Physics Matters [3 ed.] 9810194994, 9789810194994

Citation preview

a-c

Dr Ho

Feeru Tiong

''/olrie

I- Sq>

Dr Gharles

Chew

Ed.D., M.Ed.(Hons), B.Sc.(Hons), Post-Grad. Dip.Ed.

WC

Chow Siew Foong

Dr Ho Boon Tiong

B.Sc.(Hons), Post-Grad. Dip.Ed

Ph.D., M.Ed., B.SC., Post-Grad. Dip.Ed.

Marshall Cavendish Education

l,om 2ool

O 1995 Federal Publications (S) Pte Ltd O 2000 Times Media Private Limited

o

2003, 2007 Marshall Cavendish lnternational (Singapore) Private Limited

Published by Marshall Cavendish Education An imprint of Morsholl Covendish lnternotionol (Singopore) Privote Limited

Iimes Centre, 1 New lndustrial Road, Singapore 536196 customer Service Hotline: (65) 6411 0820 E-mail: [email protected] Website: wwwmarshallcavendish.com/education First published 1995 Second edition 2000

Third edition 2007 Second impression 2008 Reprinted 2009, 2010 (twice)

All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical,

photocopying, recording or otherwise, without the prior permission of the copyright owner. Any requests for permission should be addressed to the Publisher. Marshall Cavendish is a trademark of Times Publishing Limited The websites cited in the book were reviewed and deemed suitable at the

time of printing. rsBN 978-98"t-01-9 499 - 4

Printed in Singapore by Times Printers, www.timesprinters.com

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The publisher wishes to thank the following organisations and individuals for granting permission to reproduce the images listed.

Front cover photo: Photolibrary; Back cover photo: Kiss Botond / www.istockphoto.com Unit I Measurement: Satellite in Orbit NASA/JPL; Figure 1.2, Overhead Bridge Sign, Tan Kar Hui; Figure 1.5, Hamburger, Edyta Pawlowska; Figure l.6, Nanoguitar, Cornell News Service; Figure LZ Mount Everest, Alison Zhang DeSandies; Figure LZ Football field, Ufuk Zivana; Figure l.J Chopsticks, Ana Schaeffer; Figure l.B, Metre Rule, Rowdy Boeyink; Figure 1.9, Tape lVleasure, Rowdy Boeyink; Figure 1.10, Measuring Width of Pond, Rowdy Boeyink; Figure 1 .1 1 , Measuring Depth of Pond, Rowdy Boeyink; Figure I .14, Vernier Calipers, Rowdy Boeyink; Figure I .1 5, Vernier Calipers Outside.Jaws, Rowdy Boeyink; Figure 1.20, Sundial, Steve lrvine copyright, Analemmatic Sundial at Keppel Henge; Figure 1.21, Clock, Rowdy Boeyink; Figure 1.23, Caesium Clock, National Research Council Canada; Physics Today, Nano lmage Bug, Courtesy of Sandia National Laboratories,

MMiT Technologies Skydivers, Joe l\/cBride/Corbis; Runner Finishing, Oleg Prikhodko; Figure 2.1, Snapshot Finishing Line, SEIKO and EAA; Figure 2.2, Donovan Bailey Running www.sportingheroes.net; Figure 2.3, MRT, SIMRT Corporation Ltd; Figure 2.3, Airbus A3B0 (SQ), I\,4r Sim Kok Chwee; Figure 2.3, Bulletfrom Rifle, Andrew Davidhazy, Rochester lnstitute of Technology; Figure2.7, Speedometer in a Car, Rowdy Boeyink; Figure 2.13, Rocket Blasting off, NASAJSC; Figure 2.13, Car slowing down, Rowdy Boeyink; Figure 2.14, Swissotel The Stamford, Rowdy Boeyink; Figure 2.35, Feather Falling Angela Bell Unlt Forces: Tug of War, Ted Streshinsky/Corbis; Figure 3.3, Runners at starting position, Jim Parkin; Figure 3.4, Wakeboarder, Calina Barskaya; Figure 3.5, Broken Bridge FEIIIA, Robert A. Eplett/FEI\4A News Photo; Table 3.3, Forces: Soccer player, Ralf Hettler; Table 5.3, Forces: Rollerbladers, Ivlarco CauzlCORBIS; Table 3.3, Forces: Speed cyclist, Daniel Norman; Table 3.3, Forces: Badminton player, Claro Cortes lVlReuters/Corbis; Figure 3.22, Tennis player, Andre Bogaert; Figure 3.24,|ce-skater gliding, Erik Seo; Figure 3.33, Wear and tear on bike, Rowdy Boeyink; Figure 3.35, Air Hockey, Kevin Russ; Physics Today, X-33, NASA-DFRC Unit 4 Mass, Weight and Density: Hot air balloons, joy Powers; Electronic Scale, It/ari lMansikka; Figure 4.4, Solar System, Ceorge Argyropoulos; Figure 4.5, Tides, Hopewell Rocks Tidal Exploration; Figure 4.6, Electronic Scale, Rowdy Boeyink; Figure 4.8, Spring Balance, Learning Resources lnc.; Figure 4.9, Egyptian Beam Balance, Stencil Kingdom; Figure 4.10, lnternational Space Station, NASA-IMSFC; Figure 4.14, Space Shuttle, NASA; Figure 4.21 , Hot Air Balloon, Steven Allan Unit 5 fuming Effect of Forces: Tightrope walkeq Regis Bossu/Sygma/Corbis; Blades of a wind turbine, Joe Cough; Figure 5.11, CD plus magnets, Rowdy Boeyink; Figure 5.25, Standing book, Tan Kar Hui; Figure 5.25, Tumbling boo( Tan Kar Hui; Figure 5.26, Laying boo( Tan Kar Hui; Figure 5.28, Racing car, Ahmad Faizal Yahya; Figure 5.34, Jenga Tower, Alex Bramwell; Figure 5.36, Surfer on ocean waves, lan lVlcDonnell SU

Unlt 2 Kinematics:

,

Unit 6 Energl, Work and Power: Joscelin

Yeo swimming Photo courtesy of Joscelin Yeo & Team Singapore; Figure 6.1 , Rotating Wind Turbines, Kevan O'A,4eara; Figure 6.2, Food Label, Rowdy Boeyink; Figure 5.4, Archer, Joe Cough; Figure 6.21, Rollercoaiter, Raoul Brouns; Figure 6.2g, Hunicane Destructions, Doug Webb; Physics Today (l), Runneq calina Barskaya; Physics Today (2), Running Shoes, Rowdy Boeyink Unit 7 Pressure: Egyptian Curu on Bed of Nails, Hulton-Deutsch Collection/CORB|S; lvlanometer, Clayton Hansen; Figure 7.4, High heels vs Sneakers, Hermann Danzmayr/ Kristian Peetz; Figure 7.,], Plastic bagwithout extra handle, Cerald Koh; Figure7.2, elastiCbagwith extra handle, Cerald Koh; Figure 78, Dennis Sabo; Figure 7,l0, Pascal's Vases, Steven Wonnell / Johns Hopkins University; Figure 7.12, Hydraulic Carage Lift, A/arcel Pelletier; Figure 713, Hydraulic Car Jack, Piter Loredo; Figure 7.22, Mountain Climbel Tim Vlemmix / USAC; Figure 7.27, Scubadiver, fiennis Sabo; PhysicsToday, Desalination lnstallation, Photo courtesy of Hyflux Ltd; PhysicsToday, Class of Water, Davide Cu[lielmo Unit 8 TemPerature: Figure 8.1, Karen Ng; Figure 8.3, Arpad Benedek; Figure 8.4, Laurie Knight; Figure 8.6, Tom Sciweich http:/,/wvrnau.schweich. com; Figure 8.12, NASA; Figure 8.16, Peter J. IVlouginis-lvlark, University Hawaii Unit 9 Kinetic Model of Matter: Emperor ltloth, Birte Person; IMolecule, -WaD- (www.istockphoto.com); Figure 9.1, Clacier, lvan Roth; Figure 9.1 , Running tap, Elena Korenbaum; Figure 9.1 , Kettle, Lise Gagne; Figure 9.2, Rafal Zdeb; Figure 9.6, Cansovsky Vladislav; Figure 9.1 I Andy Hill , Unat l0 llansfer of Tlrermal Enerry: Emperor penguin chicks huddling, Photolibrary; Old faithful geyser in yellowstone, Ben Renard-Wiart; Figure 10.15, Johnny Lye; Beautiful house, page 214, ngirish (www.istockphoto.com); Physics Today, lcicles on thatched roof, Thomas Kirkeskov; Physics Today, A/lount Fuji, Bart Parren

Unit

lt

Tlrermal Properties of Mat{er: Hurricane Katrina, Photolibrary; Figure 1.I.1, lMartin Cerny; Figure I1.2, Tamara lrlurray; Figure 11.1J Hanna Kubica (small ice cubes), Steve Cray (large block of ice); Figure 1 1 .23, Johnny Lye; Figure 1 1.24, Rowdy Boeyink; Figure 1 1.25, kligas (www. istockphoto.com); Physics Today, Shaun Lowe Unit t2 Light: Toilet with one way mirrors, Rivelazioni; Figure 12.2, Nicholas Sutcliffe; Figure I2.7, Rowdy Boeyink; Figure 12.34, Rowdy Boeyink; Figure 12.41, Bradley lMason; Figure 12.42, Rivelazioni; Figure 12.49, Sandra vom Stein; Figure 12.52, Rick Comez tr,Iasterfile; Figure ,12.69, NASA; Figure I 2.70, Leif Skoogfors/Corbis; Figure I 2.71 , Photolibrary; Physics Today, lnstitute of lVlaterials Research and Engineering (llURE), A*Star, Singapore Unit l5 Waves: Mexican wave in stadium, Joseph Sohm/VisionsofAmerica.com; Figure 13.1, Emrah Turudu; Figure 13.26, Photolibrary

/

Unit t4 Electromagnetic Wares: People talking on phones, Antonio IVlo Cettyimages; Satellite Dish, David Cilder; Figure i+.4, AngloAustralian Observatory/David lMalin lmages; Figure 14.6, Royalty-Free/Corbis; Figure 14.7, Royalty-Free,/Corbis; Figure l4.8, Melissa Kir; Figure t4.9, Photolibrary; Figure 14.10, Photolibrary; Figure 14.1l,Amanda Rohde; Figure I4. 12, AndrewTaylor; Figure t4.,]3, lgor Kostin/Corbis; phys-icsToday, Tom Cufler; Physics Today, Peter Chen

/

/

Unit 15 Sound: Elephants drinkingfrom lake, LarryWilliams zeta / Corbis; Figure 15.1, Photolibrary; Figure 15.14, NASA; Figure 15.12, Allen Johnson; Figure I5.18, Photolibrary; Figure 15.21, Kevin Russ; Figure 15.22, Fanelie Rosier; Figure 15.22, Ryan Tacay; Figure 15.22, photolibrary; Figure 15.22, Phil Date; Figure 15.25, RoyalV-Free/Corbis; Figure 15.25, Kenneth C. Zirkel; Figure 15.22 Ana Abejon; Figure 15.28, Franklin Lugenbeel; Figure 15.36(a), Standard Royalty Free; Figure 15.36(b), Donald Johansson; Figure 15.36(c), Ir/ark Evans; Physics Today, Batowa; Physics Today, burning house, Julie de Leseleuc Unit l6 Static Electricity: Lightning striking oak tree, Lars Lentz; Plasma ball, Cary Unwin; Figure 16.9, Thomas Mounsey; Figure 16.2J Allen Johnson; Figure 16.28, The American QRP Club lnc.; Figure 16.36, John C. Palumbo, @2003 Regents, University of Arizona Unit l7 Current Electricity: Hindenburg explosion, Sam Shere / Motion Picture and Television Photo Archive; Light bulb, Hsianyu Kuo; Figure 171, Janis Dreosti; Figure 1712, Ross Thomson; Figure l7.37 Kurt Friehauf / Kutztown University of Pennsylvania Unit t 8 D.C. Circuits:

Electric eel, Photo courtesy by Undenruater World Singapore; Crocodile clips, Clayton Hansen; Figure I B.l B, lmage courtesy istockphoto; Figure 18.35, Juan Jose Cutierrez Barrow; Physics Today, Justin Honocks; physics

of Singapore Tourism Board; Figure 18.25, Ever

/

Today, Lars l\/ladsen

Unit l9 Practical Electricity: It/an repairing

electricity transmission lines, David Seawell / Corbis; Electric Surge, Daniel Brunner / iStockphoto; Figure 19.7, Night view of Singapore River, Daniel Cole Stockxchange; Figure l9.B,.Juicer, John Shepherd iStockphoto; Electric Drill, lngvald ,|3, kaldhusseter ,/ iStockphoto; Figure 1 9. Air conditioner, Calvin Ng / istockphoto; Figure 19. I 6, overloaded power socket, Rowdy Boeyink; Frgure 1 9. l7(b), Cirl in swimming pool, Rob Friedman; Figure 1 9.21 , Rocker switch, Rowdy Boeyink; Figure I 9.22, Dimmer switch, Rowdy Boeyink; Figure 19.25, Power socket, Rowdy Boeyink; Figure 19.29, Electric fan with double insulation symbol, Cerald Koh; Physics Today, Taser gun Courtesy of

/

/

Associated Press

Unit 20 Magnetism: 'Celestial Palette' - The Northern Lights - photo copyright by Donald W Getschman; Ring magnet floating on a stic( photo Courtesy By Frederiksen Company; Figure 20.1, Lodestones Courtesy of University of lllinois at Urbana-Champaign Physics Department; Figure 20.2, compass, Christine Balderas / iStockphoto; Figure 20.3, The neodymium magnet image is courtesy of Steve Spangler Science, Englewood, Colorado; Figure 20.4, Hard disk drive; Hermann Danzmayr / istockphoto; Figure 20.5, lt/agnet with iron filings, Thomas lr/ounsey,/ istockphoto; Figure 20.9, Photo Courtesy of Frederiksen Company; Figure 20.10, Mathew Hillier, Adelaide, Australia. Copyright 2004 Stockxchange; Figure 20.1l, lUaSnet attracting safety pins, Rowdy Boeyink; Figure 20.23, Hammer with magnet, Rowdy Boeyink;Figure20.26,lMagnet with iron filings, Rowdy Boeyink; Figure 20.30, lrlagnet with compasses around it, Rowdy Boeyink; Figure 20.31 (b), Ir4agnets attracting each other, Rowdy Boeyink; Figure 20.32(b) fi/]agnets repelling each otheq Rowdy Boeyink; Figure 20.40 Northern Lights, Roman Krochuk iStockphoto; Physics Today,

/

/

Superconductors, CERN accelerator, Photolibrary Unit Electromagnetism: It/aglev Train, Courtesy of Railway Technical Research lnstitute; Electromagnet, James McQuillan istockphoto; Figure21.2, Home-made electromagnet, Rowdy Boeyink; Figure 21.3, Electromagnet in a scrapyard, Photolibrary; Figure 21.1,l, Solenoid Courtesy of University of North Texas; Figure 2 1 . 15, Magnetic Resonance lmaging machine, Corbis; Figure 2l . I 6, Brain scan, Photolibrary Unit 22 Electromagnetic lnductlon: Band, MediaCorp TV Channel U; Windmill, Don Farrall Getty lmages; Figure 22.7, Design Continuum; Figure 22. 1 6, Carmen l\,4art[nez Ban0s; Figure 22.17, Jacques Crozier; Figure 22.21 , )amie Wilson; Figure 22.23, Sami Sarkis / Cetty images; Figure 22.32 Alan Heartfield; Figure 22.34, Royalty Free/Corbis

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The publishers would also like to thank the following: The University of Cambridge Local Examinations Syndicate (UCLES) and the Singapore Examinations and Assessment Board (SEAB) for permission to reproduce some of the questions from the Singapore-Cambridge CCE 'O' Level examinations. The answers in this publication are given by the publishers. UCLES and SEAB bear no responsibility for these answers. Any queries or comments on the answers should be forwarded to the publishers directly. Past year-examination questions marked (L) are reproduced by permission of

the University of London Schools' Examination Board.

