Solutions manual for Reif, reissued 2009.Full description
Solutions manual for Reif, reissued 2009.Descripción completa
Full description
Descripción completa
Fundamentals of Physics Extended 10th Edition Halliday Test Bank Download at:https://goo.gl/ytbWVg fundamentals of physics by halliday resnick and walker 10th edition pdf free download fundament...
Solutions manual for Reif, reissued 2009.Descrição completa
Fundamentals of Physics Extended 10th Edition Halliday Test Bank Download at:https://goo.gl/ytbWVg fundamentals of physics by halliday resnick and walker 10th edition pdf free download fundament...
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Halhday.Da,·jd Halllday.D3l·;,j Fundam."tal5 of ph)',ics.-8!h ph)',ics.-8th elf ExwndedlD3\·id Halliday. Robert Re'nkk.Joad R e,,, k~. Joar! Walk Walh... •. Fundamentals i'd ..• ExwndOOlDa"id H'l~d,y. Rober! p. ern. em. lndude, index. [miu"", Extended VOtslon: ve1Slon: [SBN ISBN 978--0-~71 - 7S80I 7580I"J ·J (acid-I'oo (acid-r.,", 1"1"") pap''') Ph)~icr--T"I!booh T"xttoooh I. Rosnii:k. Resnick. RoIli'.! Walke •. ka,l ka.1 [[Ill.I. Title. T,tle. I. Ph)~ics---Robert 11. Walko,. QC2l.3.HJ52008 QC2J.3.HJ52008
''''-
P,inted P.inted in tbe United Unite
10 9 8 7 6 5 4 3J 2 I
2OO6().I]J75
Volume 1
Volume 2
PART 1
PART 3
Chapler 1
Measurement
Cnapler 21
Electric Charge
Chapler 2
Motion Along a Straight Line
Chapler 22
Electric Fields
Chapler 3
Vectors
Chapter 23
Gauss' Law
Chapler 4
Motion in Two and Three Dimensions
Chapler 24
Electric Potential
Chapter 2S
Capacitance
Chapter S
Force and Motion -
I
Chapter 26
Current and Resistance
Chapter 6
Force and Motion -
II
Chapler 27
Circuits
Chapter 7
Kinetic Energy and Work
Chapter 28
M agnetic Fields
Chapter 8
Potential Energy and Conservation of Energy
Chapter 29
M agnetic Fields Due to Currents
Chapter 30
Induction and Inductance
Chapler 9
Center of M ass and Linear Momentum
Chapter 31
Electromagnetic Oscillations and Alternating Current
Chapler 32
M aX\IVell's Equations; M agnetism of M atter
Chapler 10 Rot ation Chapler 11
Rolling, Torque, and Angul ar M omentum PART 4
PART 2
Chapter 33
Electromagnetic Waves
Chapter 34
Images
Chapter 3S
Interference
Chapter 36
Diffraction
Chapter 37
Relativit y
Chapler 12
Equilibrium and El asticity
Chapler 13
Gravitation
Chapter 14
Fluids
Chapter lS
Oscillations
Chapler 16
Waves- I
Chapter 17
Waves -
Chapter 18
Temperature, Heat, and the First Law of Thermodynamics
Chapter 38
Photons and M atter Waves
Chapter 39
More About M atter Waves
Chapter 19
The Kinetic Theory of Gases
Chapter 40
All About Atoms
Chapter 20
Entropy and the Second Law of Thermodynamics
Chapter 41
Conduction of Electricity in Solids
Chapter 42
Nuclear Physics
Chapter 43
Energy from the Nucleus
Chapter 44
Quarks, Leptons, and the Big Bang
II
PART 5
Appendices / Anwers to Checkpoints and Odd-Numbered Questions and Problems / Index
This page il/fellfiol/o/ly intenTionally left blallk blank
Meas ureme nt U Measurement
1
~. Motion
buiding.? b...u-"g,1 , -, wt..tll~1 'Nhat I. Physics? 2 1·1 '1·2 -2 M.,.""nng Measunng Thongs 2 '-3 1M The kllemltJOnal Intematon,1 System S)'$tem 01 of UnlU Units Z 2 1-3
outf..sd« wi>«. 10 fo Nn run 10 '0 ulm atdt 1/a hisIh high How do.. doet an Ill! OlAf . . know know...h.. fly ball? b.M1? 4-1 What I, Is Physoa? PhYSICS7 59 4-2 Position and [);splacem.nt S9 PoWon..d~1 4-3 Awrage A.....-age V.loclty velocIty and Ind InlUnuneou. Inuanllneout. Velocity v.1oclly 61 4-4 AWRgII Average AcceleratIOn Accel.olllOfl and Insuntan«>us Instlntaneoul
.- ,
..
1-4 1-4 1-5 1·5
Changing Unots Units 3 ChI"9W'Sl LAngth 4 Length 1-6 Time 5 Mass 1-7 M ... 7 1·1 R • .,.;e" & Summary Ravie .. s... .......1')' 8 Problems 8 ProbI.ml
.
U.. Motio n Along Al ong a Stra Straight It. ight Line
""vi.,.
13
How (CM ... • woodp«Jc., woodp«ker ....,viw 1M tl>. ,aw,.. ••"",. imp.cl~ impacts its b..1e b.lak on .1 • tfH of itl ....1 2-1 Whit Wha t II lsf't1ysia? 2·1 pt.,y$ia1 14
2-2 2·2 Motion Mooon 14 2-3 PosltlOfllnd Position and D,tp!lcarMnt Dispillcement 14 2·3 2-4 Aver.gl Averag. Valoclty Velocity Ind lind Average Spe.d 15 ,.\....,~ Sp..d 2-5 I",unu Instantaneous Velocity lind Speed ......... V.1oc,ty Ind 5pMd 17 2-6 Acceleration AccoMr;.uon 19 2-7 ConlUnl.l.o;ca"""IIOfIASpKLlIClw Constant ,!,ccelerlltion: A Special Cllse 21 2·1 2-8 Another LooIc lit Constant Acceleration 24 2·' An~LookIT.ConsUnIAcc~11OII 2-9 Ft..-F"I Free-Fall Acceleration 24 2·9 Aec
U Vector
nd Three Dime Dimensions in Two aand nsio ns
58
the ",o'HId gro~.lfld t..come bet;ome fLjJ fLid lind and ,.l1ow sallow up How (un .. th.
.,
"
..
AcceleratIOn 63 Ac:celer311Of1 4-5 ProjectIle Proj.ctlle Motion MotIon 65 4-6 ProjectIle Projecti~ MotIOn Motion Ana An.lyHd lyzed 66 ~ 4-7 Uni#otm Uniform Cirwllr Circular Motion MOIlOn 70 '-7 4-8 Reiat .... e Motion in O11e Dimension RelatIVe III Ona D,m.nllOlI 72 71 .~ 4-9 R.lat ..... Mo tion ill in T TNo Re~tNe Motion .... DImensions Dim.",ion, 73 Review & Summary SlImmll')' 75 aue.t Qllesliolls ion. 76 I Probl.ms Probleml 77
"
.-,
U
"
Fo Force rce and Mot Motion ion - II 87
What Wfwl is i. 1M th. fear fe. factor f.,_in in ,idi"Sl riding th.lion me LUI a' urol't all aa roller coaster? RI.-I.,1 501 What Whal Is f't1ysics? pt.,~o7 88 5-2 Newtonian N~orNn Mechanic. Mtch.Ilic.1 88 5-3 Newton', ~·.Fntll' First La"".. 88 S-4 Fon:. F~ 89 .. H 5-5 .5 Man ~II 90 S-6 Ne-Nlon", Newton', Second s.c:ond Law lIIw 91 H 5-7 Some Particular Force. PlftlO.l", Fon:
.,
How ... ge blocks How did tl>. lhe .rldent .00.,,' Egyptia", Egypl;'n. mo.,. mow the 1M hhugoe bloch into 1'"tO place p!.ce to bbuild ... iklln. lhe Greilt (ireal Pyrllmid? Pyr.,...id? 6-1 6·' Whatlsf't1ysic.? What I, pt.,~kl? 117 6-2 6·2 Friction Friclion 117 11 7 6-3 '·3 Propertie Prope"lus of 01 Friction Fric;toon 118 118 6-4 The Drag Force and Termina 64 Drag F()fl;e ",d TermInall Speed Speed 122 122 6-5 '·5 u"i10flTl Uniform Circular Circuli. Motion MotIOfl 124 Review RIIV_ && Summa»' SuITllNlI)' 129 aQuestIOnS ... estlons 130 II Problems P~. 131 131
__ _ Contents
U
Kinetic Energy and Work
il.IJ U.IJ Rotation 241
140
What pro~rty prop
How un CIIn II SmIIU smaN snapping shrimp ."IIP snllP it. its claw.o cL.w so firmly hllt th .. sound stun. stuns it. its PMY? p",y? t hat 10-1
What I. Is Physic.? 242
7-2
What Is Energy? 141
7·)
Kinet ic Energy 141
10-2 10-3
ne Rotational Variable. Vanables 242 AIe Are Angular Quantities Quant ities 'lectors? Vectors? 246
7-4 7-5
Work 142 Worl: and Kinetic Energy 143 Work
10-4
Rotat ion with Constant Angular Acceleration 247
10-5
Relat ing the Linear and Angular Variables 249
7·6
Work Done by the Gravitat ional Force 146
10-6
Kinet ic Energy 0/ 01 Rotation 252
7·7 7-8 7·8
D<>ne by a Spring Force 149 Work emile D
10-7
Calculating t he Rotational Inertia 253
10-8 10-9
Torque 256 2S6 Newton's Seeond Neilton'. Second Law lor Rotat ion 257
7-9
152
Review Revi
10-10 Work and Rotat ional Kinet ic Energy 260 Rev;"w & S
U
Potential Energy and Co Conservation nservation of of Ene Energy rgy
166
lii lili l Rolling, Rolling , Torque, Torq ue, Momentum M o mentum
Why can a /argelandslide mo"" mow almost 30 Ii"..... Ii"",," as fa, far across .. valley a. IIa .mal/landslide?
8·'
What Is Physics? 167
8·2
Energy 167 Woo and Potential E""rgy
8-3
Path Independence of Conservative Forces 168
8-4
Values 170 Determining Potent ial Energy Valu".
8·5
Conservat ConsefVat ion 01 Me<:hanical Energy 173
8·6
Reading a Potential Energy
8·7 8-8 8·8
Work Done on a System by an External Force Conservat ion 01 01 Energy 182
ell"'"
175 179
Review & Summa,), 186 Quest ions 187 I Problems 189
What i. is th .. magic behind th .. ons ..t of II a baU .. t danc .. r'. r's midair rotation during IIa tour jet .. ? 11-1 What l.Phy.ic.? 276 WhatlsPhysic.? 11· 1 11-2 11·2 Rolling as Translation and Rotation Combined 276 11-3 The Kinet ic Energy of Rolling 277 11·3 11-4 The Foa:es 01 of Rolling 278 11·4 11 ·5
TheYo·Yo 281
11-6 11·6 11·7 11-7
Torque Revisited 281 ;.v,gula AIlgula r Momentum 283
11·8 11-8
Newton's Second Law in Ang ular Form 285
11-9 11·9
Angula r Moment um 01 of a Syst em The Angular
01 of Particles 287 11-10 11· 10
U
Center of o f Mass and Linear Momentum M omentum
201 20 1 How un can II m;ll mal .. bighorn sheep sh.ep surviv .. th ..... .. s .. veM ve", h..lld collision coNision with which it glli"" dominanc .. ? 9-1 What Is Physic.? Physics? 202 9·1
and Angular 275
The >.ngular Angular Momentum of a Rigid Body Rotating
About a Fixed >.xis >.xi. 287 of Angular Momentum 290 11-11 11· 11 Conservation 0/ 11· 11-12 12 Precessionol aGyroscope 293 Rev;"w & Summary 295 Questions 296 I Problems 297
9-2 9·2
The Center of Mass 202 Neilton's Second Law for a System of Particles 206
9·4
Linear Momentum 209
9-5
of a System of Particle. Particles 210 The Linear Momentum ofa
9-6 9-7 9·7
Collision and Impulse 210 Conserva tion of Line ar Momentum 214
9·8 9·9
Moment um and Kinet ic Energy in Collisions Collisiom 217 Inelast ic Collisions in Qne Dime
12·J 12-3
The Requirements of Equilibrium :>07
12-4
The ne Center of Gravity 308
9-10 9·10
Colli.ion. Dime
9-11 9·12
Collisions in Two Dimensions 224 Systems with Varying Mass: ), Rocket 224
12· 12-5 5 12-6 12·6
Some Examples of Static Equiliooum 310 Indeterminate Structures 314 Elasticity 315
Review & Summary 226 Quest ions 228 I Problem. 229
m
Equilibrium and Elasticity Elast icity
305
Why i. """" th .. sfight uk tih of th .. l.. aning towsr tower in Pis;! dang .. rous? PiSil 12-1 What Is Physics? Physic.? 306 12· 1 12-2 12·2 Equilibrium 306
Who! What ·mon.t ·mon.!.... • !uro lurks at th t h.. c.. nt.... of our MUky Milky Way Galaxy? 13-1 What I. Is Physics? 331 13-2 Ne Newton's ..... ton·.l.a Law ..... of Gravitation 331
What cau.e. cau. e. the .ometimlls .Om
What Is Physics? 414 Type.o/Waves Typeso/Waves 4414 14
13-3 13·3 13-4 13-5
16-3 16-4 16-5 16-6 16-7
Transverse and Longitudinal Waves 414 Wavelength and Frequency 416 TheSpeedofaTravelingWave 418 Wave Speed on a Stretched String 412 Energy and PONer 01 of a Wave Traveling Along a String 423
13-6 13-7 13-8 13-9
Gravitation and the Principle of Superpos.ition 333 Gravitation Near Earth·s Earth's Surface 335 Gravitat ion Inside Insde Earth 337 Gravitation Potential Energy 338 Planets and Satellites: Kepler's LaNs LaNS 342 Satell Satellites: ites: Orbits and Energy Ene rgy 345
Einstein and Gravit ation 347 RevieN & Summary 349 Question. Questions 350 II Problems 351
U I Fluids 359 How do ... IIII ""'ri surf.... "",rf? surf? 14-1 What Is Physics? 360
14-2 14-3 14-4
What Wha t I. Is a Fluid? 360 Density and Pressure 360 Fluids at Rest 362
Archimedes' Principle 367 Ideal Fluids in Motion MotiOf1 370
14-9 The Equat ion 01 of Cont inuity ]71 14-10 BernO
1I1-1 0scillations 386 How can you .top stop th osciHation. of the.. natural but annoying asciNation. a tall building buildw.g in .. II wind? 15-1 What Is Physic.? Physics? 387
II
15-2 15-3
Simple Harmonic Motion 387 The Force Law lor Simple Harmonic HarmOf1ic Motion MotiOf1 390
15-4 15-5 15-6
An Angular Simple Harmonic Oscillator 394
15-7
Energy in Simple Harmonic Motion 392 Pendulums 395
Harmot1ic Motion and Uniform Simple Harm""ic Un iform Circular Motion 399 15-8 Damped Simple Harmonic Motion 400 15-9 Forced OscillatiOf1s Oscillations and Re5or\ance Resonance 402 Revie' Revie'N li & Summary 403 Questions 403 I Problems 405
16-8 The Wave Equ ation 425 16-9 The Principle of Superposition Superpositi"" for Waves 426 16-10 Interference a/Waves 427 16-11 Phase ... 429 16-12 Standing Waves 431 16-13 Standing Waves and Resonance 433 Review & Summary 436 43.6 Questions 436 I Problems 438
li~j Ii~j Waves-1i Waves-II
445
What lNhat caus ... th th.... musical echo from the stairs st";rs at IIt;on an ancien! ancient Mayan May.>n pyramid? 17-1 What Is Physics? 446
17·2 17-3
174 17-5 17-6 17-7 17-8
Sound Waves 446 The Speed 01 of Sound 446 Traveling Sound Waves 449 Interference 451 Intensity 453 Inten.ity and Sound Level 45] Sources of Musical Sound 457 Beats 459
iM W Temperature, Heat, and the First Law of Thermodynamics 476 How can ;> be..tI. betltlil detect d.. tect II.. forest /ire /i", at a larg large.. distanc di.tanc .. without seeing or srnelSng srnelNng it? 18-1 What Is Physic.? Physics? 477
18-2 18-3
Temperature 477 The Zeroth Lawai Thermodynamic. Thermodynamics 477
18-4 18-5
Measuring Temperature 478 The Celsius and Fahrenheit Sca Scales les 478
xii
Contenu COI1t. nu
'"
118-6 ~'
Therma l ExpanKN'l EJ.pa"sion 482 Th.'mal Temperature and Hut Heat 484 118-7 ~7 Tempe"'t" .. ..-.d 18-8 The AbsorphOfl of Heat by SoIods Solicit lind and lJquods Liquids 48S 485 Absorptoon 1 ~' 18-9 Closet look Look It at Hut Heat lind and Work 488 A CIoN< 1~' 18-10 The ~ First lI'" Law of Thennodynamoa Th.rmodynamics 490 11-10 18-11 Some Special Cases 0 1 the First FilSt 1I laN 01 Serre Sp.c; .. 1 Cuu of .. of 11-11 ThermodynamICS 491 Thennodynam..:1 18-12 Heat Tran.fer Mechani1ms 493 1"'12 HUITrln_Mechanosml RevIew SumrNlry 497 Rw .. w & Summllry QuestIOns 498 I ~ Problems SOO 500 Cluestoonl .98
.L.°J The Kine Kinetic ",'J tic Theory of Gases 507 What 'pp"rJ ~n wnen aII QI(/x>nM.J arbonatord ~I ccalMS ..... th. the fog!h.t fog th.1 IIppHn drink;' opened? drirJr. ;,~7
19-1 Ph~ia? Sa! S08 What II PhY.le.? 19-2 Avogadro's Number 508 A~.dn;l" Numblor 19-3 1de,1 19·3 Idea l (in., Gases 509 19-4 Pressure, Tempe Temperature, RM5 Speed 512 P,.nure, rature, and RMS 19-5 Translational Kinetic Energy 514 T'an,l.tIO".1Kine tie 19-6 MeanFreePa Mun F... P. th 515 19-7 TheDistributio.-.oIMolec ular5peec1. Speedl 517 Th. D,Unb\llion of Molecular 19-8 The Heatl of .n an idelll Ideal (ill Gas 520 Th. Molar Molir Specific HU ll ol 19-9 Degrees Freedom and MoI.. Molar 5p
t.j)) Entro py t ,{IJ Entropy
aand nd the Second law Law of The rmodynamics 536 Thermodynamics v.-twl ;, the _.~ .... bet_n b.r!_n aII fUbb., n.obb..- band's o.nd'. stretch st.-lOt"" What;' tt...:onMC1ion
and time1 11M the dir«tion wKfion of 01_7 20-1 What I. Ph~ia? 537 20.1 'NNIIIPhyso? 20-2 Irrewr'Slble and Entropy l~bIe Proc.sses Prou_llnd Entropoy 537 20.2 20-3 Change '" En tropy 538 20.3 Ch'nge In Entropy 20-4 The of ThermodynamiC$ 542 Th. Second L-BIH L.. .. ofThfimodyNmia 20·5 Entropy in the Real on Re,l World: World . Engines Eng""" 543 20-5 20-6 Entropy;n Real World: Entropy'" the Rul World R"frigeraton R.fngera ton. 548 20-7 The Th. Efficiencies Efficiene... of R.al Engi..... Engln-M 549 20-8 A Statist it;al View Vi.w of Entropy 550 20.8 SI""t ical Revie w& 55 4 & SummaI)' Sumn'lllry S54 Revi.w Question s 555 I Problems Quution, I Pn)bleml 555
t.li t.fJ l. Electric Charge 561 How can c.n a• video vid.o monitor """nil.... in aII .urgicM .urgiaJ room increase ina..... th. the rilk riM of 01 bact«",' &..;t.,iIIl contamination? t;or!tll ....... llon 7
21 21·-11 21 21 -2 ·2
Wh.t I, Physics? Phy*-'CS? 562 What Is Eleclric Charge 562 E\ec\rll;Charv-
'"
CondUCIorslnd 21·3 Cooductors IWld Insullll(q Insulatoll 563 Coulomb's L..' Law Coulomb'. ,'I 54S 21~ 565 21. Quantized Sl1 Charge Is QUIIflIJ:ed 21·5 571 21 -5 Charv-I. 21~ Charge I. Is Conwrved Conserv.d 57' 572 21-4 ChIIrge Review & SumrnIIry Summary 573 Revoew Questions 573 I I'IobIemt Problems S1S 575 Ouestoons
t-t .. Electric Ele ctric Fields Fie lds 580 J"~" Howden. 11M fh men Howdoes a bee be.t ..... .... electrosr.tic. eI
".,..7
22-5
22-6 22·7
22-8 ZZ·9 22-9
Charge 583 Chllfge The Electric: Du. to.n Electric Field Due to an Electric Eleclric Dipole 585 Th. Electric Field Due D~. to a I line Lin. of Charge 586 Charg. Th. D~. to. The EIKtnc Electric Field Due to .. Ch.,g.d Charged Disk S90 590 Di"" A an Electric 591 A Point Pomt Charge Ch.rge in .... Eleetnc Field Fi.1d 591 In .... F.. 1d 594 Dopole in A DIpole an Electnc; Electric Field
t.f:':J J"-itJ Gauss' law Law 605 How can )0<1."- if jt •• you? How an lightning '91It"ing harm h.ot"".1'0".'" " does do... not nol $u IIT".)'OU7
23-1 23-2 23·2 23·3 23-3 23~ ".. 23·S 2l-S
,3-4
23~
23-7 '~7 23-8 2l~ 23-9
What Is Physoal Physics? 606 WhIt Flu.; 606 Flux Flu.; of an In ElectrIC Electrll; F",1d Foeld 607 Flux of Gauss' Law WI Glust' L...... 6t:H Law Coulomb', laN GaulS' L..· .. and 1nd Coulomb's L.... 6" 611 Gauss' A Cha.ged ChIIrged Isolated I.al.ted Conductor CondIKtOr 612 Applying Gauss' G_,' law: L.. .... , Cylindrial Cylondnc.1 ApplyIng
tl;J t"l;.I Magnetic Mag netic Fields Fie lds 735 \Nhat vvnat cau CilUS .... ... an aurora and why i. it so 00 thin?
J'+1 Jr+1 Capacitance Ca pacit a nce 656 How can a spark ... t up an explosion ..xplosion in "irborne airborne powder? 25-1 What Is Physic.? Physics? 657
,>2 2>2
Capacit.nce 657
25-3
Calculating Calcu lating the Cap.citance 659
25-4
Capacitors in Parallel Para llel and in Series 662
25-5
,>6 2>6 25-7 25-8
Energy Stored in an Electric Field 666 itt, •a D",lectric Capacit or ..Nith Dielectric 670 D",lectrics: Dielectrics: An Atomic 'I",w View 672 Dielectrics D",lectrics .nd and Gauss' LaN La .. 672
What Is Physics? 736 What Produce. Produc e. a Magnetic Field? 736
28·J
The Definition of oHi B 736
28-4 28-5
Crossed Fields: Dis.covery Dis.covel)' of the Electron 740 Crossed Field.: Fields: The Hall Effect 741
28·6
A Circulat ing Charged Particie Particle 743
28·7
Cydotrons Cyclotrons and Synchrotron. Synchrotrons 748
28·8
Magnet ic Force Fo.-ce on Oil a Current·Carrying Wire 750
28·9
Totque TDfque on Oil a Cu Current rrent Loop 752
28·10
The Magnetic Dipole Moment 754
Review & Summary 755 Questions 756 I Problems 757
Jr.f·1 J'.f'·1 Current and a nd Resistan Resista nce ce 682 What pnte precautions .... tions should you take tak.. if caught outdoors during .. fightning storm? during.
