Physics from planet Earth - an introduction to mechanics

604 Pages·2015·17.843 MB·English

by  Amato, Joseph C., Galvez, Enrique Jose

PHYSICS
PHYSICS FROM PLANET EARTH
PHYSICS FROM PLANET EARTH
An Introduction to Mechanics
An Introduction to Mechanics
“Astronomy is overflowing with exciting discoveries, ranging from Earth-planets orbiting other stars to exotic phenomena
such as black holes and neutron stars. This book brilliantly leverages these topics to entice students to a deeper study of
classical mechanics.”
—David Charbonneau, Professor of Astronomy, Harvard University
“… a special and unique text for teaching basic mechanics. … the authors are excellent writers, possessing literary acuity
and sensitivity in unusual measure.”
—Lyle Roelofs, President, Berea College

“A refreshing departure from mainstream textbooks on classical mechanics that any ingenuous and inquisitive student will love.”
—Stefano Moretti, Professor, School of Physics and Astronomy, University of Southampton
Physics from Planet Earth - An Introduction to Mechanics presents a clear and concise exposition of classical mechanics with
an emphasis on the conservation laws. The book guides you on a journey beyond standard approaches that use blocks, projectiles,
and inclined planes to grander themes involving interplanetary travel, exoplanets, asteroid collisions, and dark matter.
Unlike traditional introductory books, this one:
• Introduces the three conservation laws (momentum, energy, and angular momentum) as fundamental laws
of nature from which secondary concepts, such as force and torque, are derived
• Organizes topics around the conservation laws, avoiding the typical “math overload” encountered at the start
of standard courses
• Motivates and illustrates many topics through real, contemporary applications in astronomy, planetary science,
and space travel
After reviewing the basic mathematical tools needed to study mechanics, the text addresses the conservation of momentum. It
next introduces force, with special attention to Newton’s Law of Universal Gravitation. The text then presents evidence for a second
conservation principle: energy. The book also explores the conservation of angular momentum and a variety of applications,
including pulsars, orbital eccentricity, and gyroscopes. It concludes with a discussion of dark matter, dark energy, and the ultimate
fate of the universe.
Joseph C. Amato
Enrique J. Galvez
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PHYSICS FROM PLANET EARTH
An Introduction to Mechanics

PHYSICS FROM PLANET EARTH
An Introduction to Mechanics
Joseph C. Amato
Enrique J. Galvez
CRC Press
Taylor & Francis Group
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Boca Raton, FL 33487-2742
© 2015 by Taylor & Francis Group, LLC
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Version Date: 20150619
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To our former colleagues, who helped shape our careers while laying the groundwork
for a dynamic, intellectually vibrant department at Colgate University:
Jack Dodd
Hugh Helm
Charles Holbrow
James Lloyd
Shimon Malin
Victor Mansfield
and
Donald Holcomb (Cornell)

