Physics Grade 12 : Concepts and Connections II

816 Pages·2002·70.06 MB·english

by  Brian Heimbecker

b o o k t w o
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
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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

Table of Contents
To the Student x 2.6 String-and-pulley Problems 93
2.7 Uniform Circular Motion 98
A Forces and Motion: Dynamics 1
2.8 Centripetal Force 103
1 Kinematics and Dynamics Centripetal Force and Banked Curves 106
in One Dimension 4 Centrifugation 107
Satellites in Orbit 109
1.1 Introduction 5
STSE — The Tape-measure Home Run 112
1.2 Distance and Displacement 5
Summary 114
Defining Directions 7
Exercises 115
1.3 Unit Conversion and Analysis 7
Lab 2.1 — Projectile Motion 122
1.4 Speed and Velocity 8
Lab 2.2 — Centripetal Force and Centripetal
1.5 Acceleration 9
Acceleration 123
1.6 An Algebraic Description of Uniformly
Lab 2.3 — Amusement Park Physics 126
Accelerated Linear Motion 10
1.7 Bodies in Free Fall 19
3 Extension: Statics — Objects
The Guinea and Feather Demonstration 19
and Structures in Equilibrium 127
Acceleration due to Gravity 20
3.1 Keeping Things Still: An Introduction
1.8 A Graphical Analysis of Linear Motion 24
to Statics 128
Velocity 24
3.2 The Centre of Mass — The Gravity Spot 128
1.9 Dynamics 32
3.3 Balancing Forces … Again! 130
1.10 Free-body Diagrams 33
3.4 Balancing Torques 134
1.11 Newton’s First Law of Motion:
3.5 Static Equilibrium: Balancing Forces
The Law of Inertia 34
and Torque 139
Inertial and Non-inertial Frames
3.6 Static Equilibrium and the Human Body 148
of Reference 35
1.12 Newton’s Second Law of Motion: F(cid:2)(cid:3) (cid:2)ma(cid:2)(cid:3) 36 3.7 Stability and Equilibrium 155
net
3.8 Elasticity: Hooke’s Law 159
1.13 Newton’s Third Law: Action–Reaction 39
3.9 Stress and Strain — Cause and Effect 161
1.14 Friction and the Normal Force 44
Stress: The Cause of Strain 161
1.15 Newton’s Law of Universal Gravitation 48
Strain: The Effect of Stress 163
Calculating Gravitational Forces 50
3.10 Stress and Strain in Construction 170
STSE — New Respect for the Humble Tire 52
STSE — The Ultimate Effect of Stress on
Summary 54
a Structure 172
Exercises 55
Summary 174
Lab 1.1 — Uniform Acceleration: The Relationship
Exercises 175
between Displacement and Time 61
Lab 3.1 — Equilibrium in Forces 181
Lab 1.2 — Uniform Acceleration: The Relationship
Lab 3.2 — Balancing Torque 183
between Angle of Inclination and Acceleration 62
2 Kinematics and Dynamics B Energy and Momentum 185
in Two Dimensions 63
4 Linear Momentum 188
2.1 Vectors in Two Dimensions 64
4.1 Introduction to Linear Momentum 189
Vector Addition 64
4.2 Linear Momentum 189
2.2 Relative Motion 70
4.3 Linear Momentum and Impulse 190
Relative Velocity Problems 71
Force-versus-Time Graphs 195
Problems Involving Non-perpendicular
4.4 Conservation of Linear Momentum
Vectors 74
in One Dimension 199
2.3 Projectile Motion 78
4.5 Conservation of Linear Momentum
2.4 Newton’s Laws in Two Dimensions 85
in Two Dimensions 203
2.5 The Inclined Plane 89
Table of Contents v
4.6 Linear Momentum and Centre of Mass 211 Three Types of Damping 308
STSE — Recreational Vehicle Safety and Collisions 214 Applications of Damping 309
Summary 216 Shock Absorbers 309
Exercises 217 STSE — The International Space Station 310
Lab 4.1 — Linear Momentum in Summary 312
One Dimension: Dynamic Laboratory Carts 222 Exercises 313
Lab 4.2 — Linear Momentum in Lab 6.1 — The Pendulum 316
Two Dimensions: Air Pucks (Spark Timers) 224
7 Angular Motion 317
Lab 4.3 — Linear Momentum in
7.1 Introduction 318
Two Dimensions: Ramp and Ball 227
7.2 A Primer on Radian Measure 318
5 Energy and Interactions 229 7.3 Angular Velocity and Acceleration 322
5.1 Introduction to Energy 230 Angular Velocity 322
Isolation and Systems 230 Relating Angular Variables to Linear Ones 323