PreFaEe Physics Matters is the revision of the well received Physics: A Course for'O'Level (2nd Edlfion). Packed with a myriad of features, this textbook facilitates the effective learning of Physics and makes the subject inspiring and riveting for students. Covering the latest GCE'O'Level Physics syllabus set by the Ministry of Education Singapore, this edition presents Physics in an engaging and accessible manner through the use of stunning visuals, real life analogies and simple language to aid concept development and reinforcement. Along with this, ample worked examples and practice questions are provided at relevant junctures to help students apply concepts they have learnt. Students and teachers will find Physics Matters a refreshing update of the previous edition-revitalising the way Physics is taught and learnt.

Learning Outcomes Found at the start of each section, this lists the salient points that students will be learning in the following pages to help them stay focused.

lnteresting Chapter Openers lntriguing examples related to the topic, to stimulate the students' interest in what they will be learning.

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Physics Today Located at the end of each unit, these articles showcase relevant, interesting and intriguing applications of the concepts taught in that unit.

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Therrnal Phgsics

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Unit 8 Temperature

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What is Physics?

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Physical Quantities and SI Units 1.3 lVleasurement of Length 1.4 Measurement of Time Concept Map

2 2.1 2.2 2.3 2.4

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Kinetic Model of Matter The States of Matter Pressure in Gases Concept Map Practice Questions

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Speed, Velocity and Acceleration

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3 Forces

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Unit 9

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Turning Effect of Forces M

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5

Energy,Work and Power

6.1 Energy 6.2 Work 6.3 Power

7 7.1 7.2 7.3

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43 44 46 47 48 53 59 65 65 67

9.2

Unit

10 10.1 10.2 10.3 10.4 10.5

Unit

11

11.1

lt.2 Mass,Weightand Density

4.1 [Vlass and Weiqht 4.2 Inertia 4.3 Density

Unit

Practice Questions

77

Practice Questions

Unit

l3 16

7

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Speed-Time Graphs Acceleration of Free Fall Concept Map

142

Temperature and lts lVleasurement Common Temperature Scales ThermocoupleThermometer Concept IVlap

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8.1 8.2 8.3

68 69

74

11.3 11.4 11.5

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166

Transfer of Thermal Energy Transfer of Thermal Energy Conduction

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Convection

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Radiation Applications of Thermal Energy Transfer Concept lVlap

176

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185

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Thermal Properties of Matter

188 189 195 199

Heat Capacity IVlelting and Solidifi cation Boiling and Condensation

Latent Heat

168

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179

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75

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Pressure

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Pressure in Liquids

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Unit 16 Static Electricity 16.1 Electrostatics

12 Light

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216

r What is Light?

217

12.2 Reflection of Light 12.3 Constructing Ray Diagrams 12.4 Refraction at Plane Surfaces \2.5 Total Internal Reflection 72.6 Thin Converging Lens 72.7 Ray Diagrams for Lenses Concept Map

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224 229

16.3 Electric Field 16.4 Hazards and Applications of Electrostatics

322

238

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245

Practice Questions

248

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15 15.1 15.2 15.3

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16.2 Insulators and Conductors

Practice Questions

Wave Production and the Ripple Tank Concept Map

262 263

268 274 277 278

280

28t

Concept Map Practice Questions

284 289 289

Physics Today

29t

Sound

292 293

What is Sound?

Transmission of Sound Reflection of Sound t5.4 U ltrasound 15.5 Pitch and Loudness Concept Map

Practice Questions Physics Today

Waves

3t5

279

256 257

Unit 13 Waves 13.1 Describing Waves 13.2 Properties of Wave lVlotion

314

298

Unit 17 Current Electricity 17.1 Electric Current 17.2 Electromotive Force 17.3 Resistance 17.4 Resistivity Unit 18 18.1

330

33t and Potential Difference

347

348

D.C. Circuits Series Circuits

350 351

354 355 361 363

Concept Map

366

Practice Questions

367

Physics Today

377

Practical Electricity 19.1 Uses of Electricity 19.2 Measuring Electrical Energy 19.3 Dangers of Electricity 19.4 Safe Use of Electricity at Home

300

Concept Map

303 305 309 309 313

Practice Questions Physics Today

Magnetism Magnets and Materials Magnetic Induction Magnetisation and Demagnetisation lvlagnetic Fields Temporary and Permanent Magnets Concept Map

372

373 375 380 382 390 391 393 394 395 398 399 402 407

Practice Questions

410 410

Physics Today

4t3

Unit 21 21.1

Electromagnetism lvlagnetic Effect of a Current 21.2 Force on Current-carrying Conductors 21.3 Forces on a Current-carrying Rectangular Coil in a Masnetic Field

Unil 22

339 344

Practice Questions

Unit 19

20.5

335

Concept IVlap

18.2 Parallel Circuits 18.3 Resistors in Series and Parallel 18.4 Potential Divider 18.5 Transducers

Unit 20 20.1 20.2 20.3 20.4

324 328 328

4t4 4t5 42t 426

Concept Map

429

Practice Questions

429

Electromagnetic Induction

432

22.1 Electromagnetic Induction 22.2 Allernating Current Generators 22.3 Transformers 22.4 Converting A.C. to D.C. 22.5 Cathode-Ray 0scilloscope Concept Map

Practice Questions

433 438 442 448 450 454 455

Answers

457

Index

46t

I

I

.-

1-

r-

1.1 What is Physics? In this book, you will study one of the key disciplines of Physics.

Science-

Physics is the study of the natural world around us-from the very large, such as the solar system, to the very small, such as the atom. The study of Physics is commonly divided into major topics such as Ceneral Physics, Thermal Physics, Light, Waves and Sound, Electricity and Magnetism. All these topics are related to two main ideas: matter and energy. Figure 1.1 shows a concept map of what Physics is all

about.

is

the Science that deals with the ideas of

Matter /4 _-

-a)'-at-'

Energy

-' _. .-^a

-r+rl I

can be studied in

can be studied in

terms of its

terms of its

properties

relationships with energy

relationships with matter

properties

in the fields of

Thermal Physics

Light, Waves and

Electricity and

Sound .'..f'

Magnetism

'-.,'

The knowledge of Physics we have today is the result of the work of many scientists over centuries. These scientists built and tested their ideas on matter and energy, and verified their ideas or theories by doing experiments.

'.'1.,

e,Figure 1.1 What is

Physics-a pictorial

0vervtew

When we do experiments, it is important to obtain reliable results.

In order to obtain reliable results, accurate measurements must be made. This is why we begin the book by going through some methods that we use to make accurate measurements. General Physics

5

1.2 Physical Ouantities and Sl Units

Measurement is an important part of Physics. In Physics, we are especially concerned with what standards of reference are used and how accurate the measurements are. atigure 1.2 This sign found on an overhead bridge warns vehicles above the height of 4.5 m not to pass underneath it.

[ffEtE

Gt-oop

Albert Einstein

(I879-t 955)

Ask somebody to mention a physicist

and probably you will get 'Albert Einstein' as an answer. Einstein's

Physical quantities and Sl units Aphysical quantityis a quantity that can be measured. It consists of a numerical magnitude and a unit. They are found in signboards and labels almost everywhere in our daily lives, like in the sign shown in Figure 1.2.

There are altogether seven basic physical quantities, or base quantities. Length and time are two of them. Table 1.1 shows the seven base quantities. vTable

1.1 The seven base

quantities and their Sl units

discoveries changed the way we look

at the world. His work dealt mainly with the fundamental ideas in Physics: matter and energy. Einstein was the first to relate these two in the famous equation E = mC2. For the last twenty

Base quantity

Name of Sl unit

Symbol for Sl unit

Lengh

metre

m

IMass

kilogram

kg

years of his life, he worked in Princeton,

Time

second

S

sentence: 'Not everything that counts

Electric current

amPere

A

can be counted, and not everything that can be counted counts'. Do you

Thermodynamic temperature

kelvin

K

Luminous intensity

candela

cd

Amount of substance

mole

mol

USA.

ln his office he placed this

agree?

The units of these seven base quantities are known as the SI units, from the French Le Systeme Intemational d'Unites. Out of the seven basic quantities and their corresponding SI units, you will learn five of them in this course. They are length, mass, time, electric current and temperature.

rFigure

4 Measurement

1.3

Albert Einstein

All other common physical quantities such as area, uolume and speed are derived from these seven quantities. They are called derived quantities. For example, speed is derived from length (i.e. distance travelled) and time.

Table 1.2 gives examples of how some common physical quantities are derived from the base quantities. vTable 1.2 Some common derived quantities and units

Physical quantity

How it is derived from base quantities

Symbol for unit

Area

length x width

m2

Volume

lengthxwidthxheight

m3

Speed

lengh time

m s-r

Why do we need Sl units?

v Figure 1,4 Ancient Egyptians defined the cubit as the length from the elbow to the thumb. However, this soon caused widespread confusion as the arm length varied from person to person. To solve the problem. the pharaoh decreed that the standard cubit, or the 'Royal Egyptian Cubit', was to be marked out from his own arm. With this standardisation of length, the Egyptians achieved surprising accuracy, and went on to build the great pyramids. Do you think the cubit is a useful unit for measurement?

In the past, people used parts of their bodies and things

around them as units of measurement. That was how measuring terms like foot, yard and horsepower came about. Unfortunately, such methods of measurement created much confusion (Figure 1.4). It was not until 1968 that scientists agreed to adopt one universal set of units-the SI units.

1 cubit...

Prefixes for Sl units Using decimal notation, the distance between air molecules would be represented as 0.00000001 m. It would be cumbersome if we need to mention this quantity a number of times.

It would be more convenient if we use prefixes to represent the above quantity. In this case, it can be expressed as 0.01 pm (micrometre) where p represents the 10-6. The prefixes listed in Table 1.3 are very useful in expressing physical quantities that are either very big or very small.

submultiple

Another convenient and acceptable way of expressing the same quantity (0.01 pm) is to use the standard form. In this case, it will be expressed as 1 x l0r m.

vTable 1.3 Some common Sl prefixes Pref ix

Symbol

grSa-

C

106

meSa-

NI

103

kilo-

k

l0-r

deci-

d

I0-2

centi-

c

l0-3

milli-

m

l0-6

micro-

u

l0-e

nano-

n

Factor 'l0e

Some other common quantities expressed in standard forms are:

kilometre (km) is I x 103 m .'one milliampere (mA) is 1 x 10aA o three megajoules (M) is 3 x 106 J o six microcoulombs (pC) is 6 x 10{ C . eight nanoseconds (ns) is 8 x 10-e s o one

General Physics

5

WORKED EXAMPLE 1.1 Donovan Bailey of Canada broke the l0O m sprint world record at the ,l996 Atlanta Olympics, with a time of 9.84 s. With this record, he became the'world's fastest man'. ln contrast, a dog runs at a speed of 30 km h-i. lf the dog chases Donovan Bailey, will the dog catch up with him?

Solution First, we calculate the average speed of Donovan Bailey

Averape sD€€d

1,09,' = distance trme = 9.84 s = 10.2 m s

I

ln order to make meaningful comparisons of speed, the units must be the

same. So Donovan Bailey's speed should be converted to km h-'.

l0.2msr= lO.2xlms' lkm 60 s min = lO.2 - rl-T', 1s l0O0m, lminx99th = 36.7 k'h = so.z k, hSince 36.7 km a distance

of

h I > 30 km h-', Donovan Bailey will outrun the dog over

I OO

m. But as he begins to tire, his speed will drop and the

dog may eventually catch up with him!

1.5 The '0uarter Pounder with ^Figure derives its name f rom a weight Cheese' measurement. Americans weigh everything in pounds, from burgers to basketball players,0ne pound (1 lb) is

Ideas

l. 2,

approximately half a kilogram.

5. fil[ilf

rc1

A physical quantity has a numerical magnitude and a unit.

There are seven base quantities: len$h, mass, time, electric current, temperature, luminous intensity and amount of substance. The units of these seven base quantities are known as the Sl units. All other units are derived from the Sl units.

Chuang Tzu, an ancienr

Chinese philosopher, was known as the 'peerless explainer of scale' Co

to http://www.powersof I O.com

and

find out more (Hrnt: check lO to the power of zero). Thrs website will give you a good sense of how big or small things can get Also, find out how many powers of ten are shown and what the smallest and largest powers are

Test Yourself

I.

1

Express the weight of a 'Quarter Pounde/ in grams, given

(lb) is equalto

2.

.2

I

2.205 pounds

kilogram (kg).

The world's smallest playable guitar is 13 pm long. Express the lengh in standard form. {Figure 1.6 A microscopic photo of the nanoguitar made by Cornell University researchers. lt was built using nanotechnology. (Befer to Physics Today! atthe end ofthe unitfor more on nanotechnology.)

6

Measurement

1.3 Measurement of Length Learning Outcomes You'll be able to:

I I I

have a good sense of the orders of magnitude describe how to measure a variety of lengths using the appropriate instruments (i.e. metre rule, vernier calipers, micrometer) use a vernier scale

In Physics, length is an important quantity that is measured almost all the time. For example, we measure length to know how far an object has moved, how much space an object occupies or how far apart two objects are.

The SI unit for length is the metre (m). There is a wide range of lengths in this world (Figure 1.7). It is necessary to use the appropriate instruments and methods to measure different types of length. The metre rule and tape measure are just two examples of instruments that can be used. In the following pages, you will learn more about measuring instruments and how to use them. I

0.2

500 000 000 000 000

distance travelled by light in one year

size of chopsti c ks 8848

height of Mount Eve rest 20 000 000 000 000

000 000 000

distance from the Earth to the Andromeda galaxy

6 378 000

radius of the Ea

rth

100

a

0.000 000 000 000 001

length of

radius of the

footballfield

hydrogen nucleus

a

rFigure 1.7 We need to measure a wide range of lengths as the natural world we live in ranges from the very big to the very small General Physics

7

The metre rule and the tape measure The metre rule and tape measure are common instruments used to measure length. rFigure 1.8 The metre rule is a common measuring instrument. lt is used for measuring short lengths or as a drawing aid.

A metre rule can measure lengths of up to one metre. A retractable

steel tape is suitable for distances longer than a metre. Suppose we want to measure the width of a pond that is about 10 m. Which measuring instrument should we use? We should use a retractable steel tape. The retractable steel tape should be long enough to measure the distance (Figure 1.10). How

v Figure 1.9 Retractable steel tapes, due to their flexibility and length, can

about measuring how deep the

measure most objects around the house.

pond is? A metre rule may be used (Figure 1.11). rFigure 1.10 Using a retractable steel tape to measure the width of the pond

Precision of an instrument What is the smallest unit on the metre rule? It is 0.1 cm or I mm. The smallest unit an instrument can measure is known as its 'precision'. For example, the metre rule cannot accurately measure the thickness of a piece of paper, which is obviously thinner than 1 mm. You will have to estimate its thickness. In this case, the uncertainty, known as the instrument error, is due to the limitations of the metre rule.

Avoiding reading errors When you use a metre rule, position your eye directly above the markings to avoid parallax errors (Figure 1.12). By taking several readings and taking the average, you will minimise reading errors.

rFigure 1.11 Using a metre rule to measure the depth of a pond

Do take note that for metre rules, the zero mark is often at the very end of the rule. Wear and tear of the metre rule may make this mark

unsuitable for measuring purposes. This worn end may introduce errors to the readings. Hence, it is better to measure from some randomly chosen point and subtract it from the final readins

Accurate length of object = 2.9

4

Possible zero

-

1.0 = 1.9 cm

4

object

lnaccurate length of object = 3.0

-

0.9 = 2.1 cm

D

error at this end

rFigure

1.12(al Accurate measurement

with no parallax errors

I

Measurement

r,Figure 1.12(b) lnaccurate measurement due to parallax errors

The calipers An instrument for measuring the diameters of cylinders or circular objects are the calipers. The jaws of the calipers are used to grip

the widest part of the object. When the object is removed, the distance between the jaws can be measured using a metre rule (Figure 1.13(b)). external calipers

I

internal calipers

-) rFigure 1.13(a) By inverting the jaws of the calipers, inner diameters can be measured.