J""') Magnetic Magne t ic Fields Due t o Curre Currents nts 764
26-1
Wh.t Is Physic.? Physics? 683
field without any magnetic materian f",1d mat .. rian
,~,
2~2
Electric CUlTent 683
2~3 '~3
CUlTent Density 685
29-1 29-2
2~4 '~4
Resistance .nd Resist ivity 688 Ohm's law 692 ;!., Microscopic VieN Vie .. of Ohm's law 693
2~5 '~5 2~6 '~6
2~8 '~8
Power in Electric Circuits Circuit s 695 Semiconductors 696
2~9 '~9
Superconductors 697
2~7 '~7
27-2
"Pumping" Charges 706
Cakulating the Magnetic Field Due to a Current 765
29·J 294 29·5 29·6
Force Between T..NO o Parallel Pa ra ll el Current Current.s 771 Ampere's L.w 772 m Soienoids Solenoids and Toroid. To.-oids 776 A Current·Carryir.g Coil as a
lei etic Oscillations tel .l Electromagn El ectromagnetic Oscil lations and Alternating Current 826 B26 djd .,o/4r eruption knock 0<1\\'" OIlt the powerHow did •• 01.0. e""PllOn power· grid system Ouebec1 'Ylltem of auebec? 31 -1 Wha t I. II f't1Ylicl? 31· 1 Wh,t F't1y.lc.? 827 31 -2 LC Oscilla tions, Qu,litatively Qualitatively 827 31·2 lC o.cill.IIO!'I., 31 -3 Th ] 1·3 Thee Electrical-Mechanical Electnc.~M ech,nic:al Anabgy An"logy 830 810 31 -4 LC titat .... .....1y ly 831 31·4 lC OscillatIons, o.c,n"uonl, Quan Ou"nt~"t 31-5 Damped OSCIllations in an RLC O",.,ped o.c,II~IIO!'I' In lIn RlC 31· 5 CIrCuit C~UII 834 31-6 Altemallng •• nt 835 AlwI'nIIU"5I Cur c..,.otnt 83S
"..
Forc~ OKlbtlOM O5clllation5 835 Fore..:! 31-8 Three 5mple CircUIts nv.. Somp!. c...: ...tI 837 31 ·' The Senes 5enH RlC CircUIt Cin::... t 842 31 ·'·9 31-10 Power III AkematJng-Cu.rent Pow.r .. AIr..n.ung-C.....nt 31· 10 C.n::ullS CIrCUM 846 IU6 31·11 Tr1On.~ 849 J1 · 11 Transformers R ....,ew R"" .. \III & & Summary Suorvnary 853 Ouestoans Ou.stlOll. 854 I Problems Probieml 855 ass
31-7 31·7
n..
Ie;"" Maxwe ll's Equations; Magnetism 1cJ--I Maxwell's of Matter 86 1 861 How Can a 1'00,,1 clln. """ •• 1painting p .... "ng record the \". djrKtion direction
E... th 'l'. m~nelie of Earth m.gnetie field? f;.kI? 32-1 What 32· 1 Wh.t Is I. f't1ysics? Physics? 862 32-2 Gauss' Law lor tic Fields G.uu' for Magne Mlgnetic F,elds 862 32·2 32-3 Induced IndllCed Magn MlIQfIeetic lic Fields Field, 86 4 32·3 Cllrren 32-4 Displacement OlsplKlmlnt CUl1'IIntt 866 32·4 32-5 Maxwel!'s M,,_I1', EquatlOfls Equ,,"ons 868 32· 5 32-6 Magnets ]2·6 8.. M..~ 869
'" '"
......
Ie):) 1c~1 Electromagnetic Waves 889 BB9 What g _ " a'undosI, .undog, the me brighr, ~brf~.peIf. th. m. gil ColIn Wn-: &tip#ot, aH:wfuI'p« CoIIUS. .
appear lefr «righf or righr of oJ die rile S~1 Sun? ~r.loth 33-1 Wha t 1. Is Physics? 33-1 What PhYSICS? 890 MaxNell'sRainbow 33·2 MaullI'. R.lnbow 890 33-2 Electromagnetk Wive, Wave, The TravelIng Tr..... I..g EIKuom.gnl!lC 33-3 33·3 Qualita tMliy tive ly 891 Qu"l,tl The Trlv.ling Traveling Electron'l.gn.tic Electromagnetic Wive, Wave. 33·4 Quantitatl ....1y 89' Quantitatively Transport and thl the Poyn Poynting 897 Energy T .ansport .r.d ting Vector 8" 33-5 33·5 33-6 Pressure 899 33·6 Radiation P.n.ute 3., 3~7 Pola.izatioo 90' Pollination 901 3]· Reflec tlOn.nd I... dOOfl 90S 33-88 tion and R, Refraction 905 Toullntemal 33-9 Total Internal R,flection R. ~ ection 91. 910 3~' ~,. 33-10 Polarization by Refl ection 912 PoI"nation ReflectOOfl ReVle'N 913 Review & Su,.,.",..",ry Surrrnary 91J Questions Problems 915 Quest IOn' 914 I Problem.
... ...
rn
~ Images lm age5
924
How c... _ dNrly deatfy inboth in bod..r Ind ..... If" Howe .... fj"" fith._ air ..dw .... si...Ntaneous.ly1 """"--.1 Is PhYSICS? Ph)'I'CI? 925 34-1 What I. 34-2 Image 925 34-. Two Types Type. of 011"'9' 34-, Pla PIa". M,fl'OI" 926 34·3 ne Mirrors 34-4 Spheral MIffOfI MillO" 928 10Nge' from Spherical Sphen;.l MlrTOI"I Mom:n 930 34·5 34-. Images 3U $ph"ne,1 Refracting Refl'Ktl"51 s...rfac.s Surf~ 933 34-6 SpherICal Th,n Len_ 936 Thm Lenses 34-1 34-7 Optical Instruments .41 941 34-. OptiClllnltl'umentl 34-8 34-9 Three proofs Proof. 944 34-' Thl'fl. Review & & Summary 947 Question. Questio ns 948 I Problems Probl,ms 949
'" ,..
~1-1 lnterference lnterferen ce
958
How do ~'or--oh;ftjng coI_thihillfil inb i"q on all P"f"M Pflper rorr...cy CUIT«IC)' ,hjfl .hih colors? co/or.' 15-1 '~t Is I. Physics? Phy.o? 959 959 3501 What 3502 ught as a Wave 35-2 LoghtlS" Wa.... 959 959
Contents 35-3 35-4 35-5 35-6 35-7 3S-7 35-8
Diffraction 963 Young's Young', Interference Experiment 964 Coherence 968 Intensity in Double-Slit DoubJe-Sl it Interference Interfe rence 968 rierence from Thin Films 972 Inte rierer>ce Miche Michelf>On'slnterie lf>On's Interie rometer 978
RevieN Revie N & Summary 979 Prob lems 981 Questions 979 I Problems
~I.1 ~I.'1
Diffractio n 990
What cau UUSM .... th thot.. a"esting blu. color of the ffacial .. cial skin of a mlltldral mandral baboon? 36-1 What Is Physics? 991
36-2 3~3
36-4 36-5 3~'
Diffraction and the Wave Theo
Diffraction by a Double Slit 1002 3~7 Gratir>gs 1004 36-8 Diffraction Gratings Gratings Ref>Olving Power 1008 36-9 Grat ings : Dispersion and Resolving 36-10 Diffraction DiffractionbyOrganizedLayers by Organized Layers 1010 RevieN&Summary 1012 Questions 1013 I Problems 1014
.. Re Relativity lativity
~, ~r..
1022
How can Clltl ...... detotrmin det"",,;,,e.. what lu,b lurla at al thot ccotn!er .. nt .., of th .. 5ght-yurs away? galaxy M87, MB7, 50 mimen mimon 5ght·yul'S 37-1 What Is Physic.? Physics? 1023 37-2 The Postulate. Postulates 1023 37-3 Me Measuring asuring an Event 1024 37-4 Simultaneity 1026 1026 The Relat ;"ity 37·4 ivity 01 SimuJtaneity 37-5 Relat;"ity 01 37·5 01 Time 1027 The Relativity 37-6 The Re lativity 01 lengt Lengt h 1032 37-7 The Lorentz Transformation 1034 37-8 Some Consequences of the lorentz Lorentz Equations 1036 37-9 The Relat Relativity ;"ity 01 of Ve10cities Velocities 1038
37-10 37-11 37-12
Doppler Effect lor Light 1039 A Ne'NLookat Ne", Look at Momentu m 1043 A NeN Look at Energy 1043
1e1:1 leI:) Phot ons and Ma tte r Waves 1057 How can moll>CUles molflCUles be movotd mCNN one by enot on .. and til"" th.." im.ogotd? ;rrI8gN? 38-1 What Is f'l1ysics? f'I1ysic.? 1058 38-2 The Photon Photon,, tne the Quantum 01 light 1058 38-3 The PhotoeJectric Photoelectric Effect 1060
Photons Have Momentum Mome ntum 1063 light as a Probability Wave 1066 38-6 Electrons and Matter Waves 1068 38-7 Eq uat ion 1071 SchrOdinger's Equation 38-8 Heisenberg's Uncerta inty Principle 1073 38-9 Barrier Tunneling 1074 Sarrier Review & & Summary 1077 Quest ions 1077 I Problems 1078
384 38~
~l.·l ~.·l
More About Matte r Wa ves 1083
How can you corr corr.1 ..1an ..otlotctron? Iotctron? 39-1 What Is Physics? 1084 39-2 39·2 String Waves and MatterWaves 1084 39-3 Energies of a Trapped Electron 1085 394 Wave FUr>ctions Functions 0/ a Trapped Electron 1089 39-5 39·5 An Electron in a Finite Well 1092 39-6 39·6 More Electron Traps 1094 39-7 Twoarid Three-Oimerlsional Three-Dimensional Electron 39·1 Traps 1096 39-8 39·8 The Bohr Model of the Hydrogen Atom 1097 39-9 SchrOdinger's Equation and the
Hydrogen Atom 1100 Review & & Summary Sum maI)' 1106 Quest Questions ions 1107 I Problems 1108
r:r'l r: r'l AIl Abo ut Atoms 111 2 What lNnat;s is so diH"",nt diff..,.,nt .bout about
40-1 40-2 40·2 40-3 40·3
~ght
from IIala b ... r?
4~9
What Is Physics? 1113 Some Properties of 01 Atoms 1113 Electron Spin 1115 Angular Momenta and Magnetic Moment s 1116 Dipole Moments The Stern--Gerlach Stern-Gerlach Experiment 1118 ne t ic Resonance 1121 Mag net The Pauli ExciusiOf1 Exclusion Principle PrincipJe 1122 Mult iple Electrons in Rectangular Traps 1123 Period", Table 1126 Build ing the Periodic
40-10
X Rays and t he Ordering of the
40-11
Elements 1127 Light 1131 Lasers and Laser light
404 40·5 4~5 4~' 4~7
4~'
xvi xvi
Contents Cont..,u AN.rotunol A Na tural NudNrRNCtor Nuclear Reactor 1205 The!monuo;lea, Thermonuclear FullOl'l; Fusion: n. The BIIIIC Basic Proc. .. 1207 Proceu 1207 Thermonuclear FuSIon '" on Ihe the Sun.nd Sun and n-n-.u.: ..... FulOOl'l
4]·5 43-5 4].6 43-6
40-12 HOHlMersWotk HONLaserlW()I'\( 1132 1132 40.12 R...... ..... iew & SulTll'Nlry Summary 113S 1135 R H & Question s 1135 I Problems 11 1137 Q ..."'toonl 113S f ProbI.m. 37
43-7
Other Other St.rs Stars 1208 Controlled .... FullOl'l Controlled TI-monucl n-monucle. Fusion 1211
E!U Conduction Conductio n of Electricity Ele ctricity [:il in Solids 1142 'Nhy do n;>d: n>d: guitMisti gvit•• ts shun ,hun """';st.,,."mpfr..,. tr';"''';$!OI".mpff~ fo, oldWhy lOT oldf ...hiOMd lube tub. 1I~;fj.,'? • ...pWi_? 'IIJhjon«l 41 · 1 What Is Physics? 1143 Wh.lotl.Ph~? 41 ·2 Th. ElectnYI Electric.;ll Prop.rt Propert'eI Solid. 1143 41-2 The ... of SoIdi ·3 Energy Level. ,n InaII ~~ ~talli ... ... Solid 41 ·J Etwrtgy SoIod 1144
H I Quarks. lLepto ns. and the eptons. Big Bang Ba ng
12 18
How un" /y uni_.. be ~'«I c.. a pftologr."n photog,;oph 01 of dw the •• e./y t.a~ ... 11 44-1 Whit PhysICS7 1219 44· 1 Wh. t I, l. Physics? 44-2 PanIC . ., PartICle., PMlocles 1219 44·2 Pa rt icle. Particle. , PartICles 44·] No 44·3 An Int.,lud. I"teo-Iude 1223 44-4 Thel. ptonss 1226 44·4 The Lepton 44·55 T,... 44· The H.dronl Hadrons 1227 Still Anolher Co nserva tion La" La'l 1229 44·6 Another Conservation 44·7 Th. Eigh tfold WilY Way 1230 44-8 Th. Quatk Qu~rlo. Mod.I 44·8 The Model 1231 .... 9 Th. BiOIw; Fon:H M.ssenger 44·9 The B. sic Forces and MelS8f>ger Part Part"ICle. . . 1234 APIiUMfOfReoflKbon 44-10 A Pause for Reflectoon 1236 ....... Is &panding ~ndng 1237 44-11 The Uno Universe CoimIC Background Radiallon RadoooDOn 1238 44-12 The Cosmic 44· 1J 44-13 44-14 44-15
Daric M,," .. 1238 Oatk Matter 123B Bog Bang BIIng 1239 The Big ASummirogUp A Summ,ng Up 1242 ReYMl'N & & Sul'T'VNry SulTll'Nlry 1242 1242 Revie-N a..-toon. 1243 I Problem. 1243 Question.
_
Appendices Appe ndices
The In ternational System of Unit. IntlfTlauon.l Unlfl (Sf) (51) A-1 A. l Scom. Fundament.al Fund"mental Constanta eon.tantl of 01 PhYlics PhysIQ A_' A·3 Some s.:.m.Aslronotnocal Dati A-4 A-4 Some AstlOflomica i Data o Conv ConYlf'llOfl Fac;~ M A·S D .... ion Factors E Math Malhemati<;al FQnT\4Jln A-fl E .. matica l Form"l .. A-' F Propenl .. of theElem«l1l A·12 F Propt!rtie s of the Elements A· 12 G Periodic Periodic Table Table of of tile Ih, Elements Elements A. A·1S 1S G A. A
B C C
What loVh"t phYlies ~h)'lics und.rlie. und.rliH the th. image that thai ha. hal ho,rifi.d ho,rif..d the the world world ,ine. ,incI World World W.o, WoO, In JI1 43· 41·1' 43-2 43·2 43·3 U ·J 43-4 41-4
Wha t IIIPh~1 PI1Ylics? 1196 WhaII 1196 Nucio. Fission: Fissoon; The The Basic Bllsoc: Proc." Pnx... 1197 1197 Nuclear A A Model Mod.! !Of' for NlIClear Nucle... Fission FiM>Qn 1199 1199 The Nuclear Reactor 1201 The Nuclea. RNaor 1201
Answers o CheckpOints Answen tto Checkpoints and and Odd·Numbered Odd·N umbered Questions and Problems Problems AN·1 AN. 1 Quest ions and Index Index
1-1 1·1
Fun wit h a big cha ll e nge. Th at is how I have regarde d ti o ns. and solve quantitati ve pro bl ems. This process is ph ysics s ince the da y whe n Sharon . one of the stud ent s not easy for e ith e r stud e nt s or instructors. Indeed. the in a class I taught as a graduat e stude nt. sudd e nly de course associa ted with th is book may be o ne of the most chall engin g of all the cout"ses taken by a student. manded of me:' What has a ny of this got to do with my life?"" O f course I imm ediat e ly responde d. ··Sha ro n. Ho we ve r. it can a lso be o ne of the most rewarding because it re vea ls th e wo rld 's fundame nw l clockwork th is ha s e verything to do with yout" life- th is is phys ics. ,. from whi ch all scie ntific a nd e ngin eering applicati ons She a,ked me for an e xample. I tho ught and spnng. thought bill could not come up with a sin gle one. That Ma ny users of the seve nth editi on (bo th instrucni ght I c reat ed The Flying Circlls of Physics fo r Sharon to rs a nd stud e nts) sent in comm ent s a nd sugges tio ns to improve the book. These improveme nts are now incorbut a lso for me ~cause I re alize d her complaint was porat ed int o the narra tive a nd pro ble ms th roughout mine. I had spent sL'( years sluggin g my way through many doze ns of ph ys ics te xtboo ks tha t we re ca refull y the book. 111e pu bli she r Jo hn Wiley & So ns a nd I writt en with the ~st of pedagogical plans.. but the re rega rd the boo k as an ongoing p roject and e ncoura ge mo re input fro m lI sers. You can se nd suggesti o ns. corwas some thing mi ss ing. Phys ics is th e mos t inte restin g rect io ns. and pos iti ve or nega tive comm e nt s to John subject in the world ~cause it is abom how th e wo rld wo rks. .. nd ye t the text books ha d bee n tho roughl y Wiley & Sons (http:www.wiley.com/college/hallida y) wrun g o f any connec tion with the re al wo rld . The fun or Jea rl Wal ke r (mail address: Ph),s ics De partme nt. was mi ssing. Cleve land State Unive rsit y. O eve land. OH 441 IS USA : 1 hnve pa cke d a lo t of re al-wo rld p hys ics into this fax number: ( USA ) 216 687 2424: o r e mail address: HRW boo k. co nnecting it with the ne w editi on of 7711': phys [email protected]: or lhe blog site at ,",'WW.flyi ngcircu sFlying Circlls of Physics. Much o f the ma te llal comes ofphys ics.com). We may not be able to respo nd to a ll from the HRW classes I teach. whe re I can judge from sugges tio ns.. but we kee p and study eac h o f the m. th e faces and blunt comm e nt s what mate ria l an d prese ntati ons work and what do no t. 11le no tes l make on Major Content Changes my su c~sses and failures th ere he lp form th e basis o f th is boo k. My message he re is the smn e as I had with • Flyin g Circus mate ria l has ~e n incorpo rated in to eve ly stude nt J"ve me t sin ce Sharo n so long ago: ·· Yes.. the text in seve ra l ways: chapter o pen ing Puzzle rs. Sample Problems.. te xt ex,1mples. and end -of-cha pter you cal! re ason from lxlSic phys ics co nce pts all the way to valid conclusions about the re al wo rld . and that unProbl ems. The pu rpose of th is is two-fold: ( 1) ma ke th e subject mo re int e res ting a nd e ngaging. (2) show the de rstand ing of the t" eal world is wh e re the fun is.·· I have many goa ls in writing this ,-------~-----, stude nt that the wo rld a round the m ca n ~ exa mine d and unbook bu t the overridin g one is to provide instructors with a tool by which they can ders tood using the funda me ntal principles of physics. te ach stude nts how to effect ive ly read sc ie nti fic ma teria l. ide nti fy fun dam e ntal concepts. reason through sc ie nti fic ques-
xViii • Links to The Hying CirCIiS of Ph)'sics are shown th roushout the teXI nUl leriltland enj-Of..dUlple r problems with a biplane kon. [n the e l((~l ronic ~ ~'e rsioll of this book. ~ Iicking on Ihe icon ~ tak es )'ou 10 the corresponding item in F/)'ing CirellS. The bibliogmphy of F/)'/I/g Circlls (o\'er 10 000 refe re nces 10 scie ntific and enginee ring journals) is located at _-w.nyingcircusofphysics.com. • The Newlo nian ga\'itlllional 1.11". Ihe Coulomb law. and the Biol-Sa\'8 r1 law arc now introduced in unit,·ector nolation. • Most nlthe ~haptcr-Opcning pU7..zle~ ( the examples o f appl ied physics design ed to \"mice a reackr into each chapter) arc new (uld come straighl from research joumals in many differ\" nl fl\"lds. • Several Ihousand of Ihc end-of.chapter problems have ""'-' n rewril1en 10 Sirelllliline both the presentation and the (U! swer. Muny new problems of the mod· craie :md diffi~ull elliegolies hllv e been included.
Chapter Features 0 ll l' n in~
l)!IaIHs, A c uri o us puuling s ituntion opens ench chnptcl' and is exp illine d so mewhere within the chllpter. to e ntice a st udent 10 read Ihe chapter. TIlese features. which arc 11 hnllmark of FWldlll/wnw/j of Pllpics. are bused on current research as reponed in scientific. ellsinee ring. med ical. and ~g.'l.1 journals.
The sam ple prob!cms with thi!lnbel-Build )'ou r skill" are Iypically lonser. with more guidunce. Key I dt.'a_~ in the sample problems fIXus a studml on lite basic co nce pts III the root of the so lution to 8 problem. In effec t. Ihese key idens say. "We stmt our solution by using this basic con~ept. 8 procedure that prepares us for soh 'ing 111.111)' o thcr problems. We don't s ian by grabbing nn equ.1t ioll for n quick plug-andchug. a prIXedure Ihat prc pnrcs us for nOlhing."
Pruhll·nt -soh-inj.: laclil"" coll taiu he lpful instructions to guide the beginning ph ysics ,ludc UI lIS 10 how 10 solve problems an~ avoid common errors. R l',-i l'W,~ SI"llI n a r~ is a brief o Ullin e nlthe cha pter COlllents that cOll1ains Ihe cssenl iu l COIlC\"pIS but ""bich is not a subslitUie for rending Ih e chupter, QUl'st iu II~
ate like the checkpoints and require reasonunderstanding rUlher Ihllll Cll lculutioliS. A,lj'Wr:f 10 litl' odd- liJ/J/l ber<'d
inS and
P ruh l ~ ms are grouped und er see li o ll lilies ~lIId are labeled according to difficullY. AI/swers It) Ihe Qdtl.mUlIbert'd proble'lIs Urt' III lill' back of Ihe book.
Ico lls ro r a!ldition~ 1 hl'lil. When worked-oul so lutio ns a rc provided either in print or e lec tronica lly for certain of th e odd-numbered problems. the statem('nts for those p roblems include a trlliling icon to alen both stude n t and im lruclor as to where the solut ions are l0cated. An icon gu ide is provided here alld a t Ihe beginning o f each sc i of pro ble ms:
Wlml is phys iCl!~ The na rrative of eve ry cha pte r now begins wilh Ihis questioll.llnd with al answer thlll pertains 10 thi! subject o f the dl.'l.pt\"r (A plumber once asked me. "Wh.1t do you do fo r .1 liv. ... - -......... - - - ................. ~ ... _ I mg?" I rephed.- I 4~,=:::z:=::=::;,.::.::II::II leach pllysics.'· He Ihoughl for sc\'eral minules ll11d Ihen asked. "'VIlal is pllYSICS?- n le p lumm-r's career was SSM Solulion is in Ihe Sluden t Solutions ~'I(lnua l . e nlirel), based on pllysics. yel he did nOl even know WWWSolulion is al whal physics is. Many s ludeulS in introductory physics http:// ....ww.wilcy.oom lco l!cgelhaJliduy do not know whal physics is but assume that it is irrel· ILW Interaclive LearningW:,rc so luti on is (01 evant 10 Iheir chosen career.) hltp: llw\\'W.wilcy.oom/co llegeihllllidllY Chl'{kp.. lnt ~ ~re Sloppi ng points that effectively as k Ad!li l io n ~ 1 prohll'IIIS. These problems are /lo t ordered Ihe student. "C,n you ~Ul5wer Ihis question with some or sorted in ~n)' wily so Ilml II stud e nl must determine I'.", &o nin g basod On th;) nnc-raliv;) or .a mpl~ probl"", which p.1rts of the chnpler ~pply to nlly given problem. thlll you just re~d?" If 1I0 t. Ihen Ihe student shou ld go back over Ihnt prev'lo us malerial before traveling Additional Features deeper into Ihe chapl er. For eXll mple. sce Oleckpoint I on page 62 and Che~kpoint 2 on page 2&1. AlJ5wers Rl' ..souing 't: r~ us Jl l u~'\I rHI-dl ll ~. A primary gtllli of /Q (II/ checkpoilWJ (Ire in rite bllck oflhe book. this book is to teach stude nt s to reaSOIl through cllRl-
__-_ _- -_..
._.,. _ _ . _ _.",..._c-of_ .........._ ____ ~
Sa mple IIr"hll'lII' are chosen to demonstra te how proble ms eml be so lved with reaso ned so lutiolls rather thllll quick .1nd simp listic plugging of numbers inlo a n equ.'l.lion with no regllrd for whnt the equ.'l.tioll means.
c
lenging si tuations.. from basic prindples to It so lution. Altho ugh so me plug-and-chug homework problems remain in the book (on ptlrposc ). most homewor k problem~ e n:pllasize r\"asonillg.
