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"th e M a n g a G u i de to ™ comics inside! PhYsICs PHYSICS hideo Nitta Keita takatsu trend-Pro co., ltd. Praise for the Manga Guide to Databases “Without a doubt, The Manga Guide to Databases was the most enjoyable tech book I’ve ever read . . . I loved this book and highly recommend it.” —rikki kite, linux pro magazine “Whether you’re new to the whole concept of databases, or a hard-core database geek, you need to have The Manga Guide to Databases. Really, you want this book.” —josh berkus, postgresql core team “For an American audience, this is certainly an off-the-beaten-path approach to technical training. However, its ability to effectively plunge into a topic that can be a morass of arcane theory is undeniable. Over the years, we’ve learned to expect the unexpected from No Starch Press.” —macdirectory “This is a fun book, there is no denying that. If you’re in the market to learn more about databases and you hate normal tech books this is a great pickup.” —the caffination podcast “If I was going to teach a class or introduce a non-technical person to the world of databases, I would most likely start here.” —blogcritics.org Praise for the Manga Guide to Statistics “This is really what a good math text should be like. Unlike the majority of books on subjects like statistics, it doesn’t just present the material as a dry series of pointless-seeming formulas. It presents statistics as something fun, and something enlightening.” —good math, bad math “The Manga Guide to Statistics is a solid introduction to the world of statistical analysis done in a fun and accessible way.” —active anime “Inoue’s art is clean, cute and simplified, and it works with machine-like efficiency—the artist not only knows and speaks the language of manga, but does so fluently.” —newsarama “The Manga Guide to Statistics offers a visualization of statistics that can’t be found in any mere textbook.” —anime 3000 Wow! The Manga Guide™ to Physics The Manga Guide™ to Physics hideo Nitta Keita Takatsu TREND-PRO co., Ltd. The Manga Guide to Physics. Copyright © 2009 by Hideo Nitta and TREND-PRO Co., Ltd. The Manga Guide to Physics is a translation of the Japanese original, Manga de Wakaru Butsuri [Rikigaku hen], published by Ohmsha, Ltd. of Tokyo, Japan, © 2006 by Hideo Nitta and TREND-PRO Co., Ltd. The English edition is co-published by No Starch Press and Ohmsha, Ltd. All rights reserved. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval system, without the prior written permission of the copyright owner and the publisher. 13 12 11 10 09 123456789 ISBN-10: 1-59327-196-4 ISBN-13: 978-1-59327-196-1 Publisher: William Pollock Author: Hideo Nitta Illustrator: Keita Takatsu Producer: TREND-PRO Co., Ltd. Production Editor: Megan Dunchak Developmental Editor: Tyler Ortman Technical Reviewers: Keith Brown and Whitney Ortman-Link Compositor: Riley Hoffman Proofreader: Cristina Chan Indexer: Sarah Schott For information on book distributors or translations, please contact No Starch Press, Inc. directly: No Starch Press, Inc. 555 De Haro Street, Suite 250, San Francisco, CA 94107 phone: 415.863.9900; fax: 415.863.9950; info@nostarch.com; http://www.nostarch.com/ Library of Congress Cataloging-in-Publication Data Nitta, Hideo, 1957[Manga de wakaru butsuri. Rikigaku hen. English] The manga guide to physics / Hideo Nitta, Keita Takatsu ; Trend-pro Co., Ltd. p. cm. Includes index. ISBN-13: 978-1-59327-196-1 ISBN-10: 1-59327-196-4 1. Physics--Comic books, strips, etc. 2. Physics--Popular works. I. Takatsu, Keita. II. Trend-pro Co. III. Title. QC24.5.N5813 2009 530--dc22 2009012720 No Starch Press and the No Starch Press logo are registered trademarks of No Starch Press, Inc. Other product and company names mentioned herein may be the trademarks of their respective owners. Rather than use a trademark symbol with every occurrence of a trademarked name, we are using the names only in an editorial fashion and to the benefit of the trademark owner, with no intention of infringement of the trademark. The information in this book is distributed on an “As Is” basis, without warranty. While every precaution has been taken in the preparation of this work, neither the author nor No Starch Press, Inc. shall have any liability to any person or entity with respect to any loss or damage caused or alleged to be caused directly or indirectly by the information contained in it. All characters in this publication are fictitious, and any resemblance to real persons, living or dead, is purely coincidental. contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Prologue Does Physics Bother you? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 1 Law of Action and Reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Law of Action and Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How the Law of Action and Reaction Works. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equilibrium vs. Law of Action and Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gravitational Force and the Law of Action and Reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . Newton’s Three Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scalar Quantities vs. Vector Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vector Basics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Negative Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Difference Between Two Vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiplying Vectors by Scalars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Equilibrium and Vector Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Newton’s Three Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drawing a Free-Body Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Expressing Newton’s Third Law with an Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gravity and Universal Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 15 20 23 30 33 37 37 38 38 39 39 40 41 42 43 2 Force and Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Velocity and Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simple Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory: Finding the Distance Traveled when Velocity Varies . . . . . . . . . . . . . . . . . . Newton’s First and Second Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory: Finding the Precise Value of a Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Motion of a Thrown ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three Rules of Uniform Accelerated Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adding Vectors: The Head-to-Tail Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Composition and Decomposition of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Newton’s First Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Newton’s Second Law of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Orientation of Velocity, Acceleration, and Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 46 50 53 58 58 66 73 75 85 86 87 90 90 90 An Object Does Not Have Its Own Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 The Unit for Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Measuring Mass and Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Determining Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Understanding Parabolic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Using Calculus to Find Acceleration and Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Using the Area of a V-T Graph to Find the Distance Traveled by an Object . . . . . . . . . . . . . . . . 