The vernier calipers The vernier calipers (Figure 1.14) consist of a main scale and a sliding uernier scale. It is a useful tool that is used to measure both the internal and external diameters of an object. The vernier calipers are able to measure to a precision of 0.01 cm. Figure 1.15 on the following page shows how to use the vernier calipers.

eFigure 1.13(b) Calipers can be used to measure outer diameters, The calipers are then measured using a metre rule.

main scale

inside jaws-used

sliding vernier scale

to measure the internal diameter of an object

vernier scales-a smallsliding scale

attached to the main scale that allows us to read a fraction of the

F.

smallest interval

jaws-used to measure the external diameter or width of an object

outside

Avoiding reading errors when using the vernier calipers Before using the vernier calipers, we need to examine the instrument for zero error. This is to check that the zero mark on the main scale

coincides with the zero mark on the sliding vernier scale when we are not measuring anything between the jaws. Table 1.4 on the following page shows how we should deal with zero errors on the vernier calipers.

tail-used to measure the depth of an object

rFigure 1.14 Parts and uses of

the

vernier calipers

GeneralPhysics

9

How to use the vernier calipers Step 2

inside jaws

Read the main scale directly opposite the zero mark on the vernier scale. ln this case, the

main scale

0l

2

78

6

reading on the main scale is 5l mm or 3.1 cm.

l0 cm

vernier scale

The 4th vernier mark coincides

4

3

with a marking on the main scale. This gives a reading of +0.+ mm or +0.04 cm to be added to the main scale reading.

Eil

ET

Grip the ball bearing gently using the outside jaws of the calipers.

The diameter is found by adding

the main scale reading to the eFigure 1.15 Using vernier calipers to measure the diameter of a ball bearing

vernier scale reading:

3l

mm + 0.4 mm = 51.4 mm

Avoiding reading errors when using the vernier calipers vTable 1.4 Checking and correcting zero errors when using the vernier calipers

Checking for zero error 0

Ir

r rr lll,L Yl I I I I I ll

lf

I

0

main scale

II

Observed reading 3

I

vernierscare

rrr

I I I

0

10

The two zero marks coincide-

no zero

I

main scale

lilt

|l I I r|T;rnierscare I lYl I ,1..

rl |! lYl I

I

I I

main scale

I

vernierscate

t0

4

3

lrrrrl I |,il I I I I I I I lYl 0r0

010

main scale

I vernierscare

lxr

I I I I I I lYl

0

Reading

r

I

10

4

lYl rl r I rl 0

r I

main scale

vernier scale

0

Zero mark on vernier slightly to

the left-negative zero error of -0.03 cm (count from l0).

l0

M.urr,.runt

(+0.03) = 3..l4 cm

=3.17 cm

main scale

rrIr I vernierscate

-

from the reading,)

the right-positive zero error of +0.03 cm.

I

3.17 cm

(The positive zero error is subtracted

Zero mark on vernier slightly to

0 I r rrL

3.14 cm (No zero error correction required)

Reading = 3.14 cm

error_

0

4

Corrected reading

3.,l I cm (-0.03) = 3.14 cm (The negative zero error is added to

-

the reading.)

Reading=3.11cm

The micrometer screw gauge The micrometer screw gauge is used to measure lengths to

a

precision of 0.01 mm or 10 micrometres (Figure 1.16). It can measure the external diameter of wires and ball bearings. We use it mainly to measure anything less than 1 cm-too small for the vernier calipers to measure. How to use the micrometer screw gauge

Eil

Step 2

Turn the thimble until the anvil and the spindle gently grip the object. Then turn the ratchet until it starts to click.

cross sectio

datum

n

line

Read the main scale reading at the edge of the thimble. ln this case, it is 8.5 mm.

rEE

thimble scale 0

of wire mm

anvil spindle

0

The thimble scale has 50 divisions, each of which is 0.01 mm. Take the thimble reading opposite the datum line of the main scale. ln this case, it is 40 divisions, which

45 5

40


Figure 1.21 The photo shows a unique type of sundial. To tell the time, you step right into it form the shadow and shadow shows the time!

lflfriTlllrc;vut

"

your

own

equatorral sundial with jJSt a piece of cardboard, straw and a protractor. Find out how to do so on http://wvrw. ma rshal lcavendish.com/education/sgl student.

For scientific work, time intervals have to be fixed and cannot change. What recurrent motions can you think of that can be used to measure time?

Using a pendulum to tell time

R

A simple pendulum can be used to measure time more accurately.

It consists of a heavy object called a bob, like a metal ball, attached to a string. The string is fixed at one end. If we swing the pendulum, it will move back and forth at regular intervals . Each complete to v)

R=W

r,Figure 2.40 0ne coin will fall vertically downwards, whereas the other will be projected sideways. Do both coins hit the ground at the same time?

B= air resistance (increases with speed) W= weight of paper (constant)

W

I vo

l=

Yr)

r,Figure 2.39 Successive intervals showing how velocity and air resistance change as a piece of paper falls through the air

O

From f = 0 s to t= I s, the velocity of the paper increases from zero to v, rapidly (i.e. acceleration is great).

O

u/m

O

-

R

=4s

B'. A

t= I stot=3 s,thevelocityof the paper continues to increase from v, to v, From

(where

vr)vr)

v,). However, the rate of increase of velocity from v, to v, or from v, to v, is less than that from zero to vr over the same time interval of I s (i.e. acceleration is smaller).

s'

43 V,

O v1

From f= 3 sto t= 4 s and beyond, the velocity of the paper does not increase any more but remains at a constant (i.e.

vt = maximum constant velocity reached). This maximum constant velocity is called the terminal velocity. When terminal velocity happens, the vq =

Al

A

A

A

3

fls

Area A,

Area

,4 2

4

3

2

0

Area A,

acceleration is zero.

Area A

The speed-time graph shown in Figure 2.41 is used to represent the motion of the piece of paper as it falls. Note that the areas 4,, A2, A3and.44 under the graph represent the distances dt, d2, d, and d respectively.

Figure 2.43{b} Falling head-first

l. r)

ln the absence of air resistance, all objects fall under gravity with constant acceleration. This constant is g the acceleration of free fall. h is approximately 10 m s,.

2.

Kinematia

parachutist increases with time with a decreasing l2 s before reaching a constant speed of

acceleration for the first

could grab her and open her parachute. Robertson and Williams landed safely.

42

Describe the motion of the parachutist between A and D. State the value of the terminal velocity before and after the parachute opens. Calculate the average value of the acceleration between B and C.

(Jun00/P2lQ I )

Debbie Williams. To slow down he went into a spread-eagle position eventually, so he

(l

Time/s

r.tigure2.42

Cregory Robertson

adjusted his body to fall head-first. He increased his speed and soon caught up with the unconscious

A24681012141618

When there is air resistance, an object falling under gravity experiences decreasing acceleration until terminal velocity is reached. This occurs when the air resistance is equal to the weight of the object.

M l.

An object is released from restfrom an unknown height. lf the acceleration

due to free fall, g is 10 m s-2, sketch the speed-time graph for a time interval of 5 s, assuming negligible air resistance.

(a) (b)

2.

What is the speed of the object just before it hits the ground? What is the unknown height?

ln the presence of air resistance, why does a feather reach terminal velocity faster than a hammer, if both are released from rest at the same substantial height?

Conce

Ilnrtl?rralo

tMa Kinematics Length

/

Time

f

m

s

(Sl Unit)

(Sl Unit)

m s-r (Sl Unit)

Velocitv

'

_

Displacement Time taken

Soeed

'

_

Distance moved Time taken

m

s-r

(Sl Unit)

Area under speed-time graph gives distance travelled

Varying velocity/speed

Constant velocity/speed

I

Acceleration

y--u a= Lv At - At

wherey=finalvelocity

m

s-2

(Sl Unit)

u = initial velocity Af = time taken

Constant acceleration

:

e.g. a free-falling object under

e.g. a free-falling object under gravity

gravity in the absence of air

in air has a decreasing acceleration

resistance has a constant

due to air resistance

acceleration a=

J ='

Varying acceleration:

rD

3 =:!'. n Itt

OJ

g= I0 m s-2

General Physics

45

Section B Structured Questions t. (a) Define average speed. (b) Figure 2.44 below shows the route taken

Practice Questions Section A Multiple-Choice Questions

by a cyclist as he cycles past the places marked A, B, C and D before returning to A.

The average speed of a car is 35 km h-1. How far can it travel in 45 minutes?

A C 2,

129

km km

B D

26.25 km 467 km

6p mA6am 12 km

A car accelerates uniformly from 5 m s-r to l3 m s-] in 4.0 s. What is the acceleration of the car in m s-2?

A C

5.

o.z8

0.50 m s-2 0.80 m s-2

B D

lO km

1.25 m s-2

2pmD

2.00 m s-2

B9am

A ball which is thrown vertically upward at 1.2 m s-r

decelerates uniformly at I O m s-2. How long will it take to reach zero velocity?

A 0.12s C 2.4s 4.

B D

Bkm

7km C 12

6.Os

12.0s

noon

Figure 3.35 Have you ever played Air Hockey at arcade centres before? The puck seems to fly across the surface of the table because there is almost no frictional force acting between the puck and the table. The puck floats on a thin cushion of air, hence the name Air Hockey.

p

Friction as a useful force Car tyres

Friction plays a very important role in the motion of a vehicle. Without friction, a vehicle will not be able to move as the tyres will just spin around at the same spot. Avehicle travelling on a road with little friction may skid and lose control. Slippery road conditions on a rainy day can reduce friction greatly. It is extremely important that under these conditions, car tyres are able to grip the road properly to prevent skidding. Therefore, they are designed with treads-grooves that channel water under the tyres into them. In this way, the tyre is able to grip the road surface well. Parachutes

A parachute works by harnessing air resistance, a type of friction in air, to oppose the force of gravity. As an open parachute has a large surface area, it helps provide enough air resistance to slow down the fall of skydiver. The skydiver will then be able to descend safely. Rock climbing Rock climbers need to grip the rock surface well with their hands and feet, in order to climb a mountain. Chalk powder is usually used

to improve their grip (Figure 3.36).

ldentifying forces and free body diagrams Throughout this unit, simple block diagrams with arrows are used to represent forces acting on a body. Such diagrams are commonly called free body diagrams. When you solve problems on forces in Physics, you need to consider the effects of all forces acting on the various objects. Drawing these diagrams will help us see the situation better, and thus help us solve the problem more easily. Figure 3.37 on the following page shows some examples of free body diagrams. These will give you a good idea

on how to identify forces when solving a problem.

> Figure 3.36 Rock climbers always carry

their back. By dipping their hands into the chalk they reduce the sweat on their palms, thereby increasing friction and improving their a bag of chalk on

g

rip

o

Apple hanging on the tree . Weight llll and tension force from tree,

f

Apple falling to the ground . Weight W and air resistance R (depending on the question, air resistance may be ignored)

T

O

Bird flying in the air . Weight lry and lift from wings,

. Thrust exerted by wings,

f

I

and

air resistance, R

P Squirrel pushing an apple Push force P and friction f

.

. Weight W and contact force from ground,

rFigure

3.37

O

/

Apple on the ground

. Weight

lz7

and contact force

from ground, F

Drawing good free body diagrams takes practice. The following worked example will give you a good start at learning how to solve these kinds of problems.

WORKED EXAMPLE 3.4 A truck engine of mass 5000 kg is pulling a trailer of mass 1000 kg along a level track at an acceleration of 0.l0 m s-2 (Figure 3.38). The resistances are

l0 N per 1000

kg for the truck engine and S N

per 1000

kg for the trailer.

m = 1000 kg m = 5000 kg

a=0.10msr

€

forward thrust by engine Fe

towbar (a)

rorces

3.3g

Draw a free body diagram of the engine and the trailer. (i) the tension in the connecting tow bar between the engine and the trailer, and (ii) the forurnrd thrust exerted by the engine.

(b) Glculate

62

rFigure

F

Solution (a)

acceleration a = 0.10 m

acceleration a = 0.10 m

s-2

trailer B,

s-2

truck engine forward thrust

TT

m = 1000 kg

F"

m = 5000 kg R"

(D

(iD eFigure 3.39

(b) (D

Firsl examine allthe forces acting on the trailer. Refening to the free body

diagram (a) (i), we have

f

a

and the resistance of the trailer

Using F"", = rna where

f,*

trailer, we have Flu, = T

.'. T=rt1d +

(ii)

total of two forces acting on the trailer-tension

-

is

&.

the resultant or net force on the

Rt= n'td

&= I000 x 0.10 + 5 = 105

N

Now, examine all forces acting on the engine. Again, referring to the free body diagram from (a) (ii), we have three forces acting on the engine-fonvard thrust 4 exerted by the engine, tension resistance on the engine R".

UsingFet=ma we have F*r= Fu -

f

and

(

+ R) = ma :. Fe=ma + (f + R") = (5000)(0..l0) + (105 + 50) = 655

N

WORKED EXAMPLE 3.5

pr0p eller

A hovercraft moves on a cushion of air which is trapped underneath i! as shown in Figure 3.40. The trapped air reduces friction. (a) The hovercraft starts from rest and, as it starts, the propeller produces a foruuard force F of 22 000 N. The mass of the hovercraft is 25 000 kg. Glculate the initial acceleration of the hovercraft. You may assume there

cushion of air

is no friction.

(b)

rtigure

the force F is unchanged. Suggest, in terms of the forces acting on the hovercraft, why the speed is now constant.

(c)

3.t10

Some time later, the hovercraft reaches a steady speed, even though

of l6 m s-r, the force F is switched into reverse and the hovercraft gradually slows down. Figure 5.4.l shows a graph of the variation of speed with time. State how the graph shows that the acceleration is not constant.

When the hovercraft is travelling at a speed

(Nove8/P2lQl )

Speed/m

s,

16

8

10 20

I rme/s 30

r, Figure 3.41

General Physics

63

Solution

(a)

Civen: forward force F= 22 000 N, mass m =25 000 kg UsingF= ma,wehave a = .'. u = 0.BB m s-2

h

(b)

m=

contact force equals weight

air resistance Pequals F

Fonrvard

forci F

k7= 250 kN

eFigure

3.t12

The forward force Fcauses the hovercraft of mass m to accelerate forward

with an initial acceleration a. As the speed of the hovercraft increases with time, the air resistance R acting against its motion will also increase as it is proportional to the instantaneous speed of the hovercraft When the speed of the hovercraft increases to a certain value y such that the air resistance is equal to the constant fonruard force, the resultant force on the hovercraft gtven by F- R becomes zero (Figure 5.42). Hencg the final acceleration a hovercraft

(c)

IrlrflTfirfirr|ro 64

Forces

=F

will become zero, which explains why the

=R constant will cruise a{fhis

speed of

rz.

The graph is a curve, showing that the change in speed in equal time intervals is not the same. Therefore, the acceleration is not constant.

Concept Map Forces

which can produce Vector

Quantity

changes in the motion of a body

N

(Sl Unit)

Free body

diagram e.g.

e.g.

e.g.

Causes a stationary

Causing an object to speed

object to start moving

up or slow down

Causing an objectto change direction such as moving in

a circle at constant speed

Friction which is explained by

--+

Positive and

negative etreds

J

Newton's Second Law of Motion

Srven

by

Fna= lflt!, where

+

= resultant (net) force (in N) r7r = rtosS (in kg) Fnet

a

T1

Opposes motion between two surfaces in contact

o -t

= acceleration (in m s-2)

r)

rD

VI

5.

Practice Questions

Two objects, A of mass 3.0 kg and B of mass 2.0 k& are stacked one on top of the other as shown in

lf all the surfaces are regarded

Section A Multiple-Choice Questions

Figure 3.44.

I

frictionless, what is the acceleration of A when B is being pulled by a horizontal force of I0 N?

2.

Which of the following is a vector quantity?

A Time B C Velocity D

Energy

as

Temperature

Figure 3.43 shows four forces acting on a block. What is the resultant force?

10N

rFigure 3.44 3N 2N

A 5Ntoleft C llNtoright

rFigure

3.t13

B

6 N to right

D

No resultant force

7N

A C

0ms-2

B

2.0 m s-2

3.0 m

D

5.0 m s-2

s-2

General Physics

55

4.

Air

Weight

resistonce

Resultont force

A

70.0 N down

70.0 N up

zelo

B

700 N down 700 N down 700 N down

zero

700 N down

700 N up 700 N up

zelo

c D

(b)

A parachutist of mass 70.0 kg falls with terminal velocity. Which combination gives the weight, air resistance and resultant force acting on him?

The total force opposing the motion of the box and parachute at a particular instant during its fall

50 N. The combined mass of the box and parachute is 5.0 kg. Calculate the resultant downward force on the box and parachute is

(c)

700 N down

(take g= l0 m s'). Briefly describe the motion of the box and parachute at this time. At the end of this fall, the parachute is caught on a tall tree. The box is then cut loose and falls from rest to the ground. The time of fall is 2.4 s. Calculate

(i)

(ii)

Section B Structured Questions

l.

the velocity with which the box strikes the ground,

the average velocity during its fall,

(iiD the distance fallen.

