TO THE STUDENT

You have the potential to make a difference!W;!I )'07 The Center of Gravity 308 ne Some Examples of Static Equiliooum 310 Indeterminate Structures 314 Elasticity 315

Review & Summary 226 Quest ions 228 I Problem. 229

Review & Summary 319 Questions 319 I Problems 321 Q uestions

Contents _

rn Gravitatio n

330

i(.] Waves-l 41 3What cau.e. the .ometimlls dangerous ascalations of cau. e. .Om be..tI. detect II forest /ire at a larg .. distanc .. betltlil d.. tect .. /i", large di.tanc without seeing or srnelSng it? srnelNng 18-1 What Is Physic.? 477 Physics?

Pendulums 395

Harmot1ic Simple Harm""ic Motion and Uniform Circular Un iform Motion 399 15-8 Damped Simple Harmonic Motion 400 15-9 Forced OscillatiOf1s and Re5or\ance 402 Oscillations Resonance Revie'li & Summary 403 Revie'N Questions 403 I Problems 405

18-2 18-3 18-4 18-5

Temperature 477 The Zeroth Lawai Thermodynamic. 477 Thermodynamics Measuring Temperature 478 The Celsius and Fahrenheit Sca les 478 Scales

xii18-6 1 ~'

Contenu COI1t. nu

Therma EJ.pa"sion Th.'mall ExpanKN'l 482 18-7 Temperature and Heat 1 ~7 Tempe"'t" .. ..-.d Hut 484 18-8 AbsorphOfl Solicit and Liquids 485 The Absorptoon of Heat by SoIods lind lJquods 48S 1 ~' 18-9 Closet Look at Heat and A CIoN< look It Hut lind Work 488 1~' 18-10 The ~ lI'" of Thennodynamoa 490 First Law Th.rmodynamics 11-10 18-11 Some Special Cases 0 1 FilSt laN 01 11-11 Serre Sp.c;..1Cuu of the First 1I .. of ThermodynamICS Thennodynam..:1 491 18-12 Heat Tran.fer Mechani1ms 1"'12 HUITrln_Mechanosml 493 RevIew SumrNlry Rw .. w & Summllry 497 QuestIOns .98 I ~ SOO Problems 500 Cluestoonl 498

'"

CondUCIorslnd Insulatoll 213 Cooductors IWld Insullll(q 563 Coulomb's Law 565 Coulomb'. L..','I 54S 21~ 21. Charge Is Quantized 571 215 21 -5 Charv-I. QUIIflIJ:ed Sl1 21~ Charge Is Conserv.d 572 21-4 ChIIrge I. Conwrved 57' Review Summary Revoew & SumrnIIry 573 Questions Problems 575 Ouestoons 573 I I'IobIemt S1S

'"

t-t.. Electric Fields 580 J"~" Ele ctric Fie ldsHowden. bee ..... electrosr.tic. to r:oI/ect 11M fh ... Howdoes a be.t .... eI2 2>225-3 25-4 25-5

Capacit.nce 657 Calculating the Cap.citance 659 Calcu lating Capacitors in Parallel and in Series 662 Para llel Energy Stored in an Electric Field 666 Capacit or .. itt, D",lectric 670 Nith a Dielectric D",lectrics: An Atomic 'I",w 672 Dielectrics: View Dielectrics .nd Gauss' LaN 672 D",lectrics and La ..

,>6 2>625-7 25-8

RevieN & Summary 675 Revie .. Question. 675 I Problems 676 Questions

Review & Summary 755 Questions 756 I Problems 757

Jr.f1 Current and Resistan ce 682 J'.f'1 a nd Resista nceWhat pnte .... tions should you take if caught outdoors precautions tak.. during .. during. fightning storm?26-1,~,

J""') Magnetic Fields Due t o Curre nts 764 Magne t ic CurrentsHow can th e hum,.., brain produce It detectable magnetic en .. a d .. tectable magn .. tic field f",1d without any magnetic materian mat .. rian 29-1 29-2 29J 294 295 296 What Is Physics? 765 Cakulating the Magnetic Field Due to a Current 765 Force Between T.. o Parallel Current s 771 NO Pa ra ll el Current. Ampere's L.w 772 m Soienoids and Toroid. 776 Solenoids To.-oidsA CurrentCarryir.g Coil as a

Wh.t Is Physic.? 683 Physics? Electric CUlTent 683 CUlTent Density 685 Resistance .nd Resist ivity 688 Ohm's law 692 ;!., Microscopic VieN of Ohm's law 693 Vie .. Power in Electric Circuits 695 Circuit s Semiconductors 696 Superconductors 697