Pre/ace C lmpt e r~ tof reaso nabl e I,·n I,·ngth. gth. To avoid producing a lx>ok lxx>k thick thic k enough to stop a bullet (and thus also a student). I have mad madee the chapters of reasonable length. J explain eenough nough to get gel a student studenl going but nOi nOI so much Ihm a studenl student no longer must mu st analyze and fuse ideas. After all. a student will need th thee skill of analyzing and fusing ideas long after Ihis this book is read and the course is completed. lp a hl ~ calcuof H" n" 'l o N" r- ~'lp e r,ll r~ llhu uhu tors. ors. Whe Whenn vector calcnlations in a sample problem can Gm be performed direclly directly calculator.lhe solution on-screen with a vector-capable calculator. the so lution of the sample sa mple problem indicates that fact faci but still ca carrries Ihrough through Ihe th e traditional component componenl aualysis. When vector calculations cannot be petformed performed directly oonn-xplilins why. screen. the solution solulion eexplains U~ U~
Graphs 'is pIlUJ,'S. These are problems that Ihat give a thm requires much more mo re graph and ask for a result Ihal than just reading off a data point poinl from the graph. Rather. the solution requires an understanding of th thee physica arrilllgement in a problem and the principles physicall ammgement behind the associated associmed equations. eq uations. TIles.:; TIlese probl problems e ms are more like Sherlock Holmes puzzles because a student must decide what data are important. For examples. see problem 50 on page SO. problem 12 on page 108. and problem 22 on o n page 231.
xix
• \'o \'" luu1l' lun1l' Chapters 1I- 20 (Mechanics ( ~-Iechanics and Th emlOdynamics). hardcove hardcover. r. ISBN 978-0-47004473-5 • \'ollln1l' \'olun1l' 2 - Chapters 21 21--44 -44 (E&M (E&M.. Oplics. Optics. and Quantum Physics). Physics). hardcover. ISBN 978-0-47()"04474-2 978-0-470-04474-2 I- II. 11. paperback. [SBN 978-0-470• P:ut I - Chapters 104475-9
Th ere have been seve several ral signiflc.lnt ndditions to the WileyPLUS course th.at accompnnies Fwu/allll'n/a/s Fwu/alllenia/s of Physics: Physia: • All of the eend-of-chapter nd -of-chapter problems have been coded and ilnd are now available for assignment.
Prohirms ph)-~i~s. based on published reProblcllls with appli"d ph)-~ifs. search. appear in many places. either as Ihe Ih e opening puzzler of a chapter. a sampl samplee problem. or a homewo homework rk problem. For example. see Ihe the opening puzzler for Olapter 4 on p.1ge 58. Sample Problem 4-8 on pages 69-70, and homework problem prob[;:m 62 on Oil page 302. For an example of homework problems that thai build on a continuing story. see problems 2. 39. and 61 61 on p..1ges pages 131. 134.and 136.
• Every problem has hns an associated Hint that c.1n made available to the students at th thee instructor·s discretion.
Pro bl ems with non·1 s~ illmtioll Prubl itunti oll s. Here is one of seve several ral hundred such problems: problems: Problem 69 on JXlge page 113 relat lates es a lrue true story of how Air Canada flight 143 ran out OUI of fuel at an altitude of 7.9 km because th thee crew and alld airport personnel did not consider the .,irport th e units for th thee fuel (llll (11ll impol1anl impol1mll lesson for students stude nts who tend te nd to "blow off· units).
• For every chapter. approximately 6 problems are available in 11a tutorial formal format th.at that provides ste step-byp-bystep. interactive problem-solving guidance. guidmlce. Most are marked here in this book with th thee icon Ql (,· (,·Guided Guided Online··) but more are being added. added .
Versions of the Text
• There are approximately 400 additional Sample instnlfl or's Proble Problems ms availnble to the student at th e instnlct discrctilm, discreti on, 111e llle Sample Problems are written in the same style and fonnat as those in the text. i.e .. they th ey are inte intended nded to give the stude studell1 nt transferable proble problem-solving m-solving skills rather than specific recipes.
• For evelY evel)' chapter. approximately approximate ly 6 problems are requiles quires the th e studenl student to availnble llvailnble in a version that re eenter nter an algebraic nlgebraic answer.
To accommodate accommodat e the individual nee needs ds of instrnctors and students. the eighth eighlh edition ed ition of FUlldallll'/!Ia/s of Physics is available in a number of differenl different versions.
• There are vector drawing and vector diagram fll nct iona lity to asproblems that use "drag·n "drllg ·n drop·· functionality seSl; ses.<; the students· ability llbility to draw vectors and vector diagrams.
TIle Ih Rcggui ul ar Editi Edition on consists of Chapters through 37 (IS BN 978-0-470-04472-8).
I
• There are simulation problems that require the student to work with a jllva java applet.
TIle E ..~h·ndrd ~ t l·nd ~d Editi on contains six additional chapters on quantum physics and cosmology. Chapters 1--44 (IS BN 978-0_47 I- 75801-3). 978-0-471-75801-3).
Th e overall purpose of this new material is to move th thee on-line homework experience beyond simple prob. Right/Wrong grading and provide meaningful problem solving guidance and support. 5llpport.
Both ed editions itions are availilble avaibble as single. s ingle. hard-cover hard-cove r lx>oks. lxx>ks. or in the following alternative versions:
Preface
Instructor's Supplements In~ tru(1"r'~ Sohlliom Solutio ns Mlinual Manllal by by ~n-Ikn Se n-Ben Uao. Liao , 11I ..lnlclnr·, L1Wre nCe uLive rmo re Nallonal National I..abonll Laborntory.l1lis vermore ory. This manual I..a"Tente provides wOl'ked--oul solUlioos solmions for 11011 1111 problems pro blems found pro ...des workcd..{)ul at the Ih e end ooff eath each chapte chaple r. lit
cI"r Cmnpwnio Co mp ,minn hlustru .. lnl cl"r n Sill' http: // ....ww.wiley.comlcollegel1lullidlly http://www.wiley.oornlco llcgenl;' Il kllly i'll.iulnll 01riSlll1an. • hInl'l_trud"r's rllt"I"r'S I\I II um11 by J. Richnrd Olr'ls tl1wn. U.S. Coas t Gumd Guurd Academy. This rcsourw reso urce conlains co ntains lecture COIISI tes outlining the most imporuulI importa nt to pICS pics ooff each no lU cll.1pte r: demo ns trat ion experime nts: la borato ry and und ch,'1 pter. Ocmonslla lioo expcnmenU; loborntory comput e r projects; projects: fUm film and ,ideo video sources; sources: answers answe rs 10 to CQmput all Quc:slions. Questions. Elercises.. Exe rcises. Problems. and ~d;JlOirllS; Q loCCkpoin ts: correi.,tion to the Questions. Exe rcises. and IIa correLl tl(Jll guide guKk 10 Qu..."'ShOM. Ele~i:se5. blems in Ihe pre"ious edition. edi tio n. It .also aand nd Pro Problems the pre\'ious lso oontains con tains a11 comple te list Ii$t ooff aU all problems for which solutions aare re availlible to ssllIck
• Wil~<) Sitl1ulali o tl~ by Andrew \\1[ \') Plt),sil':> l)h~'~ i~ Silllu[alinns Andre w Duffy. Duffy, Bosto Bostonn University. Universi ty. SO imeractive interactive lis imulatio imulptio ns Jls (Jlwa (b va applets) applels) thllt class room de mo nstmli o ns.s. Ih~. t clln cun be used for forc1assroom monstration • Wiky ifs I)l'mo n~ tmti "n'~ by llo. WII ~ ~' Php I'hy~i.·., 1J(,l1Iom t rnti"n by David DJvitl Mniu M ~li ullo. Rutge rs University. Universily. This is 11a collectio n of disital digi lill videos videos of 80 nstrations. They can 80 standard siandard physics physiai demo de mons1nIllOIl!. can be shown in ci. ' I5I; or accessed from th e stude nt companshown III class or (rom the l tude nt companion re is lin uide 100 site. si te. The There an acconlp.lnying aa:onlpon)ing Instructo r's G Guide tlk, r" questions. LlICludcs "clicke - cider" questIOns. thatt includes • 'Ih rd Christman, T." lt llank 1.lallk by by J.1 Richa Richard Cbns tman. Us. Coas Coastt Guard Guard Acad emy. re than Acade my.The The Test Bank Bank includes includn mo more th., n 2200 "200 mul-mulliple-choice ilable in questions. liolls.. TIlese lbese items ite ms are al"e also Il lso avn avallabl", in "1,lc-choa ques Ihe the Compute Compu terized rized Test Test Bank Bank which which provides prm'idel full full editedi ting 7oC tests lUg fe8\lJres (eBlUres to to help help you you customi ClIstomi7.e II~"S (availlible (avoilable in in both bolh 1IBM BM and lind Macintosh Macintosh versions), versio l1s). •• All All of o f the th e IIU/mcwr " lJ"/mclOr s"s SO/Uliolls SO/HI/OilS lilli/Will Mlllullil ill In MSWord, MSWo rd , and es pdf fil files alld pdf •• All le fo room proAll text text illustrations. iIIust rations.. suitab suitablc forr both bot h class clnSlirOOlll projec tio n aand nd printing. .teCtion printing.
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On· linl."" h01IllI."""'o rk 'lIId and (Inil."l:in~. I,uiahl!:, In In addition IIdd,ll(Jll to 10 OIl·lill.' hHIII{'..-ork WlleyPLUS. Wdey/'L US. FIilIl/a/llellluls FliudamO:llla/s of of Physks. Ph)'slt;s. eighth eigh th edition edition also PL US lInd PA, which ako supports suppon s WebAssign WebAssignPLUS and CA CAPA. which are are ootthe herr programs prosrams Iha1 thaI gh'e gn'e instructors instrut toB the the ability abillly 10 10 deli" e rr lind izzes on _line, delive a nd grade g rnde homework ho mework and nnd qu quin:es oo·line.
Webe bK-kll<,~rd, Webe rr ~lId a nd lIUlaf kh" ard, A A ~'ariety varie ty of of matenats ma te ria ls h.'1~'e h.-w e been prePMed for easy mcorporation Ul eIthe r WcbCT been pre pmed for CaS)' incorporation in eithe r We bCT or board arc or Blackboard. Blackbollrd. WebCT We bCT and lind Black Blackboard nrc !X""'uful powerful aand nd eM)'· to- use O\web-based eb-based course-manage me n t ')"S' e nsy-to-use course,ma nagement 1i)'Ste ms hnee ms thnt thnt /llIow nll ow mstfUC"tors instructors 10 10 se s.! lt up complete comple te o n· n-lin courses .l.ing, ~tu courses wllh with chIll chnl rooms.. rooms. bulle lin tin bo.lrds. boards. quir quizzing. stu-· denl tl1l ckl11g.c tc. de nltrn cking. etc.
Student's Supplements Stmll' nt CUIIII'~ CUm l)w lIi niUlI Stlldc .. n ,sitl·. itl', This web site htlp' J {""""'W." iley.comfmlk."'ge1balhda)· ht tp:Jfwww.wi ley.comlcoilegel1laliiday was de"eloped deve loped 5pedfICaUy specificall y for fo r FUlIlldllltlllUfs fill/ dill/lmlilis of Physics.. eiptt desigDed to furthel aSS1S 1 eighthh OOlilOn, edition. and is designed furthe r assist siudents In lbe Siudy o f phyYcs .. lbe site ind udes u· s tudent s in the s tudy of physics. The siw includes .KIl solulions to sd cded end-of-c bapler problems (v .. h tc::h a le tions selected elld_of-chapte r (which nre .....,,' ico icon t): self-CJui se lf-qUl 7.7.es: ide nlirted ntified wllh wi th a w www n in the tex text): v.es: simulatioo o n how 10 simula tion ee~crctSeS: xercises: tips on to mllk makee besl best use ooff a/I prognlllll1lable progrnmnlll ble CAlculator: cal culator. and th e IUlemctive Inte rnctiv e thaI are described belo below. L.elll"ningWnre LearningWare 11ItOri tllt oriallis ls thai w, Stlldl'lll Stud )y (;u idl'. 'The n U,! student stud ts studyy guide consIs cOllsists Studl'nt Guidl'. of an ovc Tyiew of the c hopte r's importmll co nce pts.. ove rvie w chllpters importllnt concepts. hints for fo r solving e nd..{)(-ehapler UClitionslprobblems. lcn\S" nd-of-chapter qquestions/pro lind prllCttc::e and practice quizzn quizzes... SllId('nl', by J. J. Richard Cbristnl.11 Cbristm.'1n. S"lut i,,"~ Munua Manuall b\' 1. Stud l' nf_ Soluli."" U.S. CoaS and E",,'Md rnnp,. U.s. Coas It Guard Academy 'and Edward De Derringh We nt.... .....orth orl h Institute, Inst,tute. This Thl$ manual provides provKloes stude I tudent Went nt comple te wo rked-OUl solutioas to 15 pe~ent of wilh wi th worJ,: ed--oU\ solutions IS pe rcent o f the problcms prObif.' lnJ found fo und at nt th thee end of each cha c hllopter ptcr ""thm within the tex ese ppro ro blems are lire indic.lted indicated ,,;th with an I n ss ssm text.t. "l"h These m Icon. icol1. lul rntl"ti"l' ~ r:"' Ij, f,' tl'llruin~\\'~n', t .'uruinI-tWHrf,', This Th is software guides stu~IU · Int through solutio ns 10 10 200 of the the elld-of-chapte e nd·of·chllpterr dents throu gh solutions lllcse problems are lire indicated indica ted with ..... ith an an ilw ilw problem!.. proble ms.. 111ese iron. lhe l be so w lutio lullo ns process procc!ilS is is developed inte IIl te racti ractivel)'. icon. vely, IIopproprin tc feedback feedback and lind access access to error-spccirlc e rroro$JlCClrtc:: with nppropriate help help for the the most mOSI cOlllmon common mistakes.. mistakes.
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U""klUp ilio n, An electronic eleclronic ve \'en;l(JII Ul' .'o kl op I-Ed : ditioll, rsion oo f FIllIlIi",u:nlllls of Physk.t 1'11,.s icJ. eighth e ighth editio edition w ntauung the the Fill/dum /millis of n containing complete, te. ex Clte tended nded ,'el1>OO version of o f the the te lext is aVnilnble aYl\ILnble fo fo rr comple xt is download a l: dov.. nload nt: WVo'w.wl ley.comfool legeJdeskto p www.wiley.comlcollegeldesktop Wil ey Deskt Dc~ktop Edi tions Hre are aII cost cost effective effec tive alie "I' ernlltive mative Wiley op Editions pril11ed lext. text. to the the printed to I'h p i{s in ~u~~ ;1II S""und SCf,,"t! Lallgml Lungnag.': Mlisler/IIII I'ro /)/rm Ph~"!' gl': MU5/er /lIg Problem 5oM" by lliomas 1110111."<5 Barre Bnrrett. ll . of of Ohio Ohio Stnte Stnte Univcrsit University,y. Sol" illg8 by This brief brief p.1perback papelback teaches teaches the the student studenl how how to 10 anpThis pcffecllv~ly. l )t The Thl! prooch probl.....,,, more re effICie efrlCiently lind effective proac h pro blems mo nt ly and st ude nt willlcnrn wil1leam how how to 10 recognize recognize common common patte pallern~ In student rns in ph)"Sic:s proble problems. break problems problems down down into into mnn.-Igenlan.1g<'· physics ms. break nble able steps.. steps. nnd and npply aPf'ly appropt"iale appropiatc ledmiques. techniques.111e lhc book book takes the the stude student step-by-5tepp through thro1l!h the the solutions solutIOns to to takes nt step--by_ste uamples. numerous nUllle rous examples.
Acknowledgments
xxi
Acknowledgments A great many people have contributed co ntributed to this book. J. Richard ClJrismwn. of the U.S. U.S. Co.. C0<1st 1st Gnard Academy. hass once again created many fine supplements; snppl ement s; his hi s ha recomme recommendations ndations to this thi s book have been invaluable. Sen-Ben SenBen L ~10 of La wre nce Li ve vennore nnore National Whitenton nton of Southem Southe rn Polytechnic Polytec hnic Laboratory. lames White State University. and JetTy je tTY Shi. of Pasadena City College. performe perfollnedd the Herculean task of working wo rk ing oout ut solutio solutions ns for evely eVillY one of the hom homework ework problems in received ive d the book. At l ohn Wiley publishers. the book rece support from Stuart lohnson. the editor who oversaw the entire wh o coordinated the th e e ntire project. Torn Tom Kulesa. Kulesa . who state-of-the-art package. and Geraldine Osnato. 0 5nato. state-of-th e-art media p..1ckage. who managed a super team to create all an impress impressive ive supplements thee suppleme nts p..1ckage. p•.1Ckage. We than k Elizabeth Swain. th production editor. for pulling all the pieces togethe togetherr during the complex production process. We also thank Lesure . for her he r design of both th e text and the th e Maddy Lesure.
book cove cover; r; Lee Goldste Goldstein in for her p..1ge page make-up: make -up: H elen Walde Waldenn for her he r copyediting: Anna Me Melhorn lhorn for thee illustration iliustT11tion program: and Lilian Brady managing th for her proofreading. Hilary Newman was inspired inspire d in the search sea rch for unu unusual sual and inte interesting resting photographs. \Vdey ey & Sons.. SOIl5. Inc. Inc. and learl Both th e publisher lohn \Vd Wal ke kerr would like to thank the following for comments and ideas ide as about nbout the 7th edition: edition: R ichard David Wic Wick. k. Clarkson Woodard. University of R orida: Dnvid University: Univers ity: Patrick Rapp. University Univers ity of Puerto Rico nt at Mayagiiez: Nora TIlornber. Raritan Valley Community College: L..1urellcc urellce I. Gould. Univers ity of Hartford: Greg Childers. California State Univers University ity at Fulle Fullel1on: non: A Asha sha Khakpour of C1lifornia State University at F ullerton: loe F. McCullough. Cabrillo College. Fmally. our external reviewers hnve have be.:n bc.;,n outstanding and we acknowledge here e ach member of that llcknowledge he re our debt to each team .
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Measurement Whe" a n earthquake strikes a populated region, jt can shake apart buU
dense fluid in~tead of solid ground.
How can a building sink into the ground? lhe . n, 'N ef I, In tills (hapl'er.
1
1-1 WHAT IS PHYSICS?
Sci"""" and engi""",ing am ba",d on mea,u,emenlS and comparison~ 11111~ "'~ need ,ule. aoout how Ihiogs are n"'''''''M an~ rompared . and~. ",.d cxpeon",nts 10 cstab~sh lh" "ui1< for lb""" measuw"",n" and compa,;.ons.. 0,,,, 1'"'pose of ph~~ics ("nd enginee,ing) i. 10 design and co"duel lhose "XJX',imOllls. Fo, exampl~. pbysicists slri", 10 dewlop clocl:s of exl,...tne accu.acy so lhal auy lime or limo i"letval caD"" 1',"';",1)' dele,mirwd and compared . You m.ay wonde, " 'hNlli'r "'''h oew,,,,,,)' is >emally "'....4'<1 or worlh 11hl ~fforl. H.'fe is 00. example 01 lIIc wOrlb: \l'lho"1 docks 01 exlro"", .'IIX:lIr"'1'. III" Global ANiiouing S),;tem (GPS) IIIaI is now ,ilaJ 10 worldwide M\'ig"ion would be "",,,,"~
1-2 I Measuring Things W. disco"" physics by learuing how 10 ""''''"''' IhO quanlili", invol",J i" physics. Among IhO.., q uanlili., "e k"gill. limo. m.,s.. lemp",alUre. p,ess",e. aud ek>C1ric CtIrrenl. W. ""''''"''' each physirnl qua"lily in;1S 0"'" u"ils.. by compafloon "-;Ib a ,, " ndard. Til<' oni, is a uniq",,- name ..... a'>Sign 10 lII<'a5U'''' ollh" quanlily- for examph>, mcl", (m) for lh. qua"lil)' i.:lnglh . Th. Slanda,d cor,osJlOnds 10 e:xaclly 1.0 "nil of 100 q"anlily. As )'0" will """ Ibe Slaudard lor lenglh ...-hieh correspond, 10 ~"ac1!)' 1.0 m. is llw diSlan", Ir.",led b)' tighl in a """uum du,ing a ''''lain f,action 01 a ",co"d. We can define a un;1 and ilS 6Iandard in any way ~a,,, 10. Ho_v" •. lbe i n1llOrlani lbing is 10 do '" in s"cb a ..-ay Ihal scienliSis a,ound Ih. wo,ld ,,-ill .groo Ihat ou. definilions bolh ",nsibl" an" p,aclical. On", we sci "P a Slanda'''-"y.lo, "'nglh - _ ",usl wo. t oul p,oce· d"'~5 by " 'hieb any knglh ".-haw,,", .1x! il lhe ,adi", of a byd,ogo" ",om. II", ... he;,lba>e of • sl al,,0O3, d. or the diSlan", 10 a Sla •. can 00 OXI"", ..>d in lern" of Ib" stanJard. Rulers. " 'bieb al)p,oxim",~ our kngln 5Ianda.d. gi"~ '" 00. sucb p'o«->du.. for meas",ing lenglh. How~"",. many 01 0"' oompa,;.ons nm" Ix! indirecl. Vou ca!lllol use a ,"i.:l,. for oHmple. to ",.asum Iho radius of an alom 0' Ibe d;';lanCil to a"" •. ll!ere a,e so many phys",al quanlilies IhOl;I" a problem 10 o,g.niz. Ih,m. H:t"unalely. Ibc)' •• 0 ""I all in~eJl"n""nl; for example. 'Jl"'i'd ;.; Ibe ."io 01 a lcnglb 10 a H",e. Thus.. ",f1al we do IS piLl oUI-b)' ,nietoalional agrec"",nla 5maU numlx>r of pbysical qu,nlitii's_sucb os Io nglh "ud lime. and assigo Slandard:s 10 I"'m alono. Wo IlIi'n defi,,,, aU olt"" physical quanlih,'" in 1o ..", of In"", ba5~ q"amme qua"lilies "' n&lh and lime and 11k~' base Sl.ndar"~ Ba>e "aDda,do; muS! t>o bolh aoo.'SSible and in'·an,bi.:l. If we dofi"" 100 lenglb 51all""',d as Iiii'
l,n", ool",,"n o"e's nose and Ibc indox fingi)' on a" oUlSltelch.~ a.m. "'e "''' la;nl)' h3\" an acressiblil SIa"e st.nda,ds Ihal am ocressibi.:l 10 Ih"", "ho "ood llwm .
