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Mad About Physics Can Be Read with Profit by Any- One Who Has Had Some Exposure to Introductory Physics and Wants to Learn More About Its Application to Real Phenomena Frontmatter 9/27/00 1:12 PM Page i MadMad aboutabout PhysicsPhysics Frontmatter 9/27/00 1:12 PM Page ii Also by Christopher Jargodzki Christopher P. Jargocki. Science Braintwisters, Paradoxes, and Fallacies. New York: Charles Scribner’s Sons, 1976. Christopher P. Jargocki. More Science Braintwisters and Para- doxes. New York, Van Nostrand Reinhold Company, 1983. Also by Franklin Potter Frank Potter, Charles W. Peck, and David S. Barkley (ed.). Dynamic Models in Physics: A Workbook of Computer Simu- lations Using Electronic Spreadsheets: Mechanics. Simonson & Co., 1989. Frontmatter 9/27/00 1:12 PM Page iii MadMad aboutabout PhysicsPhysics Braintwisters, Paradoxes, and Curiosities Christopher Jargodzki and Franklin Potter John Wiley & Sons, Inc. New York • Chichester • Weinheim • Brisbane • Singapore • Toronto fcopyebk.qxd 1/2/01 2:10 PM Page iv Copyright © 2001 by Christopher Jargodzki and Franklin Potter. All rights reserved Published by John Wiley & Sons, Inc. Illustrations on pages 18, 28, 33, 81, 83, 84, 85, 96, and 105 copyright © 2001 by Tina Cash-Walsh Design and production by Navta Associates, Inc. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authoriza- tion through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4744. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, email: [email protected]. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional person should be sought. ISBN 0-471-43698-4 This title is also available in print as ISBN 0-471-56961-5. For more information about Wiley products, visit our Web site at www.Wiley.com Frontmatter 9/27/00 1:12 PM Page v To my late father—Zdzislaw Jargocki C. J. To my Mark Keppel High School science teachers Ms. Hager and Mr. Forrester, who first challenged me in chemistry and physics to bring out the joy in doing science F. P. Frontmatter 9/27/00 1:12 PM Page vi Frontmatter 9/27/00 1:12 PM Page vii Contents Preface . ix Acknowledgments . xiii To the Reader. xv Chapter 1 Temperature Risin’. 1 Chapter 2 Color My World . 13 Chapter 3 Splish! Splash! . 25 Chapter 4 Fly like an Eagle . 41 Chapter 5 Good Vibrations . 53 Chapter 6 Opposites Attract . 65 Chapter 7 Bodies in Motion . 79 Chapter 8 Stairway to Heaven . 101 Chapter 9 Life in the Fast Lane . 1 1 1 Chapter 10 Born to Run . 121 Chapter 1 1 Third Stone from the Sun . 131 Chapter 12 Across the Universe . 143 vii Frontmatter 9/27/00 1:12 PM Page viii Answers Temperature Risin’. 155 Color My World . 166 Splish! Splash! . 175 Fly like an Eagle . 185 Good Vibrations . 194 Opposites Attract . 209 Bodies in Motion . 219 Stairway to Heaven . 239 Life in the Fast Lane . 247 Born to Run . 255 Third Stone from the Sun . 269 Across the Universe . 283 Index . 298 viii Contents Frontmatter 9/27/00 1:12 PM Page ix Preface his is a book of just under four hundred puzzles about singing snow, hot ice, vanishing elephants, T primary colors, Cartesian divers, perpetual motion, aerodynamic lift, smoke rings, foghorns, virtual pitch, singing wineglasses, magnet keepers, levitating mice, superwomen, tightrope walkers, antigravity, strange pendulums, tensegrity structures, jumping fleas, and automobiles—to mention but a few of the many sub- jects. The questions range over the entire field of naked- eye physics—those phenomena we can observe without specialized research equipment. Three additional chap- ters delve into the physics of sports, earth sciences, and astronomy. Here the questions might deal with high- jump records, curveballs, golf ball dimples, waves at the beach, lightning and thunder, negative charge of the Earth, meandering rivers, orbit rendezvous, the Moon’s trajectory around the Sun, and planetary exploration— again, to mention but a few of the topics. The puzzles range in difficulty from simple ques- tions (e.g., “Why can you warm your hands by blowing gently, and cool your hands by blowing hard?”) to sub- tle problems requiring more analysis (e.g., “Bricks are stacked so that each brick projects over the brick below without falling. Can the top brick project more than its length beyond the end of the bottom brick?”). Solu- tions and more than three hundred references are pro- vided and constitute about two-thirds of the book. As these examples would show, most of the puzzles contain an element of surprise. Indeed, the clash between commonsense conjecture and physical reason- ing is the central theme that runs through this