THE MECHANICAL UNIVERSE

Transcription

1 THE MECHANICAL UNIVERSE MECHANICS AND HEAT, ADVANCED EDITION STEVEN С FRAUTSCHI PROFESSOR OF THEORETICAL PHYSICS CALIFORNIA INSTITUTE OF TECHNOLOGY RICHARD P. OLENICK ASSISTANT PROFESSOR OF PHYSICS, UNIVERSITY OF DALLAS VISITING ASSOCIATE, CALIFORNIA INSTITUTE OF TECHNOLOGY TOM M. APOSTOL PROFESSOR OF MATHEMATICS, CALIFORNIA INSTITUTE OF TECHNOLOGY DAVID L. GOODSTEIN PROFESSOR OF PHYSICS AND APPLIED PHYSICS, CALIFORNIA INSTITUTE OF TECHNOLOGY AND PROJECT DIRECTOR, THE MECHANICAL UNIVERSE The right of the University of Cambridge to print and sell all manner of books was granted by Henry VIII in The University has printed and published continuously since CAMBRIDGE UNIVERSITY PRESS Cambridge London New York New Rochelle Melbourne Sydney

2 CONTENTS Preface xiii Chapter 1 INTRODUCTION TO THE MECHANICAL UNIVERSE The Copernican Revolution Units and Dimensions A Final Word 9 Problems 10 Chapter 2 THE LAW OF FALLING BODIES Historical Background Galileo's Law Do Heavy Bodies Fall Faster Than Light Ones? Medieval Laws of Falling Bodies 14

3 2.5 Experimental Determination of the Law of Falling Bodies The Average Velocity of a Falling Body Instantaneous Velocity: The Derivative Acceleration A Final Word 22 Problems 23 Chapter 3 THE LANGUAGE OF NATURE: DERIVATIVES AND INTEGRALS 3.1 The Development of Differential Calculus Derivatives and Slopes of Tangent Lines Leibniz's Notation. Analytic Definition of the Derivative Rules of Differentiation and Derivatives of Special Functions Antidifferentiation, the Reverse of Differentiation Antidifferentiation and Quadrature The Leibniz Integral Notation Applications of the Second Fundamental Theorem to Physics A Final Word 51 Problems 52 Chapter 4 INERTIA If the Earth Moves: Aristotelian Objections The Earth Moves: Galileo's Law of Inertia Relative Motion Projectile Motion: A Consequence of Inertia Calculating a Particular Trajectory A Final Word 68 Problems 68 Chapter 5 VECTORS Coordinate Systems Vectors Addition and Subtraction of Vectors, and Multiplication by a Scalar 5.4 The Scalar Product of Vectors The Cross Product of Vectors Derivatives of Vector Functions in a Fixed Coordinate System Position Vector Expressed in Polar Coordinates Uniform Circular Motion A Final Word 105 Problems 106 Chapter 6 NEWTON'S LAWS AND EQUILIBRIUM The End of the Confusion Newton's Laws of Motion 774

4 CONTENTS 6.3 Units of Mass, Momentum, and Force Projectile Motion as an Application of Newton's Second Law Equilibrium: Balance of Forces Equilibrium: Balance of Torques A Final Word 734 Problems 734 Chapter 7 UNIVERSAL GRAVITATION AND CIRCULAR MOTION The Genesis of an Idea The Law of Universal Gravitation Acceleration of Gravity on the Earth Why the Moon Doesn't Fall to the Earth Circular Orbits Other Examples of Uniform Circular Motion A Final Word 759 Problems 760 Chapter 8 FORCES The Fundamental Forces: Classification and Unification The Strength of Gravitational and Electric Forces Contact Forces Application of Newton's Laws Friction Driving on Curved Roadways Motion in a Resistive Medium The Oil-Drop Experiment A Final Word 796 Problems 797 Chapter 9 FORCES IN ACCELERATING REFERENCE FRAMES Inertial and Noninertial Reference Frames Galilean Relativity Inertial Forces Inertial Forces in a Linearly Accelerating Frame Centrifugal Force Effect of the Earth's Rotation on g Centrifuges A Final Word 275 Problems 276 Chapter 10 ENERGY: CONSERVATION AND CONVERSION Toward an Idea of Energy Work and Potential Energy 227

