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300 CREATIVE PHYSICS PROBLEMS

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300 CREATIVE PHYSICS PROBLEMS with Solutions

Laszlo Holies

ANTHEM PR ESS LONDON· NEWYOR.K · DELH I

Anthem Press An imprint of Wimbledon Publishing Company

www.anthempress.com This edition first published in UK and USA 20 I 0 by ANTHEM PRESS 75-76 B lackfriars Road , London SE I 8HA, UK or PO Box 9779 , London SWI9 7ZG, UK and 244 Madison Ave. #116, New York, NY 10016, USA Copyright English translation

©

©

Laszl6 Holics 20 I 0

A. Gr6f, A. Salamon, A. Tasnadi , T. Tasnadi , Cs. T6th

Sponsored by Graphisoft Foundation The moral right of the authors has been asserted. All rights reserved. Without limiting the rights under copyright reserved above, no part of thi s publication may be reproduced, stored or introduced into a retrieval system, or transmitted , in any form or by any means (electronic , mechanical , photocopying, recording or otherwise), without the pri or written permission of both the copyright owner and the above publisher of this book .

British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library.

Library of Congress Cataloging in Publication Data A catalog record for this book has been requested. ISBN-13 : 978 I 84331 869 9 (H bk) ISBN-IO: 1843318695 (Hbk)

TABLE OF CONTENTS

How to Use This Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v

Physical Constants alld Other Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

vi

Part I. PROBLEMS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

I . Mechanics Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

I. I

Kinematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

1.2

Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

1.3

Statics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

1.4

Fluids. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

2. T hermodynam ics Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

2. I

Thermal expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

2.2

Ideal gas processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

2.3

Fi rst law of thermodynamics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

3. E lectrodynamics Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

3. I

Electrostatics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

3.2

Direct current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

4. Magnetism Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4. I

Magnetic field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.2

Induction (motional eml) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

4.3

Induction (transformer emt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

4.4

A lternating current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

5. Optics Proble ms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

III

Part II. SOLUT IONS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

6. Mechanics So luti ons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

6.1

Kinem ati cs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

6.2

Dynami cs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

6.:1

Stat ics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

:12:1

6.4

Fluid s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3:14

7. Thermodynamics So luti ons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

:142

7. 1

Th ermal expa nsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

342

7.2

Ideal gas processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

345

7.:1

Fi rst law of therm odynami cs .. ..... . ......... .. ....... . ... . .

:197

8. Electrodynami cs So luti ons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

429

8. 1

Elec trostatics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

429

8.2

Direct cu rrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45 1

9. Mag neti sm So lut ion s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

470

9. 1

IV

Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

470

9.2

In duc ti on (moti onal em l) ... . .. . .... .... ........ .. . ........ .

477

9.:1

Inducti on (transformer emf) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49:1

9.4

Alte rn ating current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

508

10. Opti cs Sol uti ons.. . . . . . . ... .... . .... . . ... ..... ... . .. . . .. ... . . . .. .

520

How to Use This Book

The bes t way of understandin g the laws of phys ics and learnin g how to so lve ph ys ics problem s is th ro ugh prac ti ce. Thi s book features almost three hundred probl ems and soluti ons worked out in detail. In Pa rt I, Problell1 s are arranged themati call y, starling in Charter I with probl e ms about mechanics, the branch of phys ics co ncerned with the behav iour of phys ica l bodies when subj ec ted to forces or disp lacements, and the subseque nt e nec t of the bodies on their enviro nme nt. Chapter 2 offers problems in thermodynamics, the study o f e nergy conversion between heat and mec hanical work , while the electrodynamics prob lems in Chapter :1 deal with the phenomena assoc iated with mov in g electrica l charges and their interac ti on with el ectric and mag neti c fields. Chapter 4 ' s rroble ms on magnetism seek to understand how materi als respond on the mi croscopi c le vel to an appli ed magneti c field . Lastl y, the optics probl ems in Chapt er 5 address the branch of ph ys ics th at studies the behav iour and phys ica l pro perti es of li ght. While the pro bl ems are arranged by topi c, the pro bl e ms within a sin gle topi c are ofte n arran ged by in creas in g le ve l of diOicull y. Indeed, many of these phys ics problem s are diOicult - ye t we e nco urage stude nts to try and solve the prob lems on their ow n, and to onl y co nsult the SO IUliO/ ls sec ti on in order to compare their ow n alle mpts with the correct results. We e ncourage creativ ity in problem- so lvin g, and these phys ics probl ems are intended as a means of deve lopin g the stude nt' s knowl edge of phys ics by appl yin g them to co nc rete prohlems.