100 3 Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Momentum and Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Understanding Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory: Difference in Momentum due to a Difference in Mass . . . . . . . . . . . . . . . Change in Momentum and Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory: Finding the Momentum of a Stroke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Newton’s Third Law and the Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory: Outer Space and the Conservation of Momentum . . . . . . . . . . . . . . . . . . . Real-World Explorations of Impulse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reducing the Impact. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Improving Megumi’s Serve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Momentum and Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impulse and Momentum in Our Lives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deriving the Law of Conservation of Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elastic and Inelastic Collision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Units for Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Conservation of Momentum for Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Law of Action and Reaction vs. Law of Conservation of Momentum . . . . . . . . . . . . . . . . . . . . . Propulsion of a Rocket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 106 109 111 117 120 120 126 129 129 133 139 140 141 143 144 144 146 147 4 Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Work and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . What Is Energy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory: What’s the Difference Between Momentum and Kinetic Energy?. . . . . . Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Work and Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory: Work and the Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Work and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory: The Relationship Between Work and Kinetic Energy. . . . . . . . . . . . . . . . . Braking Distance and Speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Conservation of Mechanical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transforming Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conservation of Mechanical Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 153 162 164 169 172 175 178 180 184 184 187 viii contents Laboratory: The Law of Conservation of Mechanical Energy in Action . . . . . . . . . . . . Finding the Speed and Height of a Thrown Ball. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratory: Conservation of Mechanical Energy on a Slope . . . . . . . . . . . . . . . . . . . . . Units for Measuring Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Potential Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Springs and the Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity for Throwing Upward and Height Attained . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Orientation of Force and Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finding an Amount of Work with Nonuniform Force (One-dimensional) . . . . . . . . . . . . . . . . . . Nonconservative Force and the Law of Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . Friction: A Nonconservative Force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Friction on a Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Colliding Coins and the Conservation of Energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 194 195 200 201 202 203 204 205 207 207 208 210 Epilogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 Appendix Making sense of Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 contents ix Preface It is essential to the understanding of physics to correctly “see” what you wish to examine. In classical mechanics, in particular, you need to understand how physical laws apply to transient, moving objects. But unfortunately, conventional textbooks rarely provide adequate images of such motion. This book attempts to conquer the limits of those conventional textbooks by using cartoons. Cartoons are not just simple illustrations—they are an expressive and dynamic medium that can represent the flow of time. By using cartoons, it is possible to vividly express changes in motion. Cartoons can also transform seemingly dry laws and unreal scenarios into things that are familiar, friendly, and easy to understand. And it goes without saying—cartoons are fun. We have emphasized that in this book, as well. As an author eager to know whether or not my intent has succeeded, I can only wait for readers to make their judgments. This work has been finished to my deep satisfaction, except for the omission of one chapter—due to page count constraints—featuring a trip to an amusement park to explain circular movement and the noninertial system. The main character of this book is a high school student named Megumi Ninomiya who finds physics rather difficult. It is my sincere desire that this book reaches out to as many readers as possible who think “physics is tough” and who “don’t like physics,” helping them find pleasure in physics like Megumi does—even if it’s only a little. Last but not least, I would like to express my deep appreciation to the staff at the OHM Development Office, scenario writer re_akino, and illustrator Keita Takatsu—their combined efforts have resulted in this wonderful cartoon work that would have been impossible for one individual to complete. hideo Nitta November 2006 P R O L O G U E Does Physics Bother you? Shh- Blap! My god! Sh hto ck ! Shazam! to c k! Wh iz! Pow! stay in the game, Megumi! i GOttA concentrate... several hours ago... how did you do on the physics test? Well, then, what was your answer for question 9? We’re comparing answers. 9) Suppose you are hitting a ball with a tennis racket. Which is greater, the force of the ball pushing the racket or the force of the racket pushing the ball? Select the correct answer. A. B. C. i selected c. D. The force of the racket pushing the ball is greater than the force of the ball pushing the racket. The force of the ball pushing the racket is greater than the force of the racket pushing the ball. The force of the ball pushing the racket is the same as the force of the racket pushing the ball. The relationship between the force of the ball pushing the racket and the force of the racket pushing the ball depends on the weight of the racket and the speed of the ball. Oh, no... i PicKED A. Why? Feeling so brilliant ee Tee-h hee - What do you mean, sayaka? Tee-h eehee Oh dear, Megumi. have you forgotten Newton’s third law? Don’t you remember?! it’s the law of action and reaction. th e of ket ce rac for Th e on th e ball th e of ce e ball for th Th e t on cke ra The force of the racket on the ball and the force of the ball on the racket are always equivalent. Therefore, the right answer is c! Jeez! 4 Prologue By the way, have you also forgotten about our match after school? screw up in the game, too! Eh, well... Of, of...of course not! ...Well... Be careful not to… Click Grrrr... i can't stand her! What? Cla ng ! e! Ac Tee Easy now. -h ee -h ee Pa ng The force on the ball has to be larger! Oh, no. i can’t concentrate. i... i just can’t help thinking about it... Oops! Net! if the forces on the racket and th..."

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