2~2

2~3 '~3 2~4 '~4 2~5 '~5 2~6 '~6 2~7 '~7 2~8 '~8 2~9 '~9

Dipole Magnetic Dipoie 778 Summary Review & SummaI)' 780 Quest ions 781 I Problems 782 Questions

RevieN & Summary 698 Revie .. Question. 699 I Problems 700 Questions

m Circuits27-2

705~

How can ~ pit crew avoid a (ire wha .. fueling cr ..w ~ fire whae charged race car? chargttd rac .. 27-1 Wh.t I. Physics? 706 Is "Pumping" Charges 706

~ ItJ lndu cti o n

and Indu ctan ce 791 ct a nce 791

How can magnetic induction melt metal in It foundry? ~ mag""tic 3013~2

What Is Physics? 792 Two Experiment. 792 Expenments

xiv,~,

Contents COI'tento 32-7 327 32-8 32... 32-9 329 Magne tIsm and Electrons MlIgnet,sm "nd Electron. 870 Magnetic Materials 87 4 MlIgnebC M"t.. liIl. 874 Diamagnetism 874 Do~MtJsrn 874 Paramagnetism P.-m"9MMm 876 Ferromagnetism Fem:mllgMbtm 877

,...

30-3 ,~, 30-4 ,~. 30-5 ,~. 30-6 30-7 '~7 30-8 ,~. 30-9 30-10 31)..10 30-11

Faraday's Law 01 Induction F"racby'. L",w of InciuctOOfl 793 Lenz's Law Lenz'. L",w 795 Induction and Ene.gy Tr;onsleu 798 IndllCtlOn..d EMrgy Transfers "8 Induced Electnc Fields !nd1lC.dEIKtncF.-1dI 801 Inductors and Inductance 1fld1KtOJ1;..d Inductal'Ktl 805 SeK-lnducoon 806 S.If-lnc!lICtoOn acw. RL Circuits Rl.. C'IWfU; 807 Energy Stor.d ,n I MlIgMlle FI4'id 81. Stored in Magnetic Field 810 Energy Density d a Magnet;'; Enecv1 o.n"ty of " MlIgMtK Field F.-lei 812 Mutualinductoan 30-12 Mutu"llndllCtOOfl 814 R......... & Summ.uy 816 R"" ,.w Sull'"l!T\llry Questions 816 Problems OuntOOfl. 8 16 I Probitmt 818

32-10 3210 3211 32-11 ReYOe'N & s..n-.n-y 881 Revie>N Surrrnary Questions 882 Problems 883 Outostoons 88.2 I PIobI.m. 88J

en..w

Ie):) Electromagnetic Waves 889 1c~1 BB9 What a.undog, me &tip#ot, ~brf~.peIf. m. ColIn Wn-: g _ " 'undosI, the brighr, aH:wfuI'p th. gilCoIIUS. .

lei . Electromagn etic Oscillations tel l El ectromagnetic Oscil lations and Alternating Current 826 B26djd 01.0. eruption OIlt the power How did .,o/4r e""PllOn knock 0d: guitMisti shun """';st.,,."mpfr..,. fo, oldf ...hiOMd tub. ...pWi_? 'IIJhjonl lube 1I~;fj.,'? 41 1 What Is Physics? 1143 Wh.lotl.Ph~? 41 2 Th. Electric.;ll Propert'eI Solid. 41-2 The ElectnYI Prop.rt... of SoIdi 1143 3 Energy Ina ~talli ... SoIod 41 J Etwrtgy Level. ,n II ~~ ... Solid 1144

....

.H

41 S 41.5 41.6 41 6 Semiconducton 11 SO Som.~ 1150 Semiconductor. Doped s.mocooductotS 1151 41 7 41 8 .1 Th, p-n Junction 1154 The pn The Junction Rectifier 1156 Th, Junctia!1 Rea,I .., 115' 41 9 4' 41 10 Th. UghlEmittirog 4\.10 The lightEmitting Diode (LED) 1157 41 11 Th e T,aro.istor 4\.11 Thl Transistor 1159 11 60 R....i.w & Summary 1160 ..... & Question s 1161 I Probleml 1162

