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Physics Olympiad : basic to advanced exercises PDF

380 Pages·2014·6.538 MB·English
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PHYSICS OLYMPIAD Basic to Advanced Exercises 8887_9789814556675_tp.indd 1 2/12/13 3:06 PM TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk PHYSICS OLYMPIAD Basic to Advanced Exercises The Committee of Japan Physics Olympiad World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 8887_9789814556675_tp.indd 2 2/12/13 3:06 PM Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Committee of Japan Physics Olympiad. Physics Olympiad : basic to advanced exercises / The Committee of Japan Physics Olympiad. pages cm Includes index. ISBN-13: 978-9814556675 (pbk. : alk. paper) ISBN-10: 981455667X (pbk. : alk. paper) 1. Physics--Problems, exercises, etc. 2. Physics--Competitions. I. Title. QC32.C623 2013 530.076--dc23 2013037572 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. In-house Editor: Song Yu Typeset by Stallion Press Email: [email protected] Printed in Singapore December9,2013 15:25 9inx6in PhysicsOlympiad:BasictoAdvancedExercises b1653-fm Preface to the English Edition The Committee of Japan Physics Olympiad (JPhO), a non-profit organization approved and supported by the Japanese government, has organized Physics Challenge, a domestic competition in physics, for high-school students, every year since 2005 and has also selected andsentthebestfivestudentstorepresentJapanintheInternational Physics Olympiad (IPhO) every year since 2006. The main aim of the activity of our Committee is to promote and stimulate high- school–level physicseducation in Japansoasto achieve aworld-class standard, which we have experienced during the IPhO. Physics Challenge consists of three stages: the First Challenge, the Second Challenge, and the Challenge Final. The First Challenge selects about 100 students from all applicants (1000∼1500 in total everyyear);everyapplicantisrequiredtotakeatheoreticalexamina- tion (90min, multiple-choice questions) held at more than 70 places on a Sunday in June, and to submit a report on an experiment done by himself. The subject of the experiment is announced several months before the submission deadline. The Second Challenge is a four-day camp held in August; all students in the Second Challenge lodge together for the whole four days. Each student takes a theoretical examination and an experimental examination; both are five hours long just like the examinations in the IPhO. Thebest10–15 students whoshow excellent scores in the Second Challenge are nominated as candidates for the Japan team for the IPhO. They are then required to participate in a four-day winter camp at the end of December and a four-day spring camp at the end of March. They are also required to have monthly training via email; the training consists of a series of questions and takes place from September to March. At the end of the spring camp, these v December9,2013 15:25 9inx6in PhysicsOlympiad:BasictoAdvancedExercises b1653-fm vi Physics Olympiad: Basic to Advanced Exercises candidatestaketheChallengeFinal,whichconsistsoftheoreticaland experimental examinations. The best five students are then selected to form the Japan team for the IPhO. This book contains some of the questions in the theoretical and experimental examinations of previous Physics Challenges. ElementaryProblemsinthisbookaretakenfromtheFirstChallenge competitions and Advanced Problems are mostly from the Second Challengecompetitions.Throughthesequestions,wehopethathigh- school students would become excited and interested in modern physics. The questions from the Second Challenge reflect the process ofdevelopmentofphysics;theyrangesfromveryfundamentalphysics of junior-high-school level to the forefront of advanced physics and technology. These problems are, we believe, effective in testing the students’ ability to think logically, their stamina to concentrate for long hours, their spirit to keep trying when solving intricate problems,andtheirinteresttodoscience.Wedonotrequirestudents to learn physics by a piecemeal approach. In fact, many of the basic knowledge of physics for solving the problems are given in the questions. But, of course, since the competitions at the IPhOrequire fundamental knowledge and skills in physics, this book is organized in such a way that the basics are explained concisely together with some typical basic questions to consolidate the knowledge. This book is not only meant for training students for physics competitions but also for making students excited to learn physics. We often observed that the content of physics education in high school is limited to basic concepts and it bears little relation to modern and cutting-edge science and technology. This situation may make physics class dull. Instead, we should place more emphasis on the diversity and vastness of the application of physics principles in scienceandtechnology, whichisevidentineverydaylifeaswelluseful for gaining a deeper understanding of our past. Therefore, we try in this book to bridge the gap between the basics and the forefront of science and technology. We hope that this book will be used in physics classes in high schools as well as in extracurricular activities. We deeply appreciate the following people for their contri- butions to translating the original Japanese version into English December9,2013 15:25 9inx6in PhysicsOlympiad:BasictoAdvancedExercises b1653-fm Preface to the English Edition vii and editing the manuscript: Kazuo Kitahara, Tadao Sugiyama, Shuji Hasegawa, Kyoji Nishikawa, Masao Ninomiya, John C. Gold Stein, Isao Harada, Akira Hatano, Toshio Ito, Kiyoshi Kawamura, Hiroshi Kezuka, Yasuhiro Kondo, Kunioki Mima, Kaoru Mitsuoka, YusukeMorita,MasashiMukaida,YutoMurashita,DaikiNishiguchi, Takashi Nozoe, Fumiko Okiharu, Heiji Sanuki, Toru Suzuki, Satoru Takakura, Tadayoshi Tanaka, Yoshiki Tanaka, and Hiroshi Tsunemi. January 2013 The Committee of Japan Physics Olympiad December9,2013 15:25 9inx6in PhysicsOlympiad:BasictoAdvancedExercises b1653-fm TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk December9,2013 15:25 9inx6in PhysicsOlympiad:BasictoAdvancedExercises b1653-fm Contents Preface to the English Edition v Part I. Theory 1 Chapter 1. General Physics 3 Elementary Problems . . . . . . . . . . . . . . . . . . . . . . 3 Problem 1.1. The SI and the cgs systems . . . . . . . . 3 Problem 1.2. The pressure due to high heels and elephants . . . . . . . . . . . . . . . . . . . . 4 Problem 1.3. The part of the iceberg above the sea . . 5 Problem 1.4. The altitude angle of the Sun . . . . . . . 7 Advanced Problems . . . . . . . . . . . . . . . . . . . . . . . 8 Problem 1.5. Dimensional analysis and scale transformation . . . . . . . . . . . . . . . . . . . 8 Problem 1.6. Why don’t clouds fall? . . . . . . . . . . . 11 Chapter 2. Mechanics 15 Elementary Course . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1 Motion with a Constant Acceleration . . . . . . . . . . 15 2.1.1 Projectile Motion . . . . . . . . . . . . . . . . . 16 2.2 Equation of Motion . . . . . . . . . . . . . . . . . . . . 17 2.3 The Law of Conservation of Energy . . . . . . . . . . . 18 2.3.1 Work and Kinetic Energy . . . . . . . . . . . . . 18 2.3.2 Conservative Forces and Non-conservative Forces . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3.3 Potential Energy . . . . . . . . . . . . . . . . . . 21 2.3.4 Examples of Potential Energy . . . . . . . . . . 22 Gravitational Potential Energy . . . . . . . . . . . . . . 22 Elastic Potential Energy . . . . . . . . . . . . . . . . . 22 ix

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