To test the safety of a car and its passengers, a test

(Nov8s/P2lQ I )

vehicle was propelled at various speeds towards a fixed metal barrier. ln one such test, the mass of the

dummy driver was 75 kg. The speed of the dummy driver immediately before impact was 30 m s-'. lf the time interval between the impact and the dummy coming to rest was 0..l 5 s, calculate the (a) deceleration of the dummy driver during

(b)

4.

A motorboat travels due North at a steady speed of 3.0 m s-rthrough calm water in which there is

impact.

no current. The boat then enters an area of water in which a steady current flows at 2.0 m s-' in a Southwest direction, as shown in Figure 3.45. Both the engine power and the course setting remain

average force on the dummy driver caused by

unchanged.

the impact. Explain why the wearing of a seat belt could reduce injury to a car driver.

;{wi,

N

(L)

2.

Atowtruckof mass I500 kgistowinga small carof mass l0OO kg. The horizontal force exerted on the is 1000 N and the system

boat

car through the tow bar

of tow truck and car has an acceleration of 0.50 m

Draw the forces acting on the tow truck and the towed car.

(b)

Calculate the

(D friction

(iii)

5.

on the towed car due to the road. foruard tractive force of the tow truc( given that the friction opposing the tow truck is 750 N. resultant force on the tow truck and car, regarded as a single object.

A metal box, attached to a small parachute, dropped from a helicopter. (a) Explain in terms of the forces acting, why its velocity increased immediately after

(i)

(ii)

66

Forces

being dropped; it reached a uniform velocity after a short time.

sj

s,.

(a)

(ii)

3.0 m

is

I

rFigure

3.45

(a) Explain how the above

paragraph gives information, not only about the speed of the boat but also about its velocity.

(b)

(c) (d)

By scale drawing, determine the magnitude and direction of the resultant velocity of the boat. Calculate the distance the boat now travels in 5.0 minutes. The mass of the boat is 3000 kg. Calculate the additional force which needs to be applied to give the boat an initial acceleration of

0.025 m

s-2.

(Nov8s/p2let )

rlrmEtnfirr.o

E=

t-

ii-

the Forcoor

Grauitu: I

I

r

I

multi-mil lionaire Dennis very first space tourist. He was launched into space in a Russian Soyuz capsule for a week-long stay at the International Space Station that cost him US$20 million. In an interview published after his landing, he said "it is

hard for me to fully convey what weightless for eight days".

A zero-gravity'water stadium' with floating'blobs' of water that one can dive through or throw at each

other will serve as unusual entertainment. Zerogravity stadiums will house existing terrestrial games like football, only that they will be played in brand-new ways. The possibilities are endless.

it was like to be Companies are presently working to popularise space tourism. This is good news for the average

Space tourism is by no means a new idea. Back in

person who cannot afford a 20-million dollar ticket.

1967, newspapers reported the viability of space tourism, including even the possibility of 'Hotels in Space'. Recent technological advancements have made space tourism a closer reality with the

The Space Tourism Study Program ofthe Japanese

development of NASA's prototype spacecraft X-33.

41997 report published by NASA concluded that space tourism was an industry potentially worth billions of dollars. The lack of gravity in space opens up many new possibilities, like space sports.

Rocket Society aims to bring the price down to US$10 000 with a turnover of I million passengers a year. As the number of space vehicles grow, the number of flights will increase, and the price will eventually plunge.

to Europeon a holiday, one could instead opt to take the X-33 to the Moon, perhaps for a game of zero-gravity football! In the future, insteadof flying

General Physics

67

\t\\

4.1 Mass and Weight Learning Outcomes

When we say that a person weighs 100 kg, we actually mean that the person has a body mass of 100 kg. When we buy a 5 kg bag of rice, we actually mean the mass of the bag of rice is 5 kg and not its weight.

rFigure

4.1 The number and composition

of atoms and molecules make up the mass of a body.

In Physics, weight and mass are two very different quantities. In everyday language, we often misuse the term weight when we mean mass. So, what is the difference between mass and weight?

What is mass? or property It is a of a body that cannot be changed by its location, shape and speed. The amount of mass a body has depends on the number and composition of atoms and molecules that make up the body (Figure 4.1). The SI unit for mass is the kilogram (kg).

Mass is a measure of the amount of matter

Large masses (e.9. a truck) are usually measured in tonnes (1 tonne = 1000 kg) while small masses (e.g. a pencil) are usually measured in grarns (l gram = 0.001 kg)

which pulls them back down to Earth. This force is the result of the gravitational pull exerted by the Earth. Weight is a force and has direction. The direction is downwardtowards the centre of the Earth. Since weight is a force, its SI unit is the newton (N), not kilogram (kg). This force is also called grauitational force or grauity.

What is a gravitational field?

rFigure 4.2 When we say a person weighs more than another, we are comparing the Earth's gravitational force acting on each person. The weighing scale is simply an instrument that allows us to measure and compare who has more gravitational force acting on her. So, shouldn't weighing scales reflect newtons and not kilogramslhen? Are our common weighing scales wrong? You will find out later.

...

,: i

\\> 'r*

The Earth's gravity is experienced by any object near it. The region

surrounding the Earth where gravity is experienced is called the gravitational ffeld. The force experienced is the strongest on the surface of the earth gnd gets weaker further away.

rt qcNtLnhnJ 6dl t, a ryqo(i,.u tona oLIW' Q1r1a (P{ wa t f,rnvtat fil#irt^ex ,n

hf,th

rFigure 4.3 Earth is surrounded by a gravitational field. Field lines are drawn to represent the gravitational field. General Physics

69

il

"S

@i

t

eFigure 4.4 The sun is an extremely massive star. All planets of the solar system, including Earth, are held in orbits due to the Sun's gravitational pull.

LEELGGh-o.,p

What is gr-i-i\rit;ltional field strengtn?

Singapore's local 'g' The value of the gravitationai field

The weight of an object depends on the strength of the gravitational pull. For example, an object weighs much less on the Moon than on Earth. This is because the Moon's gravitational pull is much less

strengh 'g' depends on the mass of the planet you are at and the drstance f rom

the planet's centre of grav ty. Since the Earlh rs not a perfect sphere, the value of the Earth's g is different for every part of the world. An accurate measurefirent of Singapore's ocal g vrras made at the PSB Burldrng rn Science Park. The vaLue was found to be: 9 780

610

8l N kgI.

g -

As Singapore's and crea is quite snra

,

the variation of thc gravitational lie d stren$h between the soutlrern rrost and the nofthern most po nt s genera ly

than the Earth's. The mass of the object, however, stays the same whether on Earth or on the Moon.

Gravitational field strength g is defined as the gravitational folse acting per unit mass on an object. On Earth, the gravitationai-fielcl strength is about l0 N kg1. This means that a 1 kg mass experiences a force of 10 N due to Earth's gravitational pull. On the other hand, the same I kg mass on the Moon experiences a gravitational force of only 1.6 N. Hence, we say that the r{ravitational field strength on the Moon is 1.6 N kg r.

neglrgrble (a) High tide

> Figure 4.5 There is a

gravitational force of attraction between the Earth and the l\4oon. As the Earth is more massive than the IVloon, this force of attraction causes the I\4oon to orbit round the Earth. However, we can still see the effects of the I\4oon's pull on Earth the high and low tides of the oceans are caused by the lVloon's gravitational pull.

70

Mass, Weight and Density

(b) Low tide

$A S-rIFstEI!;htlinrt

How are mass and weight related? The weight or amount of gravitational force acting on an object is dependent on its mass. The more mass an object has, the greater

the gravitational force acting on it.

We have learnt in Unit 3: Forces that F= ma. Since weight is gravitational force, from this equation, we can see that weight is directly proportional to the mass of a body. ln Unit 2: Kinematics, we learnt that all objects falling freely accelerate at the rate of 10 m s-2. This acceleration is the same as the Earth's gravitational field strength, which we will denote as g too. Therefore we can write:

W:

mE

where

No one knows how or why gravitational force exists, but Sir lsaac Newton, who discovered gravity, came up with the list below to describe this force: All masses attract one anotherwith this force. The larger the masses, the stronger the force. The smaller the distance between the masses, the stronger the force.

l

2. 3.

I,l/= weight (in I\^), m = mass of object (in kg) and

g= gravitational field strength (in N kg-t)

WORKED EXAMPLE 4.1 A mobile phone has a mass of 75 g. Find its weight if g is 10 ttt kg-t

Solution ft/ass of mobile phone

--75 g=75 x

l0{

kg =

0.075

kg

rFigure 4.6 Most common laboratory instruments for measuring mass actually measure weight, but are calibrated to give the readings in mass e.g. the electronic balance with digital read-outs

Weight of mobile phone = mass of mobile phone x g = 0.075 kg x 10 N kg-t - 0.75 N

What do common weighing instruments measure? Common weighing instruments like the electronic balance, spring

balance and bathroom scales actually measure the weight of an object, and not its mass. These machines, however, are calibrated to give readings in grams (g) or kilograms (kg). This means that an object will have different mass readings for different gravitational field strengths. For example, if an astronaut steps on a bathroom scale on the Moon, the reading will be lower than that taken on Earth. This is because the gravitational field strength on the Moon, 1.6 N kg-t, is less. From this, we can see that a weighing scale calibrated for use on Earth cannot be used on the Moon. A different weighing scale calibrated to suit the Moon's gravitational field strength will have to be used. This weighing scale will then give accurate mass measurements on the Moon.

fi/ass: 70 kg

l\4ass:

g: 10 N kg-l

g:

Weight:700

kg

kg I t2

N

)

'

N

The same weighing scale on the Moon will however register 11.2 kg. This is because the weighing scale is not calibrated for use on the Moon.

A weighing scale on Earth registers 70 kg.

Earth

70

1.6 N

Moon

r,Figure 4,7 The lastest way to lose weight!

General Physics

7l

How is mass measured? To avoid the hassle of using different weighing scales for different gravitational field strengths, the mass of an object can be measured easily using the beam balance. Figure Ll7 Determining the p- Y relationship of a gas at constant temperature

synnge arr

piston

As the gas is compressed, you can observe from the pressure gauge

that the pressure increases. This tells us that when the volume of a gas is decreased, its pressure will increase. 162

finetic

tvtoOel

of Matter

In general, the pressure of a fixed mass of gas, p, is inversely proportional to the volume of the gas, V, when the temperature is held constant. In symbols, we can express this as I Dq.,v

or

k P

whereftisaconstant

V

From the above, we derive the relationship pV= k. This is useful when the pressure or volume of a gas at constant temperature changes: p, lz, = pzv2, where p1, pra,re the initial and final pressures respectively,

and 4, Vrare the initial and final volumes respectively. When a graph of p against I/is plotted, the result is a smooth curve as in Figure 9.18. However, if p is plotted against

1

,a

straight line

is obtained (Figure 9.19). p

p

lEIGhlot=t Another possible way of *=-nr* lhe p-V relationship of a gas by using a graph is shown in Figure 9.20 below. I, and I, are the fixed temperatures of a fixed mass of gas in two different containers.

pV

V

rFigure

vs t/is

9.18 Graph of p

a

V

rFigure

9.19 Graph of

f

vs

straight line

smooth curve

f

is

a

T2

T1

p

We can use the kinetic model of gases to explain the inverse relationship between pressure and volume. When we halve the volume of the container, the number of molecules per unit volume will be doubled. This would mean that the frequency of collisions of the molecules with the walls will also be doubled. Hence, the pressure will double. In fact, if we reduce the volume to one.third of its original volume, the pressure will be three times the initial pressure. Thus, we see that the pressurep is inversely proportional to volume 7.

7,,

T,

rFigure

9.20

I molecules exert pressure as they bounce off the walls of the container

C

,,,?

Or,,

I

o =

,,? eo'

rrt(F

ee,

e =-

I ,,? Olr ,ro

6.rr

ae.

external pressure dou bled

rFigure 9.21 Kinetic model of gases can be used to explain why the pressure of a gas is inversely proportionalto volume.

ThermalPhysics

165

WORKED EXAMPLE 9.2 A sample of gas is contained in a cylinder enclosed by a piston as shown in Figure 9.22. The pressure of the gas can be raised by slowly moving the piston

to compress the gas into a smaller volume without raising the temperature of the gas (Figure 9.23). gas prston

ffi cylinder

rFigure

(a)

9.22

rFigure

9.23

Explain in molecular terms why the pressure of the compressed gas is

greater after compression.

(b)

The gas in the cylinder in Figure 9.22 can also have its pressure raised

by keeping the piston fixed and heating the cylinder, as shown in Figure 9.24. Explain in molecular terms why the pressure of the gas rises as it is heated.

Heat

Solution rFigure

9.24

(a)

As

the gas is compressed, the frequenry of collisions of the gas molecules

with the walls is increased due to the smaller volume of space. This

lEiGiltot=r

causes the increase in pressure of the gas.

(b)

From Worked Example 9.2, we can see that there are d 'ew ways to increase the pressure of a gas: Reduce the volume of the container

molecules will lead

.

to

.

collisions of the gas molecules with the container walls. lncrease the temperature of the gas by heating to enable the gas

hitting the container wall more frequently and with more force.

lnject more gas molecules, keeping the volume constant. N,4ore gas'nolecules per unit volume will increase the frequency of collisions

164

to higher frequency of collisions with the walls as

well as greater impact on the walls. Both these factors contribute to the increase in pressure of the gas.

increase the frequency of

ldeas

molecules to move faster, thereby

.

Heating increases the average kinetic energy of the gas molecules which leads to the increase in the average molecular speed. Faster moving

finetic rUoAel of l/atter

l. 2.

Pressure in gases is due to the collision of molecules with the walls of the container. Using the kinetic model of gases, we can explain that

(a)

the pressure of a fixed mass of gas, p, is directly proportional to its temperature f if its volume is constant.

(b)

the volume t/ of the gas increases proportionally with the increase in temperature f while pressure remains constant.

(c)

the pressure of a fixed mass of gas,p, is inversely proportionalto the volume of the gas, t/, when the temperature f is held constant.

Test Yourself 9.2

ffiilFl?fif'Ii€

Concept Map

ry

consists of

J Brownian motion obserued in liquids or gases

Tiny particles (atoms or molecules)

in continuout random motion

Solids

.

. .

closely packed atoms

or molecules

strongintermolecular bonds atoms or molecules vibrate about fixed positions

Liquids . atoms or molecules occur in

. .

clusters

Gases

.

slightlyfurtherapartcompared

.

to solids free to move about between

.

clusters

atoms or molecules are very far apart negligible attractive forces high speed, independent

J ='

and random motion

t=!'.

betvveen atoms or molecules

occuPres

can exert

J

J

Volume

rD

(1

o = og-

o +r

Pressure due to gas molecules bombarding the walls of the containers

p"f, o,

OJ = ?rF

r+

pY = constant

(D

(at constant 7)

-

ThermalPhysia

165

5.

Practice Questions

A B C D

Section A Multiple-Choice Questions I How does the motion of liquid molecules differ from that of gas molecules?

molecules

Liquid vibrate about mean positions

A

their

B C

Oos molecules vibrate randomly

6.

randomly vibrate energetically rotate and vibrate vibrate randomly randomly and energetically D move randomly move randomly

A gas is heated in a sealed container of constant volume. Which of the following will not increase? The average speed of the molecules. The pressure of the gas. The number of molecules per unit volume. The temperature of the gas.

move

filled with air and tightly stoppered at room temperature. The flask is then placed in melting ice. The flask stays the same size. A flask is

melting ice

at high speeds

2.

+

Which of the following statements is correct for Brownian motion? lt applies strictly to gases only. Smoke particles in air in a Brownian motion

A B

experiment can be observed to dance in

C D 5.

a

regular, predictable fashion. Smoke particles will be observed to slow down if the air temperature drops.

eFigure 9.25

The motion of smoke particles in air is due to the smoke particles colliding with each other.

ln the flask, what happens to the pressure of the air and the speed of the air molecules?

According

to the kinetic molecular theory, the

A B C D

pressure exerted by a gas is caused by the gas molecules colliding with each other at high

A

B C D 4.

speeds.

bombardment of the gas molecules on the walls of the container. random motion of the gas molecules. gas molecules being very far apart from each other.

7.