Insulaton 1n...u.lotS 1144 M.tals M-ul. 1145

law" ,,.,

H I Quarks. l eptons. and the Lepto ns.Big Bang Ba ng 12 18How un" pftologr."n 01 dw /y uni_.. be ~'I 1 c.. a photog,;oph of the e./y t.a~ ... 1 44-1 Whit I, Physics? 1219 PhysICS7 44 1 Wh. t l. 44-2 PanIC. ., PartICle.,, PartICles 1219 442 Pa rt icle. Particle. PMlocles 44] No Int.,lud. 1223 443 An I"teo-Iude 44-4 Thel. ptons 1226 444 The Lepton s 445 T,... H.dronl 1227 44 5 The Hadrons 446 Still Anolher Conservation La" 1229 Another Co nserva tion La'l 447 Th. Eigh tfold WilY 1230 Way 44-8 Th. Qu~rlo. Model 448 The Quatk Mod.I 1231 ....9 Th. B. sic Fon:H and MelS8f>ger M.ssenger 449 The BiOIw; Forces Part ICle. 1234 Part" . . 44-10 A Pause for Reflectoon 1236 APIiUMfOfReoflKbon 44-11 The Uno....... Is &panding 1237 Universe ~ndng CoimIC RadoooDOn 44-12 The Cosmic Background Radiallon 123844 1J 44-13 44-14 44-15 Daric Matter 123B Oatk M,,".. 1238 Bog BIIng The Big Bang 1239 ASummirogUp A Summ,ng Up 1242 ReYMl'N & SulTll'Nlry 1242 Revie-N & Sul'T'VNry 1242 a..-toon. Question. 1243 I Problem. 1243

''''

"w

r: ..~ Nuclea r r:".. Nuclear Physicsm.1ong

1165 11 65

What au_ the ,acNtion danger to ar CNWS flying ~I CIIU_ m. redUlion dJInger 10 , .. ct-. th.long po/;',",Odu.. 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"_

, , , , ,C.

~i". _

..p~iIo _

,~ ,

10- ' 10- ' 10- ' 10- ' 10- "

0' J panieular tinl' i"lerva! '"

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.

lO-" lO-l. ~ a","' rd~ so Ihat ulllm"lol}' e~,,)' "",-"suring d..",ioo "",iveall ronlaim aboul IcnJ ~m 01 string!

,h.

1-6 1TimeTun., h'" 1"0 "'Pl be abk> !o an''''''' ''''0 qlk'slio",: "lI'n

tho mlic>, tim, o/t 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 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 .1ca50nal ,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\e,oid&", s...011 OlOun,';n

Ocean 'me,EJep/l'.' Gn, Sped of du ,'"Id rali" e for a ""'pIc of too ground:< - - - -.

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 .. 0sliluling Ihi:! oxpression inlo Eq. 1 10 and Ihen sub sliluliDg for v.. _ f.om Eq. 1 11 lead 10P-J - ~ V..... _ ~

v.._(l ll)

V,''" 1 + ,

1 + ,'

(1 13)

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:

SUt>sh IUI,n g PliO, - 2.600 X 10' 19lm' and 100 Cfllical val"" of, - O.ilI . .." find Ihal bqU.Oipul.,I Iil:. algebnJ< quan'iti..

Wl'~

"''''r...

too,.

,i.,.

""If'''' de .. red uni" ",maiD.

me",.

~!It,

Lengt h The "",,'er ~ defuted .. ,he 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 12 .re .. ed ' 0 "",plify me" .",,,,,,n' _ation.

51 Units lb. nil ,)"tm empll. s.ized '" 'h~ book ~ ,h. Intorna,ioo al S)'"'''' of Uni" (SII. The '~ree ph)"""1qu 'i .

The JKOD d ~ ""tine are "n' wo,lrIwKloe by ~ ,ignal. I. i. 1.0yd7

)

!"'in" . Dd pic..: 11 f>Oin" .3

2

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 Oin" ?

Sp .dn~

,di.,

Her... are '0 r.", over a ren.ur EngliII.,.... I ~ '''' ". ... ~OCODd .. _ d " b..od . . ,.w-.. ......,., are roo .. in~ ....,""" "an (hip.ly","",fICl " ... 1.l....

n

(F\&. I.,';). n.. ..... ~ n W"'" is .lOOO

m. 110'0' "'any ""bic n,ime'en 01 k ore ,ho dod: B .. od1 (Au ""'" ",,~i ... , .odin!' f", po-e"10 6..... )

......

"".09..0

'" I

,

I

'"

,. I ,. ,l', otoIe.. U.

." I ,.

.01'1B

FlCi . , ..

.9 U)"h .... ~ . .....,B i. tho U..1Od SUlnt

d.l'" oI._ek ,ne dock> ,eat. Jw 'ify )u, cboke. .. ..

,.bIe.

atom. :tnd a c,.,bon "''''" .,. 1.0 u, 16 u, and 12 u. respectively. (I/jnt: Cat. are """.. im .. krI""",, '0 kill a mole,)

""'* ,-,"

A"",,,, ,,"",. tBN' C """"" ,,~t... t"HI

-

WO>,

11.."

'2:I'>!:rI

It""" ". "","57 '2ily il>CJ .... , in ,im.?

