Paul J. Nahin - In Praise of Simple Physics: The Science and Mathematics behind Everyday Questions

In Praise of Simple Physics

Oliver Heaviside (1988, 2002)

Time Machines (1993, 1999)

The Science of Radio (1996, 2001)

An Imaginary Tale (1998, 2007, 2010)

Duelling Idiots (2000, 2002)

When Least Is Best (2004, 2007)

Dr. Eulers Fabulous Formula (2006, 2011)

Chases and Escapes (2007, 2012)

Digital Dice (2008, 2013)

Mrs. Perkinss Electric Quilt (2009)

Time Travel (1997, 2011)

Number-Crunching (2011)

The Logician and the Engineer (2013)

Will You Be Alive Ten Years from Now? (2014)

Holy Sci-Fi! (2014)

Inside Interesting Integrals (2015)

In Praise of Simple Physics

The Science and Mathematics behind Everyday Questions

PAUL J. NAHIN

PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD

Copyright 2016 by Princeton University Press

Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540

In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TR

press.princeton.edu

Jacket illustration by Anne Karetnikov

All Rights Reserved

on page 116 is from Darkness at Night: A Riddle of the Universe by Edward Harrison, Copyright 1987 by Edward Harrison; by permission from Harvard University Press.

Library of Congress Cataloging-in-Publication Data

Nahin, Paul J., author.
In praise of simple physics : the science and mathematics behind everyday questions / Paul J. Nahin.
pages cm
Includes bibliographical references and index.
ISBN 978-0-691-16693-3 (hardcover : alk. paper) ISBN 0-691-16693-5 (hardcover : alk. paper) 1. Physics. 2. Mathematical physics.I. Title.
QC21.3.N34 2016
530dc232015031463

British Library Cataloging-in-Publication Data is available

This book has been composed in ITC New Baskerville

Printed on acid-free paper.

Typeset by Nova Techset Pvt Ltd, Bangalore, India
Printed in the United States of America

1 3 5 7 9 10 8 6 4 2

For Patricia Ann

Contents

Foreword

Physics is a glorious brew of diverse ingredients. No single approach is sufficient when grappling with Nature. Experiment and observation are essential, of course, but so, too, are concepts, pictures, imagination, mathematics, and physical intuition, topped off with logical consistency. We are explorers in a maze with mysteries at every turnnot for the faint of heart!

Learning physics and teaching physics (two sides of the same coin) are, likewise, all over the map. There are laboratories, lectures, problem sessions, computer calculations, and booksany approach that can help us understand. And books themselves take different approaches. Some are top-down, starting with physical laws and then developing examples and applications. Others are historically based, developing physics as the author imagines it was invented or might have been invented if real history were not so full of diversions and blind alleys. Yet other books are conceptually based, avoiding all mathematics like the plague. And still others are packed with mathematical analysis but are thin on concepts, illustrations, and applications. Each approach has merit.

In In Praise of Simple Physics, Paul Nahin takes a different, refreshing slice through the subject. He shows us some really interesting examples of applying simple physical principles to a variety of special cases, questions, and puzzles.

There are a myriad of topics here: we learn about wringing more of our energy from renewable sources in the chapters Energy from Moving Air and Energy from Moving Water. There is the futuristic chapter, Rapid Travel in a Great Circle Transit Tube. We find out how best to catch a baseball, how to measure gravity in our garage, and why the sky is dark at night. We learn about an error committed by the great Isaac Newton himself. We even learn how to figure out which of three light switches in the basement controls a lightbulb in the attic, with only a single trip up the stairs!

I learned a lot from this book. I have been doing physics and teaching physics for a long time, but there is always more to learn. For example, I have long enjoyed using dimensional analysis to help solve mechanics problems, by requiring consistency in the fundamental dimensions of mass, length, and time in equations. Yet, several of the beautiful examples given in this book I had never seen before!

This book does not pussyfoot its way around analysis. The reader is presumed to know some beginning differential and integral calculus. There is no sweeping math under the rug: if the way to solve the problem lies through doing an integral or two, Nahin does not wave his wand and say, Now after performing the integration, here is the result. He dives right in and shows you all the details. So if you are already well versed in simple calculus, you can skim these parts while admiring his straightforward, clear development; but if you are tentative or rusty, every step is there for you to read, so you can catch up on what you never quite learned or what you may have forgotten.

If you have read any of Nahins previous books, you will not be surprised that this one is also chock-full of entertaining, informal, and sometimes surprising examples on many topics. Whether you are a practicing scientist, a layperson with some background in math and physics, or a student at any level (as long as you have some calculus or are willing to learn), you will enjoy delving into the delightful chapters in this book.

T. M. Helliwell
Burton Bettingen Professor of Physics, Emeritus
Harvey Mudd College
Claremont, California
February 2015

Preface with Challenge Problems

Physics should be made as simple as possible.

But not simpler.

Albert Einstein

Teaching thermal physics
Is as easy as a song:
You think you make it simpler
When you make it slightly wrong!
Mark Zemansky

A mathematical argument is, after all, only organized common sense.

George Darwin

Ive made a curious observation about how the typical person on the street (assuming that this is actually a meaningful concept) reacts to the announcement of any new, amazing scientific discovery. Usually its astonishment but, occasionally, the reaction is over-the-top. An example is the announcement a few years ago from a research group at CERN (the famous high-energy particle physics laboratory near Geneva) that they had observed faster-than-light neutrinos. I remember what