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1-3 I The International System af Units U.~
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~ .92
'"' ScienliflC nOla lion "" romp"te" som"limes lal"" on an "'""" b,iefer look. as in
3.56 E9 and .t92 E- 7. ,,·ho,. E st"ndo; fOI "expo""nl of leo." II IS b,ief", slill "n c~ lcuJal""'." helC E is "'placed ,,-;th '" emply space. As • IUlI"e, con",,,;"/ICC ",be" d.:>ab"g with la'g" '" wry ,mall su'elll ""l'i . ...., usc 100 pwfixes lisloo in Thble 1-2. A, y"u can SN. eactl p,efix "'P,"SC"l'i a ""flain PO""" olIO, 10 00 "scd" a mulliplicalion loclor. Anochiug "prefix to an SI unil has Ih. elf..., 01 Illullipl}'in& by th" ""ociaIOO facto,. Thu" ...., can express a pa'ticular el.'Clric POW"' as
so,,'"
""y
m".-
1.17 X 10" ".-atlS - 1.27 gig''''' 'lIs - 1.27 GW
,~.
, .~
10"
)Qua-
,.' ,,,. ,.' ,.' or
,. ,.'" W
,~ ,
10- ' 10- ' 10- ' 10- ' 10- " Io-LI
2.15 X 10-' s - 2.15 "an06ilCOuds - 2.15 u"
(1 -5)
Som" p,"fi_'''''' as """d in millilile', "' "li""'I"', ki1ogra m, and ""'gab}'le, "" p,obably familia, 10 you.
1-4 1Changing Units We oli"n ",-",d 10 ch,ng" Ih" u"ilS in "'hien a ph)~ieal quanlil)' is o'I',",,,,d. W" do so b)' a n"'lhod call<'d cl,a,n-I",! COIW
00,
P",f", ... / 0' 51 Uni ..
10-"
0' J panieular tinl' i"lerva! '"
lmin _
j
1
'"'
Th"" Ihe ra li05 (I min)1(60,) and (60.)1(1 min) c~n be used as oonv.,.,i011 I or 60 - I; e arh ml",bu and its "",, focto ... This is not lhe same as ..-riling muS! be Ireated l<>gelh.r. Bi'CiIu,", multiplying any quan tily by Willy I"a'..,. Ih" qua" I!l y uneh.n!l"d ...., can inlrOOUCi! oo,wetSion faCIO .. "-h.. e~", "'" find Ih~", " ...ful. In chain -buk ooo'",."on, ...., use Ihe faCIO .. 10 ca"",,1 u""-amoo unil' . For example. to oonv" " 1 n,;n losecoods."'"have
-k -
2 min - (2 m,n)( I) - (2 """)(
I~) -
120 ..
(I-fi)
II you iOlrOOu", a oonve,.,;on faCIO' in surb " way Ih.1 u"w"nted units do nol can",!. ;"wrt Ihe f.cto, "nd Iry again . In con~"rsi",,~ Ih ' ""ilS Gbraic ,ul", as , ... riablo s ,nd numbe, .. Apf"'ndix D giws conv"";,," foclor, 001",",," SI "n
lO-" lO-l<
When. accmdiJlg (0 in 490 RC. !O tning w01d of lhil Mar",bon 10 AlIII'll' Gw~k ,-k-lOry ove, Ibe Pcrsi'"" h. plOoobl)' Jan al " spa>d of abom 23 noos I"" bour (,;dc'Slb ). The ride is an aocicnl G"'
'.-r,1e
lbi>.cnn is. Brilisll voIu",,, for f,.sIlly mug/II h<>rrings: 1 Cfall - 170. 47~ lil.r.; (L) offish. OOoot 7SJ oorrings. Suppos.:! {hal. 10 tX' d,c " ..'lOOlS in Saudi Arab... _" shipment of 1255 m..,;l 00 CO\'ido is an Arabic u!li! d !.>oglb: I covidara!J0fI?
=
From Appendi.\ D ~'e _ Ihal I L isequiva!.>nl 10 lOCO em'. To oonve'l lrom c~bk ",nl;mewrs to
cubic """,dos, ...., must cub< Ih. 00""",,100 "lio N n• • en """limN'" and oov;
1155 nans - (m5cnos) (
170.H4 L , cr"n
X
lOOOcm' ,. '---
X
I OO\1dO ) ' '"~€
~o . _ ucm
- 1.903 x 10'cm·ioo.'.
PROBLEM -SOLVING TACTICS
Tactic 1: Significant FigurllS aoo D..amai PI"an If you c>kul.,ed 11.. ...we, '0 S"",pIe Probl,m I_I ";,lIou' you, c.Uculotor ."tom . ,bHy ,o"odin~ i, oft ,n. oumbe, 4.m 666 666 67 X 10- ' migh' IIJ .. appe • ...t in tI.. di,pI.y. The preci!ioo implied by tlili nurnbe, io me:rni.o~",. W. ,ounoded ,b . ...""'''0 U x [0- ' Un/, .., ... ot ' 0 "'ply ,b", j,
is mor. proci
23 ,idWh oomi", of '''-0 digi'" call. d ",".~iooI:.!inal , .. uiu of rolrwatioru art of teo ,ounded ' 0 m.tcb ,be Ie"" rrumbel of ,i.!."ilk.,,' figur .. in ,b, gi""n d., .. (Howeve,. ,om" ..... . . .,,'" 'iylifir"'" figure ;, h pl.) IVn.n 'be Itf'mOO1 of the digi" '0 be di"" .. ded io 5 or mor •• ,be 1:0<' ,em';oin~ digi' ~ """,
fi~ure!
... llA and ll .1279 ;, lOUJldtd '0 'hree 'i.!."ilkoot
'0
ligure ... 11.3. (The ...,,.'" sample probltm. in 'bio boo ~ .re wu>ll}' pre .. .,td with ,be . ymbo} _ io".><1 of _ ."". if rounding io involved) Wb. n , "umbe, ouch .. 3.15 0' :l.15 X 10';' p,ovid.d i. • problem. ,n. numb.. ofsignrlioan, fisures;, awareo'. bu,
0'"
how abou, 'be "umbe, JX1JI Is i, known '0 only .iy>ili_ (3 X HI)? 0, i. i, kDOWlJ '0 '"' maoy .. Iou, signifioan, tigu .... (HO I X IO')? I. ,hi< book . ..-e .. sum. ,h., ,u ,n . ..,m in surh Yv .... numbt" as 3000 or. ,isoificao'. bu, you hod be" ... not mak< 1!'umpbOO .I ..... he, .. 000" ooof".. sign/fic"", fig"'" ...;,. l places. , .. ptdiv.ly.
can' tisur.
'h'
Coo,,,,,,,
'''0, ..
'hr"
1-5 I Length I" 1792. Ihe ne,,·oorn R~publir 01 Fran"" e~"b~sh.d a "e~ S)'S1em 01 .'eighls and meas",es. l IS oornerstone was Ibe me'er . defin...><1 to Dc o ne '"n -millionlh of Ih . dis Ian"" lrom 100 nonb pol.>. 10 the ~q"a1or . Laler . 101 pnctical rea",,,,, IhlS Eanb sla"dard ""as 3OOodo ....><1 and IIhl "",lei "alTh' to Dc d euw 01 • plalinum-iridium bar. 100 """_ dart! .."' .. ba,. ".-hion ......, kepi al lbe 1l1leIJlJlio"al Bureau 01 Weights "nd Me"u, .. ,I(m Paris. Acrural' OOJ''''' 01 the bar ..-ere ",,"I to slandardizing laboralo-ere u""d to prod",," o th« . "'" Ihroughoul 100 world . The"" >OCunda,y slill moOro """""hI.>. ~ a","' rd~ so Ihat ulllm"lol}' e~,,)' "",-"suring d..",ioo "",ive standard """,,r bar Ihrough "oomplial1ed chat" 01 ro",pari"'n~ Ev" nluaUy. a S1"nd",d mo re precise lb.u Ih . disla"". b,m.."," I11'O fi"" scratch", 00 a ",.,1.1 bat ".-as ""luired. I" 1960. a now standard for 100 "",TO, .
"and,trd, ..
l.o l Timo
b,...,d on 100 lI-"-ek>nglh ollighl."", adopled SpocilkaUy. Ihe ,I,"dard 101
Ib ~
",..Ie, "'" ,ed.:lfi""" 10 00 I 650 763.73 ~'"WJ..'1lglhs of a p.arhcub, O1ange-red ~glH
e mined by alo"" of hyplo" -86 (. p.anicul., i<;ololX\ 0' I)l"'. of ~ryplOn) in " go, did Ij",,, inter,""1. I" th" " -01ds of !h . 17th (rio"",al Conlcn'"". 0" Weighl' sud M" "nr ..:
r
Themete,;' the Ie.gtb 01 tb<-patb t",.. IO
This lime inlo"'al w," ch""n SO th,l !ile 'p".d of light c i:s CI.1cdy
c - 299 791 ~ 58 mr~ sp'ed of ligh! h.d Ixoco"", o,uen", ly p,ecise. SO ;1 mad.>
M.asur e"", ,,!s 01 too ..,"'" !o adopl !"".IpilCd olligll! ., a tango olleng!b,.fro", Iha! 01 !he universe (lop I;",,) 10 !bose 01 so",e very sOIali objoc1s.
j
Some Appro.im .... l.e"9'h. Leogt. io M ..."
M" a.. ,em,n'
fi,,,
Oi".IlC' to tbe gawie. fofmod O;,!>"", to tbe Amdrornod. golny 0;',. • .,.. to tbe o ... by"", Pr,m"" C.nuuri 0;',."", to PI.to R:odi", 01 E .,.th Heigl" 01 Mt_ Ew,e" llOCkn"" 01 ,b;' pas, Leng'h 01 . t)piocol
m•
2 x II" 2 x 10"
4 x 111' 6 x 111' 6 x HI' ~ X
10'
I x 10- ' I x II}-"
Rodiw 01,
hydro!"n "''''''
5 x IO- H
R:odiw 01 , Jlf ot""
I x 10- "
PROBLEM-SOLV!NG lIlCTlCS
Tactic 2: Order of Magnjlud~ The ON" <>/ "'~gnN"J< of , o.mo., is ,be powe' 01 "n ..·ke. ,b, ."",!>eo- is .xpres>tnd B art 4. Oft",,_ 'nsill'''iog >nd .ce"", prole .. ioo:w wiU esti_
m". tbe "",Ill, 01 • ,.kulatio. '0 ,b. ",ar<>l or"", 01 m.y,;_ ,»de, FOf OW" " """ple, ,be ne .... ' Ofck, 01 m'gW,IKle ;. 4 fOI A ODd 5 for R SIOclr COII1DIOO wben ""tailed Of prod .. do .. '''i"irOkulatioo are not kn""",, or eao.iiy /OIlJId. S, .,pI, Pro blen, 1_3 giv.. an ,x:omple.
The world', I.,gest b,1I 01 ,;I,ing i, aOOUI 2 01 in .. dius.
lenglh d - ~ mm.l1ien . wilh a cfOSS-s..'CIiooal area 01 J' and a lenglh I .. lb. Slring oocupi<':5 " 10,,1 vol u"", 01
To 'be "ear<':51 01<1.>, 01 magniludio. whal is IIl;o 100al leng!b I. of lile Slriog i" ,w ball?
We collid 0( CO\Irse.lale IhIl ball aparl and measu," '00 100al le ng!b I•• bill !ba' lI'oold Ial:o grea! ell011 alld m,t. IhIll>aU's boJil
,h.
."i,m'''''';'
V _ (cfOOS-Si'Clion,1 area )(lo"Blh) - d'l_
This is approximate')' oqu'l to 100 volu"", 01100 b"lI. gi",,, by f.-R-' . wbicb is aboll' ~R-' oocau", ". is ,bou, 3. ThUs. we baw
,I'L _ ~R'
1· - 7
-
~ R'.
4(2 m)' (4xlo-'m)'
- 2 x lOOn, _ IOOm - l(lT t m. (A"' .... ') (Nole Ilta! you do nOi n""d a ~akula!or 10' such' sim p~fi.>d cakula!ioo.) To !"" n"arcsl Older of magni!ude. 'be l>all ronlaim aboul IcnJ ~m 01 string!
1-6 1Time Tun., h'" 1"0 "'P<'Cti. Fo, l be abk> !o an''''''' ''''0 qlk'slio",: "lI'n
j Som. Appro.; ....... TIme 1"... rY~ "
.T,m.
M ..........
In'ervalin
n.
Lif.tim. of ,h. pr"'"" (pr...wn«l) Ag. 01 the unive, ..
Shof .. " hI> liSI" p.1ot. Lifetime of 'he m",' 1LII",bIe panicle The 1'I>nd rim ..
2 X 10' 9 X JI)' S X IO-L
1 X 10-' 1 X 10-1<
I X 10-" I x 10-4>
tho mlic>, tim, o/t
'Ih~ ~
•• "" .. "" ... be .."., •.
Any ph<'nomenoo Ihal .o""als itself is a JIOSsibk:> lime slOnd3fd. Earlh's rotation . ,.-hkll ""wrm;",, , (he length of the day. II" N~" used i" lhis 'CO)' [Of «,olU""'; Rg. I -I sho"-' one "0,..,1 . xample of ..."Urn ba..,d 011 thai ,malioo. A q"JrlZ clod:, io ",hich a q""'lZ ring is m,o" to "ib'"I~ continuonsl)', can be ~~bbt"l~d agaiR<;l Earth ', ,mJtion ,ia astrooomical obs<,vJtiorrs and u>cd to "",a",,~ lime ,"Ierval, in Ibe laOOratory, Ho~ev<'1, Ihe ca~b'" tlO" caoool be ~~"i.d oul . 'i lb Ib~ .ccu,aq ~~11..'O" Slandard 101 Coo,dioaloo Univ",sal Tim.> (UTC) in Ibe Uniled Sl.to~ liS lim~ signals aro available by sbo,!~,v~ radio (sl'lion, WWV and WWV\I ) "nd by leh.."hono (3OJ-49"\1-7111). T'llli! signal:; (a"d ,,,IJloo inlo,m'lio") ate .1<;0 ,,'ail"ble IfOm tbo Uniloo Slat"" Naval O.,...,,,,.lory at .."b"I' hl1p://1ycl • dock e XI'''"JeI)' a= .. "ly.1 ~'ou, partirnl" localioo, )'OU .muid baw 10 "eronnl for Ihe Iravol lim" req"i.oo f01 I"os.:! ,ignal, 10 reach you.) Figuw 1-2 'ko ..~ ",rialioo, in th' "'nglh of 0"" day on Eartk owr" 4-),,", I"'rioo, as deW,min.'ca50nal ,nd repeti!iou~ •••• n'peC! tk~ fOlaling E.1f!k "hen loom is a di/fctenre bet'"""" Earth and >tom as timekeopers. Too "a,iahon is d"" 10 {id.1 ,/foCls ""u",d by {h e "",oon and 10 larg<'--scal" wjmb . TOO 13th General Conf",e""" on Wciglns and Me"",.", in 1967 ,dopled >standard scroud b.sed on Ik e ""'"U"' dock:
r
',me .at,.
OneJ«ODd ,sthe by 9 192 631 77000
.,om.
h"-,,
Alo",ic docks are .I() con,isWnl Ibal. '" principlo, t",o "",iu", docks lIIOuld 10 run f01 «OJ ~'~ars before th~ir reading' .,ould dilf'" by ",oro Ib"" I s. Even ,ocb aa","'1' pakls i" comparISon ..,{b (hJ! 01 dod, <>"'''"tty being dcvelop
,b.
FIG. 1·1 WheD metric IeOl ..... propooed in I ,h. bour ,""'lioN to J'fovkle . W_bow cia)'.
,n.,
m.
The ide.didnOl catch 0 ... u.. .,"er 01 tim IO-bour "",,,b ";re]y pm _
vid. d .... .n dial 'h" l.,. 000""._ .ioo al Il_holU ,...... Do ,be , .... am<- lim.7 PnktnJ
1-7 1 Mass The Standard Kilogram The SI Slandard 01 mass is, platinum-lfi diulll qhn'" baw 00<0 ",nt !O Slandardi",ng 1000rat01;"< in othe, countri"" and the n,",,,,, of other bodi.. can bi! ""(ermined by b.l.ocing the", against a oop~', Table 1-5 sho..., SOal~ masse, oxp""S<'d in kilogram,. ranging 0'..... oout 83 ordor, 01 magllltude. The u.s. COP)' of the mlldard kilogram i, ho""'" in a ,'ault at NIST, h is ,oalO\'od, no mOfil th.n a ~'o.r. for tho>. pu"""," 01 cbecking dupli,a t" copi~' tbal ar" ""'" ol", ... bere. Sin"" 1S89, it has be"n !a k,," to France t...'ice lot ,.romp.rison ..'uh tbe prim'f)' standard
0"""
A Second Mass Standa rd The m"""" of atolll'S ca" 00 oompared ..' th one anotb01 mor" pr"';sdy than they ~"O 00 oompared witb tbe Sla"dard b]ogr.m, Rlr thIS W"""" ...." b'~e a second mass standard It i, tbe carOOu-12 atom . " hirh, by ;nt",n"l ",o.1 agr",,""""t, has 00.:.1l assigoed " m", of 12 . ",mi e m ~'" uni., (uj, Tho ,elation ""tw",," tbe t...., gmt, is I" - 1.66053886 X lO-n kg.
So"", App 'o . ....... M..... M . .. in Kilogram.
(I -7) O bjt
..ith an """"naint}' of :!: lO in tho las! t1l'0 ded"", ] pIa""" Sciont "t' can . " 'ith of oU",r alO"" relareasonable prOO,ion. ~xp"rimen taJl )' ""!e,mine tho>. ti", to the m.ss of carbon-12 , What pre", ntly tack is a «,[jab'" me.ns of eXI"ndu'8 Ihat p,o>ci,io" 10 mom CO"'"lOn "nits of ",", .. sud! as a kilogram,
,,,0
MI, ii.iM
"JaSi'' '
K . ....lllLOi"",... 0", g" "")' ~
Density
M_ A>\e,oid&", s...011 OlOun,';n
As we shall discuss furl ber in Chapler U. Ihe density p 01 a ma{('rial is Ihe mass "'... "oil ,..,tn"",:
Ocean 'me,
, --, . m
1A>""li~s
(I -3)
arc l)'pirally lisled io kilogram' pe' cubic meter 0' 8rarrtS PC' cubic (1.00 gram P'" cubir "'"Iimol~r) lS ohon used '" ccnl,metor, Tho do""ly 01 .... a oomparison, Fr"", SIlO1\' has .OOUI to'l'> 01 Ib.1 d.:>nsil)': plahn" m has a don,ity tha! i, about 21 !JUlilS Ib.1 of w.{('r,
'ill
A be. ,')' ob/,-'C! can 'ink into Ihe ground du,iog ao
e.. l hqu. ko if the sha king c."ses the ground to unde,go Ilq"SSlbili!)' olliq lli'faclion " ' sand)' ground call be predicled in term, of tt.:> ,'"Id rali" e for a ""'pIc of too ground:
v_
'.-
< - - - -.
(1-9)
Here, V..... is lhe !Olal Vo! "flle of the sand sr""' in lbe sampl<> , 00 V..... is 100 lotal volume ""IWOOO ttl< grains (in the ,<>ids), If ~ excililds a cmical n.l u" of 0,80.
EJep/l'.' Gn, Sped of du<;, Penicillin molo<:ule U ..... ;umalom '
0 00
EI""lfOll
I x to" 2 x to" 2 x to" 7 x to" 5 x to" I x to" 7 x to' 5 x to' j X to- J 7 x to-" 5 X to- ll 4 x 10-" 2 x 10-" 9 x to- J1
liqlli'/oclioo can occu, dUflllg ,u e,nbqual:e. What j, Ihe C01rosponding saoo ""osily p......7 Sotid >iliroo diO1iOO {lhe prim:lf}' oompeo""1 of .. 0<1) bas a """"ty of p,." - 1.(,00 X 10' kglm', ~
Tho
""">il~'
01 Ihe sand p_
in a samp"'lS
,,;;;;;:;;~< unil ,'OIU "'" - lbal os.. Ihe ra lio ollh. 10lal mass "'-.. 01 the ,,"d gr'''lS 10 Ihe 10lal vol ume I b~ .. mpt~:
m._.
P-o - ~'
v• •
v", .. of (1 -10)
Calculatlo ...:
Th~
loul volume V.,..of a sampl~i'
V.- _ V..... + V ...... Sut>slol uling for V..... from Eq . 1·9 .nd soh'ing for lead 10
Sut>sliluling Ihi:! oxpression inlo Eq. 1· 10 and Ihen sub· sliluliDg for v.. _ f.om Eq. 1· 11 lead 10 P-J - ~ V..... _ ~
v.._ (l · ll)
From Eq. I-&Ihe 10lal mass m ..... 01100 ,",ad g.ains is Ih. product of Ihe dellSil}' of silicon dioxide and 11K> 10lal volume of lhe sand g.ains:
V,''" 1 + ,
1 + ,'
(1 · 13)
SUt>sh IUI,n g PliO, - 2.600 X 10' 19lm' and 100 Cfllical val"" of, - O.ilI . .." find Ihal bqU<'faclion OCC"rs "hen Ihe sand dcnsily exeoods
..,.
2.600 X 10' 19l rn'
(1 · 12)
(An' .... e')
REVIEW & SUMMARY Meaou.amen! In Ph ysl" PbY"'" i. i>......t "" ........ . m..,' of p/I.)'>ical qu",,'i' i... Ct,,.;,, p/l.y.ic.al qu,,,,;,ioes bav. t - . , """"" .. qU"~li " (.""h .. Ie'S,b. and cb h.. bee" defined '" term< 01 • " • ..t. ro .r>
,i.,•.
The JKOD d ~ ""tine are "n' wo,lrIwKloe by ~ ,ignal. !omic doc<. in ...Drhrdizin! b borat<>rieJ.
nme ~gh'
51 Units lb. nil ,)·"tm empll. s.ized '" 'h~ book ~ ,h. Intorna,ioo al S)'"'''' of Uni" (SII. The '~ree ph)"""1qu • • 'i .
,. " rn.pI. yed i. T. bIe 1· 1 art .>t.ptor~ S, ... d"w. "hicb mm' be boob """,..,ible and ;.." riable. b. vt t-n .. ,.bbr.bed fill 'bese ba.., q. "'u;,ioes by intor"",ioo al .SfffmeDL The .. ".oo.rn. art "",d;. all physical .... ... re· lIlen'. fill both b ... q.,.'ili ... r>rr,;,i .. derived from ,b • .,. Scirntilic not.,ioo .oo ,h. p.. fu .. ofT. bIe 1·2 .re .. ed ' 0 "",plify me" .",,,,,,n' _ation.
,b.
"rm.
M aos The kiloy ... ;. defined in of , platirrum _ iridilUll " ... d:ud m"" kepi lit. . Paris. fur "".... ,"" •• t> on 'D . 'omic scale, 'be atomic""", uni" defined in "'m. 01 ,he "om = boo!·12.i. ",":illy •• od.
De nsity volume:
lb. de •• i,y
p
Cha nging Unlto Coo,..,,;oo 01 uni1. m>f I>t p.,fOlmed by .,;"g d!~In · U"k c"",',-"s in which ,he OIigio. 1data are ",.hipli«l succ ...... d y by ronv,,""" f><1or. ""illen '" unily
M<. 1..5 Length • 1 lb. macrome1" (1 _) ~ 0I1e. railed ' lte mk"",. (. ) How m. oy micron. mat. up 1.0 om? (b) Wbat ITact;OII 01 • ce.,ime'" .qual. 1.0 "m? H"", many micron. >I. i. 1.0yd7
«)
•2
Sp .dn~
in 'hio book .. "" ge .... aIIy doDe in units 01 I pic .. . Dd 6 pi~ _ I inclt. If • 6g>l" ..... m;,pI, cM in ,be p . ge proot. by 0.80 <"Ill, .. ha, ,.... ,he .,;",1.,,,,,,,,., in (a) pic... and (b) f>Oin" ?