""'ge'

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? ~

.re

19 Su""""" 'hat, "hile !}'ing 0nd, .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...20 Gold. ",lOCh .'" '. ~ th. moo. docrUe m,,>1 :tnd cIT" ....",ri.g 14.0 an by I 7.0 an .. bein~ Iill.d ..-on id.ntic>! pfi.. 01 '''''< wat., fill1 (c) W'Ie' b .. . de .... y 01 lOCO kYm-'. How mucb rn . .. does , ...,t.. in ,b, doud ha",,1

,be

,Ila,

,...Ie,

M1'ii'"p,..,bl ~ m

32

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 "aoJr olll !Illf,,, of dril 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) i/i""",.?

I "",d.,d boolle

I lIIagnWD _ 1 """dard

"""j..,

)

I je,oboam _ 4 ,,:rnd .. d boolles I "boboam _ 6".ndard bool'"

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_ II"" .Iroo' len~'h ol2Om. 7) depoh of II m beigh' ol6.0 m, and . .. . . d.,d ,loped ,oof (""n ....1 '''''''gular f""" 00 , endo) of beighl 1.Om . J. 1011" ""Iu~td 10 oo,ain 1.0 kg of bydrog , A h)' Wb>1 m"" of ...... , ... feU 00 '''''b"" adeMiry of 1.0 X 10' kg''''.

'own in i'rOOl.m 'I? W",o,

Probl,m.lK

47 A pe""" II . 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.

,b.

.o.

hlD". 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"llbio "'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 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

t..t~

.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) . U .. !be l."sth "bl. in Appr!be "ated ''''ge.",b., ... tb. lowe< .al"" .nd tb. uppc' vol .... '''ptively.loo (.J 'he C)'lind,,, 1'_S,b in ........ (b) .1>0 C)'line 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

sa

m.",,,,,,,

h.,..

w,..

Old Briti>l! Meaowe>

,unk."

.>ide"""

...,pooa _ 2>al"I"""" de.."t"""", _ 2 ...,pooa. .. bl"poon _ 2 de"",n.pooo> ..",up _ 8 ..1>I"pooB' bo-e.kf .."up _ 2 te>cup' 1 00, 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. - - - - -. _ t>.1 dl

(2-4)

NOle Ih.1 " is Ihc rale al" hi po;silioo x ;s changing "il b lime .1 giwn insIJ"I: d IhJI i~ " is Ih. de';-"Ii,,, of -' "ilh ''''J'OCl 10 r. AI", nole Ih.1 ,'al any ; trfoti.", ~

1M posilioo 01 a p.1.lie'" mo\1ng 00 IUl .< ,,-,is is giV('n b)x - 7.8 + 9.21 - 2.11'.(2-5)

- 2. 1 mI,'.Takiog Ibe d",ival;v~ 01 Eq. 2-5. W~ 1... il~

..ilh -< ill ,,,,,lets and ",",nds. Wbol is iI' ,-.Iocily al I - 3.5 s1 Is Ihe ,-.IOCIly conSlIUlI. ot ts il conlinuousl}' changing?

,,0

" - T, - d, (7.8 + 9.2f - 2.11') . "whieh tK>olh magnilU"" and dlf.x:1ion (il i, yel anolh", "0 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 fe1 as Ihougb )"ou 3te p,o",,' .", ,.bethe,

""""",..ti""

~ 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'ei1ioo 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?

loU""';"~

wW W

,,' - "I + "1Jlx - r,l r - "a - if", + VI' r - "a _ "' _!-"

x, -

'' - ', + 0' ''0' + !to.'

>

>,

'!-"'k . """ thot to. """,boo.,.. u...!s'i!Uli"g .he", v.lue, IIlto Eq. 1-16, "'. bal"

0' - (7A9 m/s)' + 2,,( 1.87 X 10- ' m),0.Q -

- 1.500 X 10' mis'.

Figure 2-9 gi'.s a parlide's ",[ocily " "' il m",'", along an x axis ~iilh ",,"slanl What " ,IS ",I 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

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),

(8 n~")' - 1'1 + 2,,(20 m - 0).Ho .... ''''.. l "01I' OOilllo, I', "0' a.

(2 -19)

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"dI'. -

S.cond try. In" .ad o f directly invo"'ing lbe .equeSl.d

9.5

ml~

(A""".... )

~ Ch.opt ... 2 I Motion Akmg. Strlligtlt (j,..ComllHlnt: Some problem'S ;,,"01,.., an equationlhal indud., the r"'lU0> ,/Od'Jim'" ;""grol ('" II",id,,;mlil'/,lnI(J8")

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

,.ha,

Sample Problem

mNO!~ that Munday's displacem,,"t y - J. is a baSIOlioo is Iho f,,,,,lal l "",ol')I'.

