Physics Olympiad : basic to advanced exercises

380 Pages·2014·6.538 MB·English

by  Committee of Japan Physics Olympiad

PHYSICS
OLYMPIAD
Basic to Advanced Exercises
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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,
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In-house Editor: Song Yu
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Email: [email protected]
Printed in Singapore
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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
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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
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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
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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