Frequency of collisions with wolls

Averoge distonce

increases increases

decreases

c

rncreases increases increases

unchanged

unchanged unchanged

D

unchanged

increases

increases

Averoge

speed A B

Speed of molecules increases increases decreases decreases

When a gas of fixed mass is heated under constant Pressure,

I ll

the average speed of the gas molecules

lll

the average separation of the gas molecules

A fixed mass of gas is heated while being kept at

constant volume. How do the propertres of the molecules of the gas change?

Pressure decreases increases decreases increases

the volume of the gas increases. increases. increases.

A C

I only

ll and lll only

B D

ll only l, ll and lll

oport

Section B Structured Questions t. (a) Describe the motion of molecules

(b)

(c)

in the solid, liquid and gaseous states. State the relative strengh of intermolecular forces in the three states of matter.

How do the above two characteristics,

i.e.

motion of molecules and stren$h of molecular forces, affect the shapes and volumes of solids, liquids and gases?

166

finetic

tvtoOel

of Matter

2.

Using a microscope, smoke particles can be seen moving inside a glass tube. They appear as tiny spots of light that move in various directions. The air molecules inside the glass tube cannot be seen with the aid of the microscope. The apparatus is illustrated in Figure 9.26.

A-

4.

(a)

What is seen moving when Brownian motion

(b)

Why is a microscope necessary in order to

is observed?

observe Brownian motion?

(c)

Explain how Brownian motion provides evidence for the kinetic molecular model of matter.

eye

5. mrcr0sc0pe

Figure 9.29 is a diagram of a bicycle pump.

handle

oiled leather washer

Figure 10.26 Convection currents in refrigerators

v7

\

n

cool

air

!!

Common applications of radiation a

1. Teapots Since shiny surfaces are bad emitters of radiation, shiny teapots can keep tea warm for a longer time than black teapots. In addition, since shiny surfaces are bad absorbers of radiation, shiny containers can

O

keep cold liquids cool for a longer time than black containers.

r Figure

10.27 Shiny teapot

2. Greenhouses A greenhouse is used in cold climates to help plants grow better by trapping heat. During the day, infrared radiation from the Sun passes through the glass roof of the greenhouse. This warms up the soil and plants in the greenhouse. As the contents in the greenhouse get warm, they start to emit infrared radiation. The infrared radiation emitted by the contents in the greenhouse is slightly different compared to the infrared radiation emitted by the Sun and is unable to pass through the glass roof. Therefore, the infrared radiation emitted by the contents in the greenhouse gets trapped. The amount of infrared radiation in the greenhouse gets built up over time. This causes the temperature in the greenhouse to increase. glass roof infrared radiation from the Sun

lass sides g

>Figure 10.28 A greenhouse

182

transfer of Thermal Energy

3. Vacuum flasks The vacuum flask (or thermos flask) is designed to keep liquids hot by minimising heat loss in four possible ways, namely conduction, convection, radiation and evaporation.

The stopper is usually made of plastic which is a poor conductor of heat.

hollow plastic stopper

Conduction through the trapped air above the liquid is minimal since air is a very poor conductor of heat.

trapped air

Conduction and convection through the sides ofthe flask a re prevented by the va cu um between the double-glass

vacuum

double-walled glass bottle

walls of the f lask.

To minimise heat loss th rough radiation, the wa lls of the

lass a re silvered so as to reflect the radia nt heat ba c k into the hot liquid. Convection and evaporation can only occur when the plastic stopper is removed during use. Heat loss by radiation is harder to stop as radiant heat can pass through a vacuum. g

thin silvered walls of glass

hot liquid

outer case

cork to hold flask in place

rFigure

10.29

WORKED EXAMPLE 1O.1 Two horizontal plates of the same area are separated by a distance one above the other and enclose a layer of water between them (Figure 1 0.30). The upper plate is maintained at temperature Ar and the lower plate at temperature Explain the primary modes of thermal energy transfer when 0, 0,.

02.

)

upper p late at

01

lower plate at 0, r,Figure 10.30

Solution When 0,

)

0,, the primary mode of thermal energytransfer is convection. When

the lower layers of water are heated, they expand, become less dense and rise. This results in cooler upper layers descending to take their place. Thus, for

convection to come into play significantly, the lower plate must be at a higher temperature than the upper plate. Conduction does play a part in transferring energy through water, but water is known to be a poor conductor.

Thermal Physics

185

WORKED EXAMPLE 1O.2 Figure I0.31 shows a typical vacuum flask designed to keep liquids hot Part

c

of the vacuum flask is enlarged. State and explain the function of each of the

pars labelled A to

C.

Solution A

rFigure

10.31

A: Thin silvering wall to minimise thermal energy loss by radiation since B:

shiny surfaces are poor absorbers of radiant heat. Vacuum to prevent thermal energy loss by conduction and convection since both these processes require a material medium forthermalenergy transfer.

C:

Hollow plastic stopper to minimise thermal energy loss by conduction since plastic is a poor conductor of heat. When in place, the stopper also prevents thermal energy loss by convection and evaporation.

IfiFil: ELF.Grrr How do penguins keep warm? The dense feathers on the penguins trap a lot of air in between them. Together with the thick layers of fat under the skin, they provide good thermal insulation which allows the penguins to withstand temperatures below -40 "C. ln addition, penguins huddle close together, sometimes in packs of thousands, to protect themselves from the cold. Huddling reduces the surface area of the body exposed to the extremely cold weather and this reduces heat loss through conduction and convection. At the same time, loss of heat through radiation is also reduced. Every so often, penguins shift position to allow those who have been on the edges to warm themselves up in the centre of the group. Penguins are indeed considerate creaturesl

.rnflrfi?+Trm€ 184

Transfer of Thermal Energy

Conce tMa Transfer of Thermal Energy

-{

by the processes of

OJ

i

J

C,onvection by means of

Conduction by either molecular

currents in the medium

vibration orfree electron difhrsion

(iquid or gas)

in solids

vt +r rD

Radiation by the emission of infrared radiation

-t

o -.+r -{ J

rD .t

leading to

3

J Everydayapplications such

as cooking

OJ

m

utensig heat exchanges,

cavity wal I i nsulation, household hot water systems, ref rigerators,

J -l

rD

vacuum flask, etc.

oq

5.

Practice Questions Section A Multiple-Choice Questions t. According to the simple kinetic theory, how

energy transfer by radiation only.

A B C D

is

thermal energy transfened from the hot end of a glass rod to the cold end? The molecules from the hot end move to the cold end. vibrate more and pass on the energy to the neighbouring molecules. send out infrared radiation to the cold end. move from place to place, collide with the colder molecules and transfer the energy to them.

A B

C D 2.

ln a vacuum flask, the vacuum prevents thermal

4.

conduction only. convection only. conduction and convection.

ln the following experimental setup, equalvolumes

of hot water were poured into the containers and the temperatures of both containers and contents were the same. After an hour, the temperature of container P was found to be lower than that of container Q.

ln a hot water tank, the heating element should be placed at the bottom because conduction cannot take place when the heater is at the top of the tank. the heated waterwill rise and form a convection

A

B

C D

current.

0

P

radiant heat travels faster in the upward direction.

e,Figure 10,32

the heater must be covered by water at all

This shows that P is a better

times.

than

of heat

Q.

A conductor B C radiator D

absorber conductor and radiator IhermalPhysics

185

5.

A heated body is allowed to cool in air. Which of

3.

the following statements is incorrect? The processes of convection, conduction and radiation are in operation. Loss of heat by conduction through the air is

A

Figure 10.34 shows an electric kettle used to heat water to its boiling point. warmed air and evaporated water rise from spout

B

C D

inefficient because air is a bad conductor.

Loss of heat at moderate temperatures under ordinary conditions is mainly through

thermal energy conducted through the plastic

convection. Loss of heatthrough radiation is most effective for small temperature excesses.

t

The temperature

-10'C to 0 oC as

Thetemperature remains steady at 0 "C as the ice melts. This is shown on the curve bythe plateau

shown bythe portion

or straight line portion

of the solid ice on heating rises from

s

water (liquid)

P0 of this curve.

0R. This happens in spite

There is a change

of thermal energy being

in temperature.

When allthe ice has melted, the temperature of the liquid water rises from 0 'C to 20 'C as shown by the portion RS of this curve. As in the case

of the solid ice, there is

a

change in temperature.

absorbed. There is no change in temperature.

Based on Experiment I 1.3,we can make the following observations. rFigure

11.9

l. 2.

196

fnermal Properties of Matter

The melting point of ice is 0 "C since this is the constant temperature at which ice melts to become water. During the change of state from ice to water, there is no change in temperature even though thermal energy is being absorbed.

Where has the thermal energy supplied as indicated by the straight line QR in Figure 11.8 gone to? This can be explained by using the

kinetic model of matter as shown in Figure 11.10. molec ules

thermal energy a

bsorbed

eFigure 11.10 Melting in action

How does a solid melt? The molecules in a solid are held by strong intermolecular bonds. For the solid to melt, these bonds have to be broken. Since energy is needed to break the intermolecular bonds, the thermal energy supplied at section QR of the curve is used to do work to break the intermolecular bonds between the molecules of the solid. Once the intermolecular bonds are broken, the molecules can now

move out of their fixed positions. We say the solid has melted, that is, the change of state from solid to liquid has occurred. This explains why there is no change in temperature during melting. The thermal energythat is absorbed without a change in temperature is called the latent heat of fusion of a substance. Latent heat means

hidden heat. It will be discussed in greater detail in Section I1.5. The temperature of a pure substance only changes upon heating when there is no change of state. You can observe this when solid ice is heated from -10 'C to 0 "C, and when liquid water is heated from 0 "C to 20'C.

Solidification and freezing point The reverse process of melting is called solidification-changing from a liquid to a solid. A pure substance will solidify or freeze at a temperature equal to its melting point. For example, water freezes to form ice at 0 'C. We call this temperature of 0 'C the freezing point of water. Experiment 11.4 shows how to obtain the freezing point of a substance by using a cooling curve.

Figure 11.29

cold water

On Figure I 1.28, draw the variation with time of the temperature of the wax in this second experiment. You may assume that the heat

needed to warm up the test-tube itself

Pure steam enters at I00 "C and the jug initially contains 500 g of water at 20 "C. Eventually, the water in the jug reaches a temperature of I OO 'C. The specific heat capacity of water is 4.20 J g-t o6-t

is

negligible.

(Decee/P2/QB)

5.

and the specific latent heat of vaporisation of water

Some details about nitrogen are given in the table below. Melting point

c

Figure I 1.29 shows steam passing into a jug to warm up some cold water. ln this question, you

is 2250 J g-'.

(a)

Specific heat Specific latent heat of Boiling point capacity of liquid vaporisation J g-t 'g-t c Jg'

(b)

State what is meant by the specific latent heat of vaporisation of water.

Explain why the mass of water in the jug increases.

-210 -r 95

(a)

At

1.4

200

(c) (d)

-209 'C, will nitrogen be a solid, a liquid or

a gas?

(b)

Define what is meant by specific heot copooty.

(c)

Using data from the table, showthat less energy

warm liquid nitrogen from -21O "C 'C than is needed to boil it.

is needed to

to

-.l95

(Deco2/P2/Q6)

6.

(Dec00/P2lQs)

8.

This question is about the rate of evaporation from a pool of water.

(a) Complete the table below by entering 'increases' or 'decreases' or 'no effect', as appropriate, in each of the empty boxes of the

Lemonade can be cooled by adding lumps of ice to it. A student discovers that 70 g of ice at a temperature of 0.0 "C cools 0.30 kg of lemonade from 28 'C to 7 'C. The latent heat of fusion of ice is 0.33 tMJ kg-r. The specific heat capacity of water is

Calculate the energy needed to warm 500 g of water from 20 'C to 100 "C. Calculate the final mass of water in the jug when its temperature has reached 100 'C.

second row. Temperature of water

Surface area of water

Wind speed over water

increases

increases

increases

4.2lJ kg-t ;1-r.

Determine (a) the energy gained by the ice in melting, (b) the energy gained by the mehed ice, (c) the energy lost by the lemonade, and (d) a value for the specific heat capacity of the lemonade.

(June5/P2/Qt)

Effect of each increase on rate of evaporation from the pool of water

(b)

State your reasons for your answer to (a).

(Dece6/P2/Qs)

ThermalPhysics

215

9.

Figure I L30 shows the apparatus used by a student

to measure the specific latent heat of vaporisation of water. A heater is placed into a beaker of water which stands on top of electronic weighing scales so that the mass of the beaker and water may be measured.

(a) (b)

Define what is meant by the specific lotent heot of voporisotion of water. As soon as the water is boiling, the student notes down the reading on the scales and starts a timer. Every 100 seconds the student notes

down the reading on the scales. The results obtained are shown in the table.

Time/s 0 Reading

scale/g

()

203.22

100 2OO 300 199.79

r

98.2

400 196.s0

Draw up a table to show the total mass of water evaporated after 100 s, 2OO s,

300 s and 400 s. That 0 to 200 s and so on.

is,

from 0 to

I OO s,

(ii)

(c) (d) (e)

The heater supplies energy at the rate of 58 J s-'. Add to your table values showing the energy provided by the heater in 100 q 200 s, 300 s and 400 s. That is, from 0 to 100 s, O to 200 s and so on. Plot a graph of energy supplied (y-axis) against mass of water evaporated (x-axis). Start your axes at (0,0). Determine the gradient of your graph. How is the specific latent heat of vaporisation of water related to this gradient? The voltage of the power supply connected to the heater is doubled. Describe and explain the effect this has on the readings obtained, and on the final result. power supply

insulation heater

water

beaker electronic ing scal e

rFigure 11.30

(Junee/P2lQe)

rrrrtflnil!ilImo 214

trermat Properties of Matter

FTY

i Civil Defence

Force

At the same time, as the mist vaporises to

years has employed

become steam, its volume expands (by at least

to extinguish fires more quickly

1600 times!) and displaces the air from the

and with little damage to property. How are water

surroundings. This deprives the fire of the oxygen

mists able to extinguish fire more effectively than

it

guns

needs to continue burning.

conventional jets of water? What is the Physics behind it?

During tests conducted by the SCDF, a fire the size of a three-room

H

DB flat can be put out with

We know water mist consists of many tiny water

just 36 litres of water in less than three minutes.

droplets. With the volume of water fixed, the combined exposed surface area of the droplets is much larger than the exposed surface area of a jet of water. Therefore, in a fire, the water mists will vaporise much faster than jets of water. With faster vaporisation (i.e. latent heat of vaporisation), more thermal energy from the fire can be removed effectively, helping to put out the fire faster.

Whereas conventional water jets require 3600 litres of water and at least 10-15 minutes to put out the

fire! Also, water mists are able to absorb

the toxic gases released when household materials burn; thus protecting the victims. Since less water

is used in this method of fire extinguishing, not only is water saved, the amount of property damaged is also minimised

(like furniture

and

home electrical appliances), thereby facilitating

fire investigation later

on. ThermalPhysks

215

This art exhibit in Europe ls actually apublic toilet one-way mirrors. You can look out while uslng remain invisible to passereby. How is this poseible? secret behind one-way mirrons? You

will find out in

!-{;.

l"' i

--"'-.-.

**t

,-h:==

12.1 What is Light? Learning Outcome You'll be able to:

I

understand how light travels and how we are able to see

LEb.rtl Look through a straw with one eye. You should be able to see objects that are in line with the opening of the straw. eye

4

Light is a form of energy. We are able to see everything around us because of light-from watching TV to taking photographs to playing sports!Without light, our world would be in total darkness and we would practically be blind. Our eyes detect light in a range of colours-red, orange, yellow, green, blue, indigo and violet. To a scientist, these seven colours form a spectrum, while to a layman they are commonly known as the colours of the rainbow. When these seven colours are mixed, they form white light.

straw

pencil

rFigure

12.1

Flex or bend the straw slightly whrle looking through it. Are you still able to see objects that were in line with the opening of the straw? No, you would not, as light entering the straw does not bend. What does this tell you? Light travels in straight lines!

,..A

avi

#

.lfi$.h:-r 1,.'.

Also, light travels at an amazing speed of 3.0 x 108 m s-r in vacuum. At this speed, it is possible for light to circle the Earth more than seven times in just one second!

How does light travel? Light travels in straight lines. The Try It Out!on the right will help you determine that. Can we then trace the path of light? Yes, we can.