'0...... baseball

",aigh' up ;n'o Ur. The "I"";"'" off, loU .ppIy for ri";ng" "",U .. forfaU"'gob_ jerd. 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",

Tactic 6:

eitbe' .... pos;';"" or ..... ""sa'i",,_ Th .. ;' nu. "" "",.. ,wb".lI.. body "Iocated:ond "" maUo, bow /,." 0';' IOh:o,

.ui,

dir""io. i, .. DlO'-in!o In S..nple Probl.m 2--8. ,be """,Ie' . ';011 of ,be baU ~ n'l" '" {dow",..,dl 'b,OIIO"'" ;" !iglr', wbtlher ,lie bill ~ ,i,inS or Caning,. Tactic 7:.;bili';e~

Un1k>Hy discord _OI "",m '0 fi" E.,rui ,bem cartop""c.b. g.A .. .... ..,.,.."

,na,

,""ugh'

,b.

2-10 I Graphical Integration in Motion AnalysisWh 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"'-'v.d I",m pooi . tiOA x, '0 poo.;tioo..l b., cleptodo 0t""'" tb. parti_ , .. Dl""" i. th .. time int1 ;. ,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.1o1ioru O(T. blel_1 apply"!

.,.iclo

_ _ Ch.opt_ 2 I Mation Along. Strlligtlt (j,..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, ...

'>n_

,h.

''''''age

cD,

Xo _ - 2011L The ,,;gao 01 ,h. partide', i.in. 1 velocity v, (>1 time ',) ,nd ro...""" ocale .. ,ioo a .. e. r''P''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~ ". lid indic~te how the . ..,." lor (I) 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 'peO ......9' ,net, A \lord Ih.. !. (a) FOf lOtI ..pauo diu:uu d btllWtll I'" IU'H Qn 'Iou , """"'..,,~ , ....iII ....ion .. )'! II 'hI "p""'lion io I....;". IM1 """""'~ ....... or. ,be (b) .pd - ' Ie) lIi,ect, ... (lIpm..... "dowmu..",)of'b. ohock ....! ~

TH politi ... of I"'''id. """;'! - , 110 . .. oxitr t>y.r _ ~,75 + 1.50" ....... '" , io ;" """""" CakW ... (0) 'boo ue"!' ~ Io "';,h ,. _ S.70 X 11)' mf~ lI'hal ;, it> """)tT"ion , II1>nt 7 ....

.27

Nooo .. . ... dng A' with oorutan, acctl .. .. ,ion. Th. tigur,', venk al ",aliog '. .. se' by .T, _ 6.0 m.\\ba' >t. ,be (.) magnitude . nd (bJ dir.rooo 01 ,he. portid. " """,ler>! iort?

diter 00Dd0e ...... from tb. >ir ""to . 'f'Of' 'h>< ;, .,t,.,b.d '0 tb. mu,hroom . dr"" grow, 011 ()[I' .ide of ,n. 'pm' and film !'''''''' on tb. "' ... >ide. Th, .pm. ;, bent""'" 1' tb. dr",,', weigh'. bIl, ... 11 tbe film the drop. the drop', water .ucklenly 'l".odo into the film .. d ,he 'f'Of' ' poi_S' upw. ,d ", .. pidJy th., it .. >llmS oIf iIl,o the air. Typically. the .pm...""b. . . >peed 01 1.6 mi, ill a 5.0 pm I,uncb: its .peed it ,he. re dwo.d to "'to in LOrn", 1' ,be .... u ... s th., d.,a and "'UmiD! co",ta"' occtl .. .,iOlU. lind the """,Ieration ill, .."" of g dur_ ins (.) the 1.lUICh and (b) the >peed reducti"". ~

"ache.

.29 An . I"k .. hid. "am fTOm ... , and """"Ie .."" ., r.le 0I 1.0mJs' in . "raigh' Ii"" uMil i, "oclte >peed 01 20 mr.. The v.hide ,b ... >low. >< a oi l ,0 mi.' UD _ ,il i, stop< (a) How moch ,1m I. poe' f,ol[l "OI' '0 "op7 (b) H"... f .. 00.. ,b. vellkle " .",1from '0"'",,7

COD'"' ' """...

"",.""It .."

.tar,

30 A world', land 'I""'d ,,in .Iev"", XiOlwo .potecelerat" fTOm , .., .nd ,b back '0 ,," ., 1.22 H""" for do., cob ",ov< ...-kile ,,,,,,,lfIa'ins 'olull 'p'edf,om .. ,,? (h) How lon~ 00.. i, take '0 m:a. ,h. """,,"" 190 m ,un,,,ani.~ and .nd_ inpt , ..,7

,_i.oce

mi.'. (.)

,h.

