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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

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 CANCOPY (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).

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 suggestions, 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

Table of Contents
To the Student

A Forces and Motion: Dynamics
1

Kinematics and Dynamics
in One Dimension

1.1
1.2

Introduction
Distance and Displacement
Defining Directions
1.3
Unit Conversion and Analysis
1.4
Speed and Velocity
1.5
Acceleration
1.6
An Algebraic Description of Uniformly
Accelerated Linear Motion
1.7
Bodies in Free Fall
The Guinea and Feather Demonstration
Acceleration due to Gravity
1.8
A Graphical Analysis of Linear Motion
Velocity
1.9
Dynamics
1.10 Free-body Diagrams
1.11 Newton’s First Law of Motion:
The Law of Inertia
Inertial and Non-inertial Frames
of Reference
ma

1.12 Newton’s Second Law of Motion: F
net
1.13 Newton’s Third Law: Action–Reaction
1.14 Friction and the Normal Force
1.15 Newton’s Law of Universal Gravitation
Calculating Gravitational Forces
STSE — New Respect for the Humble Tire
Summary
Exercises
Lab 1.1 — Uniform Acceleration: The Relationship
between Displacement and Time
Lab 1.2 — Uniform Acceleration: The Relationship
between Angle of Inclination and Acceleration

2
2.1
2.2

2.3
2.4
2.5

Kinematics and Dynamics
in Two Dimensions
Vectors in Two Dimensions
Vector Addition
Relative Motion
Relative Velocity Problems
Problems Involving Non-perpendicular
Vectors
Projectile Motion
Newton’s Laws in Two Dimensions
The Inclined Plane

x

1
4
5
5
7
7
8
9
10
19
19
20
24
24
32
33
34
35
36
39
44
48
50
52
54
55
61
62

2.6
2.7
2.8

String-and-pulley Problems
Uniform Circular Motion
Centripetal Force
Centripetal Force and Banked Curves
Centrifugation
Satellites in Orbit
STSE — The Tape-measure Home Run
Summary
Exercises
Lab 2.1 — Projectile Motion
Lab 2.2 — Centripetal Force and Centripetal
Acceleration
Lab 2.3 — Amusement Park Physics

3

Extension: Statics — Objects
and Structures in Equilibrium

Keeping Things Still: An Introduction
to Statics
3.2
The Centre of Mass — The Gravity Spot
3.3
Balancing Forces … Again!
3.4
Balancing Torques
3.5
Static Equilibrium: Balancing Forces
and Torque
3.6
Static Equilibrium and the Human Body
3.7
Stability and Equilibrium
3.8
Elasticity: Hooke’s Law
3.9
Stress and Strain — Cause and Effect
Stress: The Cause of Strain
Strain: The Effect of Stress
3.10 Stress and Strain in Construction
STSE — The Ultimate Effect of Stress on
a Structure
Summary
Exercises
Lab 3.1 — Equilibrium in Forces
Lab 3.2 — Balancing Torque

64
64
70
71
74
78
85
89

123
126

127

3.1

B Energy and Momentum
63

93
98
103
106
107
109
112
114
115
122

128
128
130
134
139
148
155
159
161
161
163
170
172
174
175
181
183

185

4

Linear Momentum

188

4.1
4.2
4.3

Introduction to Linear Momentum
Linear Momentum
Linear Momentum and Impulse
Force-versus-Time Graphs
Conservation of Linear Momentum
in One Dimension
Conservation of Linear Momentum
in Two Dimensions

189
189
190
195

4.4
4.5

Table of Contents

199
203

v

4.6
Linear Momentum and Centre of Mass
STSE — Recreational Vehicle Safety and Collisions
Summary
Exercises
Lab 4.1 — Linear Momentum in
One Dimension: Dynamic Laboratory Carts
Lab 4.2 — Linear Momentum in
Two Dimensions: Air Pucks (Spark Timers)
Lab 4.3 — Linear Momentum in
Two Dimensions: Ramp and Ball