5 10.3 Kinetic Energy and the Conservation of Energy Gravitational Potential Energy Potential Energy and Stability Heat and Energy Mechanical Advantage and Efficiency of Machines Power A Final Word 253 Problems 254 Chapter 11 THE CONSERVATION OF MOMENTUM The Universe as a Machine Newton's Laws in Retrospect The Center of Mass The Law of Conservation of Momentum Rocket Propulsion Energy and Momentum Conservation in Collisions Center-of-Mass Coordinates Impulse: Collision Forces and Times A Final Word 288 Problems 289 Chapter 12 OSCILLATORY MOTION Finding a Clock That Wouldn't Get Seasick Simple Harmonic Motion The General Solution of the Differential Equation of Simple Harmonic Motion Examples of Simple Harmonic Oscillators Energy Conservation and Simple Harmonic Motion The Simple Pendulum Gaining Insight Through Approximations Damped Oscillations Forced Oscillations Describing Resonance Damped Forced Oscillations Swinging and Singing Wires in the Wind A Final Word 327 Problems 330 Chapter 13 ANGULAR MOMENTUM Rotary Motion Torque and Angular Momentum Angular Momentum Conservation Force and Torque 342

6 13.5 Kepler's Law of Equal Areas Vortices and Firestorms Conservation of Angular Momentum and Energy A Final Word 355 Problems 356 Chapter 14 ROTATIONAL DYNAMICS FOR RIGID BODIES Rotation of a Rigid Body About a Fixed Axis Center of Mass of a Continuous Mass Distribution Moment of Inertia A Calculation of Moments of Inertia The Parallel-Axis Theorem Energy and Work in Rigid-Body Rotation Analogies Between Rotational and Translational Motion 14.8 The Physical Pendulum The Torsion Pendulum Combined Translations and Rotations Kinematics of the Rolling Wheel Rolling Down an Inclined Plane Coriolis Forces A Final Word 407 Problems 407 Chapter 15 GYROSCOPES An Ancient Question The Gyroscope Angular Velocity of Precession The Earth as a Gyroscope A Final Word 426 Problems 427 Chapter 16 KEPLER'S LAWS AND THE CONIC SECTIONS The Quest for Precision Kepler's Laws Conic Sections The Ellipse The Conies and Eccentricity Properties of the Ellipse Cartesian Equations for Conic Sections A Final Word 448 Problems 448

7 X CONTENTS Chapter 17 SOLVING THE KEPLER PROBLEM Setting the Stage Polar Coordinates and the Unit Vectors г ando Solution of the Kepler Problem Celestial Omens: Comets Energy and Eccentricity Orbits and Eccentricity Kepler's Third Law Planetary Motion and Effective Potential Applications of Orbital Dynamics Calculating the Orbit From Initial Conditions A Final Word 472 Problems 473 Chapter 18 NAVIGATING IN SPACE Freeways in the Sky Navigating in Space Transfer Orbits Gravity Assist A Final Word 487 Problems 489 Chapter 19 TEMPERATURE AND THE GAS LAWS Temperature and Pressure The Gas Laws of Boyle, Charles, and Gay-Lussac The Ideal-Gas Law Temperature and Energy A Final Word 507 Problems 503 Chapter 20 THE ENGINE OF NATURE The Age of Steam Work and the Pressure-Volume Diagram The First Law of Thermodynamics Adiabatic and Isothermal Processes The Second Law of Thermodynamics The Carnot Engine A Final Word 525 Problems 526

8 Chapter 21 ENTROPY Toward an Understanding of Entropy Engines and Entropy Entropy and the Second Law of Thermodynamics An Implication of the Entropy Principle A Final Word 544 Problems 544 Chapter 22 THE QUEST FOR LOW TEMPERATURE Cooling Off The States of Matter Behavior of Water Liquefaction of Gases The Joule-Thomson Effect A Final Word 559 Problems 560 Appendix A THE INTERNATIONAL SYSTEM OF UNITS 563 Appendix В CONVERSION FACTORS 565 Appendix С FORMULAS FROM ALGEBRA, GEOMETRY, AND TRIGONOMETRY 569 Appendix D ASTRONOMICAL DATA 577 Appendix E PHYSICAL CONSTANTS 573 SELECTED BIBLIOGRAPHY 575 Index 579