5.2 Work 233 More About Centripetal Acceleration 325
Work from an F(cid:2)(cid:3)-versus-(cid:3)d(cid:2)(cid:3)Graph 237 7.4 The Five Angular Equations of Motion 327
5.3 Kinetic Energy 239 7.5 Moment of Inertia 332
Kinetic Energy and Momentum 241 Extension: The Parallel-axis Theorem 337
5.4 Gravitational Potential Energy 243 7.6 Rotational Energy 339
5.5 Elastic Potential Energy and Hooke’s Law 249 7.7 Rotational Kinetic Energy 342
Conservation of Energy 253 7.8 The Conservation of Energy 344
5.6 Power 255 7.9 Angular Momentum 347
5.7 Elastic and Inelastic Collisions 260
7.10 The Conservation of Angular Momentum 348
Equations for One-dimensional
7.11 The Yo-yo 352
Elastic Collisions 260
Energy Analysis 352
Graphical Representations of Elastic
Force Analysis 352
and Inelastic Collisions 266
STSE — Gyroscopic Action — A Case of
STSE — The Physics Equation — The Basis
Angular Momentum 354
of Simulation 270
Summary 357
Summary 272
Exercises 358
Exercises 273
Lab 7.1 — Rotational Motion: Finding the
Lab 5.1 — Conservation of Energy Exhibited
Moment of Inertia 365
by Projectile Motion 280
Lab 5.2 — Hooke’s Law 281
C Electric, Gravitational,
Lab 5.3 — Inelastic Collisions (Dry Lab) 282
and Magnetic Fields 367
Lab 5.4 — Conservation of Kinetic Energy 283
8 Electrostatics and Electric Fields 370
6 Energy Transfer 284
6.1 Gravity and Energy 285 8.1 Electrostatic Forces and Force Fields 371
A Comparison of (cid:3)E (cid:2)mg(cid:3)h 8.2 The Basis of Electric Charge — The Atom 371
p
and E (cid:2)(cid:4)(cid:5)GM(cid:4)m 289 8.3 Electric Charge Transfer 373
p r
Kinetic Energy Considerations 290 Charging by Friction 374
Escape Energy and Escape Speed 292 Charging by Contact and Induction 375
Implications of Escape Speed 293 8.4 Coulomb’s Law 377
6.2 Orbits 295 The Vector Nature of Electric Forces
Kepler’s Laws of Planetary Motion 298 between Charges 384
Kepler’s Third Law for Large Masses 300 8.5 Fields and Field-mapping Point Charges 388
Extension: Orbital Parametres 301 Force at a Distance 388
6.3 Simple Harmonic Motion — 8.6 Field Strength 394
An Energy Introduction 303 Coulomb’s Law Revisited 395
Hooke’s Law 304 Electricity, Gravity, and Magnetism:
6.4 Damped Simple Harmonic Motion 308 Forces at a Distance and Field Theory 398
vi Physics: Concepts and Connections Book Two
8.7 Electric Potential and Electric Terminology 488
Potential Energy 400 Phase Shift 490
8.8 Movement of Charged Particles in Simple Harmonic Motion: A Closer Look 491
a Field — The Conservation of Energy 404 Simple Harmonic Motion in
The Electric Potential around a Two Dimensions 492
Point Charge 409 10.3 Electromagnetic Theory 494
8.9 The Electric Field Strength of a Properties of Electromagnetic Waves 494
Parallel-plate Apparatus 414 The Speed of Electromagnetic Waves 494
Elementary Charge 415 The Speed of Light 495
STSE — Electric Double-layer Capacitors 418 The Production of Electromagnetic
Summary 421 Radiation 497
Exercises 422 10.4 Electromagnetic Wave Phenomena:
Lab 8.1 — The Millikan Experiment 430 Refraction 500
Lab 8.2 — Mapping Electric Fields 433 The Refractive Index, n— A Quick Review 500
Snell’s Law: A More In-depth Look 502
9 Magnetic Fields and Field Theory 435
Refraction in an Optical Medium 504
9.1 Magnetic Force — Another Force
Dispersion 505
at a Distance 436
The Spectroscope 506
9.2 Magnetic Character — Domain Theory 437
10.5 Electromagnetic Wave Phenomena:
9.3 Mapping Magnetic Fields 438
Polarization 507
9.4 Artificial Magnetic Fields —
Polarization of Light using Polaroids
Electromagnetism 441
(Polarizing Filters) 508
Magnetic Character Revisited 442
Malus’ Law: The Intensity of
A Magnetic Field around a Coiled
Transmitted Light 509
Conductor (a Solenoid) 443
Polarization by Reflection 511
9.5 Magnetic Forces on Conductors
Polarization by Anisotropic Crystals 512