In Figure 12.2,light from the torch is traced by drawing straight lines to join one point to another. Arrows are added to indicate the direction in which light travels. Such lines are called light rays. A beam of light is actually a bundle of light rays

light ray

A beam of light is made up of a bundle of light rays

rFigure

12.2 Light rays shining f rom

torch travel in straight lines. There are three types of light beams: parallel, convergent and divergent. So, what type of beam does a torch produce? a

Light, Waves and 5ound

217

(luminous object)

light from the lamp

1

I reflected light from the picture

4

picture on the wall (non-luminous oblect)

What are luminous and non-luminous objects? Not all objects give off light of their own. Objects that give off light are known as luminous objects. We are able to see such objects directly, e.g. the images on a TV screen. Objects that do not give off light are known as non-luminous objects. We are only able to see such objects if there is a light source or luminous object nearby.

How do we see? We are able to see when light rays enter our eyes. Figure 12.3 shows how our eyes see a lighted Iamp (a luminous object) and a picture

(a nonJuminous object). In this case, we are able to see a nonluminous object when light from the nearby luminous object is reflected off the nonJuminous object.

This phenomenon tells us that light can be reflected. This is an important characteristic of light which we will be studying in the next section.

Key ldeas

I. 2.

Light is a form of energy. Light travels in straight lines called rays.

Test Yourself 12.1

l.

A student drew rays on the picture in Figure 12.4 to show how the eye sees the apple. Explain why the light rays are drawn incorrectly.

rFigure

218

Liqht

12.4

12.2 Reflection of Light Learning Outcomes

What are the laws of reflection? We can set up the following experiment to help us find out more about the reflection of light.

EXPERIMENT 12.1 Objective To illustrate the laws of reflection

Apparatus ray box, plane

minol protractor, piece of paper

Procedure

I. 2.

Set up the apparatus as shown in Figure 12.5. Vary the angle of incidence

i and measure the corresponding angle

of reflection r.

3.

Compare the values of i and r. Are they equal?

|ELGNota!

oint of incidence mtrr0r

lncident ray: Light ray hitting the reflecting surface.

r reflected

Point of incidence: The point on the reflecting surface where the light

incident ray

ray hits.

Normal: The perpendicular to the reflecting surface at the point of incidence. normal

rFigure

ray box

12.5

Results

l. 2.

lt is observed that for each angle of incidence r, the corresponding value of angle of reflection r is the same. lt can also be observed that the incident ray, reflected ray and the normal at the point of incidence all lie in the same plane (i.e. a flat

Reflected ray: Light ray reflected from the reflecting surface.

Angle of incidence i: The angle between the incident ray and the normal.

Angle

of reflection r:

The angle

between the reflected ray and the normal.

surface). Light, Waves and SounO

219

From the results of the experiment, the two laws of reflection are as follows:

First Law of Reflection The incident ray, reflected ray and the normal to the reflecting surface all lie in the same plane. Second

law of Reflection

The angle of incidence is equalto the angle of reflection (i.e.

i=

7).

Types of reflection-regular and irregular Is it true that only smooth and shiny surfaces like mirrors reflect light? How about dull surfaces like the palms of our hands? Do they reflect light too?

All surfaces reflect light. The difference lies in how smooth the surfaces are. The smoothness of a surface

will affect how light is reflected. 12.6 Pages of this textbook may ^Figure seem smooth. but don't be fooled! lf you look under the microscope, the surface

>Figure 12.7 Why does a shoe shine after polishing? What happened during pollshing that made it shine?

is very irregular!

vTable 12.1 Characteristics of the two types of reflection

Type of reflection

(a)

Regular reflection

-

occurs at smooth surfaces e.g. mirrors, polished metals incident

rays

Parallel light rays incident on the surface are reflected in one direction only (i.e. all rays have

the same incident and reflected angles).

reflected rays

(b)

For such surfaces, the normals at all points of

incidence are parallel.

smooth surface

2

lrregular reflection occurs at rough surfaces e.g. sandpaper,

(a)

-

cloth incident

reflected angles of each ray are different from

rays

those of another ray).

reflected rays

(b)

rough surface

220

Liqht

Parallel light rays incident on the surface are reflected in all directions (i.e. the incident and

For such surfaces, the normals at all points of incidence are not parallel.

WORKED EXAMPLE 12.1 Figure l2.B shows a ray of light incident on a mirror.

(a) (b) (c) (d)

State the two laws of reflection.

Complete the diagram to show the reflected ray What is the angle of incidence? What is the angle of reflection? rFigure

Solution

(a)

12.8

The two laws of reflection are:

(D

The incident ray, reflected ray and the normal at the point of incidence all lie in the same plane.

(ii)

The angle of incidence is equal to the angle of reflection.

(b) The reflected ray is shown in Figure 12.9. (c) Angle of incidence i = 90o - 50" = 40". (d) Using the second law of reflection, angle of reflection

r r = i = 40".

r

Figure 12.9

WORKED EXAMPLE 12.2 Figure 12.'10 shows a ray of light P striking D

a mirror AB. The mirror AB and the mirror CD make an angle of I20" with each other. Continue the ray

P

to show the path it takes

P

after reflection at both mirrors.

(a) (b)

1200

Find the angle of incidence at AB.

c A

Find the angle of reflection at CD.

B

rFigure

12.10

Solution

(a) Angle of incidence at AB, i = 90o (b) o=l8o'-4ABD-20" = lB0o - 12Oo -20" = 40o

:. ir=99" = 90o -

g

20" =7O"

P

40o

= 50o Hence, 12=i2=50"

C

A

0

rFigure

l2.ll

WORKED EXAMPLE 12.3 140 cm

A lizard (Figure 12.12) is slowly

A

ceili

moving along the ceiling of a room

and stops at position L. Find the distance AL such that it can be seen

50 cm

lizard 120 cm

B

by the eye in the mirror.

eye

eFigure 12.12 Light, Waves and Sound

221

What kind of image is formed in a mlrror? Hold up a piece of paper with the word 'Physics'written on it, and stand in front of a full-lengh mirror. You can see that

your image formed by the mirror is upright. Your image is also the same slze as you.

TheTry It Outlon the left and F.:rperiment 12.2 will help you detdrmine the characteristics of an image formed by a plane mirror.

E)(PERIMENT 12.2

Can you read the word 'Physics' correctly? You will notice that the word has undergone a left+oright inversion, or a lateral inversion.

Objectrve To find the characteristics and position of an image formed by a plane mtrror

Apparatr-ts plane minor, three pins, graph paper, wooden holder

Proceclure

l. 2. 3.

Set up the apparatus as shown in Figure 12.14. Observe the images formed.

d, and d, by counting the number of squares between the pins and the mirror surface, and between the image and the mirror surface. Compare these two distances. What can you Find the distances

conclude?

2lD

ugrt

Results

l.

mirror

The following observations were made regarding the mirror image. The image is:

(a) (b) (c) (d)

2.

same size as the object laterally inverted \t)

upright

\rf

virtual

The distances d, and d, are equal. We can conclude that the distance of the image from the mirror is equal to the distance of the object

softboard

from the mirror"

graph pa per

r,Figure 12.14

From the experiment and Try It Out!, the characteristics of a mirror image are as follows: Characteristics of a plane mirror image:

t. 2, 5. 4. 5.

lt is of the same size as the object. lt undergoes lateral inversion. It is upright. lt is virtual. The distance of the image from the minor is equal to the distance of the object from the mirror.

lELEhote! virtual image is an image that cannot be projected or captured on a screen. It is produced by rays which seem to come from the image but do not actually pass through it. A

A real image, on the other hand,

is

an image that can be captured on a screen (e.9. the pictures you see in a movie theatre). The rays for real images

you see come directly from the picture captured on the screen.

WORKED EXAMPLE 12.4 (a) There are 9 letters in the word SINCAPORE.

(D

Hold the word up and stand in front of a mirror. Write down the appearance of these letters in the boxes provided when the word is reflected by the mirror.

(iD

How many of these letters appear to be different when the word is reflected?

(iii)

(b)

Write down the letters that appear to be the same.

A driver of car A looked at his rear-view mirror and saw another car B (Figure 12..l5) behind him. lf the registration number of the car B is SDE 789H, as shown in Figure I 2.1 5, write down the registration number of car B, as seen by the driver of car A in the rear-view mirror.

rFigure

12.15

EEil (a)

(i)

f (ii)

FI

6

o q

(iii) o, A,

o n

?

I

(b) HeB\ raz Light, Wavesand Sound

225

r--qz-=ta il!ffininct Front-to-back lnversion Apart from lateral inversion, there is another perspective to describe the image formed by a plane mirror, known

ldeas

l.

The two laws of reflection are: (a) The incident ray, reflected ray and the normal at the point of incidence all lie in the same plane.

as f ront-to-bo ck i nve rsi on.

lmagine yourself standing in front of a mirror. Now, with your right hand, point towards the right, You will find that your

(b) The angle of incidence is equal to the angle of reflection

2.

image also points to the right, Next, point towards the left. What does your image do? lt also points towards the left. Now, point your finger at your image. Your image points back atyou, opposite to the direction you are pointing atl This

phenomenon is known as front-to,back inversio n.

(i.e. 4i = 4r). The image formed by a plane mirror is: same size as the object, inverted laterally, upright, virtual and the distance of image from the mirror is equal to the distance of the object from the mirror.

Test Yourself 12.2

t. 2.

Draw a diagram to show clearly the incident ray, normal, reflected ray, angle of incidence and angle of reflection. What is the relationship betuveen the angle of incidence and the angle of reflection? What are the characteristics of an image formed in a plane mirror?

12.3 Constructing Ray Diagrams Learning Outcome rFigure

12.16 When you look into a mirror, do you see your front or your

You'll be able to:

M

back? You only see your front. This is because the image has been inverted

front-to-

ba c k.

Ray diagrams for plane mirrors

N/

o

point object 0

rFigure

12.17

o

@

I\il

0

I

.--ll----ll 1

-{

You have learnt that the distance of a mirror image behind the mirror is equal to the distance of the object in front of the mirror. We will use this principle to locate the position

of the image behind the mirror (Figure 12.18).

O

Oi

A rFigure

Lisht

We have learnt earlier that mirror images are virtual images that cannot be captured on a screen. However, by drawing ray diagrams, it is possible for us to locate the position of a mirror image. Figure 12.17 shows a point object O in front of a plane mirror M. The point object O is represented by a dot, while the mirror is represented by a straight line, with shading to show its silvered back.

A

224

apply the principle of reflection in constructions, measurements and calcu lations

12.18

O

Measure accurately the perpendicular distance between object O and the mirror surface. Mark off the same distance behind the mirror to Iocate the image l.

@

M

-ll- - {

Join the image I to the eye by drawing straight lines as shown (Figure 12.19).

O O

Use dotted lines for the lines that are behind the mirror surface. We use dotted lines to indicate that the rays coming from behind the mirror are virtual. Use bold lines for the lines that are in front of the mirror surface. We use bold lines to indicate that the rays reflected off the mirror surface are real.

Figure 12.45

.+ 1.0 m

Solution

Civen:

tan0=f 2

.'.0 =26.6" Hence,i =90o -0=63.4" Using Snell's law sin r

sirlql4' - g!1n 1.33

r = 42.2o

tanr=!9 d

rhererors

'l-1i'; d*F rl

depth of

pool d=

1.0 m

?

n = 1.33

2.0 m

ld I

.H

1.0 m

rtigure l2.tl5 rod

light rays as seen by the

Daily phenomena and applications of refraction 'Bent'objects

liquid

We now know that refraction causes the 'bending' effect of objects

placed in another optical media (e.9. a rod in water). From Figure 12.47 we can see that light rays travelling from water to air bend away from the normal. However, as our brain tells us that light rays travel in straight lines (i.e. the dotted lines), we end up seeing the rod as'bent'.

path of light rays a

rFigure

12.41 Ray diagram of the 'bent'

image of a rod in a glass of water

Light, Waves and Sound

255

Misperception of depth

As shown in Figure 12.48, the effect of refraction can make swimming pool seem shallower than it really is.

a

light ray seen the eye

apparent depth

real depth

water actual path of

light ray

o rFigure 12.{8 a point

Ray diagram of the image I of

0 at the bottom of a swimming pool

The archer fish's secret

Found in the waters of Singapore, the archer fish shoots a jet of water with pinpoint accuracy knocking its prey off a branch. How is it able to overcome the visual distortion caused by refraction?

tFigure 12.49 A bear instinctively overcomes visual distortion and succeeds in catching its prey.

One way the archer fish could overcome this visual distortion is by positioning itself under the prey. This way the prey as seen by the fish is less distorted, as light rays entering the water surface perpendicularly are not refracted. This would help the fish overcome refraction and aim like a marksman!ln a similar manner, bears catch fish by overcoming visual distortion. In this case, the bear accurately

judges the position of the fish swimming underwater, and is able to catch it (Figure 12.49). News reader prompter Have you ever wondered how a news reader is able to read the script and yet maintain eye contact with the camera lens? The news reader reads the script off a partially reflected image, which is formed on a one-way mirror. The camera is positioned behind the mirror, and therefore, the newsreader appears to maintain eye contact with the camera lens.

236

Lisht

4*

WORKED EXAMPLE 12.12 A thin rod is placed in a beaker of water, as shown in Figure

.l2.50.

Calculate the values of 0 and x. rod

Solution Using Snell's Law and the principle of reversibility of light, x B A ._ stn0

"-

sln

10.0 cm

3OP

sin 0 = 1.33 sin 30'

0 =41 .7" tan

io.= x

10.0 cm

r#

= 10.0 tan = 5.77 cm

30'

water of ref ractive index n = 1.33

300

(q)

ll!ll

urand )",> 7r.

rFigure 13,24 lf you place a plastic sheet at an angle, the change in speed of the waves will cause them to bend. Light,Waves and Sound

275

Reflection of waves Figure 13.25 shows how reflection of waves can be demonstrated. A straight barrier standing upright in the water causes the incoming incident waves to be reflected. v Figure 13.25 A straight barrier is placed at an angle to the straight dipper You can see the waves reflecting at equal angles to the normal (4i= 4r) in the inset.

incident wavefronts

straight barrier straight barrier incident

water WAVES

-2-.- -- ^ a-*"-"--

normal

reflected water waves

reflected wavefronts

ns How do tsunamis originate? Tsunamis have been in the news for the terrible devastation they cause to Lives and

property They are essentally waves with high amplitudes and long wavelenghs. They usually originate fronr earthquakes or landslides. Earthquakes occurrrng on the sea floor displace a huge amount of water frorn its rest positon Thts water will try to regain its equilibrium and, in the process, waves are formed. These waves travel at incredible speeds towards land, and possess tremendous amounts of energy. By the time they reach the shore, they can reach heights of up to severa metres and speeds approaching that of a 1et planel ALI this energy enables thern to wreak havoc on the shore (Frgure 13.26)

Ke

Ideas

The following terms are used to describe wave motion:

l. 2. r,Figure 13.26

5. 4. 276

wares

Crests and troughs:These are the high points and low points that characterise transverse waves only. For longitudinal waves, the terms compressions and rarefactions are used.

Amplitude (A):The amplitude of one oscillation is the amplitude of the wave. lt is half the vertical distance between a wave crest and a wave trough. lts Sl unit is the metre (m). Wavelength (i): This is the shortest distance between any two points (such as two successive crests or troughs) on a wave that are in phase. lts Sl unit is the metre (m). Period (I): The period of one oscillation is the period of one wave. lt is the time taken for a wave crest to move through a distance equal to its wavelengh.

5.

Frequency f): This is the number of complete waves produced per second. lts Sl unit is the Hertz (Hz). Frequency and period are related by the equation:

6. 7.

Test Yourself

l. 2. 3. 4.

I=t

Wave speed (u): This is the distance travelled by a wave in one second. lts Sl unit is metres per second (m s-';. The speed of a wave can be computed by the equation: u = t L Wavefront: A wavefront is an imaginary line on a wave that joins all points which are in the same phase of vibration.

1

Displacement/cm

3.2-1 3.3

0.1 5

Figure I 3.27 shows the displacement-time graph of a periodic motion.

What is the (a) period, (b) frequency and (c) amplitude? State the relationship between the speed of a wave and its frequency and wavelength. Sketch a graph to show how the displacement of a particular point changes with time when a wave of amplitude 0.4 m, speed 5.0 m s-l and wavelen$h 10.0 m passes through it. lVlark the amplitude and period on your graph. Water waves move from the deep end of a pool to the shallower end. State the changes (if any) to the frequency, wavelength and the speed of the wave.