v

Physical Constants and Other Data

Gravitational constant Speed of light (in vacuum) Elementary charge Electron mass Proton mass Neutron mass Charge-to-mass ratio of electron Unified atomic mass constant Boltzmann constant Plank constant A vogadro constant Gas constant Permittivity of free space Permeability of free space Coulomb constant Compton wavelength of electron

G c e

6.673 X 10 - 11 Nm 2 kg- 2 2. 998 x 10 8 ms- 1 1.602 x 10 - 19 C 9. 109 X 10 - 3 1 kg (5 11 .0 keV) 1.673 x 10 - 27 kg (938 .3 MeV) 1.675 x 10 - 27 kg (939.6 MeV) 1.759 x 1011 Ckg - 1 1.661 X 10- 27 kg 1.381 X 10- 23 JK - 1 6.626 X 10 - 34 Js 6.022 X 10 23 mo] - l 8.315 Jmol- 1 K- 1 8.854 x 10- 12 CV-1m- 1 2 411 x 10 - 7 Vs C - 1 m - 1 8.987 x 10 9 VmC - 1 2.426 x 10 - 12 m

Mean radius of the Earth R Sun-Earth distance (Astronomical Unit, AU) Mean density of the Earth p Acceleration due to gravity 9 Mass of the Earth Mass of the Sun I light year

6371 km 1.49 x 10 8 km 5520 kgm - 3 9.807 ms- 2 5.978 x 10 2 4 kg 1.989 X 10 30 kg 9.461 X 10 15 m

Surface tension of water Heat of vaporisation of water Tensile strength of steel

0.073 Nm - 1 2256 kJkg - 1 = 40.6 kJmol 500-2000 MPa

vi

'Y

L

1

Part I PROBLEMS

Chapter 1 Mechanics Problems

1.1 Kinematics Problem 1. A tra in is mo vin g at a speed rails. The tra in whi stles for a time o f T . whi stl e? The speed o f sound is c = 330 m /s; train does not reach the ra ilway ma n until the

o f v to ward s the railway man nex t to the H o w lo ng d oes the railwayman hear the v = 108 km / hour = 30 m is, T = 3 s; the end o f the whi stl e.

Problem 2. The speed o f a moto rboat in still wate r is fo ur times the speed o f a ri ver. Normally , the motorboat takes o ne minute to c ross the ri ver to the port straig ht ac ross on the other bank. One time, du e to a moto r probl e m, it was not able to run at full power, and it took four minutes to cross the ri ver al o ng the same path. By wh at fac tor was the speed of the boat in stili water reduced ? (Assume that the speed of the water is uniform throughout the wh o le width o f the river.) Problem 3. Consider a trough o f a se micircular cross secti on, and an inclined pl ane in it that lead s fro m a po int A to point B ly ing lo we r th an A . Prove that wherever point C is chosen o n the arc AB , an object will always get from A to B faster a lo ng the slopes AC B than alo ng the origin al s lope A B . The c ha nge o f direc ti o n at C does not involve a ch ange in speed . The e ffects of fricti o n are negli g ibl e. Problem 4. The acce le rati o n of a n objec t is unifo rml y Inc reas ing, and it is ao = 2 == 2 m /s at to = 0 sa nd al = 3 m /s 2 at t l = 1 s . The speed o f the obj ect at to = 0 s

is Vo = 1 m /s . a) De termine the speed of the o bject at t2 = 10 s. b) De termin e the v -t fun cti o n o f the mo ti o n, a nd the n plot it in the v - t coordin ate syste m. c) Estimate the di stance covered by the object in the first and last seco nd o f the time interval 0 < t < 10 s .

3