CONTENTS
Preface for Instructors xi 2.10 Application: Calculating the Number
Preface for Students xv of Hours of Daylight 49
Authors xvii 2.11 Summary 52
Problems 53
Section I Mathematical
3 Using Vectors to Describe Motion 59
Toolbox 1
3.1 Introduction 60
3.2 Displacement and Velocity 60
1 Surveying the Skies 3 3.3 Constant Velocity Motion 63
3.4 Uniform Circular Motion 64
1.1 Early Astronomy 4
3.5 Relative Velocity 67
1.2 Eratosthenes and the Earth’s Radius 5
3.6 How to Measure Relative Velocity 70
1.3 Aristarchus, Hipparchus, and the Distance
3.7 Hubble’s Law 76
to the Moon and Sun 10
3.8 Hubble’s Law and the Expansion of the Universe 79
1.4 Ptolemy and the Earth-Centered Universe 14
3.9 Summary 82
1.5 Copernicus and Galileo 16
Problems 83
1.6 Mapping the Solar System 18
1.7 Measuring the Earth–Sun Distance 20
1.8 Measuring Intergalactic Distances 24 Section II Conservation of
1.9 Summary 26 Momentum 93
Problems 27
4 The First Conservation Law: Mass,
2 Vectors 33
Momentum, and Rocketry 95
2.1 Introduction 34
4.1 Introduction: What Is a Collision? 96
2.2 Position and Displacement Vectors 35
4.2 One-Dimensional Collision 97
2.3 Unit Vectors 36
4.3 Elastic Collisions and Energy 102
2.4 Vector Arithmetic 36
4.4 Three-Dimensional Collisions 103
2.5 Angles between Vectors 39
4.5 Momentum Conservation and the Principle
2.6 Vectors without Coordinate Axes 42
of Relativity 106
2.7 Comparing the Copernican and Ptolemaic
4.6 Application: Rocket Propulsion 111
Worlds: Vectorially 45
4.7 Application: Multistage Rockets 116
2.8 Dot Product Revisited 48
4.8 Summary 119
2.9 Application: The Law of Cosines 48
Problems 120
vii
5 Collisions and the Center of Mass 129 7 Circular Motion, Simple Harmonic
5.1 Introduction 130 Motion, and Time 213
5.2 What Is the Center of Mass? 130 7.1 Introduction 214
5.3 Motion of the Center of Mass 132 7.2 Uniform Circular Motion and Centripetal
5.4 Using the CM to Analyze Collisions 134 Acceleration 215
5.5 Example: The Superball–Basketball 7.3 Applying Newton’s Laws to Circular
Collision 138 Motion 217
5.6 “Slingshot Effect”: Speeding Up Spacecraft 7.4 Newton’s Laws at the State Fair 221
in Midflight 139 7.5 Einstein’s Happiest Thought:
5.7 Planetary Fly-Bys in Two Dimensions 140 Weightlessness 223
5.8 Chadwick’s Discovery of the Neutron 143 7.6 Simple Harmonic Motion 230
5.9 Relativistic Collisions 146 7.7 Prototype Oscillator: The Mass–Spring
5.10 Application: Particle Accelerators and System 230
Colliders 150 7.8 Example: Collision with an Oscillator 237
5.11 Summary 154 7.9 “Simple” Pendulum 239
Problems 155 7.10 Coupled Oscillators 241
7.11 Relation between Sinusoidal Oscillation
and Circular Motion 244
6 Acceleration, Force, and Newton’s Laws 167 7.12 Longitude Problem 246
7.13 Just a Second! 247
6.1 Introduction: Galileo and
7.14 Summary 249
Sixteenth-Century Ballistics 168
Problems 250
6.2 Acceleration 170
6.3 Parabolic Projectile Motion 173
6.4 Application: Clever Monkeys vs. Shrewd
Hunters 176 8 Kepler’s Laws and Newton’s Discovery
6.5 Newton and the Principia 177 of Universal Gravitation 265
6.6 Newton’s Laws of Motion 179 8.1 Introduction: The “War on Mars” 266
6.7 Inertial and Gravitational Mass 180 8.2 Kepler’s Laws 268
6.8 Using Newton’s Laws: The General 8.3 Vector Cross Product 273
Procedure 184 8.4 Application: The Cross Product and
6.9 Friction Forces 187 Kepler’s Second Law 275
6.10 Application: Drag Forces 188 8.5 Inverse-Square Dependence of the
6.11 Oblique Motion 192 Planetary Force 277
6.12 Multiple Bodies: Choosing the “Best” 8.6 Newton’s Grand Synthesis: Universal
System 194 Gravitation 279
6.13 Two Common Errors 199 8.7 Shell Theorem, or Newton’s “Superb
6.14 Application: Rocket Thrust 201 Theorem” 281
6.15 Summary 203 8.8 The Apple and the Moon 283
Problems 204 8.9 Law of Universal Gravitation 284
viii Contents