... " "OOPin be ',...,0 .... 10m 7 (b) Wbat i. lite , ... ,.,j be'ween " . ';00>1 (e) If .... bway 1r:li. ""I'" for 20. at . ",b ,,.lion. ,..hat i, th. m:OOmwu >peed 01 ,he ,rnn.f,om """ .... ,_ '0 tbt l1ext? (d) a ..pb x. ". up ond .""".. ,,'" the iIlt"">! an_up '0 ,h. next. 37 Con A and B """" ill tbt ...". dirtclioo in ~, !>rI.. Th. pOiOOo x of n, ! givffi ill Fig. 2_ 26.trom time, _ 0 '0 , _ 7.0. The figun'" ",nn! ocaIint .. ," by x, - .11.0 m. A' , _ 0. car B is atx _ 0. with , ve_ 0(" locity 01 12 ..~ >Ad 'g>'i", FIG. Z_Z6 ProblemJ7. .,ioo '" (.) \\b., mmt _. be sud! """ Ib..c"", (""""".,.,ily) "'" by side (""""".wi!)'" the ...... voIue of x) '" ,_ ,t o.? (b) JU """ val"" of _.. 00... ..,.,)' tim .. ore the can.ide by side? ) s.t,etch the pOitioo .T of cor B"' ..... time , txt R~ 1r2b. H".. """')' times will ,he " ... be side by side if th. ""!niIade 01 """,I" ",ioo _. .. (dJ ,hl1 .. d (.) "'" til .. th. (.)1 38 you .... drivillg 'word a "affio .ignal ,.,1teo i, "" yello .... Your.peed i. ,b. Ie!>! 'p'.d limit of ''0 _ 55 kmlh, YOllr be" doI Iw """".. t vekxity 0110 kmlh. ,b. can p....odr ott... . , x _ 445 m.... d ~ it ... . """"an' ve Iocity 0I-W kmlb. ,k,y P"" e.dt ott... " x _ 76.6 .... are (0) the initial ",loci!), and (b) the 1tt is tlte """,Ie .. m' y>itude oI:,b. led cat1

,=O. Tho E..... car Il:ti.,i""

.. ~

00.

o,b~ " 'I'),,..in

" . nltrIg doH Ik. ",'kag. 1>1:. lo,",,,,b lb. goo""? (b) With wh., 'I"', d dot. i'M tb. grourxl? ... 50l.nin~

.41

w"""

42 W..... bigh-"",ed P" "'"E" II .""I ~ at 161 tmlh .ourtd ber>d. ,he gino i. ,boded '0 .... ,nat alooomOl;'. bas improplnlCli"". 90 m '0 , ... volley be.". , ... bridB" (. ) [0 b~ much ,im. does i! paM throoglr ,.e la" 10% 01: i,. lam Wb .. i. its (b) "'beo it begins tint I.. t 10% of it< fall ond (C) 'OIhe. it ceacbe.,h. vall,y beoe"" the bridge?

'1"''''

51 A key fall! f.om bfid!le ,hat .. 45 In obove the ...,.ttl. It lall. di.oetl), ;"to mod,1 boa, . Dl()Yio! orith """" .. t .. k>city.'Jr.at ;, 11 "' from ,he point 01 impact wh. " tb. key ;, " Ie"""d. Wb >1 istb . spud 01 tbe boat1 ........ 52 At time I _ O ppI. I .. dropped /r"", , bridge 011'0 . rooclw.y be.t >t h the bfidB'; """""'hot b'tT. ppIe 2 ;, 'hrown doMt 110m th . ...... bfiSh'. Figure 231 gives 'be wniocai po>itio .. y 01 tb. apple< durin! tb. falling. un ,il both apple. nave ru' tb. roadw,y. ",tb opproxirn , "l y ... nat '1"''''' ~ .pple 2 thI","" t 110 kmilL Your "gum,", e1i",r" your . ",ruioo 110m the pobc< Ie< 20, (Jong rnooglr for yoo to look .. the phme and )" U. - [ "",,'t do that!-). A! tbe beginning oI:!Iu, 2.0 ~ ,h. police oIiX" begir>; bntinB,uddonly" 5.0 mI,'.(., Wb>t ~ ,b... ~'ion bet"""'" the when )'OW ."",tion finally r;, 1I0OI to. 12 .0 ..... (.) lObo, i. ,he .... sni'ude d it< """.g. "",.1 . .. ,,,,,, dwill8 .h>1 rootact . Dd (b) io the "" .. "!!. "pOf_1 58 A 'OC. ~ ,hro..... vtItic. lly upward Irom grounod 1e".,1 >! o. At' _ l.5, i, !W'" ,he ,opol > tall tow" . D d 1.0. I.,,, i, , ..ebe. iu maximum heigh', lIb., ;, ,he h.igh' d ,he t"....,.. 1