0.1

0.05 0

0.05 0.1

0.15

0.2

Ime/s

-0.05 -0.1

-0.r5 ^r

Figure 13.27

rhEirffio

Goncept Map Waves

.

transfer energy

. classified as transverse

. no transfer of material

or longitudinalwaves described by

Quantities

. amplitude . wavelength . period . speed . frequency . wavefront

Direction of oscillation

. perpendicular wave

to direction

of . along the direction

of wave

motion-transverse, motion-longitudinal, e.g.

e.g. water waves or

light

sound waves

represented by graphs

Displacement-time graph for one particle . x-axis is time . y-axis is displacement . information that can be extracted: amplitude, period, frequency

Displacement-distance graph for all particles

.

x-axis is distance along wave

.

y-axis is displacement

. information

that can be extracted: amplitude,

wavelength

O)

=

rD tt1 Light, Waves and 5 ound

277

6.

Practice Questions

from deep to shallow water in a ripple tank. Which diagram shows how the waves are refracted?

Section A Multiple-Choice Questions

t.

2.

B D

molecules. matter.

force.

Cde

7.

1

1-

D hallow

Which of the following describes waves as they move from shallow water to deep water? Frequency Wovelength Speed

with different frequencies.

A decreases increases increases B no change increases decreases C no change increases increases D increases no change decreases

Which one of the following is an example of

string

-t-*

'\+il 'l

allow

travel.

longitudinal waves? Waves in a ripple tank Light waves in air A vibrating guitar string Sound waves produced by a vibrating guitar

de

l'siatto*

shallow

A B C D 4.

B

deep

energy

When a transverse wave passes, the particles of the medium oscillate A parallel to the direction of the wave travel. B in phase with each other. C perpendicular to the direction of the wave

D 5.

A

A wave transfers

A C

Water waves travel more slowly as they move

Section B Structured Questions I. Figure .l3.29 shows a student creating waves on a long elastic cord. The student's hand

Figure 13.28 shows a transverse wave. lf the speed of these waves is 2 cm s-', which of the following pairs of amplitude and wavelengh is correct?

makes one complete up-and-down movement in 0.40 s, and in each up-and-down movement, the hand moves through a height of 0.30 m.

DisplacemenVcm

T

+0.006

I

I

0.01

Time/s

rFigure

- 0.006

A B c D 5.

13.29

r,Figure 13.28

Amplitude/cm O.O2

0.003 0.003 0.006

The wavelength of the waves on the cord is 0.80 m. For this wave, determine the

Wovelength/cm 0.006 o.o2 0.04 o.o4

(a) amplitude, (b) frequency, (c) speed.

and

(Jun9o/p2/ea) 2.

frequenry 3 Hz produces water waves in a ripple tank. Which of the following values of wavelengh and speed are possible? A vibrator of

Wovelength/cm

A3 B 15 c36 D4

278

o.r,

waves

Speed/cm s-t

dlmm 1.0

0.5

dcm

0

1

-0.5

5

-1.0

rFigure 12

(a)

13.31)

Figure 13.30 is a graph of variation of d, the displacement (r-axis), with s, the distance from the vibrator (x-axis), for ripples on the surface of water in a ripple tank.

5.

Determine the (i) amplitude, and (ii) wavelength of the ripples.

(a) Distinguish between transverse

and

longitudinal waves. Cive an example of each type of wave.

d/mm 1.0

0.5 0

-{.5

0.2/

\0.1

o.s

\

10.4

0.5

fls

x

Y

-1.0

rFigure

(b)

rFigure t3.iIl

13.31

(b) Figure 13.33 represents successive

Figure 13.31 is a graph of the variation of the vertical displacement d of the ripple tank vibrator with time t. Determine (D the period of oscillation of the vibrator,

wavefronts of waves travelling on the surface of water in a ripple tank. When the waves reach XY, the direction in which they travel

changes as shown.

and

(ii)

(c)

Describe

the frequency of the vibrator. Use your answers to (a) and (b) to determine the speed of the ripples.

Qunea/P2/Qa)

5.

(c)

Water waves enter a dock at a rate of 120 crests per minute. At the dock are two poles 1 2 m apart

from each other. A worker watches a particular wave crest pass from one pole to another in 4 s. Calculate the (a) frequency of the wave motion, and (b) wavelength of the waves.

how the initial wavefronts could be

(ii)

produced in a ripple tank, and how you would arrange to bring about

the refraction at )ff in the ripple tank lt/easure the wavelength of the waves before and after refraction, and hence calculate the ratio speed of water waves before refraction speed of water waves after refraction

(Nov87/P2lQ3)

6.

4.

(i)

On entering shallow water as shoum in Figure 1 3.34,

the direction of travel of the plane waves changes through 20o as indicated.

Complete the diagram by drawing lines to represent the crests of waves X, Y and Z on the shallow water. Find the new wavelengh of the

P

WAVCS.

(Nov83/P2lQ3d) x

M

Y

infrared

10-6

tr3

radio waves

l0_2

ltr'

rFigure (

1

1000

which was spotted by astronomers in 1

rFigure

14.4 Before (above) and after below) shots of the supernova SN 1 987A 987.

14.3

Liqht, Wavesand Sound

285

I.

The electromagnetic spectrum comprises transverse waves, such as radio waves, microwaves, infrared, visible lighq ultravioleq X-rays, and T-rays, which travel through vacuum at the same speed of 3.0 x l0s m s-r.

TestYourself 14.1

l.

Which of the following members of the electromagnetic spectrum are listed in order of increasing wavelength?

A B C D 2.

microwaves, ultraviolet, infrared, X-rays X-rays, ultraviolet, infrared, microwaves

ultraviolet, infrared, microwaves, X-rays infrared, ultraviolet, microwaves, X-rays

Electromagneticwaves are known to share certain common characteristics. Which of the following is incorrect? They all travel with the same speed in vacuum. They are all transverse waves. They obey the laws of reflection and refraction. When they pass from one optical medium to another, e.g. from air to water, their frequencies, wavelenghs and speeds all decrease.

A B C D

ga mma

rays

target

helmet

14.2 Uses

of Electromagnetic Waves

Learning Outcomes eFigure 14.5 Gamma Knife radiosurgery

You'll be able to: I state the applications of electromagnetic waves & describe the effects of absorbing electromagnetic waves

uses weak beams of 1-rays from several sources. They are focused at the tumour in the brain through holes in a protective helmet worn by the patient. The combined energy from the weaker beams is

sufficient to kill the tumour but insufficient to damage the surrounding cells.

Applications of electromagnetic waves l.

Gamma rays: Radiation therapy (cancer treatment)

Gamma rays can be used to treat cancer. These high energy rays are directed at cancerous tumours to kill cancer cells. The Gamma Knife radiosurgery is one such medical procedure that uses y-rays

to destroy brain tumours (Figure 14.5).

2. X-rays: Medical and everyday applications In radiography, low frequency X-rays are used to produce the X-ray

eFigure 14.6 Airport security guard examining the X-ray image of luggage passing through the X-ray machine.

284

ilearomagnetic Waves

images used by doctors to diagnose the fracture of a broken arm or even tooth decay. X-rays are also used in everyday applications like X-ray scanners in airports (Figure 14.6). They can penetrate through all types of materials, exeept for lead, to scan the contents of passengers'luggage. --.-===

I In the medical field, some X-ray applications include radiology and radiography. In radiology, high frequency X-rays are used for radiation therapy, as in the case of y-rays (Figure 14.9).

3. Ultraviolet: Sunbeds and sterilisation of medical equipment

Ultraviolet (U\) radiation is divided into three bands in order of increasing energy (frequency): WA, UVB and UVC. UV rays are the part of sunlight that causes sunburn and tans. Ultraviolet lamps that emit UVA are used in sunbeds (Figure 14.7) for artificial tanning. It is popular in countries with long periods of limited sunlight. Lamps that emit strong WB and WC radiation are commonly used as germicidal lamps for sterilisation in hospitals.

4. Visible light: Optical fibres

r,Figure 14.7 A man wears goggles to protect his eyes from the UV rays emitted by the sunbed. While artificial tanning is safer than suntanning, medical authorities have warned that excessive exposure to ultraviolet radiation by regular users of sunbeds may lead to premature aging and even skin cancer.

As we have learnt in Unit l2: Lieht,light is used in optical fibres for medical purposes and telecommunications. Also, visible light is needed in everything we do, from watching movies to using the computer to reading booksl

5. lnfrared: Remote controllers and ear thermometers Infrared remote controllers are used to control a variety of electrical devices such as TV, video or hi-fi systems. The human body, like any object, gives out infrared radiation that can be detected by sensors. These sensors can be used in intruder alarms

and even in ear thermometers! How do these

thermometers work?

rFigure 14.8 Ear thermometers were used extensively to test for fever during the SARS epidemic in 2003. They are able to detect body temperature faster than conventional thermometers.

r Figure 19.7 Most offices in Singapore use fluorescent lamps.

374

Praaicat Electricity ,]

d-

Electric motors Electric motors are used in household appliances like the fan, washing

machine, hair dryer, food mixers and electric drills (Figure 19.8). Electric motors can also be found in hard disks and DVD drives. Motors work on the principles of the magnetic effects of a current (Unit 2l: Electromagnetism). They convert electrical energy into rotational kinetic energy.

! I

I I

Key ldeas

l.

Electric kettles, ovens and heaters make use of the heating effect of electricity to function.

2.

An electric current is passed through the heating element (nichrome) in the appliance, causing thermal energy to be generated.

m l.

2,

rFigure 19.8 Some domestic appliances that work on the principles of the maqnetic effect of a current.

Cive two examples of household appliances that use the heating effect of a current.

What other types of lamps have you encountered other than filament and fluorescent lamps? Do you know which type is more efficient in converting electrical energy to light energy?

19.2 Measuring Electrical Energy Learning Outcomes You'll be able to:

I I

recall and apply the relationships P

= Vl and E = Vlt

calculate the cost of using electrical appliances in units of kWh

Have you ever noticed the power ratings on electrical appliances in your home? Have you wondered how the power ratings are measured? In this section, we will be learning about electrical power and how it is calculated.

Electrical power P ln Unit 6: Energ4 Work and Pou)er, power P is defined as the rate of work done or energy converted.

P

w _r1) - :-'

orP =

L

, -(2\

where P - power (in W), W = work done (in ), E = energY(inJ),and t = time (in s). Electricity and lr4agnetism

575

ln Unit l7: Cunent Electricity, the equation for potential difference 7 between two points in an electric circuit or across a conductor is

V

given by: V

+ P

rFigure

W

(3)

0

where V =

= work done (in J), and Q = charge (in C) W

19.9 Power Pdissipated by

the resistor as thermal energy

From(3), W=QV-(4)

lELGtuote!

Substituting (4) into (1), we get "t

Use the'triangle' method, demonstrated in Section 2.1, to find P, V and l.

potential diff erence or voltage (in \),

By substituting the equation

7

=

P=9!

(5)

Q into (5),- we get

P=Vr _(6) Hence, to calculate the power P of any electrical appliance with a current /flowing through it and a potential difference Tacross it, we simply multiply the two quantities of /and 7.

In the case of a resistor with resistance R (Figure 19.9), the rate at which electrical energy is converted to thermal energy can be calculated from any of the following three equations:

P=Vl Appliance

Power

Electric iron

950 W

LCD

ry

P=t2R

(sinceV=/R)

p

V2

R

(since /

V ) R

The SI unit for power is the watt (W). Other units that are commonly used include: I kilowatt (kMD = 1000 W or 103 W 1 megawatt (MVV) = 1 000 000 W or 106 W

125 W

32-40W

Fluorescent lamp

2kW

Electric kettle

r-2

Air conditioner

kw

All electrical appliances or devices are usually marked to show the amount of power they consume as well as the operating voltage. Take any electrical device and examine its power specification. For example, an electric kettle is marked '2000 W 240 V'. This rating means that when an operating voltage of 240 V is applied across the heating element, the kettle operates at 240 V and it converts electrical energy into thermal energy at a rate of 2000 W. The power ratings for some common appliances are shown in Table 19.2.

rTable 19.2 Examples of power ratings of some common appliances

WORKED EXAMPLE 19.1 3.0

0.70

v

flashlight bulb is connected to a i.o v battery of negligible internal resistance (Figure 19.10). The ammeter shows a reading of 0.70 A.

A

What is the electrical power used by the bulb?

A

@ bu lb

r,Figure 19.10

576

Praaical Electricity

Civen [/= 3.OV,l= O.7O A. Then the power P of the lamp is P =Vl= 3.0 x 0.70 = 2.t W Hence, electrical power used is 2.1 W.

rts

Electrical energy E F

Using P =

7

,

we can re-express the equation to find the amount of

electrical energy E used in time

E=

1.

Pxl or E = VIt

(sinceP=VD

In the case of a resistor of resistance R, the electrical energy converted to thermal energy can be easily calculated from the

How do technicians repair electrically 'live' lines without getting electrocuted? When a technician approaches a 'live'

line, the electric field surrounding the line brings his body to the same potential as the line. To ensure that the technician and the line are at the same

potential, the technician extends

following three equations:

E=Vlt= /'Rf (since V = tR)= [,

(since t =

[)

The SI unit of energy is the joule (J). Other convenient units of energy include: I kilojoule (kJ) = 1000 J or 103 J 1 megajoule (MJ) = 1 000 000 J or 106 J

a

conducting tube to touch the line. At the same time, he must be insulated from anything that is electrically connected to the ground to avoid being electrocuted. The technician wears a conducting suit, hood and gloves that are electrically connected to the line via the conducting tube. This ensures that he is always at the same potential as the line, thus he will not get electrocuted.

WORKED EXAMPLE 19.2 An electric iron with a heating element of resistance 60 a is connected to the 240 V mains. Calculate (a) the electrical power produced in the heating element, and (b) the amount of electrical energy consumed when operating the iron for 2O minutes.

lElGtuote! = l'R is useful for comparing the power dissipated by

The equation P

resistors in series since current / is the

Solution

same.

The equation P=

(b)

power P is P

=F

t/

rs usetul tor

comparing the p ot,ver dissipated by

Civen that R = 60 Q and l/ = 240 V,

(a) The electrical

i

=#

resistors in parallel since p.d.

= 960 W

l/ is the

5ame.

To use the iron for 20 minutes, the electrical energy E consumed is

E=

P

xf = 960x20x60= Ll5x

l06J

=

l.l5tVlJ

WORKED EXAMPLE 19.3 A filament lamp, rated as 60 W, 240V, is connected Io a24O V power supply. Find (a) the current flowing through the lamp, (b) the resistance of the filament, and (c) the energy produced by the lamp when it is switched on for 8 hours.

@ Civen P = 60 W and

(a)

t/= 24OV,

The current lis t =

(b) Ihe

!v = f,q = 0.25 A 240

resistance R of the filament is

p

=Vl R

v= iomR^ =i orRcanbecalculated{ (c)

i.e.R=f=#=e6oe

24o

ffi=9ooei

Converhngtime f of B hours into seconds $ves 8 x 60 x 60= 2.BB

x

lOas.

Hence the electrical energy E used up when the lamp is switched on

forB hours isE=P x t= 60 x 2.88 x lOa= 1.73 x 106J =

.l.73

IVIJ

Elertricity and Magnetism

577

Calculating the cost of electricity consumption Have you ever wondered how the amount of electricity consumed

by your household is calculated?

i-FF3

^Figure

I

The electricity meter is used to measure electricity consumption. The cost of electricity consumed is calculated based on the number of kilowatt-hours (kwh) of electrical energy used. The difference between the current month's and the previous month's readings based on the meter gives the amount of electricity used for the current month.

19.11 Electricity meter

The kilowatt-hour is the unit used for calculating the amount of electricity used. One kilowatt-hour (kWh) is the amount of electrical energy used by a 1 kW device in one hour. Take a close look at the electricity meter in Figure 19.11. Do you see the units in kwh?

lElGiNotor A common error most students make

is to mistake kWh as the amount of electrical power consumed. However, kWh is actually the amount of electricol energy consumed. lt is also known as a domestic unit of electricity.

WORKED EXAMPLE 19.4 A 1.5 kW electric heater is used to heat a large container of water for 2 hours. Calculate the amount of electrical energy used by the heater in (a) kwh, (b) J.