!"'in" . Dd pic..: 11 f>Oin" .3
Her... are '0 r.", over a ren.ur Engli
, Dd (b)
,<>di.,
...... coo ..... MIT ..". iu Ira'a.~ • 01' 36'" s...pli' _ ~'" 1\~ ... 01' 000' Smoot IS boted . . dIf Ia1Vb 01' Oha R~ s..-. I,.. d ... 01' 1Wi2. """ .... oatrieIJ co
1t"S1b II)' ltDIII' KrJo a.. AIpNo f' .... mlly ""'-lId .... t off (,.;,. poi.,) 1-Smoot"ngtkl"""'5 ,lie btod8O....1:0 . ...~ ho
n.. ,",'y don.a '''''.. of ,...
,. 20 ~b (dIf won! coni,,,,,,;.,.. d - f""rtcftI n..., II . Die< ""'...." of ''''''' i. p......, company h' pt,. 1lfII • paioful d _ in ........... , - .....1).
COOS"";"" .., Ib .. 'M pol"", ..,.._ .asily inl"f.~ (1"r. ",.. oI>ly. ,be pol..,. •••,," ori!inally upsc1 ~" .. 'be Srn_ is _ ... SI base URi,. ba' ,line =P'«l ,he onil .) Figw. 1-4 >II.,.... I ~ '''' ". ... ~
. 12 A ...... " pto ' 0 1 (a) HO'O'lo.S " a ", icr"".nlur~ i" .. inu, .. l (b) VIi" t
··4
Ibmnl~. "-
, ... _ _ lIIc Ch>rIr<
Ri_. boo
""S'.
""or
dtIM«I
poi."'"
in Sm-. (S). Willie. (W). and Z.II ( Z). "'".UIt 'b.,. ..io, ..'bew«l"_t,b 01 50.0 Sm-. In tl) "',UI.. ....:l (b) Zekl..?
•• 18 BKau .. E.nb·, 'OI . ,iOll " g..duolly slowing, ,b. Ie"t,b ol.""b d.y i.cre,....: The l 01 the d>ily il>CJ .... , in ,im.?
"e
""'ge'
••• 19 Su""""" 'hat, "hile !}'ing 0<\ • be""h ... .,. 'ke «1.>101 .. "chioS the Sun .," t as ,h. 'op ol,ne Sun d .. ,pp.... You ,be. ,,>nd, .1en. _ i"~ your .yes by • h'isht 11 _ 1.70 m, .. d >top ,b .....reb ..-b •• the 'op 01 the Sun >g. in di.. pp..'~ JI the .I • .,..d ,im. '" _ 11.1 ~ u-hal ;, .b. radius rof E.rth?
..e, ' ·7 MI..
atom. :tnd a c,.,bon "''''" .,. 1.0 u, 16 u, and 12 u. respectively. (I/jnt: Cat. are """.. im .. krI""",, '0 kill a mole,)
..27 0 ••• pe.ding SP'" in Mahy .... fOIl buy on ox wi,h • weigbt 01 2S.9 p;cul. j. ,b. local URi, ol ... igh t ~ I pirul _ 100 gim. 1 gin _ 16 rahil>. I "'hil _ 10 c""'~ md 1 diet _ 10 hoon~ The weight of 1 h""" """"poods '0 a ..... 01 0.3779 g, Wh.n yoo anans. '0 5IIip ox Ilome '0 fOUl . "oni,bed family, bow mIlCh.,.., in kilogram. mo" yo. ded .. , o. ,b •• hippin~ m... ~... tl (Hmo Ser up mul.jple ,h"'n _ ~nk ronvtJOioru.)
,be
•• 28 0,,,,., 01 fi"" Califomi. be",h .and
.re
appro,i_ m.lely .pbe,.. ..-no .n ave ...ge ,adi •• of 50 "'" and are ",ade oI .iIkoo dioxide. ",lOCh h .. a d.nsity 01 2600 kslm'. Who, m,.,. 01 >and gr';". woold bave a 'OI>! ..... f""" ""' . (,h. 1OIa1 "T" 01 all .h. individual sph .. ,,) «luI '0 ,b •• urf",. ore. 01 • ""be. 1.00 m "" .. .qe? ~
run.. """j""
•• 29 Doring b• • vy 01. lll' 0.80 kIll up >lOll! tbe d 2.0 m deep .hl" in.o a vail.y i • • mud . lidoe.A,,,,me tb>l ,be mud.nds up uniformly di oI. he mud "ni.g .oo.ea 4.0 m' II• • of ,b. v:olleyfloor? -::lG'
..30 11',re,;, poured in,o • co'lainer th .. b:t• • Ie.le The ... .. m 01 'be ,. ...,"' Vve" as. fu"",i"" oC ,ime' by '" _ 5.000'" - _lOOt + 20.00, witb '''' O. m j. gram~ >lid , in >«:<>r>
.21 (.) Aswmi.~ tb .. ",. Ie, II... "".,ity ol.xaclly I !ic.,', lind tb. m . .. 01 <>rI. cubic ... te, 01 w.Ie, in kjl~ (b) Suppooe 'bal j, , ..... 10.0 b to ruai" • cootain..- 01 5700 m-' 01 \\1ut i< ,b ... mar. ftow , ...... i" kilogram. pe' ""'_ ond,ol""t"fromtb,oon,:ti • .,1 ...
•• • 31 A venleal OOIl,.me, witll base >IT" ....",ri.g 14.0 an by I 7.0 an .. bein~ Iill.d ..-on id.ntic>! pfi.. 01 ''''' in 'he 000_ ''''." inc" .... at th. ",te 01 01..\Ocml.. .. wbat ra'e (kiloy ..... pe' minute) 00...1Ie m... 01 the candies i. tile
",be
w.",.
'"g''' sr'"
.22 lb. record for the bOIli. w .... , in 1'192 by ....... i. Millville. N.w lersey _ .he)' blew • bOI,', ";th • volume 01 19] U.s. fluid gall"". (a) How mIlCh .bon 01 1,0 nLil~OII ",IlK ,h .. l (b) [f,b. bonle ..... " filled with wa"," ,h. /ei
,""",i",,,.,, i,
.23 Eartll b ... m ... 01 5.98 X 10" kS The ave,oge rn . .. 01 ,he >101ll.! ,h., m,k •• p E""b i. 40u. How mOH Y"OIl>! art tbe,. in Eartb ? •• U 00. cubic l TadiUS 01 JO!=- For ''''s •. y"" the lowe, value >nd 'h' hi~be, v.lu., ,"'pecti ..!},. for tb . folJowin~ (.) How m.. y ,.1lK mel", 01 wate, ... in • cyti!>drical d , .di •• 1.0 k.,? (b) H ow many l _lil" pop botdes would ,b>< wat., fill1 (c) W'Ie' b .. . de .... y 01 lOCO kYm-'. How mucb rn . .. does , •• ...,t.. in ,b, doud ha",,1
,Ila,
,...Ie,
•• 25 IfOIl bas. den"'y 01 7.87 !i!om i. 917 X 10- " kS If tb, orom • .,e ",berical and 'ishlly pocked. (.) "hal is .h. volume of an i,OIl >10m and (b) "hat ~.ne di
1><._""
•• 26 A mole of atoms i< 6.02 X W" "'''''''" To ,b. ,...,." order 01 m.gn;,u
,im."
rn ...
Add~io...r P,oblom. J2 T.ble 1_7 .b"""' ..... ' old ... ",w •• 01 liquid volume. To cornplore the tallk •.-bat nwobe" ('0 ,hr ••• i!"ili< .. t ~gur .. ) 5lloold be .... ,ed in (.) ,.e wey column. (b) ,h. chaldron 001lUll". (C) bag <01"'"0. (d) ,lie pOItlo coIwn •. ",d (.Jlbe siU llk? (I) The vol ...... of I bag i, «10.1 '00.1091 m'. If .. oId>tor)' .... a wi,ch cooki"~ up some vile liquid in • ""uJdr",, of volume J.'i chaldroru.. ..-h. , ~ the volume in ",IlK mer",?
,be
M1'ii'" p,..,bl ~ m
32
,..,.y I -r I cbaldron _
'"' -
I pOIlI. _ I gi.Il _
baS
pOI,1e
gill
llW
40fJ
6-10
1102-10
""eo,
3l An ok! EnsJioh childr.n', ,byme -lillie Mi .. Muff" . .. OIl > ,uffel, ,,'inS b" ruret. ..,d "h,y, >long <=I , > 'f'ide' who ", down t.e.ide b ... .. ." The ,pOd" ,,, clown .01 bt",,,,,,, of 'h' "aoJr olll !Illf,,, of dri«l Sie, The VO/U"", "", .. u,e of • give. 1»' I luffer _ 2 poet. _ 0.50 Imp"ial bu>llel "",,, I Impe'i.:rl bwbol _ 36.3687 lire" (L ~ Wh" ..... Mi" Muff,r', in (a) poch (bl Irnpl b",bek:u>d (e) bl"" ? 14 An ok! man"",,,po Ih". l>ndo ....,.., i. Ih . lime of King ATth., b.1d 3.(10 >CTe. of plowed 1.00 pm. 0 li,.._ "ock .... ol !.I.O perche. by HIO pelebt. Wtr ...... lhoe '0101 ..... i. (.) lhe old "nil of rood. and (b) qUm m.",,? Her .. I ocre ~ an:uta of 40 pereb .. by 4 perrbe~ I ,ood i. an ..... of 40 pe«be' by I percll, aDd I pud> ~ 11.. 1.",.,," 16.5 h .
,.toe.
,.ff.. "
".>11
,,,,,,.Ir
35 A I"""" !",reh osesa ~ in Eog!.oo and ships i, homero 'be U";Ied St".. , Th . <:0, ,ricke, adve"io.d 'h" lhe 00'" f.el oowWDplioo ....... . , lb. rare ol 40 ",il .. per y.Uoo OIl ,be opt" r<»d, The 'owisl 00.. .01 .. . U", 'k" lb. U.K. galloo diff,,, from Ih. US gall"":
1 UK. gallon _ 4.545963 I ~ .. " I us.Sollon _ 3.78:'i n Oli",.. fix .nip of 750 miles (i. ''''' Uni,e;:I St" ... ). b""" m.. y y.~ 100' ol fu.1 do« (0) lhe mi" . kt. I"""" beli,,,, >lie needs and (b) 'be car "".all y ,",!uir e~ ...
Two 'Yl"" ol ""","units "",e in"", in ''''' 1910ir in ''''' U.i"d SI ..... lb. "f'I'Ie b .. rel J.ad a I'Sally .. , volum. of 7Il56 cubic inch .... lhoe cranbe,ry InneU82li cubic i""h.. If • mereb.", .. U, 20 cranbu ,y ban. ", of Sood!; 10. cu"omu ,..ho Iwob "" io rec.iving "1'1'" "'n.Is...-h .. ;" lb . disc"p"'C)' in the,bipme"' volume in U,,,,7 )6
37 The d ..cripooo 101 a cenoin b..."d of h""" painl claim. • c"'''''''S' ol 460 f,'/gal. (. ) E'p'e .. Ihio q"",,'ily in "Iu", meren pe' lirer. (b) E.p'''' 'bio quan';I)' in an SI .nil (Jee Apptndice, A and D ), \\'h . , io 'be inve,.. of ''''' o'igin>l quanl;'~ ond (d) "bal " ii, phrrk>i . iy>i/i""",.?
«)
38 In the U.ired SI. It" . doll b""" bo. lhe ",Ie oll : 12 of • ,e>! """'" (III" ". ,,,,,b lenglb ol ''''' doll b"" .. i. Ib " of 'be ,e" howe) aDd • mini"we II""", (> doll b.,.... 10 iiI "';,bin • doll howe) b. , lhoe seal. of 1 :144 of. ,,>I b"" ... Suppooe. ,,01 boo", (Fig. 1_7) II"" .Iroo' len~'h ol2Om. • depoh of II m•• beigh' ol6.0 m, and . .. . . d.,d ,loped ,oof (""n ....1 '''''''gular f""" 00 , •• endo) of beighl 1.Om . J.
h
39 A cord i. > volu." of cuI wood
.u
.0 0"" molorule ol ... It, (H,O) oon,ains 'wo " om, of by
,,,,a! """'"
m, ...".
41 A 'OIl is • of volu ... f'eq""'1y U>e '"'I";''' oom, calf boc • • " Ihere . . . ., le",' IhI .. ')'pe' of 10110: A did (h) 73rtgiol" (I m' _ 2&378 Us. oo .... Is.) " .
'oo
''''''?
42 SIT""!.I)'. lbe wi • • for • I:uS' .... dding """plio. ~ 10 be ., " _ in • "wIDing ",'_g! ... ,ocepoacle "';Ih lhoe in!e"01 d b"... m>JIY of each ,h",,1d be plUeb,e;:I and. 0"" lhe ,,,,. pt,,,1e "filled. how mucb wi"" i. lef! ""er in I",,,,, of (b) ":rnd,,d boo,,,", OlId« ) b .. ,,?
.,"ead
I "",d.,d boolle
I lIIagnWD _ 1 """dard
"""j..,
I je,oboam _ 4 ,,:rnd .. d boolles I "boboam _ 6".ndard bool'"
1 »Inr .... 7.1I
n """dard """I",
_
I balrllazar _ 16 ,randard bood .. _ I U56 L I ",buch.>dntzz.. _ 2Q .. :rnd>rd bollles
"'ga'
41 A I)'pkil cube b.. on edge jeoglb of I em. If )'011 bad a cubical box 11.." contained . mol. ol "'gar ",be~ whal .......Jd in . dge longlh be ? (One _e _ 6.02 X 10" ""il~ j 44 UoinS """ven ions :u>d do,. in ''''' chapltl. delenni.o. ,b. numb..- of b)'llr"!l.n >1011" ""Iu~td 10 oo,ain 1.0 kg of bydrog •• , A h)'
'om "'" •
45 An ""rooomicol Wlil (AU) io lbe .,,,,,se di .. """, bel ..... n and ,hoe Sun, approxim >lely 1.50 X 10' km. The ,petd of hSb,;, .boUl 3.0 X 10' mit.. Expoe .. l!roe 'peOO of Uglr' in ""ro.omkol ""its pe' minul.. .."
Earl"
B B B B fIG. 1
41> Wb>1 m"" of ...... , ... feU 00 ''''' b"" adeMiry of 1.0 X 10' kg''''.
Probl,m.lK
'own in i'rOOl.m 'I? W",o,
47 A pe""" <>II . e 23 kg pe' .....,.k. Expre.. ,h. m .., I"", '"'-.. in miUigr>nK pe' oecood ... if ,he <1- by ->e«>r>d 10..
.a
The mrn _h"!( ",,/0 i. a financial lerm U>rE' ",ough lor """"'". It i. defio.ed .. !be .. rio of the mar_ ket I"ice 01 • pig \Oit b uo:... of .H (}l .rugs to!be m .. ket I"ice 01 • us. bushel of oom. (Jb< WOfd -.rug.. i. derived from an old a"man...,m th .. m..... ·10 rut", _ b... tb. same me.run~ lor -.ru~" ... ve,bio drm EnglidL)A us.bm.belio eq.>I to 35.2.\8 L If tho oorn- ""E io listKl .. 5.7 011 tbe mart" ,bOllS< ... b.t ~ it in !bemettic .';" 01
".,k>
.>-
S5 A ... ndard in","" .. .u-.-... b .. 110!" .acb with . ri" (b.igh. ) of 19 ClI1 and • ''''' (borirootal depth) of 23 em. R... ",b "'Sg"''' tb at the .. ",. "<>
.>1"
"airc...,
56 lb. con"""" Eastelo _ ' •• mammal. t)llically has • m. " of 75 ~ .midi con .. poods to about 7.5 mole. of .. oms. (A mole of " om, ~ 6.W X 11)'" .. om~) In atooDc m... \!JIits (D) . .. bat;,.1>0 ~ .. age "',." 01 tb. i. the commo. E:utem moIe1
"om,
(Jlint: S.. !beM,." ,.hle in Appendix D.)
y"" ..... orn din.", 101400 poople., . OO PO' .. ,ving {ODe serving PO' po''''''} How.ve,. y"" bave only b.bo"",o peppe" 00 bond The 'p;cioe.r. 01 poppe";' me ._ "".d in tenn, 01 the "",..Uk h"" wll, (SHU). On . v.nge. 0... jalapofto peppe' h .. . ~ of.j(OJ SHU md b,b,.,.,o POI'P" b", •• pici""" of JOOOOJ SHU To get tb. de_ "'KI.pic:in .... bow many h>.l>anouJd Y"" ... bo.i_ tute foo: !be jabpello popp in th. ,edpo 101 the 400 WIne.. ? •9
y"",
(I'"
50 A \mil 01 .... oI.en.oed in m. .. urillg laM
"'il! is .b.
h«lD". defined as Io'm'. An opeD-pit ooaI mine """su"... 75 b""""" 011.00. d""", to • deptb 0126 m •• acb 1"'ar. Wh .. volume of .ann. in t"llbi<- lilom"',, ~ io ,tlD""OO io thi! .im.? 51 (.) A unit of tim. """,,.imes ..... d in nri io tho wt<. On. oJral:, equ." 10-- ' , Are there moo. shak .. in . . .000:><1 tb m tl>oo:< are oerondo io • ~,,? (b) H"",aru h.ave ".;tOO 101 about 1(1 ye",...·b...,. tho unive,,,, i,.bout 10" Y"" old. 11 the.ge of tbe .oiv,... i. d,fioKl .. I -unive, .. day:· wb .... unive .... day coru;... 01 ··l1.JIi"" .. fffOIIdo" . . . ... rn.al day 00II<;'15 01 oOfm.1 ""_ ODd!. bow man)' wtiveno >KOo:>ds b.ve hum.:ur, .:w.. d? 52
A..! . ,," 11, . .. "",'1""" !be old and the IJIOdem ",d
t..t~
the I..-ge .00 tl>o "'nil. ooruid" tb. 10Uooring; I. old ,ual Eogland I hide (bet ..... " 100 ond 120 """) ,.'" tb • • re . 01 1.00 ... ded to ,wtain o.e family ..;,b • ".gle pI""Sb!Of . the """,_""",iOll.1 " .. 01 a "u _ ,leD' (defined in term. of tb. cbanoe 01 a p.u1ic1e rutting and boing nhlorbed by i.) io m''''UJ.d io units of bar",- .. 1>0.. I ~n ;, I X 10-- " m'. (In DUcIe" pbysics j"gon. if • •• cleu. ;, ·1"ge:· theo ,bootio!. p.u1icle at it;' lik . >I!_ing .IJW_ let'" a bam door. "tUClr can hardly be oW..,d.) What io tb. r>tioof21 ,..pe.tal:e< to II ba,,\l 1
.re .
53 A to:adi.ional ""~ oIleogth in J. pan ~ ,b. hn (I l .o _ 1.'17 m). Wb . . .f< tb .... ti", of (.) "I..... hn. to "I"'" ",,,,,,,.00 ( b) ail due . ... lor 24.5 mi .<> put y"'" >alv. ge ,hip dio:e<1ly """ a pu-. .. >!rip. H~". when your dive" proo. tb. ocean Boo< at tbat locatioo .00 find.o 01 • ,hip. you ,adio back to Y"'" •.,u"" of informatioo . onl y.o disaw... h .. tbe ,ailing di .. """' .......upposed to be 14.5 ,,",,"c~1 mjJ<~ 0'" .. gut" mile>. U .. !be l."sth "bl. in App
,unk."
.>ide"""
57 An ....""'ornkal "oN (AU) io equ.1 .0.1>0 ""''''g' 1 p< "\ di!.ance f,om Eanb to tb • Sun •• oo..t '12.9 X 10' mi. A (pc) i, di!t:"". at FlG..4 Problem 57. ",hich a leogtb 01 I AU would ",bo.nd "" ",,!,!. 01 "XU)' I """""d 01 "'" (Fig. 1-8). A ligli'-Y'"' (Iy) io.be di>tone. tbat tigllt. tr. v.lins tbroIISb > VOl"UWD witb a .peed 01 186 OCQ rniI ~ would oove, in 1,0 ye ... &p"", !l>e E.nb _ Su. dinanc. in (a) P" """ ""d (b) ~ght _y.ar.
P''''''''
,b.
.o.
sa
10 pize A Uantic 0)""''' (...flicb com. 2b .0 -"l 1'" us. pint). lb. Iillod <»'>101 C«It:me, ohipped to you Iw tbe in"ric< n>ea5Ure of 1.0 .. X 12 ,m X 20<111. and , us. pillt ;, equivalent .0 0.47.12 H,,,,. B)' bow man)' ~' ..m io!be oo:Ot, ""'t of )"'" an.icipaled 00"",,1 59 1M cubit io "" . Drient unit of leogth b"",d "" tbe di""""" betwe.n the .Ibow.oo tl>e.ip 01 tbe middle fins" 01 ,I>e A..!.u"", ,h.at ,1>0 distaD'" "",god from 43 to 53 em. .Dd , uPI""" that anci,", du"':o!.' iodicate that • ,)'lindrical pillar was to h.v •• I,"!tb 0(9 cobits aDd a di,,",_ tff 01 2 ",bi.. fi>r!be "ated ''''ge.",b., ... tb. lowe< .al"" .nd tb. uppc' vol .... '''p«tively.loo (.J 'he C)'lind,,·, 1'_S,b in ........ (b) .1>0 C)'line <)'Ii.oder". voIu"" io oubk ....... 1 60 An old Engl~h cookbook COf''''' thio ,ecipe foo: « ..m 01 ",,,Ie ""'I" ··Boil .. ock of the lollooring """'11.JI1: I bo-.. k_ I:..tpi to the boilin! stocle Add I ..1>I.. pooa of cooked o:U and I ""'J'OO'I of ,al~ Simme, !Of 15 min.- 'Jb< loIIow_ ing table give> ...... 01 tl>e """"",iau >mOOS old (1""''''' _ rir) Briti>.b me"""". and an"",! oomJI1OII (>tiU premttrir) us. m ....."" (Th ......... ""''''00 !Of metric..ion.) fi>r liquid " "'''''''- I Britislr ""'I""'" - I u.s. .. "'f'OO'L fi>r..-y me .. "".. I Brirub ""'JlOt1 _ I us.q">t1. ln us.m .......... bow mud! (.) "oci.{b) ",.Ie tops. (e) rice.aDd (d) salt of. "'l"ired in th, 'ecipel
t.bIe
hall,,,,, _ 8 .. bl"poo
Motion Along a Straight Line A woodp
bea k into the limb of a tre" to sea",/1 for insect. to eat, to create storage space, or to audjbly oovertioo for a mate.
rh .. motion toward the limb may be vel)' rapid, but the
.toppo'ng once the Umb is reached is extremely rapid and would be fala l toa
human. Thus, a woodpecker should seemingly fa ll from the tree either dead or un· conscious every time it .Iam. a. b eak into th .. tlP6. Not
only does it survive, but it rapidly repeat. the mob"on, sending out a rn!-tat·tat signal through the a ir.
Why can a woodpecker survive the severe impacts with a tree limb?
13
2-1 WHAT IS PHYSICS? 0". purpose 01 pbysics IS 10 st udy 100 mO!ion of oo,<><:1.-ho,", las1
!he~' n""'~,
101 enrupl~, and how fa. lhey move in a giwn amoun l of lim"- NASCA R engin""" are fanatical "OOUI !hlS "'l"'CI of physICS" the)" &1",",;oe 1M Jl"rfo'maoc~ of In";, ""'" befo,~ and "u,ing a rare. G~ologlSls use Ihis ph)~ics to "",a",,~
nosing a parlially d=d ane,y. "nd motorisu ..... it 10 dil! e'min~ ho .. they might slow snlfirionll)' ".. 11;>" Ih ei. radar OOh,do, sound, " warning. Th" .. are oolln ll." ot oo, "Jampl ... In Ihi' cb"pt~ •. ,,-~ Slud}' Ih. basic ph}',i"" of "1Oliou 1\'II.2,e 111.2 objeel (raro ca., 10000nic pia .. , blood "" U, 0. "ny 01 "", ob;ocl) "'OW3 along • ,iogle axis. Such ""01io" i, "aUed QM-d"~~,,,jOl,al ,,"00'011.