"""I".,,,,,,

a projexi. Th. poo>'ion of pankle I ~ Yv'" by x _ 6.00r' + lOOt + 200 ('" mele" """ .. >Do:r.rd 5.20 m , hov. ,he """,. It hi .. ,he waro, ..-irb "nain velocity ond Ibe. ,ink< '0 ,b. borrom with >am. velocir~ II "",ne. ,h. bon"," 4.1.0 I ai, .. i, ~ dropped. (0) How d"p" ,he Iak.? or. ,he (hI and (eJ direc'io. (up or cIoron) of Dve ..!"- v. loci'y of ,b. ball for ,h c,ire foll l Suppose ,"", all ,he ",ate, i. dr.in. d fr om ,h I. ... Th. ball ~ no..- rb,o..-n from ,h. diYirlg !>o:r.rd so ,na. i, . gain reaches ,b. bonom i. 4,80. Wb" ar. the (d) m. gni_ ,ud nd (e) direb i.Ie,_ion 3. wh." , he appear, wb,. ,h.y M. di .. """, d f,om it. 1be inle'_io re "'p>Jared by dipan. How loo.!; of,,, ,b. fir .. diamond beEiru '0 fall Mil ,h. ' ..0 di:tIllollOd. be 10 m . """ 77 If , b_ alI pilcOe' ' hrow> f ..,ball .. a horizon'a1 ' 1"101160 kin/h. bow IonS dou ,h. ball,ake10 "aclr born. pi ... 1M m . w:oy? 71 A proroo., ..... aloog ,h. x..;, >OCO!. (e ) lndic. " ,h ....."'. " '0 (h) o. the y . ph. (I) 1'101 Yv",... t>M indica .. 00 i, ,he .... ,.," '0 (' ). 79 A rnorOl from ..11 IOCcele.-.,Ioo ,,,,,ld be moi.,olnedat,b.valoeirr (a)1 ... 91

(.J Wb .. ;, ill . ...."'" "",,1e..,iOll. i.

mi.'.

",,,Ie.,,ok. "". ""reI,,,",

oo.""nt

U An automobil. driVel iocr."",. ,.,. speed .. . const ... , r.t, f,om 25 kmlb 10 55 kmlb in 0.50 mlo. A bkycle rider "",ods up " 000>1..,' "',. f,om ,," 10 .lO l mlb in 05() mi . \\nat ... , ... m>gll;tu"". of (0) ,h. drivd. """,,10..,;00 . nd (b) ,b. rid,,-, "",.lfIatioo?85 To st"l' y""r 'humb and foreti.ger ,t th e Ih" dol ("" .he Iefl mFig. l-ll). !>om! eti"" ,ito., (a) H"", f.. from ,b. low" dol >llould you pIace.be 50.0 .... m"k? H""" moch hiy.er ,book! you pi""" oil. m:uks !of (b) 100, (eJ ISO. (d) 200.... d (.) 2,';(j ""? (For eumple. >lloold ,Ire (00 m. ffi>rk.r be 2 om .. . . far from tho dol '" In.. ~O m. .... l" l U '" y"" ." an"." 01 2 'ime~ 0", you fi.d >my 'un", ,be ..,we,,?)

93 Fi!w. 2_,(\ >how< si"'ple device for rne ..urins your

ti", di"""""

,.en

.r",

16 A r.d "aio t" ..ling" 72 k",lh and, gree. train ".",,1_ ingot 144 kmlh are b.oded toward . oclr otb .. oI""g " ''''igllt , 1e",,1 \\!h," tbey.re 950 m . pari . ocb .ngineer ..", the OIber', Iraio .. d . ppIi.s the br.t.. The b..k", ,I""" ncb trun >t rhe,." 01 1.0 mI,'.I. lbe", ooIIisioolU '" ."'~"" y... ond yve 'he speed of the rod "ain .. d ,be sp."""

,

,

- ,

9' Figur. 2- ~ 3 glveo ,b. >c_ eole ..""" ""IS'" 'I .... , for porticl. moYing ol",,! aD X :ru.. The . _axi. scaie i . .. t by ~. _ 12.0m/. ' .A" _ - 2.0 ~tlre par_ tid" velocity i, 7.0 mls. is iI. velocilyatl _ 6.0.1

