Competitive physics: mechanics and waves

831 Pages·2018·5.092 MB·English

by  Wang, Jinhui, Widjaja, Bernard Ricardo

Competitive
Physics
Mechanics and Waves
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Competitive
Physics
Mechanics and Waves
Jinhui Wang
Bernard Ricardo
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO
10817_9789813233942_tp.indd 2 10/7/18 4:04 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
Names: Wang, Jinhui (Former Physics Olympiad student), author. | Ricardo, Bernard, 1985– author.
Title: Competitive physics : mechanics and waves / Jinhui Wang (Hwa Chong Junior College, Singapore),
Bernard Ricardo (NUS High School of Mathematics and Science, Singapore).
Description: Singapore ; Hackensack, NJ : World Scientific, [2018]
Identifiers: LCCN 2017048390| ISBN 9789813233942 (hardcover ; alk. paper) |
ISBN 981323394X (hardcover ; alk. paper)
Subjects: LCSH: Physics--Problems, exercises, etc. | Physics--Competitions.
Classification: LCC QC32 .W216 2018 | DDC 530/.076--dc23
LC record available at https://lccn.loc.gov/2017048390
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2019 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.
For any available supplementary material, please visit
https://www.worldscientific.com/worldscibooks/10.1142/10817#t=suppl
Typeset by Stallion Press
Email: [email protected]
Printed in Singapore
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Dedication
The Physics Olympiads were some of my most enjoyable experiences in high
school and I hopeto sharetheelegance of problem-solving, prevalent in such
competitions,withmorepeople.Writingthisbookhasreallybeenafulfilling
journey that has evoked many moments of nostalgia, ranging from the thrill
of solving a problem to my past struggles when learning about physics. I am
extremely grateful to the following people who have supported me in the
course of writing — during my hardest times in National Service — in one
way or another.
Myco-author,BernardRicardo.Icansafely saythatheisoneofthebest
physics educators in Singapore. His enthusiasm and illuminating pedagogy
during his lessons for the Physics Olympiad national training team inspired
me to pursue and teach physics. It has been a joy working with him and his
many insights have added a novel perspective to this book.
Myteachers,TanJingLong,MrKwekWeiHongandMrsNgSiewHoon.
I still remember the quirky jokes that the class makes during your lessons.
Thank you for introducing me to physics and infecting me with your love
for the subject.
My students, Cui Zizai, Mao Ziming, Chang Hexiang, Guo Yulong,
Andrew Ke Yanzhe, Ryan Wong Jun Hui and many more. It was a plea-
sure to teach you and your inquisitiveness in our lessons together was a
great source of motivation during my conscription. I am also grateful to you
for proofreading chapters of this book and providing constructive feedback.
Myfriends,JiangYueandMaWeijia.Thankyoufortakingtimeoutfrom
your busy university schedules to draw numerous diagrams for this book as
I was preoccupied with National Service. This milestone would literally not
have been possible without you.
v
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vi Competitive Physics: Mechanics and Waves
My parents. Thank you for everything that you have done for me, from
cooking meals at home to discussing life decisions with me. I would not be
who I am today without you.
Finally, itis withthe greatest joy that I presentCompetitive Physics and
I hope that you enjoy the book!
— Wang Jinhui
It is a pleasure for me to present our book, Competitive Physics. The
process of this book’s production, that has been thrilling and satisfying,
could not be completed without these special people in my life whom I
would like to extend my deepest, most heart felt thanks.
My co-author, Wang Jinhui. This book was birthed out of his vision. He
isoneofthebrightestyoungmenthatIknowanditwasextremely enjoyable
to put our thoughts together. I hope this would be the start of many more
collaborations and substantial discussions.
My mentor, Professor Yohanes Surya Ph.D. I was first introduced to the
world of Physics Olympiads by him. Full of passion, he dedicated himself to
impart his knowledge and love for physics to so many people. His slogan,
Physics is Fun, has encouraged and inspired me to impact the world of
Physics Education.
My wife, Yoanna Ricardo, daughter, Evangeline Ricardo, and son,
Reinard Ricardo. Thank you so much for always supporting and praying
for the completion of this book. The times at home and on the road with
you are the times when I was most fruitfulin writing and I am truly grateful
for those good memories.
For all our readers, I hope you will find this book enjoyable and have fun
reading it as we have had fun writing it!
— Bernard Ricardo
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Preface
Competitive Physics grew outof aPhysics Olympiadcoursetaught byWang
Jinhui at Hwa Chong Institution — intended to prepare students for the
annualPhysicsOlympiadsandtoimbuedeeperknowledgeinphysicsbeyond