2-2 I Motion Iod,,; h~",ve., a lumbling IUmbl" ... e
2-3 I Position and Displacement
-
p""",,,
~dln<_
~-~-c;--:C--7_7_:, ' xl'" _" 1 02
onp./
Poo;!;OIl i",le'eTmin«l 00 .. :ro. ,hat is m.. k.d in URi", oIle,,!," (b". mel.n) :tAd ,b>1 .."nd! indelinil
To local~ an objfft "",.~s 10 flud ils posilio" relalive 10 so,"" .d",ence poinl , of'"0 Ih. "ri~in (0' lNO poinl) of aD axi, such .s Ihe x a.is in Fig. 2 -I. The "",i,i'-e difl....,ion of Ibe axis is io Ihe dirl'C,;on 01 iOCf"",inS "um""" (roo.d;nol",,), whicb is 10 Ihe righl in Fig. 2-1. The OI>pO;. Jocaled "' x - 5 m, ..-hich means il is 5 m ,n Ihe posillVe dl1<'C1io" lrom 100 origio . If il ..",e "I x - - 5 m, il ""ould be jU-;1 as la, I,om Ih" o.igin hut in Ihe opposile di.OCIioo. On Ih . . .is, a coo.dioale of - 5 m is I~ Iha" a roo,d ina" of - J "' , and bolh roo.di o"I "" "" Ie,. Ihan a roo.dina l" 01 + 5 ".,. A p i"" sign for • roo.dinale "oed 001 Ix>. sho"lI. hUI a minus sign muS! "Iwa}~ bi> sbown. A chaoge from pos;l;on x, 1o posilio"~-, "calJed a di"Ia«'"",n, .1x. wh •• "
FIG. Z.1
.1., -
x, - x,.
(2 -J)
(Tbil'ymbol .1. Ih. G,,,,, k uppe"a", d"II'. '"pro",n" a .ha"g" in a qua "lily, aod
T""- "-orld, a nd oWr)1bing io il. m""os. Evo" ",.",ingly "a' io"ary Ihings. such "' • roa""-a)', 010'" ","ilb Eanh's ,otolio", Earlh', o,bila.OII"d 100 Suo . lh" SURS 0'bil around lhi' ""Ow. ollhe M,lty Way gala.ty. "ud lb., ga l.l Iy", migfJlion ro[atiw 10 o,her gakaxi"e,al p'operlies of molioo Ihal is '''''!riClod i" ways.
'h'''''
1. The mOlio" is aloog a Slraigb' ~"" 01I1y. The ~"" sl,oled, hUI il muS! Ix>. s!r,ighl .
""'y Ix>. wrlica!. ho,izonl 'l. or
2, Force, (push"" aod p ulk) ,-""use olOli01l bUI wiU nol 00 disctr5.SoNl umil OIapre, 5. I" Ibis chapw, discllSS only Ih. mOlio" ilsdf "nd Ch'"g.3 in Ihe molion. Doos 100 ""wing obj~ct """,d up. slow do•.-n. Slop. or ,~ve"" di,eClion? If lhil molio" does .h"ng.. how is Ii"", involved ,n Ih. chang.·/
w,
J. The mo"ing obJOCI;' .ilh .. n panicle (by ..-hid! we mean, pOInl-li t " object
,ho,
c1ire<1K>n The """ .am., btl • .', is always "" 'be "",i.ive .. de of ,he
0Ii.!,in.
e",,'Y such "' ,n ","eIfO") or an objecl ,bat mo ..... lite a particle (suell pOri ion 0'0'''' ,0 Ilkl sam" di.OCl ioo and al ,hil salllil 'ale). A "iff pig slipping down a "",'gh' pla},grollnd slido mighl be ""n,.oo.oo 10 be ,no"iog like. po.il m,,"n, lb. final v.lue of ,hal quanlit}' min"s 100 ,"i1lal val .... ) Whon OHm""" ar" inserled 10. tbe pos i"o" v.lu~s X, and x, i" Eq, 2- 1. a disrl.",,,,,,o' io ,bi>posili'''' d .. "Clioo (IO Ih ~ righl'" Fig. 2 -1) al ...a}'s co""'s o ul posil""'. and" dis-
2-4 I "", ... _V<>kxhyO
pb"""",nl in Ibo upposiw di.oClinn (Iofl in lb. figure) alway' 00""" oul negali",. For eLlmple . if Ih. pafliek! moves f.om x, - 5 m 10 x, - 12 m.lben <1.< - (12 m) - (5 ml - + 7 m. The posit;vo .,.,;"11 indieale' Ihal lb. mOl;on "in 100 posili'·. direction . If. in",ad. Ih. pa.tick """ 'cs from x, - 5 n, 10 x, - I m. Ihon <\.>. - (\ m) - (5 ml - - 4 m. The "egalh... result ind>cales Ihal Ibe molloo is in Ihc nesalive dimelion. Thc aetual numoo. of n"'I~" cov.,cd for a \rip" irr"lev, nl ; dispLaeemcm involve. onl)' Ib, origin,1 an d final poslliOffl. RI. ~IJmp"'. if Ih' parlide mOV(lS from x - 5 m oul lox - 200 m and loon bact 1o x - 5 Il•. Ih' displa"""",,n l from ,la,llofinish ismenl of
b'" ..
0.
' ("'1
WII~' fo llow. is ,h~ Jim o! rna,,}, ch«Kpoims )'''''' ~.j/[ sa In ,,,,.. book. Each COl"''''''! o ut! or ,no,.. q""'jo,,, "'oou an""~" "'/" '" .."M nasOl1i"g or a m,,,,,,1 c~lculalion, and ,ach gil'" J "" a quiet dl«k of"",I' ,,,,dn",,,,,ding of" poinr jU3I d'-"""sm/. Th< "IU~"" a" /is",/ jJ, "'~ bock of ,It. book.
H 'C I( POI NT 1
Her. are
,;"ly. • Iong •• x ..... Which pain (b) - 3 m. - 7 m;
(~)
'hr.~ pail. 01 ;niti. ( ond fin>l (>OII;'iOl1<' ,,,poe-
y.. • n.ey,;ve
di'l'I"",,,,,,,n1: (.) - 3 or. + 5 m,
7 01. - 3 m1
J' f lG. 2· Z Thoyaphoh(r)lor
'M' ;,
aD arm>lueoh" - 2 mlor all,im ....
2-4 1Average Velocity and Average Speed A compact "-ay 1o """,.ioo pas"ion is ",ilb a graph of pasilioo x ploned os a funcI;on of lime I- a grapb of xl'). (Tho nOlalioo .1'(,) represen!. a lunctioo x of I. nol Ihe prod",1 x li!lli!S ,.) A. a 'imple cIampi •. Fig. 2-2 show. 1M position function ..-(,) 10. a .lalionJ1Y a.madillo (" 'bklt we I.eal as • pa,tie"') 0'''' a 7 • lime iow,' -al.l1Ie anima!", pasili01t sta}~ Jlx - - 2m. Fogure 2-.1a is morc u'I •• .:.sting. "",,"use il in,·olve. mo11on. Th;, •• madillo is appa",nlly firsl nOlic.'
v... - ~ -
x, - x, ~ "
(2-2)
Tha nolahon m,,,n, Ibal Ihe posi!ion i, x, allune I, and Ibon .., al lim • .,. A rommon u"illo. I' ... IS 100 n "' (~. per second (mls). You m~y """ other unil' ,0 1M p.oblom~ bu! Ihey are always in Ib e fo.m of leoglh!lin"'On a grapb of x versus r. I' ... IS Ibe ' lope of Ibe st.aighl lioo Ibal ,onneCls Iwo parllcu l.1 f pornls 00 1M x(,) cu,,-e: one is 100 jIOlullhal ro"esponds 10 x, and ',.
B",""u", av"rag~ ,!",cd tloos ,,," iocluJo dimcliou.;t l""~s an)' algebraic sign. Somol; mes ' . .. is lh. "Ill~ (e_.",pl 101 too absrnro of a sign ) a •• '.... Ho"",,,,,. "' is wmonsuawd ;n Samp'" P,oblem 2-1. Ih" IwoC1l" to. quil" diflo,on!.
Sample Problem
m
Yoo dri"~ a to..!-UP pd"p trud along" Slraigh! ,oad fOf 8A km al 70 kmlb. al wbi<"h poinl I"" truck runs 0111 01 gooi", and Slops. 0,..,. the n~xt 30 min. you wa!J: anCl her 2.0 l m /a'IIIO, along (be rood 10 a ga
<"J
Calculations: W. firsl wrile ~
I'
......
-
~
<1.1", ·
R.a"angi" g and suboliluling dala Ihcn gi'''' us
Wha! is }'OU' "".,all d~I"""O!.nl from lb. b<>ginnmg 01 you, d"," 10 }'our arrival al (h , 'talio"?
8.4 kO!
70 k mlb
- 0.12 h.
<1.1 - <1.1 .. + <1.1 ...
- 0.11 h + O.50h - 0.61 h.
"
(c) Wbal is )'OIIr a",rag;> velocily I ·... from lhe heginniog of }'OU' drove 10 )'our ."".,1.1 Ihe 'l"io01 Fi"d il oolh n""""icall)' and gt.plucally.
firsl positioo.
ulculation: From Eq. l I. "'0 haw <1..< - ..., - x, - lOA km - 0 - lOA km . ThUs. your ow,.U displ.ce""'"1 i, lOA km io
(Answer)
Ih~
rffi-
live di'i'Clion of Ih" -< axis. (b) Whal is Ih ~ lime iOIe,,'al <1.11,,,", 100 Iwginning 01 you, d",'. 10 }'our .",val al (h. ,talion?
From Eq , 2-2 w~ know Ihall' ... fortn< e"';" "1110 of the di",I:J<>'m<'n( of lOA ~m }Or ,'" m Ii", trip 10 100 1;,,-.., inl."u.] of 0.62 hI'" tI~ en';" trip.
Calculation: Here
w. find
- 16.8 km lb _ 17 kmlh. ,I,.ad)' know lhe walking Ii"", inh),val <1.1. .. ( - 0.50 b) . bU! ,,-. lock 100 d,i"0g 11"", .m.,,'al <1.1.. . How""et. ,,-~ k"o'" (hal fOf 100 d,i"~ Ib~ displJce. "","I ')"-. . is 8.4 l m and lhe average wooly I'~ IS 70 kmlb . Thu~ IbIS awrag<'- ,'.Iocily is lb. ralio 01 Ih~ displace""'''t for Ihe drive 10 Ih. lime Inti',,,..1 for Ihe drive.
( Aos~",)
w~
To find v... glaphlC,II)'. firsl .." graph lh. IUfICllo" X(I) " ,"d Ihe poinl lab;>l,d '" ··Slalion:· You, ."",age wlocol)' i, Ihe slop< of lhi! suaighl I"", IDn"oC1ing IbOSi' (lOIniS; Ihat IS, v ... i, lhi!
2.,5 I ln". n'''''eo
,
" I ".,l••.• '" , i • •• I • , j.L ., ..,"\••• ••
rabO of !he riu ( ~.( - lOA km) 10 Ih. nm (.1, - 0.62 h). whicb gives us ",.. - 16.8 hnlb .
Tru
, , •
~'I · O
lb.
Tlme(b\
(d ) SUPIX"" (hal to pump Ih~ gasohu~. (XI)' 101 " . and walk had: to IbB Iruek takes }'OU anolb •• 4S "bn . What is your ow ..!;" sp<.>OO from (he lK>ginniog of you, drive 10 you, ,~!U," 10 lhe ~
trurl: "jlh {h.
gasoli"~1
I- to,,, "'"1
.., ,b.
FIG. z.li line. marted -Driving" and"Walk;"!!" are "",oioo _';m. pi"'" for ,he
'''''gh'
~
poi"'
Ca/CU/,otlon: Tha !DIal di,{."", is 8A kill -t 2.0 hn -t 2.0 km - 12.4 kin Tl>.> lOul lime im~.val is 0.12 h -t O.~ b -t 0.75 h - 1.37 h. Thy,_ Eq . 2-3 give, \IS
'
... -
12A km
U7h
- 9.1 kmlb .
(Ans .....,.)
I'ROILE M-SOLVING lIlCTlC5
Tactk 1: Do You Under,!.nd tIKI Prolhm? Th. 000Il _ moodifliNhr" .imply "'" undo .. tandin& the problem. The be", , .... ofunde,,'an:liD!;, ,his:e.. Y<'" oxpI>in tbe problem? Wri1f down the ¢Ven data. wi,b unit~ ""OS the ')'fllbok of the pl",emen' II.< in pan (. ) . nd ,he oon..,~ time interval .1t in part (b).) Men'i!)' ,he lUllno'oIn aod it> 'J'IIIboI. (In the """pie p",blem. the unboI.!" ""1ori1)' "...-) The. lind ,h. """""" ,;00 beowe.n ,he ""too.... :ond the d.... (Ihe C
Tactic 2 : Ate I"" Units 01(1 Be """ 10 US< a """,,"en' ... 01 unit> .. be. ""I1",! ownh." ",'0 ,he oq.atioru. In Sample Problem 1-1. the logical oniIs in leTOW of tho give. OO>eIim .. Di>Od'oroovm unit~
Tactic 3 : Is YOUI AM"' ...· Rea.onablpU, algcm ,or in)'OllI "y",otinS ofnumbe" on • e>klll.,or.
,b.
".Iiz, .,
Tactic ,,:
Reading a Graph
an.
,b,
min., ..,...".., or b lome_
A!wa)~
""" the "Diu ("""",,<10 or len) in "'hicll ,II.....iabl'" Of • • xpr .... d
2-5 I Instantaneous Velocity and Speed You bave now ..,~ o Iwo ways 10 ""-'<:';00 bow 1""- "otJ"'lhing moves: ",..'.ag<> W(ocil)' and ,vc'"gd , y) ". Th. velocily ~I .uy insl~nl is oblailk.>d ltom 1110> a,""'~ gc velocily by sh.in ~ing tbe lim. inlo,,-.I t>.1 dose. and dos.>' 100, As ~ d •.-ind(." Ih . awrage velocily oj>p.Q,Jeb", a llmilin g value .•,.hich is Ihe wlocily "1 lbal Ur;1"nl:
, t>.., dx " - • 11m - - - -dl-. • _ . t>.1
Fisu, .. 2-1. 2-3., 2-I , . nd
2_5 .... graphs )'OIl s.boukl be . bIe '0 "ad •• siI),. lo ....... y . ph, tbe v:uioble "" ,be bOO"""al i, ,h. ,ime " ,.j,b 'be direc_ '''''' 01 in", .. inE ,ime '0 ,he !ish" 10 .a.cb, ,b ••ari.bl. "" tbe unicoi oxi. ~ pooi'ioa x of the moving p.nicle wit • re'f"'CIlO ,he origin, ..ito the p<»i1iv. dirw;oo of x u~rd
(2-4)
NOle Ih.1 " is Ihc rale al" hid po;silioo x ;s changing "il b lime .1 • giwn insIJ"I: IhJI i~ " is Ih. de';-"Ii,,, of -' "ilh ''''J'OCl 10 r. AI", nole Ih.1 ,'al any ; tr
~ Ch.opt ... 2 I Motion Akmg. Strlligtlt (j,.. S, .ed is tbe magnitude 01 ,..,Iocily; lbal is, s!"-'-">d is ~.IOClly Inal ha, Ix..... " Sl,ipp<'il"'" in words Of vj, an algebraIC sign. (OrUlion: S",,~d and 3W rage spood can b.> qui,e d,ffe,"", .) A , ... Iocny of + 5 fils and one of - 5 mfs oolh h3ve an """"ialed SJ"l"d 01 ~ mt.. The sp.",oo"",(e, in a car ",.asu",.. sp....m. nol wl<>city (il cannot d
/c
H 'C K POI N T Z Tho following "Iu"iorn y.. ,he pooilio,u(r) 01 • I'",'i 0): (I ) x _ Jt - 1; (2) x _ - .\I' - 1: (J) z _ :u,~ and (4) z _ - 2. (oj In which ,;,u,1ioD ~ u.. v.loc_ "r v of lb. panicleroru","'? (b) In wbicb" v in , ••• e~ . ';'ex dir«tiOll?
We can find {he veloci!y a! an)' !i"", from Ike ,lope of lh. x(t) CIHW a! {k .! !une.
j ""
Calculatio ...: The slope of x('j. and so"ko !Il<' "eiocil y. is in Ihe inlen'als from 0 10 1 ,and from 9 S 00. so Ihen tOO c~b i, Slalionary. Outing t OO inlerva1 1><-, Ih ~ sl"Pi' is OXIslanl and lIO"",r",5O lhe" lhe cab mo'", "')In rons!,nl .... locil)'. We cakula!~!he s10Jl" of.«,) {heo ..
.E
,,,.0
g
I>o<:ause Ihe .~,) curve " aoo"~ lh~ , a'li~) Figure 2--6a show. Ih" x doe5 iooooo i"" ••", by 20 m in Ihal inlC'v,1. How""",. Fig. l-& s nol leU '" Ihe mlu
po
m.
r
.C-:'I
_
i -----• .~',~ ~;:... ;:x 0 0 Timol_)
,.,
0
"
, • • , ~"
,
• i • •• !,
'I
,,, , ,,: ~. ,, ,
----~
•• , , • • "
,'.I"es
fJ..- - (4.0 ,",,)(8.05 - 3.051 - + 20
, . Urn
" "
~ _ ., _ Hm - 4.0", - + 4.0ml,. {J., 8.0 , 3.0,
TOO pius ,ign i"dicat" Ihat Ille cab is n,o'1n8 in Ille pos. iliv~ -< di';>. In a roo in S<>cti0fl2.6.) Gwen" 1'(') srapb ,ocll as Fig. 2-6b. we could"w01 t b""[:W,,d" 10 prn
. ,... . - ,
<>I.I ~
T
j /
." 1,
•
./...
• , , • • • ol,'(~
, .""'.i.r..;O.;
i ,, .I L• ,
0
'""'" 1- )
, , • • ,
'"
j,
.- •'" • ! ,U ± ~ = 1
~ ~
~
,*",",00 ~~~
~
FIG . ~" ( ~)Tbex( 1) l il is ,b, d"ivali", of ltoe x(r) curv. (., _ IWdrH<) The ~(') '"'Ye lor ,be cab. I, is ,toe cleriv.live of ,b. Y(r)<0ser". body migb ' 1,,1 during ,b. acrel""io ...
2-6 I Aca>k>foti.", ~
1M posilioo 01 a p.1.lie'" mo\1ng 00 IUl .< ,,-,is is giV('n b)x - 7.8 + 9.21 - 2.11'.
..ilh -< ill ,,,,,lets and ",",nds. Wbol is iI' ,-.Iocily al I - 3.5 s1 Is Ihe ,-.IOCIly conSlIUlI. ot ts il conlinuousl}' changing?
i Vcloc,I}' ts I.... firsl "",i' -ali,.. (,.-.Ih m'p.lCI 10 Ii,,,,,) of lhe posilion IU OClion x(,). u/culationo: Fot ,implirily. lh. unils have b,.-;eo omil IN from Eq. 2-5. bU I you can i~'1 lhem if }'OU like by cbanging Ih~ COi'foc..nl' 10 7.8 m. 9.2 mls. IUld
" - T, - d, " (7.8 + 9.2f - 2.11'). whieh tK><:omes (2-6) ,. - 0 + 9.2 - (3)(2.1)r - 9.2 - 6.3f. AII - 3.5s. I' - 9.2 - (6.3)(1.5)' - - 68 mls. (An,""') All - 3.5 '" Ih e parl id" is mm-lng in Ih. negalive di.eclioo of x (0010 Ih. min .... sign) wilh a sl"'"" of 68 mls Sin"" lhi> quanlily , apl"'''' in Eq. 2-6. Ibe ",Iocil)' • d"l"'n", on , .nd so is conlinuO\I'Sly ch,ngiog.
2-6 1Acceleration Wh en a pa'lie"", ",locily
I',
a ... -
-- .
(2 -7)
~
" " ..11
alIi"",
f,. The
i._,to "",ncou, locele,mi on (ot ,imply "",:.. k:Mion ) " a
".
- T,'
(2 -S)
In ..-otds.lhe. . =""a(lon 01 a p.1 l1ic1e a( any msl.,,1 i, Ihe ",Ie al ..-bieh iI' '-CIOClly " rnanlOng allhal ;flS1anl . G,aphically. Iho a=letalion aI "ny I>OUlI " 1""- ,Iop
" '('") ",
o - T, - d, dI - dr"
(2 -9)
In wo,ds. lhe """"' '''",1;00 01. pa,{icle 'l an)' inslalll i, Ik. "","nd denvali", 01 iI' ro"lion xl') "',Ib ">;p<', Whon • is conslaol (al ei lhe, 00' 4 mI').lh~ ""'ivali", " Zi'ro and so atlo;, lho> ooc.l "'ralio" . When lhi! cab fus1 begin' 10 mo,,". Ihe ,-(I) eu II... ba:s a polili"" derivaIi.. (Ill« ,Iop cab slows 10" 9-op. l",,- d.:!,;va li"~ IUld slop.:! oIlhe 1'(1) curve a,. ""gal;"~; Ihal is.a(I) is neg'tli'.... NeXi comp"'" lhe. slopo.>s of Ibo "(I) CUf\-e during Ih" 1..'0 acc~kra lion I"'riods. Th •• lope associa l"d ..ilh lb . cab', slowing do",n (commonly called "de ",~ . ,ahOll ") is 'I'~' "",,"USil Ih ~ cab Slops in hallihe I;me il look 10 gel up 10 'P'-;ed . Tho 'Ieepc' 'lop« """IUlS lhall be magnilude ollhe dOC<'lerahO"" [a.S'" {bau Ihal 01 {be aoc~k"llOn. as in~ica le d in Rg. 2-&.
FIG. 2·1 CoIOIl,1l P. St' P!' i•• rocket ,led as it;. bfOlly.t up to high ope«! I""",,,,.tiot> OIlt 01 tbe p'!") .Dd th .. Y'"Y J >pidly b"'N (""'" I· 'lOtiot> into tbe page). (C.."",y U.S. Ajrf"omo)
n." ""O""oos IOU would 1",,1 .,hilo riding in Ihe cab of FIg. 2.fi .w ",dicalM b). tho slotchoo figuros at the bolton!. Wh"n lhe cab fi.st acede"tes. you fe<>1 as Ihougb )"ou 3te p,o",,'1 nothing 'P''CIal. In olbe , w01d~ yO"' body .e""ts 10 ooc"k,a{,ons (II is all OC<>:'IOf01ll<'le.) but nol to velOCIties (il is nol a 'P'",dom"lCr). When }·ou a,e in a car !ravehng al 90 lmlh 01 at, "i'1'l.oo t..,voting at 900 ~OI l b. }·ou have no bod,,}· a"',,,,oo,. of Ih~ moho". Ho ..""" •. illh" ca, 01 1'1'00 quiel l)· change, velocity. }·ou ma}· "'-'COOl" l""nly ""'are of lb. cbang<'. pe.haps ,,'"Cn I.igb"'ood by it . Part 01 the Ih.dl 01 ,n ann"",· ""'01 p"~ ri"" i, due 10 Ih" q"ie~ ma"Bos of wlocity thai yO" ""<1..... 80 (yO" pa y 10' Ihe acceleration" not fo. th~ spnJ). A mow .xl,eme '''011'1. is sno .... in lhe pholographs of Fig. 2·7.... bieb .." .. lalen 1.. hil" • mctel sled ,.."' .ap,dl}· _=10.· aled along a 1ract and Ih"n rapidly bral"" 10 a stop. ~ La,S" a=lo,."ol15 are som.rim"~ exp'<"S5<'d in le.ms 01 g ""ils. ,,-;th
w.