volume. ix Frontmatter 9/27/00 1:12 PM Page x Einstein characterized common sense as the collection of prejudices acquired by age eighteen, and we agree: At least in science, common sense is to be refined and often transcended rather than venerated. The present volume tries to undermine physical preconceptions employing paradoxes (from the Greek para and doxos, meaning “beyond belief”) to create cognitive disso- nance. “Though this be madness, yet there is method in’t.” We believe that far from being merely amusing, paradoxes are uniquely effective in addressing specific deficiencies in understanding (cf. Daniel W. Welch, “Using paradoxes,” American Journal of Physics 48 [1980]: 629–632). Take, for example, the following question: A man is standing on a bathroom scale. Sud- denly he squats with acceleration a. Will the scale read- ing increase or decrease? Many students, guided by common sense, will say the reading will increase because the man is pushing down on the scale while squatting. The correct answer is that the reading will decrease because while the man is squatting his center of gravity is being accelerated downward, and hence the normal force exerted by the scale must decrease. In tackling paradoxes like this one the contradiction between gut instinct and physical reasoning will for some students be so painful that they will go to great lengths to escape it even if it means having to learn some physics in the process. Are these paradoxes real or merely apparent? From the point of view of the standard methods of instruc- tion in physics, the counterintuitive conclusions reached in many puzzles in this book clearly only seem para- doxical. The conclusions may be unexpected and some- times even mind-boggling. Nevertheless, except for a few puzzles involving deliberate fallacies, they follow impeccably from the fundamental laws of physics and can be confirmed experimentally. But perhaps we should honor our sense of unease and dig a little x Preface Frontmatter 9/27/00 1:12 PM Page xi deeper. After all, many concepts in physics are mere useful fictions that aid visualization or simplify calcu- lations. Examples include centrifugal forces, electric and magnetic field lines, magnetic poles, and the con- ventional sense of the electric current, to name just a few. Useful fictions can be dangerous in that a constant vigilance is required to remember their fictitious char- acter. There is a long-standing debate in physics as to whether certain well-established concepts have outlived their usefulness and should be completely eliminated. Heinrich Hertz, one of the early participants in this debate, for example, suggested that Newtonian mechanics be restated without using “force” as a basic concept. In the introduction to his Principles of Mechanics, published in 1899, he wrote, “When these painful contradictions are removed, the question as to the nature of force will not have been answered; but our minds, no longer vexed, will cease to ask illegiti- mate questions.” Ludwig Wittgenstein, who knew this passage virtually word for word, was so impressed that he adopted it as a statement of his aim in philosophy: “In my way of doing philosophy, its whole aim is to give an expression such a form that certain disquietudes disappear.” Paradoxes are an embodiment of such disquietudes and, as a result, have played a dramatic role in the his- tory of physics, often foreshadowing revolutionary developments. The counterintuitive upheavals result- ing from relativity theory and quantum mechanics only enhanced the reputation of the paradox as an agent for change. Is physical reality inherently paradoxical (i.e., crazy, to use the vernacular), or do paradoxes arise solely in our description of it and are they a signal to discard the old conceptual framework and adopt a new one? As this is not a book in philosophy, we have the right to be evasive, and instead of answering the ques- tion directly, we prefer to end with an anecdote about Preface xi Frontmatter 9/27/00 1:12 PM Page xii two great luminaries of twentieth-century physics, Niels Bohr and Wolfgang Pauli. Some decades ago Bohr was in an audience listening to Pauli explain his early attempt at reconciling the theory of relativity and quantum mechanics. Afterward, Bohr stood up and said, “We are all agreed that your theory is absolutely crazy. But what divides us is whether your theory is crazy enough.” xii Preface Frontmatter 9/27/00 1:12 PM Page xiii Acknowledgments t is difficult to acknowledge all the individuals who Ihave helped to bring this book into print.
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