the typical high school syllabus. It quickly became a collaboration with his
former trainer in the Singapore Physics Olympiad national training team,
Bernard Ricardo.
Competitive Physics is meant to be a theory-cum-problem book. The
first half of each chapter explores physical theories with illustrations of how
they can be creatively applied to problems. The latter half of each chapter
revolves aroundpuzzlesthatwehopewillintriguereaders,aswebelievethat
problem-solvingisacrucialprocessingraspingthesubtletiesofthecontents.
Therefore, we have included a multitude of problems which are ranked by
increasingdifficulty fromonetofourstars.Someproblemsareoriginal; some
aretakenfromthevariousPhysicsOlympiadswhiletheothersareinstructive
classics that have withstood the test of time.
Thisbookisthefirstpartofatwo-volumeserieswhichwilldiscussgeneral
problem-solving methods and delve into mechanics and waves — setting a
firm foundation for other topics that will be presented in the second volume.
Weenvisionproblem-solvingtobeafunprocess—fromtheinitialexcite-
ment of approaching an unfamiliar problem, to the joy of pitting all of one’s
knowledge against it and finally, the satisfaction earned from solving it after
numerousfailed attempts.Inlightofthis,ourgoalistospreadthepassionof
problem-solving — an infectious hobby. It is difficult to quantify the factors
that make a problem interesting or elegant but the following have been our
guiding principles in writing Competitive Physics:
1. Physical Significance. Quintessentially, physics is about modeling the
world aroundus.Therefore,it is gratifying tobeableto analyze everyday
phenomena and to leverage on this knowledge to improve such processes.
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viii Competitive Physics: Mechanics and Waves
For example, a problem in Chapter 3 asks: how should we run towards
a shelter to minimize how wet we get in the rain? Meanwhile, Chapter 6
elucidates the reason behindwhy two colliding billiard balls leave at right
angles relative to each other.
2. Intuition. There are many overarching themes in physics — symmetry,
the equivalence of different observational frames of reference, reversibility
of processes and many more. Not only are these usefulas sleights-of-hand
in problem-solving, they reveal crucial aspects of the common structure
of physical theories. Developing a strong hunch for them — a gut feeling
that constantly bugs you to search for ways to exploit them — may prove
to be beneficial in one’s future physics journey. As such, we have devoted
the entire first chapter, Minimalistic Arguments, to honing this physical
intuition.
3. Insight.Sometimes,aseeminglycomplex problemcanbevastlysimplified
by making an astute observation — whether mathematical or physical.
Perhaps, it is to express the solution in terms of vectors or perhaps it is
to observe that two different scenarios “feel” the same to a certain entity
and thus conclude that the entity will respond in the same manner in
both cases. Maybe it is to draw enlightening analogies between two prob-
lems that appear to be completely disparate on the surface. Ultimately,
suchproblemswhichrequireperceptivethoughtdonothavecookie-cutter
approaches and require the reader to invent an appropriate technique on
the spot. They hence implore the reader to really think and are very
rewarding to solve.
4. Fundamentals. The objectives above would not be possible without first
mastering the fundamentals of a theory — the situations that it can be
validly applied to, its assumptionsand its ramifications. As such,we have
also included many classic problems to reinforce understanding of the
basics. To this end, we are extremely grateful to Dr. David J. Morin for
allowing us to use some problems from his exemplary textbook: Introduc-
tion to Classical Mechanics.
In summary, our guiding principles are “PIIF”, as in the onomatopoeia
“pffft” when, having read this book, you scoff at a future problem after
swiftly spotting its trick. Jokes aside, it is paramount for the reader to first
attempt the problems before peeking at the solutions. Even when perusing
the solution to a problem, the reader should inspect it line by line until he
or she reaches an inspiration that sets him or her back on track in attempt-
ing the problem again. Only by experiencing the process of problem-solving
yourself can you internalize the clues in a problem that hint at a certain
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Preface ix
approach, understand why certain approaches are incorrect or desirable and
ultimately, improve. There is no short-cut to developing an intuition for
problem-solving besides trudging through an arduous but fulfilling journey
of enigmas.
Despite our best efforts; the probability of this book being error-free
is, unfortunately, akin to the odds of observing a car plate that reads
“PHY51C.”Therefore,ifthereaderdoesspotanymistakesordubiouspoints
in our discussions, we would appreciate if they are highlighted to us via the
email [email protected].