and Charges — The Motor Principle 447
10.6 Applications of Polarization 514
The Field Strength around a
Polarizing Filters in Photography 514
Current-carrying Conductor 451
3-D Movies 515
The Unit for Electric Current
Radar 516
(for Real this Time) 453
Liquid Crystal Displays (LCDs) 516
Magnetic Force on Moving Charges 456
Photoelastic Analysis 517
9.6 Applying the Motor Principle 460
Polarization in the Insect World 518
Magnetohydrodynamics 460
Polarized Light Microscopy 518
Centripetal Magnetic Force 461
Measuring Concentrations of Materials
The Mass of an Electron and a Proton 462
in Solution 518
The Mass Spectrometer 464
10.7 Electromagnetic Wave Phenomena:
9.7 Electromagnetic Induction —
Scattering 519
From Electricity to Magnetism
STSE — Microwave Technology: Too Much
and Back Again 467
Too Soon? 522
STSE — Magnetic Resonance Imaging (MRI) 472
Summary 524
Summary 474
Exercises 525
Exercises 475
Lab 10.1 — Investigating Simple Harmonic Motion 529
Lab 9.1 — The Mass of an Electron 479
Lab 10.2 — Polarization 530
Lab 10.3 — Malus’ Law 531
D The Wave Nature of Light 481
11 The Interaction of Electromagnetic
10 The Wave Nature of Light 484
Waves 532
10.1 Introduction to Wave Theory 485
Definitions 485 11.1 Introduction 533
Types of Waves 486 11.2 Interference Theory 534
10.2 Fundamental Wave Concepts 488 Path Difference 535
Table of Contents vii
Two-dimensional Cases 536 12.6 The Bohr Atom 608
11.3 The Interference of Light 537 The Conservation of Energy 609
11.4 Young’s Double-slit Equation 538 The Conservation of Angular Momentum 610
11.5 Interferometers 544 Electron Energy 612
Extension: Measuring Thickness using Photon Wavelength 613
an Interferometer 545 Ionization Energy 614
Holography 546 Bohr’s Model applied to Heavier Atoms 614
11.6 Thin-film Interference 548 The Wave-Particle Duality of Light 614
Path Difference Effect 548 12.7 Probability Waves 615
The Refractive Index Effect 549 12.8 Heisenberg’s Uncertainty Principle 617
Combining the Effects 549 A Hypothetical Mechanical Example
11.7 Diffraction 553 of Diffraction 617
Wavelength Dependence 553 Heisenberg’s Uncertainty Principle
11.8 Single-slit Diffraction 554 and Science Fiction 621
The Single-slit Equation 555 12.9 Extension: Quantum Tunnelling 622
More Single-slit Equations (but they STSE — The Scanning Tunnelling Microscope 624
should look familiar) 559 Summary 626
Resolution 561 Exercises 627
11.9 The Diffraction Grating 563 Lab 12.1 — Hydrogen Spectra 630
The Diffraction-grating Equation 564 Lab 12.2 — The Photoelectric Effect I 631
11.10 Applications of Diffraction 569 Lab 12.3 — The Photoelectric Effect II 632
A Grating Spectroscope 569
13 The World of Special Relativity 633
Extension: Resolution — What makes
13.1 Inertial Frames of Reference and Einstein’s
a good spectrometer? 569
First Postulate of Special Relativity 634
X-ray Diffraction 571
13.2 Einstein’s Second Postulate of Special
STSE — CD Technology 574
Relativity 637
Summary 576
13.3 Time Dilation and Length Contraction 640
Exercises 578
Moving Clocks Run Slow 640
Lab 11.1 — Analyzing Wave Characteristics
Moving Objects Appear Shorter 643
using Ripple Tanks 583
13.4 Simultaneity and Spacetime Paradoxes 646
Lab 11.2 — Qualitative Observations of the
Simultaneity 646
Properties of Light 586
Paradoxes 647
Lab 11.3 — Comparison of Light, Sound, and
Spacetime Invariance 649
Mechanical Waves 587
13.5 Mass Dilation 652
Lab 11.4 — Finding the Wavelength of Light
Electrons Moving in Magnetic Fields 656
using Single Slits, Double Slits, and
13.6 Velocity Addition at Speeds Close to c 659
Diffraction Gratings 588
13.7 Mass–Energy Equivalence 662
E Matter–Energy Interface 589 Relativistic Momentum 663
Relativistic Energy 664
12 Quantum Mechanics 592
13.8 Particle Acceleration 668
12.1 Introduction 593 STSE — The High Cost of High Speed 674
