while Saint Martin’s Wood
and the gully to the east of this, Herleville Wood, and the
quarry at its southern end, were all strongly held by machine-
guns in prepared emplacements. As before, the German
gunners fought with magnificent pertinacity and courage; one
Tank Commander claimed to have knocked out over thirty
machine-guns, and this claim was supported by the infantry
with him; the estimates of several other Tanks were almost as
high. These machine-guns were provided with armour-
piercing bullets, and Tanks were pitted all over and in many
places penetrated by these. There is no doubt that by

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