Solution P= 1.5 kW, t=2hrs (a) Energy usedE(in kwh) =P xt= L5 x 2 = 3.0 kWh (b) E(in J) =Px t= 1500 x (2 x60 x 60)= ].08 x l07J

Civen

WORKED EXAMPLE 19.5 Figure I 9.1 2 shows a utilities bill of a household for one month. How is the cost of electricity shown in the bill derived? -_4sd.e*.

Hroryffi

MEffi6Gtr-al5:2rZI kit,

Mf fro(Dlt{lts: k kr.F*rA*DFhmryS.ffi,bt,U

aILt

hD kMtr

Id

,ltI

0.tH

4.9

t.t, 10

ott Gq)

9.97

ro,

75t

,56

7.5t

$rG

sr

o$

0.e5

t361

*

t.o

t.a

l12

tl$l

Z,

Or ra

270

r

2Ftn

llx)

Ed

3.16

!32fl

rFigure

19.12 A sample

utilities bill

Solution From Figure

.l9.12,

under the heading'Electricity Services', the number of units of electricity consumed is 1 l2 kWh at a rate of $O.l 957 (or 19.57 cents per kWh). Therefore, the cost of elearicity consumption is 112 x $0.1957 =$21.92 which is correctly indicated in the last column of the bill.

578

Praaical Electri(ity

EM ut!

WORKED EXAMPLE 19.6 The kWh is a unit of electrical energy. What is the equivalent joules (J)?

of 1 kWh

in

Note the number of each type of appliance in your house, e.g. the number of light bulbs, the number of hours these appliances are used each day, and their power usage.

@ Energy

E=Px f = I kWx I h= 1000Wx3600s=3.6x

Hence,

I

kWh is equivalent to 3.6

l

It4ake

an estimate of your

household's daily electrical usage and costs. What would be the estimated monthly electrical bill?

106.J

tVlJ.

How close is your estimation

Utility companies, such as Singapore Power, use the unit of kilowatthour (kWh) to compute the amount of electrical energy used by households. The cost of each kWh depends largely on the price of oil or natural gas.

to your latest average monthly bill? Drd you overestimate or

2.

to calculate your

WORKED EXAMPLE 19.7

household

electricity usage? Find out more at http ://wwvv.marshallcavendish.

lf Singapore Power charges I B cents for each kWh of electrical energy used, calculate the total cost of using a 3 kW electric kettle for 20 minutes and

.l00

underestimate? Did you know that you can use an electricity consumption calculator

a

3.

W filament bulb for 5 hours.

com/ed ucation/sg/student.

Recommend ways to reduce your household's electricity consumption. Practise these and check the following month's bill to see if there is a change.

Solution Electricalenergyused byelectrickettle, E, = Electrical energy used by bulb, E, =

(ffi)

Pxt

= 3 kW r

(#)h

= lkWh

kw x s h = o.s kwh .l.5

kwh TotalenergyusedE= El + Ez=1+ 0.5= Hence, the total cost = 1.5 x I 8 = 27 cents = $O.21

Key ldeas

l.

Electrical power P can be calculated using the following formulae:

P=Vl

2. 5.

tt2

=!-=l'R

Electrical energy E is given by E = P x

t.

The kilowatt-hour (kWh) is the unit of electricity usage. the electrical energy used by a 1 kW device for I hour.

I kWh refers to

Test Yourself 19.2

I

(a) A 240 V mains power supply an air-conditioner (Figure

delivers a current of 9.0 A through

.l9.13).

Find the power supplied

in watts.

(b)

ffi "rFigure

19.13 A

typical air-conditioner

An air-conditioner is used for 1.5 hours each day. Using the answer

in (a), given that the electricity tariff is $0.1 B per kWh, calculate the cost of using the air-conditioner in a month (30 days).

fl,?ltlllll{Iff'r:}O

Electricity and Magnetism

579

19.3 Dangers

of Electricity

Learning Outcome You'll be able to: I state the hazards of using electricity

Although electricity plays a very important part in our daily lives, it can also be very dangerous. Electrical faults in appliances or circuits can cause fires and electric shocks. Electricity can be dangerous due to three reasons-damaged insulation, overheating of cables and damp conditions.

Damaged insulation Electrical appliances can only work if they have wires to carry electricity from the voltage supply. These wires are usually insulated with rubber and they are wound together to form a cable enclosed by PVC (Figure 19.14) or rubber (Figure 19.15). rFigure 19.14

PVC cable

rFigure 19.15 Bubber-insulated cable

Insulating materials become worn with time and use. For example, the electrical cables of the hair dryer and electric iron usually get bent and twisted because of the way they are used. This might cause the electrical insulation to crack and break, thus exposing the conducting wires inside. The exposed live wire can cause severe electric shock to the user if it is touched. In this case, it can lead to serious injury or even death.

Overheating of cables Overheating of cables occurs when an unusually large current flows

through the conducting wires. An unusually large current flows when, for example, a fan motor overheats and melts, fusing the live and neutral wires together. We have learnt in Unit 17: Cunent Electricity that the resistance of a conducting wire is inversely proportional to its cross-sectional area. This means that athin wire has a higher resistance compared to athick wire. The higher resistance of thinner wires will produce more thermal heat that will damage the insulation and may cause a fire.

t

rFigure 19.16 When too many electrical devices are connected to one wall socket, the current that flows through the socket may be excessive and can cause overheating of the cables.

380

Praaicat Electricity

Therefore, when appliances are being wired, manufacturers must make sure that the wires are of the correct thickness. Generally, thin wires are used for appliances that need less power, e.g. lamps, while thick wires are used for appliances that need more power, e.g. kettles.

Damp conditions Many electrical accidents occur in damp conditions. For example, it is very dangerous to leave a hair dryer on a wet sink (Figure 19.17(a)). A person using the sink could be electrocuted if the wires were exposed

or had damaged insulation. If the hair dryer with the main power switched on happened to fall into a bathtub while a person was bathing, the water would provide a conducting path for a large current to flow. As our human body can only withstand a current of about 50 mA, the large current will

electrocute the person. Other possible hazards include turning a switch on with wet hands.

Human Resistance The electrical resistance of the human body is made up of the resistance of dry skin and the resistance within the body. The resistance of dry skin is about 100 kO. The resistance within the body, which is composed mainly of fluids, rs about a few hundred ohms. Thrs explains why dry skin acts as an insulating layer by providing high resistance. lf the skin is wet, the resistance of the skin will be lowered. The resistance within the body, being very low, will allow a large electric current to flow through the body, causing an electric shock or even death.

r Figure a

19,17(a) Leaving a hair dryer on

wet sink can be very dangerous.

-ry

irE=

?

< Figure 19.17(b) Wet skin reduces the electrical resistance of the human

E:.-.

body

t.

Dangers of electricity are caused by damaged insulation, overheating of

cables and damp conditions.

Test Yourself 19.3

l.

State the danger caused by the following conditions:

(a) (b) (c)

Damaged insulation Overheating of cables Using electrical devices in damp conditions.

Electricity and tr,,taqnetism

581

19.4 Safe Use

of Electricity at Home

ln Section 19.3, we learnt about the dangers of electricity. In this section, we will learn about the safety features installed in our homes. These are: l. Circuit breakers,

2. 3. 4. 5. 6.

Fuses,

Correct placement of switch in the circuit, The three-pin plug, Earth wire, Double insulation of certain appliances.

Figure 19.18 on the facing page shows a circuit in the home. For most homes, electricity is supplied by a cable containing two wires-the live (L) wire and the neutral (N) wire. In such a circuit, the current enters the house through one wire and returns to the local substation through the other. The live wire is usually at a higher voltage ot240 V while the neutral wire is usually at 0 V. In a typical home circuit, these two wires are connected to a main fuse box, an electricity meter and a consumer unit. The consumer

unit is the distribution point for the household's electricity supply. Figure 19.18 shows the consumer unit containing a main switch and four circuit breakers which lead to the four common circuits in the house. Depending on the needs of a household, there may be more than four circuits, with a circuit breaker to each circuit. The common household circuits are:

l.

Lighting circuit-ln this circuit, the lamps in a house are connected in parallel so that each lamp receives the mains voltage of 240 V. In addition, if any lamp should fail, the rest of the lamps will not be affected since they are connected in parallel.

2,

382

PraaicalElecuicity

Ring main circuit-This circuit supplies electricityto all the wall sockets in the house. With the ring arrangement, the current can flow to any socket by the live or neutral wires. Besides the live and neutral wires running a complete ring round the house, an earth @ ring circuit is also added for safety reasons.

underground supply cable

neutral

live wire (L)

wire (N) main circuit breaker box

main circuit breaker N

L

IrIIFI

electricity meter

L

N

lighting circuit E

main switch N

L

two-way switch

I

L

I

15A

t_

N

to immersion heater circuit

consumer unit circuit breaker box

30A

o.

L

L

to air conditioner circuit N

30A

power sockets

I

L

I

I

,'i ,l\

il'

I

N

I

symbol

for a

circuit breaker

5

I

I I

I

I

L

_t I

E

I I I I

E

earth

rFigure

3.

19.18

Typical home circuitry

Air conditioner circuit-This circuit is connected to the air conditioner unit in the house. The air conditioner tends to draw more current from the mains and thus the circuit breaker has a higher current rating.

4,

Immersion heater circuit-This circuit is connected to the immersion heater that supplies hot water to the household. Like the air conditioner, the immersion heater draws more current and has a higher current rating.

Electricity and Magnetism

585

1.

Circuit breakers

Circuit breakers are safety devices that can switch off the electrical supply in a circuit when there is an overflow of current. Without the circuit breaker, this surge of current can cause damage to home appliances or even start a fire. Leakage Current r8l 204

ls rot

$i 1$l

204

IG2OA I

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Cu

Rating

'L

re Circuit Breaker

r Figure

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19.19 ConsLrmer unit

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til lr

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Earth Leakage Circuit Breaker circuit breaker box

Figure 19.19 shows the consumer unit circuit breaker box that consists of two circuit breakers. It can normally be found near the front door of a house. The circuit breakers are: (a) The Miniature Circuit Breaker (MCB) (b) The Earth Leakage Circuit Breaker (ELCB) or the Residual Current Detector (RCD) The MCB prevents excessive current flow through the circuit by tripping or breaking it. In Figure 19.19, you can see the breakers labelled with various currents, e.g. 6 A and 20 A. This means that when the current exceeds these values, the circuit breaker will trip. The electricity supply to that part of the house circuit connected to the MCB will then be cut off.

The MCB can be reset by switching it on again. This should be done only after the fault in the circuit has been corrected. If the MCB trips again, this means that the fault is still present. In this case, an electrician should be contacted to repair the fault. The Earth Leakage Circuit Breaker (ELCB) monitors the amount of current flowing from the live wire. The current in the neutral wire should be the same as that in the live wire. If there is an electrical fault, there will be a small current leakage (generally about l0-30 mA) to the earth via the earth wire (or more dangerously, through a person). The ELCB detects these small current leakages from the live wire to the earth wire. When this happens, the current in the live wire will be greater than the neutral wire. This will cause the ELCB to 'trip'.

584

Praaicat Elertri(ity

There are many causes of current leakage, but one common cause is the poor insulation in old electrical appliances. This would cause a small leakage current to flow from the live wire to the earthed metal case of the appliance. Without the ELCB, a person who touches the metal case may get an electric shock.

2.

Fuses

A fuse is a safety device included in an electrical circuit to prevent excessive current flow. It has the same function as the miniature

circuit breaker. A fuse consists of a short thin piece of wire which becomes hot and

melts when the current flowing through it is greater than its rated value. Rated value refers to the current rating marked on it. In general, a thicker wire will require a greater current to melt it. Fuses with thicker wires therefore have higher ratings. Fuses are normally rated at I A, 2 A, 5 A, 10 A and 13 A. For safety reasons, the following points should be considered when

selecting and installing fuses:

(a)

Fuses should have a current rating just slightly higher than

the current an electrical appliance will use under normal conditions. For example, a 5 A fuse is used for a lighting circuit (b)

r,Figure 19.20 A glass cartridge fuse contains a thin metal wire which melts when excessive current flows through it.

that uses 4 A. A fuse should be connected to the live wire so that the appliance

will not become charged (i.e. have a potential difference of 240Y after the fuse has melted due to an overflow of current.

(c)

Before you change a fuse, always switch off the mains power

supply.

WORKED EXAMPLE 19.A A hot water heater is rated 2880 W, 24OV.C-alculate the operating current and

suggest a suitable rating for a fuse to protect the heater from overheating.

Solution Given: Power of heater

P

=2880 W, voltage

V

=24OV

Let the operaing current be /.

p=

t//, then

t=

i =ffi =,r. o

The current / in the water heater

is l2

A. A suitable fuse is one with a fuse

rating that is slightly higher than the cunent flowing through the device. Thus,

a l5 A fuse would be suitable for the water heater.

Electricity and Magnetism

185

WORKED EXAMPLE 19.9 The following appliances are operating in a kitchen circuit: 50 W fruit blender

I.

2. 4OO W refrigerator 5. 800 W microwave oven

4.

1.5 kW electric kettle

The electricity supply is 240 V and the kitchen circuit is protected by a A/iniature

Circuit Breaker (lVlCB) with a rating of 20 A. What

is the cunent flowing through the circuit breaker when all the appliances are operating at the same time? Does this trip the tt/CB?

Solution Since all the appliances are operating at the same time, the total power P is

P= 50 + 400 + 800 + 1500 =2750W To find current /, we use the formula P= t//. Then/

=i=#=u.5A

As the current is lower than the circuit breaker rating, the circuit breaker does

not trip and all the appliances can operate safely.

3.

Switches

There is a great variety of switches. There is the one-gang switch which has a single switch on the face plate, the two-gang

rFigure

19.21 Rocker switch

switch which has two switches on the face plate, the rocker switch (Figure 19.21), the dimmer switch (Figure 19.22) and so on. All switches are designed to perform the same function. They break or complete an electrical circuit. If the switch is fitted onto the neutral wire, the appliance will be 'live' even though the switch is 'off' (Figure 19.23).ln this case, anybody who touches the metal casing of the appliance would experience an electric shock.

rFigure

19.22 Dimmer switch

metal casing is at high voltage (240 V) as it is

x

still connected to the live wire even though the switch is open

live wire

(on)

fuse

large current flows through the person to the earth causing a nasty electric shock

to the mains

Figure 21.?2lal A positively charged particle in a magnetic field is deflected upwards in a circular path

direction of positively charged particle before entering the magnetic field positively cha rged

particle

-

XX

x./t

x X. X X X XXX x X XXX X

@- +---"

magnetic field into plane of paper

x

Force

X

1

lX,'*

current

magnetrc

field

path of positively charged particle (part of a circle)

When a beam of positive charges, e.g. protons, enter the magnetic field region, the beam is deflected upwards in a circular path. This is because the moving charges experience a force perpendicular to its direction of motion. The direction of this force can also be predicted by Fleming's Left-Hand Rule. We take current to be in the direction of the beam of positive charges.

However, if we have a beam of electrons or negative charges, we follow the conventional current direction which is opposite to that of electron flow (Figure2l.22(b)).

>Figure 21.n|il A negatively charged particle is deflected downwards in the same magnetic field.

direction of electron or negatively charged particle before entering the magnetic field electron or negatively charged particle

e

magnetic field into plane of paper

X

XXXX

X

XXXX

X X

'X"-x x .\

magnetic field

+.x,] current

X

I Force

XXXX path of electron or negatively charged particle (part of a circle)

In Figure 21.22(c), the beam of positive charges or protons enter a region of a magnetic field which is directed out of the plane of the paper towards you. The beam is now deflected downwards.

424

Electromagnetism

l

direction of positively charged particle before entering the magnetic field positively charged particle

magnetic field outwards from plane of paper

oo o OO ooooo @- +----O a'..o o a O

o oao

o

Figure 21.41(a)

aa

when

(i) the current is increased, (ii)

a

the current is reversed.

(Novee/P2lQ3)

5.

Figure 21.40(a) shows a coil ABCD that can turn between the two poles of a magnet. Bare metal paper clips support and pass current into and out of the coil.

a

< Figure 2l.41(b)

>r I

In a non-ideal transformer, there will always be power loss, i.e. the efficiency 4 is less than 100%. The equation relating output power

EfficiencY,

-

QutP\rt Power

rnput power

x fio%

Thus, if the efficiency T of a transformer is 70%,we get

/Vp

(for 100

t

a sharp and

microphone Y-input Q

o

t

I

intense pulse as incident sound