Problems with the Classical or Wave Summary 676
Theory of Light 593 Exercises 677
12.2 The Quantum Idea 594 Lab 13.1 — A Relativity Thought Experiment 683
Black-body Radiation 595
14 Nuclear and Elementary Particles 685
The Black-body Equation 596
12.3 The Photoelectric Effect 598 14.1 Nuclear Structure and Properties 686
The Apparatus 598 Isotopes 687
12.4 Momentum and Photons 603 Unified Atomic Mass Units 687
12.5 De Broglie and Matter Waves 606 Mass Defect and Mass Difference 688
viii Physics: Concepts and Connections Book Two
Nuclear Binding Energy and Average Appendix B: Lab Report 752
Binding Energy per Nucleon 688 Lab Report 752
14.2 Natural Transmutations 690 Statistical Deviation of the Mean 753
Nuclear Stability 690
Appendix C: Uncertainty Analysis 755
Alpha Decay 691
Accuracy versus Precision 755
Beta Decay 693
Working with Uncertainties 755
(cid:6)(cid:5)Decay (Electron Emission) 693
Making Measurements with Stated
(cid:6)(cid:7)Decay (Positron Emission) 695
Uncertainties 755
Electron Capture and Gamma Decay 695
Manipulation of Data with Uncertainties 756
14.3 Half-life and Radioactive Dating 697
Addition and Subtraction of Data 756
Half-life 697
Multiplication and Division of Data 757
Radioactive Dating 698
14.4 Radioactivity 700 Appendix D: Proportionality Techniques 758
Artificial Transmutations 700 Creating an Equation from a Proportionality 758
Detecting Radiation 703 Finding the Correct Proportionality
14.5 Fission and Fusion 706 Statement 759
Fission 707 Finding the Constant of Proportionality
Fission Reactors 710 in a Proportionality Statement 761
The CANDU Reactor 711 Other Methods of Finding Equations
Fusion 712 from Data 761
Creating the Heavy Elements 715
Appendix E: Helpful Mathematical Equations
Comparing Energy Sources — A Debate 717
and Techniques 765
14.6 Probing the Nucleus 718
Mathematical Signs and Symbols 765
14.7 Elementary Particles 720
Significant Figures 765
What is matter? 720
The Quadratic Formula 766
What is matter composed of? 721
Substitution Method of Solving Equations 766
The Standard Model 721
Rearranging Equations 766
Leptons 721
Exponents 767
Quarks 723
Analyzing a Graph 767
Hadrons (Baryons and Mesons) 723
14.8 Fundamental Forces and Interactions —
Appendix F: Geometry and Trigonometry 768
What holds these particles together? 727
Trigonometric Identities 768
Forces or interactions? 727
Boson Exchange 728 Appendix G:SI Units 770
Feynman Diagrams 729
Appendix H:Some Physical Properties 773
Quantum Chromodynamics (QCD): Colour
Charge and the Strong Nuclear Force 730 Appendix I:The Periodic Table 774
The Weak Nuclear Force — Decay and
Appendix J:Some Elementary Particles
Annihilations 731
and Their Properties 775
STSE — Positron Emission Tomography (PET) 736
Summary 739 Numerical Answers to Applying the Concepts 776
Exercises 741
Numerical Answers to End-of-chapter
Lab 14.1 — The Half-life of a Short-lived
Problems 780
Radioactive Nuclide 747
Glossary 786
Appendices 749
Index 790
Appendix A: Experimental Fundamentals 750
Introduction 750 Photograph Credits 798
Safety 750
Table of Contents ix
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
method Flowcharts
of
process
The flowcharts in this book are visual summaries that graphically show you
onnecctti the interconnections among the concepts presented at the end of each section
c theng
Concepts and chapter. They help you organize the methods and ideas put forward in
the course. The flowcharts come in three flavors: Connecting the Concepts,
putting Method of Process, and Putting It All Together. They are introduced as you
TToogite atllher need them to help you review and remember what you have learned.
e x a m p l e 1 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.
appllyying Applying the Concepts
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