5

Energy and Interactions

Introduction to Energy
Isolation and Systems
5.2
Work
-versus- d
Graph
Work from an F
5.3
Kinetic Energy
Kinetic Energy and Momentum
5.4
Gravitational Potential Energy
5.5
Elastic Potential Energy and Hooke’s Law
Conservation of Energy
5.6
Power
5.7
Elastic and Inelastic Collisions
Equations for One-dimensional
Elastic Collisions
Graphical Representations of Elastic
and Inelastic Collisions
STSE — The Physics Equation — The Basis
of Simulation
Summary
Exercises
Lab 5.1 — Conservation of Energy Exhibited
by Projectile Motion
Lab 5.2 — Hooke’s Law
Lab 5.3 — Inelastic Collisions (Dry Lab)
Lab 5.4 — Conservation of Kinetic Energy

6

Energy Transfer

6.1

Gravity and Energy
A Comparison of Ep mg h
GMm
and Ep r
Kinetic Energy Considerations
Escape Energy and Escape Speed
Implications of Escape Speed
Orbits
Kepler’s Laws of Planetary Motion
Kepler’s Third Law for Large Masses
Extension: Orbital Parametres
Simple Harmonic Motion —
An Energy Introduction
Hooke’s Law
Damped Simple Harmonic Motion

6.3

6.4

vi

222
224
227

229

5.1

6.2

211
214
216
217

230
230
233
237
239
241
243
249
253
255
260
260
266
270
272
273
280
281
282
283

284
285
289
290
292
293
295
298
300
301

Three Types of Damping
Applications of Damping
Shock Absorbers
STSE — The International Space Station
Summary
Exercises
Lab 6.1 — The Pendulum

308
309
309
310
312
313
316

7

317

Angular Motion

7.1
7.2
7.3

Introduction
A Primer on Radian Measure
Angular Velocity and Acceleration
Angular Velocity
Relating Angular Variables to Linear Ones
More About Centripetal Acceleration
7.4
The Five Angular Equations of Motion
7.5
Moment of Inertia
Extension: The Parallel-axis Theorem
7.6
Rotational Energy
7.7
Rotational Kinetic Energy
7.8
The Conservation of Energy
7.9
Angular Momentum
7.10 The Conservation of Angular Momentum
7.11 The Yo-yo
Energy Analysis
Force Analysis
STSE — Gyroscopic Action — A Case of
Angular Momentum
Summary
Exercises
Lab 7.1 — Rotational Motion: Finding the
Moment of Inertia

354
357
358
365

C Electric, Gravitational,

and Magnetic Fields

367

8

Electrostatics and Electric Fields

370

8.1
8.2
8.3

Electrostatic Forces and Force Fields
The Basis of Electric Charge — The Atom
Electric Charge Transfer
Charging by Friction
Charging by Contact and Induction
Coulomb’s Law
The Vector Nature of Electric Forces
between Charges
Fields and Field-mapping Point Charges
Force at a Distance
Field Strength
Coulomb’s Law Revisited
Electricity, Gravity, and Magnetism:
Forces at a Distance and Field Theory

8.4

8.5
8.6

303
304
308

318
318
322
322
323
325
327
332
337
339
342
344
347
348
352
352
352

Physics: Concepts and Connections Book Two

371
371
373
374
375
377
384
388
388
394
395
398

8.7

Electric Potential and Electric
Potential Energy
8.8
Movement of Charged Particles in
a Field — The Conservation of Energy
The Electric Potential around a
Point Charge
8.9
The Electric Field Strength of a
Parallel-plate Apparatus
Elementary Charge
STSE — Electric Double-layer Capacitors
Summary
Exercises
Lab 8.1 — The Millikan Experiment
Lab 8.2 — Mapping Electric Fields

9

Magnetic Fields and Field Theory

Magnetic Force — Another Force
at a Distance
9.2
Magnetic Character — Domain Theory
9.3
Mapping Magnetic Fields
9.4
Artificial Magnetic Fields —
Electromagnetism
Magnetic Character Revisited
A Magnetic Field around a Coiled
Conductor (a Solenoid)
9.5
Magnetic Forces on Conductors
and Charges — The Motor Principle
The Field Strength around a
Current-carrying Conductor
The Unit for Electric Current
(for Real this Time)
Magnetic Force on Moving Charges
9.6
Applying the Motor Principle
Magnetohydrodynamics
Centripetal Magnetic Force
The Mass of an Electron and a Proton
The Mass Spectrometer
9.7
Electromagnetic Induction —
From Electricity to Magnetism
and Back Again
STSE — Magnetic Resonance Imaging (MRI)
Summary
Exercises
Lab 9.1 — The Mass of an Electron