19 - 9.8 mi.'
(2· 10)
(s "nil ).
'haU di'iCUSS ," &>clion 2·9. g is Ih. magnitude 01 Ihe """, ,,,.ation of a (As faili"g ob,ect oo.r Earth', ,u,f"",.) On a rollo. roJ.ste,. you may experie nce b.ief """""'talio"' up to Jg . .... hich is (3)(9.8 mls'). 0' 29 mls'. mo.~ Ib.n eno"gb 10 justify the cosl 01100 .i""-
.00",
~IIOBLEM-50LYING
TiI.CI1C5
Tactic 5; An Acce/eracion·s Sign I. commo. l:m"S' of:m occel".tion It", • "".oc:ie.,ffi< """""i.!' pooiIive """l,,,tioo ""' .... ,hat ,he .peed 01 an obi .... ~ ioe","".g. and .. ytive """""..,;"" m..... tb., tb •. 'l""'d ~ d.ecr • • ",,! (tbe obj«t is d""l .... ing). In 'his boot. however. ,he";gn 0I :tO "",,",.,ioA iodie.,es. dir«tiot> .•", ,.bethe,
. . . II tbe .;gn. 01 tho yelodty ... d of . port;"'''' "etbela/1M.". ,he .ptodof'be panir" iner ...... II tb, .. S.. "0 oppoo;1e. ,It •• pood
~ incr.""'! Of dK"aoi.g.. FOf .xample. if • car witll •• initial yelocit)· I· _ - 15 mi. i, b,lIkod to Ht"!' in 5.0 ~ then _.., _ +5.0 m.'t'.Tho >«,1 .. >,;"" ;. posUi'~. but tb. speed It .. d",,..,.,.d. Th. " ...,., i, tbe in .iyu: tbe di'e
Vc H'CKPOINT 3 A """"bat mo"""oIo.s onx ...... Wltor i. tb. 'ign of ito """ ... ,,100 if;, .. onovinS (a) in ,be p<>!;'iv. di, .... ;"" wi,b ioc:ro""ng opeN.(b) in th. posi_ ,iv. dir«t;"" wi,b do
guag<. ,he
""ob;":<"" f'f"d
ditt,,,.,,,,
=.,
""",,,,..ti,,,,
H". then ~ ,he proper ,...y 'oin",I"" 'be ';gn"
""""",..ti""
.< - ~ - 27t + ".
"·ilb Xln m,",,,, and, in seconds. (a) Boca"", position.< depends 0" lilllo t. Ih ~ pJrtielo nlUst b<> moving. Fwd tile pJ,6clo·s wlocily fuoction ,·(1) and a=J.ora1io" I"oct;"" ntl).
Ihe velocl1y is ''''0 oolh J, belore "nd 3 5 afler looclock ,ead,O.
(c) Dose,i"" Ih' paniclo', molion 101 ,,, 0.
Rosonlng: We need 10 exam;oo Ihe x (.). 1'(1). Jnd a(,'.
A! I - O.!OO ",,'Ilde ;, a!x(O) - + 4 m and is mO'ing "'Ih a velocilY 01 "(0) - - T/ mi,-!hal i:s. in !lie n,gali"e dir<'Cl;oo 0( Ibe ..- aJ;~ Jt< .=Ioral;oo is a(O) - becau,", juS! loon !be ""nic"", veloci!y is 001 rnaoging. Fo, 0 < 1<3" 100 ",,'lid.> siul has a ooga!ive Wlocil~'. so il oonlin",... !o move in Ihe ""gali"c d;,e<:{ion. Ho .."vef. i!s accel"ralion is no longe, bY! is iflCfeasing and (X'Si!ive. B•.-"",u,", !oo sign, 0( too '"Iocily and Ilia .cceloralioo are opposi1e. It.. "",!ic'" muSI be sln"-ing. lnd""d . .." al,eady how !bal;1 'lOP' n,omen!anl)' a!, - 3 s JuS! Iboo !he parlick is os far 1o the lell 01 llIi! o'igin in Fig. 2 -1 as i! ""II eWI!('1. Subslilllling 1 - 3, inlo 100 10u(I)."" find Ihal 100 panlde', """"00 )!lS1 Ihen i:s x - - SO m. lis II 3 s. Ihe "",Iicle moves 10 Ihe righl on Ih. axis. lis aoce le,alion ,,,main, posihve aud grows p.ogress""I)' lar&", tn mJgI1illlde. Th. wlOCJly " now posiIi", .• nd tl 100 grows prog,essively larg<" in mag"ilud"
~xp,,,,,, ion'
101
exP''''''''''"
2-7 1Constant Acceleration: A Special Case 10 lIl.ny I}'P'" of n"'lion. ,II. aoc.I""lioo is eil ll", co\l,;lanl 0' apPIOI;ma"ljI so. FOl oxample. you migbl a=lera" a ca. al an 'pproxim.lIdy con",nl ,"10 ".-hon
"
a "'ffie ~ghl lurn, lrom ,od 10 g"eo. Ttk>fl graph' of }'Oll' posilion. wloci'y."M """"Ie,alion would resembl~ Ib"", in Fig. 2-K (NOlO Ihal a(1) in Fl.!;. 2-& is oon SI.nl. " 'hirn ''''Ill''''' 111.1 1'(1) ,n Fig. 2-& ha~" a conSlnn! slope.) Lal", when }'OU bla ~ ~ ,00 ~ar 10 a Slop. Ihe acc"",ralioo (01 1k'CCt."lion in oommon language) mighl .Iso be 'I'ploximal"l)' conSiant. Such cases a,e so common IIID! a 'p"cial sN of equD!ioft'l bas ""en do,ivoo 101 de'ling ",illl 100m. On" apPloarnlo Ihe do.,,-alion of Ih """,icral;"" "OJOSl'O'.IOO awrag<'- ..,.:
I
velocity "").given at .",11 poi.t by the slope of tb. """'" oh(I). (c) It, (ro ....01) >«<1 .. _ >l ion, tqu>l 10 tho (ron>t .. t) .. ope of the curve 01 11/).
::t::::::::::..::=,., ,
!•
.
•,' - - - - - - - -
'"
~ "j - --.,.".='.::""-
~ Ch.opt ... 2 I Motion Akmg. Strlligtlt (j,.. He," ". is the ""loeOl)" at {his ,,
0 and v is tbo velocity at any lal", lime I. We can
{Il"'" -
"-'<"3"iI
,. - ". + a'.
(2-11 )
As • cbock, nOie Ihallk ... equ.,ion •• duG'S to ,. - \'0 lor I - 0, as ;1 must As a fu,· th., ,hod . lake tbe tkrivOIiv. 01 Eq. 2-11. Doing so yii>lds d,M, - a, ..-k"", is I"" di>finili"o 01 a. Figure 2-Sb sho .... " plot of Eq. 2-11.1ho \'(,) fUlKtion , Ih. Illocl;on is Iia;>Jf "nd thus thc plot is • Slraigbllin". III • similar maone, . .." can ,.,,·rite Eq. 2-2 ("ilh a low chang"" in oomion) .. v , .. -
x - x. , 0
and Ih"" as (2-12) in •.-bich x. is the rosi!iO" ollbe panic"'., , - 0 and ", .. is 100 avc .. g~ yelocity ""1 .... ~" I - 0 and a law. 1;""" . For Ih. Ii",,", v.loci! YIll"Clio" in Eq. 2-11.lbe a"Hag' velocity ""C, any Ii"", interval (,"y. from I - 0 10 a later l;n", ,) is thc aver.go of the velocity.l Ih. 1><>ginning of 1M interva] ( - "oJ and 100 velocily al Ibe .nd 01 Ihe in!",,-al ( - ,'). For Ihe inlorval from, - O!O !b~ la!", !ime 'IOOU. Ihe aw,"g<' ,,,loci!)' i,
"... - 1<'-, + ").
(2-13)
SUbsli1U!ing the 'igh! "de of Eq. 2-11 fo, " yields. .h", • li a le f('.rra"ge"",n!, 1'-. - I',
As a cbod:, no!e Iha( pu l1ing , - 0 )'iold:! -' - x .. as il lIlust As a fU'I IIe, cllec~ . laking Ih. , "'I"al""" Ih.t might p'ov~ useful i" ""Iai" spox-ifi. Sllualions FItS!. "Ole Ih"l "' mao}' a. five qua"I ,I"" ran possibly"" i"volved i" aoy problofil "bout con"""l a..se quanlilies io; "ar io'-ol""d in (he proble m. ';,hn- "-' Q gi.'en o r ru an "nk",,~-~. W'oare Ihen p,e"'"!ed "'Ih !h,ee olille f('mainiog quanti!>.. "lid asked !o find Iho fourlh. Equations 2-11 ""d 2-15 coc h co"lallllour of the"" qu"ntilie" bU I "01 lhil "'"'" fou,. I" Eq . 2-11. Ihe "m.-;si"g illgtedi.",., is Ih. disp]"",nwnl -' - x ~ In Eq, 2-15. il is Iho ",Iocil)' " 'Th
-
"j + 2a(x - J(.).
(2-16)
Thi' .qual""o is u",lul if ..... do "01 how, and 31e nol ,.qui,.
-' - x. - t(", +
I'}I.
(2-17)
iat'.
(2-18)
Final!)'. w~ can eliminale I'o-obl,ining x - x, - '" -
NOIe 100 ,ubU. difle,~OC
Table 2- llisl5 lhe baSIC co""anl a=1.ralion ~qualiol1'S (E'I" 2- 11 a"d 2-15) a, ..",U as lhe 'p<'Cializod cqualion, ,hal we have deri".d . To sol,.... simpl. ron"",,' ac an equalion frOlll Ibis ~SI Ii/you hove lhe ~Sl " 'ilh you). ChOOS<' au equalion for" hich Ihe only "n~ no"'n va ,iable is Ihe va,iab"'rcq"",wd in lhe problonLA 'impler pi"" is 10 ",mem00' onl)' Eq~ i -II aJId 2- 15. aoo lhen so/v~ loom "' simullaJl<'Ous equ.:llioru ..1I""e"" needed.
.y-;;
loU""';"~
H 'C I( POI NT. . The «Iu" ioru give ,be po>i1ioo x(,) 01 . panicle LO fou, . "u.,ioru; (I) r _ 3r - 4, (2) X _ - 51' + 4.' + 6; (1) r _ 2},' - ./It, (4) r _ 5t' - 1 To ",hiCJr 01 'b .... "tu:"ioru "" 'he «I." ;"'" 011>010 2-1 apply?
Sampl. Problem
't.,.,
loVe ca" us.> !he oonSlan1 -ac
c..lcwtions: B .... u"" !h o ...oodJKldo.·s ooad Slop'<. the final velocity is " - O. The inilial v.locity is ", 7.49 mls. ""d .he displac~n\cn! du,iog !h;, coJISI",, ! aocok .. !iOll is x - x. - 1ii7 X 10- ' m. Sul:>s'i!Uli"g .he", v.lue, IIlto Eq. 1-16, "'. bal"
0' - (7A9 m/s)' + 2,,( 1.87 X 10- ' m), Q -
Equ.,;"" Number 2_11 W
w W W
Mi<"ng Equ.tioo
x -
'' - ', + 0' ''0' + !to.'
0."""1 <
x, -
<0
>
,,' - "I + "1Jlx - r,l r - "a - if", + VI' r - "a _ "' _!-"
•
>,
'!-"'k . """ thot to. """,boo.,.. u...!<,d..-... b
m
lhil h~ad 01 a woodp<'Cl ., is rno'ing f,,",
0.
Eq""'iom for Mo.ion wi.h Con ..... Ac"" ....... ion·
- 1.500 X 10' mis'.
Dividi"g by g - 9.8 mli- and ,"~ing .be absolu!~ ,·.Iuo. "'. find Iha! Ibe magni!uoo of!oo he.d·s aOCek,.llOn" ,, - (1.53 X 1(0)g. (A", ....,.) Co ....... nt: This !)')>ical a=Io .. ,iol\ magnituoo for a woodpi'd •• is aboll! 70 lim", !ho OOC<'le,alion masni IUd;> of Colonel Slap!, in Fig. 1-7 and ceminl)' 1I'0ukl h.ve been le1hallO h,m . T1Ie abili.y of a 1I'()()(]p<'de' 10 wiltlSland such huS' """,lernhOl! magnilUoos;s!Xl' 1I'('U uOOo:>l'S!ood, but !boom !"'O main argun ... (1) n... ...oodp.'der", molion is ,Imoo alo"g a Slraigb! line.Some r.",an:b"fS bel",,,"" !ba! ooocu"'oo can occur III "uIllaos .nd anima" ..nc" the ooad is rapidly ro1a100 arou"d!he neel (o "d b,"in Slem), 00llhal il is "'"s ~k.I)' in SlIaigll! lin;> motion. (2) n... "'uodpilcl ds brain is anocbM S() "'01110 100 "'Ulllha! lhore is linl.:l re,idu,l ",,,,,,men! or osciU .. i"" 01 !he b.ai" jus•• Iu', lhe impact and nocha"", for tOO lis,u. oo"U"",ing !h . skulllUld b,ain !olcar.
",e
""s
"'1SU' its posilion
Figure 2-9 gi'·.s a parlide's ",[ocily " "' il m",'", along an x axis ~iilh ",,"slanl What " ,IS ",I
.=I~,"hOll.
...
loVe can use lb. oonS!a"'-""",)('.alioo equa paniclllar, w~ can us.> Eq. 2- 16 (I~ - ,i + 2,,(x - x.j). ,,.hidJ ,ela!es wloci.y and IlOSilron.
First try: No.mally wo ... an! 10 """ a" equalion Iba. includ.s .he ,equ.Sled v3fiabJ~. I" Eq. 2-16...... ~~n ide"'ily ... as 0 ""d I'. as b..';"S !h•• eque.slild v3fiabli>. Th.o .." can ide ",ily a second pair of val"~' as beiog I' and Jr. Fro", the g.aph ..... II...., ''''0 ,uch pai.s: (1) " 8 n,l. and x - 20 m. and (2) • - 0 and x - 70 "' . Fo. enmple. wo ~an ..Tile Eq. 2- 16 as
(8 n~")' - 1'1 + 2,,(20 m - 0).
(2 -19)
Ho .... ''''.•.• l "01I' OOilllo, I', "0' a. S.cond try. In" .ad o f directly invo"'ing lbe .equeSl.d
(
)
FIG. 2~ Velocity""".' positioo.
variable, Ids","" Eq. 2- 16 " 'ilh !ho ',,"0 pairs of koo"'o data, ,denlif}'ing "0 - 8 m/s and x, - 10 rn as the fitsl pair a"d • - 0 m/s and x - 70 OJ as .he s.."O)lld pai •. Then ".., cau "~Il~ (0 mI,), - (8 OIls)' + 2,,(70 m - XI m),
which gi"", "S a - - 0.64 nili- . Sul>Slitu!i"g Ihis val"" into Eq. 2-19 .nd solving fo, V. (Ibe ",Iocil)' associated wi.h !h . posl1ion of, - 0), .... fi"d I'. -
9.5
ml~
(A""".... )
~ Ch.opt ... 2 I Motion Akmg. Strlligtlt (j,.. ComllHlnt: Some problem'S ;,,"01,.., an equationlhal indud., the r"'lUnging p1Ob10m requires you 10 firstll'" an ~q"al ion lhal doe, no'
,,,,,Iu de Ibe roqu"'led va".!>'" but I"" gi"es yOU" value floWed 10 find it Some,;"",. ,"" proc~du,~ I" ~"'"
pnpu.
c"ura~ 00<:3""';1 is 50 indlfec1. How.,"", . if you build )'our 5OI\10g s~ms by solving 10[' 01 problems, Ih. proceduro g,.JuaUy mquires loss rourage and "JaY eveo "''COme obvious. Soh-ing probleRls of .ny ~jnd , ,..h.lh~ ,
ph)"iCll or social. req uire. pra<1ice.
2-8 I Another Look at Constant Acceleration* Tb.:l firs! 100'0 equalio/\<; ill Table 2-1 are {he basir eq "",iol\<; from "'hir h the mhers ar. Tn.,.,. 1010 ClIn be oblJloed by inleg"I ;"" of lb•• = I,,,. ,ioo wilh Ih. cood,lion Ihal Q is oouSlant To find Eq. 2-11 . we .. ~,il. lh. "" fin;I;O" 01 .c-
"""v;,d.
ederalion ( Eq. 2-8) .s
d,' - adl. W. 0••1 ",.ile 11>0> ,/Od'Jim'" ;""grol ('" II",id,,;mlil'<) of bolh ,ide5:
Sinro a""lotalion
a" •COOSlanl, il can bo<> lahn o uts;"" lhe in1eg
w.
(2-20)
To eva lual~ I"" c"""a Bl of inlegra lion C. 101 , - 0, ,I " 'hkh Ii,"" I' - ".. SubslilUhng lh ese values inlo Eq, 2-10 (,,-bkh musl hold fo. all ,·,1",-><; of " HK"ludmg, - 0) yields ". - (,,)(0) + C - c: SUbsl;luI;ng Ihi' inlo Eq. 2-20 giws us Eq, 2- 11 . To "",we Eq.l-15, we 1Cwril~ 100 defi",tion olveooly (Eq. 2 -~ ) as
dx - vd, .nd lh"" loko Ih. inoofi"ile in legral of bolh 5i"", 10 obl'in
NeXI , wo ,ubSlil"l~ for " ..-ilh Eq. 2 -II :
[,1"' - f("o +"')d'. Since I', i, a COllSlanl , os i5 Iho a=kralio" a. lbi, can bi? ....·.inon as
1"(~gr'I;on
now yie ld, -< - I ''; +
ia,' +
C.
(2-21)
"ho •• C ;s ,001be. con,I,n( of iUlograli01l . A t lime, - O. wo baw x - xo SUbsliluhng lho", "3Iu ",,;" Eq, 2-21 yiekk Xo - C . Replacing C "'Ih ... in Eq, 2-11 givos us Eq. 2-15.
2-9 1Free-Fall Acceleration II }'OII I"",,>d an obI'",1 " 'lh '" up '" down ,nd could ""mehow olinlJilal. 100 effects of ,i. 00 iI' flighl. )'Oll would find lnal Ih . object 3"",loral" do,,-"ward "1 "",nain CO/I'Slan l ,ale. Th.1 rale ;,; calied 100 rr..,.r. Ii IK'WI• •• 'io n. "nd ;1, magn;lude;,; "'PfCS"n ted by g. The .""ol.."'l;on i, inlk'P"n"""l of Ihe objc",f, ch,,"cleri'lics.surh os mass, densily,O' sha",,: 11 is lh. same for all objoc{"
"""OS
Two examplos 011,..,-1,11 OOC<'le,a!ion ar~ ,no..-n in Rg. 2-10. wbich i<; a of mobosoopk photos of a fea!h'" and ao appl ... As !h= object' loll. !lIey .",ebale 1kJ•.-nward-bO!h a! the san", ra!o g. Thu,. !ooir in",oa .. a! lb. saOle raw. and !boy fall !og<>!h.,. The ""Iuo of g va.;"" !Jigbd)' ..;\h 1'li!Udo and with olenl ion . Al ... a li'Vel in Earlh', midlali!Ud"" Ih. value is 9.8 m1S' (or J21!/s'j. whim is whal )·ou should u"" os an ex",,1 ""moo, lor ,hoe problem' in 'his boot unl",s o,h" ...-;"" nOled. Th~ equalions of mo!ioo 1II Table 2-1 lor conslan, a.cc<'loralioo also awly 10 f,e" lall nea. E~'!h', ,urlace: lbal i~ Ihey awly 10 au objecl io ve'heal llighL eilbe, up 0' oown." ho" !1Ie effoct5 of the air call "" IK'gkCled H o~over. nole !hal lor Iree faU: (I) The dire"lions of mOlio" are"".,. along a 'wheal )" ax", iltSl •• d of Iii.> x axis. wilh Ih. posil,ve di.ectron of y up",,,d. (nu, is imporlanl for lal'" chaplo" wh~n combin.>d horizonlal and ,-..lical mol ion, ore examiuedj (2)"J"b.> I •..,-Iall ace"Ii'''lio" i, uegah"e-Ibal is, """-""'~rd on Ih~ y axis. 10-"'ard Earlh's cenler-a"d so il has In. "alue - g ," Ihe eq"aIlOn~
'I_d,
. - The boe_falt """,ler.,ion .... Bank', .",[ace ;u _ - g _ - 9_8 ",!<'.and tbe ~'"8"Itud< of ,be """,ler. '"", ~! _ 9.8 mI, l. Do _ ,ub>';1Ute - 9.8 mI, ' lor !.
Suppose you loss a 10",:110 di,i'CIly up..-,rd "'lh ao inilial (posil;"') "("\oc;1)" v. F!G. 2·'O AI"'''r . od,"'Ppi. and Iho" calm ;! "000 il rclUlfl'i !O lbe rdo"", ",,,,I. Du,ing its fru-fall f/lg/II (Irom jltSl ruw, ils r.lo"", !O jll5l bo.:>fore;1 is ca ug/n).!1Ie eq"aliollS of Table 2-1 apply!O il' mOliofL The a.ocolofJtion " al .....ys a - - g - - 9.8 ,n"'. lli'gal;W arid Ihu,
"
"""-n-
occeie",ti"" ;ncr .... , ,be disUIIC.
be" .,.,," ,,,,,,,,.,ive irn.8.... In ,b, .1>-
2· 11 alld 1·16: ,juring th~ .. oce of .... ,Joe f... her 'M ,pple fall . scen!. lbe magnilude 01100 posil;", '"locily d<'Cfo",",,, U"hl il nlOO.ICnlarily b.>- 'ose,b ... (Ii", :;"1;II7/0"I>/,lnI(J8") romos Z\'fO. Bocau", Ihe lomalo h" lhoo SloppOO. i! i, a! i15 maximum hcighl . During Ihe """"'" I. !110 m agnimdo of 1M (now "" gati''') ,.~ loci 1)" i'lffil as..,,"
-/c
Eq~
=n.
freeloll ;. vacuum" ,be m.gni ,ude 01 """,1e"';011 g. The
,.ha,
H 'C Ie POI N T 5 (.j If y"" ''''.. ball ,,"';yn"p, i ..", "ED 01 ,be ball". di.pbcem.n, lor ,h. """"'~ from tbe T.Ie ... po;", '0 , .. hiS"" poin'? (b) Wh" iT i1 lor ,be de.oc.n,. ITom ,b. highe.l poinl bod, to , .. rele_ poin'? (e) \\11 . 1 ;.'0. boll". """,1e ...,iorI .. ;" kiy.e .. poin,1
Sample Problem
m
a..
Scpwmbe. 26. 1993. Dave Munday ",",,"I o",r lbe Canadian odge of Niagara Falls ," a Slt'<'ll>all "'l"ip[l"
NO!~ that Munday's displacem,,"t y - J. i<; a neg.I"" quanli!y-Munday fcU do"'". in the n posilrve ,oo! b..'C3U"" Munda}" ob'-iousl)' reach"" tli.> wal<'f ""face aft" 00 begins 10 lall al 1 - O.
&'<"~"""
Mu"day', fa U "-as a Ireo lolL lhoe oon'la"l -o""" Io,"lioo "'l"'lioo, 01 Table 2-1 apply.
•
• ,, • '"" "
"<)
Cakwtions: Lei us place aj-".xi<; along Ihe palh 01 his lall. wilh y _ 0 al hi' slarling poill! aod !b" posil;'" di,el.1ion up lh. axIS (Fig. 2 -11). Tlwn Ih" a.creloral,on i:s a - - g along Ih.! alis. ,"d too ..-al,-, Iovel is a! y - - ./8 m ("'galr,"" b..,<"3USC it IS below y - 0). Lm !oo falll><"gio al Woo, - O. ",Ih in,lial "'loci I)' "0 - O. From Table 2-1 Wi'- choose Eq. 2-15 (bm in)" nola lion) beca ..... n oonla,ns lhe r"'lU"'led lime < W" find J -
Y. - ,... - !gl'.
,.,
I' - -1&'4.9. 1 - ).1 5-
<),
,,
fIG. %- " The position. veloc;'y. .....J ioo 01 • freel)' laII"",- objed. bue "eel ball ri
,h.