400
404
409
414
415
418
421
422
430
433

435

9.1

436
437
438
441
442
443
447
451
453
456
460
460
461
462
464

467
472
474
475
479

D The Wave Nature of Light

481

10

The Wave Nature of Light

484

10.1

Introduction to Wave Theory
Definitions
Types of Waves
Fundamental Wave Concepts

485
485
486
488

10.2

Terminology
Phase Shift
Simple Harmonic Motion: A Closer Look
Simple Harmonic Motion in
Two Dimensions
10.3 Electromagnetic Theory
Properties of Electromagnetic Waves
The Speed of Electromagnetic Waves
The Speed of Light
The Production of Electromagnetic
Radiation
10.4 Electromagnetic Wave Phenomena:
Refraction
The Refractive Index, n — A Quick Review
Snell’s Law: A More In-depth Look
Refraction in an Optical Medium
Dispersion
The Spectroscope
10.5 Electromagnetic Wave Phenomena:
Polarization
Polarization of Light using Polaroids
(Polarizing Filters)
Malus’ Law: The Intensity of
Transmitted Light
Polarization by Reflection
Polarization by Anisotropic Crystals
10.6 Applications of Polarization
Polarizing Filters in Photography
3-D Movies
Radar
Liquid Crystal Displays (LCDs)
Photoelastic Analysis
Polarization in the Insect World
Polarized Light Microscopy
Measuring Concentrations of Materials
in Solution
10.7 Electromagnetic Wave Phenomena:
Scattering
STSE — Microwave Technology: Too Much
Too Soon?
Summary
Exercises
Lab 10.1 — Investigating Simple Harmonic Motion
Lab 10.2 — Polarization
Lab 10.3 — Malus’ Law

11

The Interaction of Electromagnetic
Waves

11.1
11.2

Introduction
Interference Theory
Path Difference

Table of Contents

488
490
491
492
494
494
494
495
497
500
500
502
504
505
506
507
508
509
511
512
514
514
515
516
516
517
518
518
518
519
522
524
525
529
530
531

532
533
534
535

vii

Two-dimensional Cases
11.3 The Interference of Light
11.4 Young’s Double-slit Equation
11.5 Interferometers
Extension: Measuring Thickness using
an Interferometer
Holography
11.6 Thin-film Interference
Path Difference Effect
The Refractive Index Effect
Combining the Effects
11.7 Diffraction
Wavelength Dependence
11.8 Single-slit Diffraction
The Single-slit Equation
More Single-slit Equations (but they
should look familiar)
Resolution
11.9 The Diffraction Grating
The Diffraction-grating Equation
11.10 Applications of Diffraction
A Grating Spectroscope
Extension: Resolution — What makes
a good spectrometer?
X-ray Diffraction
STSE — CD Technology
Summary
Exercises
Lab 11.1 — Analyzing Wave Characteristics
using Ripple Tanks
Lab 11.2 — Qualitative Observations of the
Properties of Light
Lab 11.3 — Comparison of Light, Sound, and
Mechanical Waves
Lab 11.4 — Finding the Wavelength of Light
using Single Slits, Double Slits, and
Diffraction Gratings

E Matter–Energy Interface
12

Quantum Mechanics

12.1

Introduction
Problems with the Classical or Wave
Theory of Light
The Quantum Idea
Black-body Radiation
The Black-body Equation
The Photoelectric Effect
The Apparatus
Momentum and Photons
De Broglie and Matter Waves

12.2

12.3
12.4
12.5

viii

536
537
538
544
545
546
548
548
549
549
553
553
554
555
559
561
563
564
569
569
569
571
574
576
578
583
586
587

588

589
592
593
593
594
595
596
598
598
603
606

12.6

The Bohr Atom
The Conservation of Energy
The Conservation of Angular Momentum
Electron Energy
Photon Wavelength
Ionization Energy
Bohr’s Model applied to Heavier Atoms
The Wave-Particle Duality of Light
12.7 Probability Waves
12.8 Heisenberg’s Uncertainty Principle
A Hypothetical Mechanical Example
of Diffraction
Heisenberg’s Uncertainty Principle
and Science Fiction
12.9 Extension: Quantum Tunnelling
STSE — The Scanning Tunnelling Microscope
Summary
Exercises
Lab 12.1 — Hydrogen Spectra
Lab 12.2 — The Photoelectric Effect I
Lab 12.3 — The Photoelectric Effect II