(An,wer)
~ ,
- 0.
~.
4.
,,
""'.I.....
- ~8 m - 0 - Ot - j{9.8 mlrjl'.
• • ,., • Im/"I";.',
N;. !,n FalI ~
•
.
_ " .6 _, ...
~
_H .l --29.4
~.
~."
4.'
1,
"• ,
,
~ Ch.opt ... 2 I Motion Akmg. Strlligtlt (j,.. (b) MumlJ Yeould oouo! ofllh~ Ih','" ..oond, of r,,,,, rail but rould nOl .... how /" be had fallen with each count Dil,,,.mio" his pos
(d) What ""as Muoday', v.IociI}' ., "oeh oollnl of ""'" IllU s.>rond? Was he ''''"'" of his incfCasing sJl"'
CalcWtiorw: W. 'gain"Sil Eq. 2-15 but now we ,"tlsli· '"I~. In {Um. 100 ,.,tu...." , - 1.0" 2.0 s, and 3.0" and so[", 101 Mumby', p<>;ilion J.n." ,",uits are silo'"" in Fig. 2-11.
Calculatio ...: To find 100 wIOOl;'" from the o,iginal 1I:!!a ~.,thout ",ing tbe pi>Sl!ioll'> lrom (b), lot a - - g io Eq, 2-11 "nd then substitute. in lum , thi! valu", 1 - 1.0 .. 2.0 .. and 3.0 ~ is oXllmpl~:
(c) Wh.1 WM Munday', velodly a, ""
w. ,".I.",,?
,.""h..-..:I Ih. "'.-
w.
H.," '0
' - '. - 81 - 0 - (9.8 ml,')(1.0 s) - - 9.8 mls.
Calculation: To find 18.> velocity froRlIl\;> "rigi"al data withool u.ong Ih~ tilTh' of faU from (a), we rc"~;I' Eq . 2 -16 in J DOlalKm and Ihen ,"t>sli!Ul" ~"OW" d",":
Tlleolhe, ",sul!s ,to Sh~'1I in Fig. 2-11. Once be was in lree fall , Munday was unawarc of tho incr"",mg speed b..'C3use the accele,ation du,ing tho laU ~1lS alway,; - 9.8 mis', as nOl.d in the 1",1 column of Fig. 2-11. He ... as. 01 COU'1O'_sharply aware of biuing IhO''-alO' herallse Ibon the accelo .. l;oO amupdy ch.nged (Munday sun-iv.>d too laU bU! lhen lao..'
m
In Fi[l. 2-11, a pilCh[>f loss.>s a baS<'h,lU up along J y Jlis. ""Ih.ninilial'p"odol11 nu.. ~ (a) How loog d"", 100 Nil lah to leacb ilS maximum heigbT? (1) Ooco Ih. balllea",~ the pilCh .. and before il ,elUlllS 10 his hnd, its occc\i>IOlioo is Iho f,,,,,lal l "",ol<1""lioo ,, - - g. Ikrnuse this is CO"SI,nl, Tabl. 2-1 appties 10 I~e ",olion. (2) TIle '-olocily ,. al lhe maximum ~"ighl must be O.
lains IhOSi! lou, ~a riabkl& This }'icld<;
. •
,- ,. - ,.
" 'O"'~ "'s'-P"'"'
,
:'
..
...... ,' .--. ..
-.,.,.,.""
:,' on' """"'''
" ""
""""II ""
,h.
",aigh' up ;n'o Ur. The "I"";"'" off, •• loU .ppIy for ri";ng" "",U .. forfaU"'gob_ je<1.,p"'vi
"
1""'-
"
" ""
(Ans ..~r )
Calculation: We c~o lake Ih e ball'. leloase poinl 1o be Y. - O. We can 'hen .~il~ Eq . 2-l6 '" Y nOI.1ion, ""-1 y - y. - J and ,. - 0 (.1 too ",ax,mum belgbl), and solve fo, y.W. gel
"i _
y _ ,., -
2a
0 - (12 mls,>' - 7.3 m.
(Ans ..~r)
2( 9.S mig-) ~ .O
n,
Calculations: We know,·... - - g. and di'l'lac"n"'''1 J - J. - 5.0 m, and .." ~ill"1 t, so we ehOOSoi' Eq . 1- IS. R• • -nling illo, J and selhng y. - 0 give us
" " "
-~
1.2..
(cl How long does 'he ball t"ke 1o ,.ach. po,"1 abov~ ils ,,,Io.se "",n11
,:'I
'1"-"'" ."' ........ ' : ...d _.. :.
0 - 12 ntis 9.8 ml,'
(b) Whal;,; Ihe ball'. maximum h.igh! ahove ils reloa",,poinl ?
ulculation: Knowing ,', Q, aud lhi! initial velocilY ". - 12 mI.. and 1O'.~ing I. we soh'" Eq. 2-11. .·hleb oon-
'0...... baseball
(An' ..... ')
~
.......
-''''
y - , ... Of
}gl',
5.0m - (12 m/'ll - (f)(9.8 n,I>')I'.
If we lempo,arUy omil lb. unil' (ba~iog n01ed Ihal Ih<>y are c!l1lSi'I"nl), .. e can rell~,le Ih;,; as ~ .9t'
There atO Iwo such Ii",,,,! Tlus is n01 ,eally '",posing b..>ca""" lb. ball passes IWicc 11uougb y - S.O m, once on 100 wa)' up and OOC
I'ROILEM-iOLVINCl1It.CTlCS
Tactic 6:
Meanings of Minus Signs In S"'ple Probl.m, 2_7 ... d 1-1\. "'" .... b/i,b. ..,d in Sample Probl'1ll2_8 it 10.... ,hoe pilei.. ,', h. od A nes" iv. val •• 01 y ,he. m, .., ,b . , ,.e bod)' ;, bel"", ,b. cl>ooen oriSiD. A ""!",iv. veloc;,)' mearu ,hoe body i, movin!;. ,hoe ""!"I;ve direc';"" of ,b. Y ",,;, _ ,~ .. is, oo...w>rd. Th~ ;. Hue no Ill. " ..... hoe .. ,b. body;' Ioca,ed, We ,.te d.. """,Ien';oo '0 be DeS,live ( - 9.8 mi.') in all problem. d.oIi'g ..-i1h CallinS bodia A "'g.. i"". "",ele..,;oo """0", 'bat, »';m, goo. 0., v,loci')' 01 'be body beoom",
dir""io. i, .. DlO'-in!o In S..nple Probl.m 2--8. ,be """,Ie' . ';011 of ,be baU ~ n'l" '" {dow",..,dl 'b,OII£O"'" ;" !iglr', wbtlher ,lie bill ~ ,i,inS or Caning,. Tactic 7:
Un<> 01,._
,na,
,""ugh'
)'OO migh' "'" b. ve 01., poo_ .. ;. Sompl. Probl.m2_8c. 1f)'Oll E" mOfe "" .....,n on ... tI.., do ,b • • yoo expect. do "'" .lj,olll>1k>Hy discord _OI "",m '0 fi" E.,rui •• ,bem cartop""c.b. g.A .. .... ..,.,.." .;bili';e~
,b.
2-10 I Graphical Integration in Motion Analysis Wh o" "" hav~ . graph 01 an obj.."C!'s accek:lralion ",''us lin",, "''' can inlogral~ on Ibe graph 10 filld Ih" Obj..'CI'S WIociI}'"1 gi'"en lim •. Soc,u", acee",,",io" a is dofi"'-'
'"y
", -". -r
(2-22)
adl.
The righl ,;00 ollbe <'I lator Ii"", I,. The
f. , ,
( area bel""O" .=lo,aI10" cur",)
,"" -
audl;n",axlS.lrom~lOl,
.
(2-23)
[I a "nil of occder.lion IS ) m!s' and a u"il of lim" " ) .. Ih"" Ibc 00...· spondi"g "nil of area 011 100 gr aph is
(I m/,')(I s) - I mI~ ..-hieh " (pror<'rly) a "nil of voloctly. WOO" Ihe """,,"'r31io" ""''''' is at>ovo Ib" li me "i.. lho area is fX'S,IIvC: ".-he" Ih~ curve" t..IOW lhe ,ime 1lXi~ Ih. ar"a is ""gal;'.... gimilarly. beeallSO vcloctl}' " is defined in I""", of ,h. posi';"" .< as v - dxM" Ihen
x, - x.-
f"dl,
A , ,.,
(L-U )
"
..-her" Xo is 100 p""'ilio" .1 I;"", '" 3Ild x, is Ih" pos'ho n "I limo I,. llI
r',. JI _
J..
heIW""':
(area velool)' curve). andl ,"", .. ",lrom~lol,
•
b::'L '. '
(2-25 )
[Ilh e unil 01 velooty is I mls alld Ih. unll olliffie i:s ) .. Ih'" lhe rorr.spond,ng uRi, 01 arca on ,he graph is (1011, )(1 sJ - In,. ..-hien " (pro]lo'lly) a U";I of pos,lion and drsplOC.
~
'"
flCl. 2·1 J The ... abe,woen. plOI,ed 00 hOfirorl," lime
rurv•• ,.e
aJlio, f,om lime I, '0 I;me I,';. indi_
""t.d fOf (0) al"''''' of ""","',a'K>A o v.",... I . OO{b) , !""pb 01 veloc;Iy
,'ve,,,,'"
"Whipl:lsh injUf}'" commonly occurs in a " • ...,nd col~· ,iou ,.·ho ,e a lroul ca, is lIil I,om bgan 1o aroelofJle?
From 100 ms 10 110 ms. ,egio" C bas Ih e sll'pilof . ,,,,,. {aaglo...'i{h a,~a a,,,a c - (0.010.)(50 mls') - 0.50 \l\Is. SubshtuhGg ll1c5o "olue, and I', - 0 iOlo Eq , 2·26 givo:; us
", - 0 - 0 + 1.5 mi. + 0.50 I', -
",Is.,
2.0 mi. - 7.1 k mlh.
(An' .... e')
Com""",tI: When 100 h~,d ;. just Slarl'l\g to mov~ (o ...·,'d, Ihe 101S0 .I,,,ad)' bas a sr-
W~
can
Ine lorso ,!",w al aoy lorso at') gtaph .
Calculations: W. loo,", ll1at Ibe i";tial torso spe~d is "0 - 0 al lime 10 - 0. al lb . slall of 100 "colli,ion:' W~ w.nt Ih~ to,.., ' I""d ", al time " - 110 ms. .,hicb is \\ he" 1110 h.ad begins to ""co]o,ate. Co"wini"g Eqs. 2·22 .nd 2·23. ~. can '.-rile ,. _ I' _ (area b,,{~ .. o a.e <:ele,"!iO"CU""). '0 ""dhm • • xrs,lrom"to' L (1.26)
"'pa'''.
too a,,,a into th'''' Fo, co"wn;.""", lei u, (Fig. 2·Ub). F,om 0 to.j() "IS. regioa II h.. no
",ea. - O. From .j() m, {o 100 ms, ''-'!lion B ha, tOO sbap" of , 1';"0' glo ...'ith ",~a
'fea . - kO.cI60 .)(50 mfs') - 1.5 mi•.
\00
'"
n"
fIG . 2·" (~) n.. 0(11 ALl •• adof ovo/u.o· ",' i. a ,imul>tioo of . " ..·end ooIli
,im.
1><,,,,,,,.
REVIEW & SUMMARY Position The pitj,., dir<<1io. 00 all oxi. ;.lhe dj' ..... ;011 of incIe., ,,,! poo.;ti'" ""mhe", ,b. "I'poo.;l' direction ~ tb • • • ~ • • ~ .. d~'<1k>n.
Displacement Th. fwp/<><'mtnr .I., of • p.. tioc{. is lb.
DiC'em.nt i. a """'Of quan.ity.1t iT pooit; ..,
~
tb. p.,.tiocle
b., M<>v.d '" .h. positive direclioo of Ihex """ ""d •• saliv, if tbe. particle II .. lIlOV,di. tbe. ""!iui"" dir«liOIL Average Velocity \\0." a p.njde h., m<>v.d I",m pooi . tiOA x, '0 poo.;tioo.<, d.ri"g a. im.e ",".. ai d' _ ', - I" ito ",'<1ty dllfiog Ih, l iot'TVa! i<
, • --.1,.I.t ~
n.. algeb",ioc 'ig. 01
-
~ ~ - ~.
(2.2)
I'~. indkrtid. '"<>v ... oot io".ad d.pe""" OIl it. original .1Id tin' p<>Jition<.
0. a gnoph o(x v ....... I.the .YenS' velocity for • time in_ t, ,,,01 .1r i. tbe . Iope 0( tb. ",oisht tine """",,",ins the poin" on the t " P'''''"t tbe 'WO end! 0( the lo,.tvol. "'""rag. Spud Th. "\~'"g' ' pu d '.~ 01 a p.,ticl. dur_ i.S' time intorv>.l b., cleptodo 0<1 tb. total di>t""'" tb. parti_ , .. Dl""" i. th .. time int
-
i1)' .'( t) . 00 the"""""; time clerivat iv. of pooitioo x( I~
.-- ---
d'x dt' .
dv .,
(2_8.2 _9)
0 • • IlJaph 0(" ."''''' '. , • • occe"IlI1ioo u at ""y time r i. 'be .Iope oI,he
I'rlodl}' (or
v _ .\) + .r.
(l -Il)
x - "o - Vd + ~".
_ _ 11111 . _.1.< _ _dx • .H ' .1r dr
", - vi + 2a(.•
wh"e veloci'),
sl"""
0"':
Av. rag. Ace.l. r a tion AI'"oK< tbe ...tio 0( • chan! . in v.l<>city b.v to the ti .... in .. rvol :0, in ,.,1licb the cbmS' "",ws: (l -7)
(l -15) - x,).
(l-16)
x - x, _ !<., + o}l.
(l-17)
x -.'o _ "' _ ~I'.
(l -IS)
The.., are "or ""lid ",,1> •• 'be ocreler"iOll;' .'" OOIK1>n'. F.... Fa ll Ae.-I...."'lon A. important exomple 0( Itroiy.t_1ine mOlioa witb occe .... tioo .. that 0( ... object ,;'log or fallin! f,,,,1y E arth·, ,wi""" The COII_ " . n' . ere" "'tioo "'Iu"i"". d.lCJibe ,~ .. DlO1iOOl. 00' we mak. ".0 chang .. in nor.,ioo: (I) we the 1110
00II<".'
."OJ
,.f..
Th • • Igeb",ioc >.is'' indic., .. 'be diroctioo of".... In.tant.lnus Ace. l. .ation /,.,'0","""""' «
QUESTIONS 1 Figlll' 2-15 oil".., foo, patn. aIong..ruck objeru move fTO'" • " . rting poin' '0 , final point. aU in II" ....... time lottrvill. Th. path> I"'" ""., a grid 0( "'Iually ,paced "'aitlh' lines. RaAk ,h. path> >j><'«I 0( tile oil;.n~ SI.at .... fi"•. 2 Fig.« 2_16 .. . gnopll 01 • l=''''Ie·. """,tion '!oos an .• axil ,..,,"'!tim •. (.) At time , _ O. wh>1 ;. ,be , iY' of ,he pa""' .... poo.iIi",,?], ,he p .. t~ , .... velocity pooi'i ... neg. tiv •. orO>1(b)' _ 1 ,,(e) t _ 1o.and (d) , _ 3.1 (e) How m.oy ,im.. doe. tb. panic.. ~ ,be poi.' x _ O? 1 Fig"" 2_17 giv .. tho v.1o<:i1)' 01 , partide moving on .. oX ..... Wh"t are (0) tile i.itial ood (b) the fi.1lI dir.cti"", o(tr.,..,17 1='",1e """ mOo (e) Doe. "",n'oril y1 (d) Is 'he ,ioo pooiti ve or .'g.'i",,' (.) Is it OOI1
, I
I
I
, I
,, , , ,,
•
AIBI c
"
L
'
Chihuahu... it
•
I
-ot,f-t-1,,-
0( ,
pe
FIG. I ·1§ Q u .... io.1.
,, , , ,,
,, ,,
'"' , 1,1
c I
"
flG . 2-11 Qu,,'ion .j.
'('1
5
Figwe 2_19 give. tb . v.loc_
•
i1)" 0( • porticle movi.g atOll! an I ~ at ,b. hiSlk-lt
..w. fIG. Z·"
Q .... tioo 2.
'"'''''Y.
,b.
F'Ilute 2_18 gi... tbe occe ....tioo 0(1)
ch:o" " • German , b.pIoe
,
•
ve,_
..
oo:e"""
Poi.,
poi.' o. tb. rurv" poin' .j i, >1 ,b. knoe .. poi." .. d point< 2 ... d ~ art . , 'be ,am. "igllt. II'h., ;. tbe di'e<1ioo 0( tr . vel .. f1G . 2-19 Qu,,",'iOll~ . (a) time t _ 0 and (b) poi.,.j1 (e) A, ,.rueb 01 tile six numbered points dotS the pank .. ,._ ve"", its dire<1ioo 0( "'o",l ? (d) Rank the .iI point> according ,<> tb. magnitude of tb. acrel..,.io •. !'• • ,..., fin"
,
6 The loU""ing '"'Iu " ioru give "'" velocity .'(1) 0( a pank .. in fow ';'u.uio .. , (oJ I' _ 3; (b) v _ .j,' + 2J - 6: (e) 0 _ 3r - .j, (d) .' _ 51' - J. To oI'he .. ,i,uations 00 ,b. "'I">1ioru O(T. blel_1 apply"!
.,.iclo
fiG 2-17 Qu."ion 3.
_ _ Ch.opt_ 2 I Mation Along. Strlligtlt (j,..
'>n_
7 I. Vi&- 2_20.• cream E,ri.e .. Ib,,,,". diJocUy "p ...... ,d (WI 'hr"", evenly ",.,,,d windows of el •• igb" Rank tbe windows >c_ cording t" (.J speed of 'be "eam '''''gerin. .. hile p... i" ~ Ibem. (h) th. time 'be cr."", ''-''germ. , .... 10 p... them. (0) 'he magni_ tude 01 ,b. occele ..,ioo oI ,b. rr.am tans,nn. while p ,."in ~ thorn, and (d) ,he cJ...Jlg< 4v in ,b. 'f""l"d ol, •• cre . m '''''geli •• dmiog ,b. p .... age.y .."" 6, ...
,h.
,xi,
",.",low,
cD
''''''age
• A" _ 0 . • parti
Xo _ - 2011L The ,,;gao 01 ,h. partide', i.in. 1 velocity v, (>1 time ',) ,nd ro...""" ocale .. ,ioo a .. e. r''P''<1;".,Iy. for fOIl, (l) +. +; (2) +. - , 0) - . (4) - , - . 1. ,.,1>kb ";,",,ion> ,.;]) ,b. partie" (0) .. op """",,",.. ~y_ (b) pa.. • through Ihe origi., and II."'" pas. Ihrougb the origi.?
+,
«)
,
,
9 H""gi.g ""or tbe railing of • brkJ,o; •• YO" drop an.~ (.0 initio! velocity) • • l"'" ,b,ow. 0 ..,oo.d e~ do ..... ward, lib ;". ~, city 1'(') 1m (.) dropp"d ,- , '. "', ',
r;CC7<';----
,toe
•
'U ond A(b). nd 'heB 'h,,,,,,,, 'U7 (Cw",,", at. pa,aUe" .., at. C. D • • nd E, '0 ' r< F IUId G_)
','<..,",""'. :.',.', ' ~
'.
'G
F1G. l-Z1
FIG . z.20 Qu."ioo7.
c
'F
'c
Q ... ,ioo 9,
PROBLEMS
._. . _oI_"'""". . . Me.
._
'N .......... """"'" "'..".. ~ . . . -, ,,,",,,,,,,,,,,,,,,
SSM
~ oI_
" .... '"9. V.l o<~y . nd " v.'"9_Sp.. d
Z·'
An ,u ,omobile t..vek 011 • " ..ight ,o.>
.1
,toe =n,
ing 'his SO tm nip? (A".m. ,b .. i, """'.. in ' be prui'ive .T di_ '«1iOll.) (h) What ~ ''''' ''''' ''B' 'l""'dl Graph x "",... I . nd i.We.,e bOlO' ,he velocity i, lound 00 the graph.
....
-
."'''so
«)
• 2 A car tr 'v.~ up , hill " • oorutan' 'p"ed 01 -10 k rnlb ,nd re'.ntO dowD the hiU at • COlIS" ", ~ 0160 kmlh. Caku.l." the . ... age.p
"'''''.)'011'
51\.,
.3 During a hard ey .. migh' IOf 0.50 ~ II y"" , re drivin! • car at '10 krJ.1I du,ing ,uch "noez .. how far 00.. th. car move during tll .. ,im.7 ., Th. 199'2 """Id .p H.be,. H~ """ through tho me"wed 200 m .. retch ,. .. . ",:din! &.sw '. at ....ttich h. co""""ntod. "Cogito "go zoom!" (I think. ,herelore r ~o fo .. !). In lOOt. S... WhiltinBhm b.. t Huber. 'e«JId by 19_0 km!h. Wh at was Whittingham', time 'hrough ,he 200 ml . 5 Th. posiIiOll 01 >It objtct moYin3 alon~ >II x ..is is given by x _ .lr - 4P + ,,_u-h"ox;, in mot." >J>dl in >oooodri. Fiod the po>i'iOil 01 'he object" 'he loU"",ing vol." 01 t. (a) I .. (b) 2 ~ 3 .. ODd (d) 4 ~ (.) "''bar ;, tb. obj.lid indic~te how the . ..,." lor (I) <"
«)
,im.
.o.
.6 CornP"" Y"'" avenge ",lociIy in ,b. followin! ,....., , ....q.) You ,.alk 73.2"," "p"edol L22 ml, >nod tb
_
'N """"",,,, ",""""
u.w
..."""'. ...."" . "
~ "
You ,.alk fO< LOOmin., • ..,...d 01 L21 mI, aDd ,h.n run fo, 1.00 min at 3.(l'i mI, along . ""ight tract_ (e) G-tapltx verso, I for boob "'.... d indicate ho.. t" ."""ge velocit), i, lound on tb. sraph. •• 7 III I k .. r-.ce-s. 'WIDtI I OIl "",k I ("';tk time 2 min.17.9'i .) appear, '0 be I"'te, ,h ... 'WlDtI 2 00 track 2 (2 min.2K15 . ~ Howeve,.lJ>d obrain 'he car', "",.d v, in" wind) .... ,i,u>tioo. .hould fiod overag' of Jit, ",d dil, (method I) Of .bould we divide d by tb. ,v""Ee 01 and "l (h) Wha, is 'be l,actio...1 diff.rt"", in 'he metbod. wb,n • wiod blow> alons th. c,,', ,oute >J>d the 01 ' h, "';ll(h~ ".
Ii",
w.
".ody
,toe
'wo
,,,,toe
't
"';0
•• 9 You >te '0 dri"" '0 OIl intervie .. in LU>O,htl to_ oat • eli .. ' ''''''' of JOO kin on aD y. Th. in"rvi.w ~ >t 1L 15 ....... You pi.., to drive at 100 kmlh. 50)'011 I.... " 8, 00 ...... to aU"" I00I ....,. 'ime. You drive " thM 'pe
exp''''....
{i",
''''''p
,bow,
p",,",
0"' '0
FIG. Z.U Problem 10..
.1<11
••
""pilL >lid ar. . . pan."d t>y L _ 1." ...
n ...I'M.....'" iII"& 2.-.U 0CCIIn" 'net -o.tl) 1.1_