13

The World of Special Relativity

Inertial Frames of Reference and Einstein’s
First Postulate of Special Relativity
13.2 Einstein’s Second Postulate of Special
Relativity
13.3 Time Dilation and Length Contraction
Moving Clocks Run Slow
Moving Objects Appear Shorter
13.4 Simultaneity and Spacetime Paradoxes
Simultaneity
Paradoxes
Spacetime Invariance
13.5 Mass Dilation
Electrons Moving in Magnetic Fields
13.6 Velocity Addition at Speeds Close to c
13.7 Mass–Energy Equivalence
Relativistic Momentum
Relativistic Energy
13.8 Particle Acceleration
STSE — The High Cost of High Speed
Summary
Exercises
Lab 13.1 — A Relativity Thought Experiment

608
609
610
612
613
614
614
614
615
617
617
621
622
624
626
627
630
631
632

633

13.1

14

Nuclear and Elementary Particles

14.1

Nuclear Structure and Properties
Isotopes
Unified Atomic Mass Units
Mass Defect and Mass Difference

Physics: Concepts and Connections Book Two

634
637
640
640
643
646
646
647
649
652
656
659
662
663
664
668
674
676
677
683

685
686
687
687
688

Nuclear Binding Energy and Average
Binding Energy per Nucleon
14.2 Natural Transmutations
Nuclear Stability
Alpha Decay
Beta Decay
Decay (Electron Emission)
Decay (Positron Emission)
Electron Capture and Gamma Decay
14.3 Half-life and Radioactive Dating
Half-life
Radioactive Dating
14.4 Radioactivity
Artificial Transmutations
Detecting Radiation
14.5 Fission and Fusion
Fission
Fission Reactors
The CANDU Reactor
Fusion
Creating the Heavy Elements
Comparing Energy Sources — A Debate
14.6 Probing the Nucleus
14.7 Elementary Particles
What is matter?
What is matter composed of?
The Standard Model
Leptons
Quarks
Hadrons (Baryons and Mesons)
14.8 Fundamental Forces and Interactions —
What holds these particles together?
Forces or interactions?
Boson Exchange
Feynman Diagrams
Quantum Chromodynamics (QCD): Colour
Charge and the Strong Nuclear Force
The Weak Nuclear Force — Decay and
Annihilations
STSE — Positron Emission Tomography (PET)
Summary
Exercises
Lab 14.1 — The Half-life of a Short-lived
Radioactive Nuclide

Appendices
Appendix A: Experimental Fundamentals
Introduction
Safety

688
690
690
691
693
693
695
695
697
697
698
700
700
703
706
707
710
711
712
715
717
718
720
720
721
721
721
723
723
727
727
728
729
730
731
736
739
741
747

749
750
750
750

Appendix B: Lab Report
Lab Report
Statistical Deviation of the Mean

752
752
753

Appendix C: Uncertainty Analysis
Accuracy versus Precision
Working with Uncertainties
Making Measurements with Stated
Uncertainties
Manipulation of Data with Uncertainties
Addition and Subtraction of Data
Multiplication and Division of Data

755
755
755

Appendix D: Proportionality Techniques
Creating an Equation from a Proportionality
Finding the Correct Proportionality
Statement
Finding the Constant of Proportionality
in a Proportionality Statement
Other Methods of Finding Equations
from Data

755
756
756
757
758
758
759
761
761

Appendix E: Helpful Mathematical Equations
and Techniques
Mathematical Signs and Symbols
Significant Figures
The Quadratic Formula
Substitution Method of Solving Equations
Rearranging Equations
Exponents
Analyzing a Graph

765
765
765
766
766
766
767
767

Appendix F: Geometry and Trigonometry
Trigonometric Identities

768
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 Concepts 776
Numerical Answers to End-of-chapter
Problems

780

Glossary

786

Index

790

Photograph Credits

798

Table of Contents

ix


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