"''h.,

II A rock ;' >1101 ""nically op. ,.rd from ,be edg< 01 'be lop 01 0 I. Ubuilding. Th. roI 20 kmlb and ,ben I"'UNf baok down ,b. hill . , 35 k",lh 'hrough lIS origin] Ie",l (The ,ime required for ,Ire lid (b) ;" maximum 'I"'odl (c) Oraph x. '" and. """u. "or ,b. ,rip.1 01 A cen>io '1"""" h.. . 'op spd 01 11.0 mil. If , ... 'I"int., "Ol" I,om "'" .. d """,'er"'" .. a he is .b l. '0 "'>ch hio 'op ,,,,,,,d in di .. """" of 12.0 rn. He .. ,b able '0 maio'",n 'OP 'p".dlor ,h. ,emainder 01 100 II'h.,;. hi> ,ime lor ,he 100 m ,acel (h) I. orCal. i ," by I', _ 4.0 rni~ (.) WIt .. io ,he 01 p."id , , _ (.) 5.0 , ? (b) Wlut ;, , ... veloci'y 01 flG. :u. 1'robl,,,,I04. 'ke par'iel , 1 _ 5.0 . 1 (,) "'b.,;, ,b. """,I . ""ioo ol,b, p.,.,ide" 1 _ 5.0,? (d) I\ih., i. the .v.r.ge ""I",;,y 01 ,he partid, I>'0 rn!~ (.J How I",,! i, ,b. p"ocb"'~' in ,he >it? (b) A, wh., beigb' doe. 'be fall beEin? 111 n.. z...o Gravily ReOf .., b FacUl,y .. ,h. NASA Ol,"n Rue ..,h Conlt, i""ludes. 145 m d,op 'ower. Thi< io ." e""", .. ed ,..,nical ,.,..", 'hrougb ... bich.. .nH'.S oth" poo_ . ;bdi1ie~. I m CIion. ThUs. Ihey s""cify ioomical di'pJ""""",nl we lOIS and '"pfOscnl Ibe 5aJl1C changt. Th. 'luee veCl"" 3. b. ond i'

""'"'0/" 'qro""',,,,7 - li + b.(3-1) ,,-hien ,")', th't Ih. vecto, 7 i, Ih" vOOo, ,urn 01 vOOors aod b.Th~ .ymool + ," Eq. 3-1 and II> wo,d, "sum " and "add" have diffe'''"t meanings fot VOCtors than the)' do i" too usual algebra OOcall'iol Ihey involvu !Jolh magniluc:l;> and diroclion. Figu,e 3-1 suggests a prOCi'du," fot adding Iwo-di"IC",io",i wClots Ii and b goo""'1rk-~lly. (l ) 0. pap"'. s~Nctt ,-octot --.; to some COIIve"K-"' "",10 and al Ihe P'''P''' "ngkl. (2) S~,,'ch .-000' b 10 Ih ... me seal ....lIh its 1ail allh. ""ad of v.c101 --.;. again at the P'''P''' angle. (J) The wetor ,un, 7 inod ? _ iI + 5. Coo,iderinS""'ious Of;' . " ' _ of iI .oo S. "b.r ..fA) lhoe maJIimum """sible magoirude for? and (b) the mioilllUlD poosible m'Y'i,1Ode7

~

Sample Problem

m

10 ao ori~ nl""'ing class. ~'ou h,,'e Ib~ goal o f mo",ng a.far (Sirughl Lne d .'l1a"",,) 1'001 baSIll P i< y eat." if yoo wwle,.o:o di. pI. ...." iI. b,.nd - ?, io "Y Ofd".a"ang~monl 01 ' ''''Iors"if. b. and - ... Th~y call t>c in an}' 0''''''_ becau,., 100;, vecto, sun, is Ihe sa 'ni' for an}' 0''''''. Tlhl 0''''' ' sho ..n in FIg. J-7b " 10' Ille vecto, sum

"

d - b + a + (- 7 ). U~ng Ih~ scal. giwn in Fig. 37". w~d of Ihrs voClo, sum. find,ng d -

"'0""'" Ibe kon gl h(An ...... ')

a m .

34 I Components of VectorsAdding ' "OClors gei, arrowheads would poinl low,"d negat;'-o x and y. Rosoh'; ng "CClor b;n Fig. ] 9 }'idlk a pusi"ve compoaonl b, and a ""gal;ve compon~nt by. In g~noral. a voclo, h:rs Ib'N compon e nl s.. all ho ugh 10' Ih ~ case o f Fig. 3-&

a

a

a.

FIG. (o)The"""'p"""nt5 . , of vta' if. (b) lb, """1""""1' >Ie undwI,ged ~ ,hoe """"" io 1oot '" ,he ....gnitude aad orien, .. ;.., >re m ...

J..

>lid.,

_od...

tain,e:

" . - aoosB ,nd a, - a.i0 8..d Radjans Angle> tnal",I.,iv. 10 lb. posil;"" dir"",;oo 01 Ih. x aID ... "",itiv. if the~ art .... in Ib, COOllI1trdocl""" direI. ,no =ne >ZIg\n> (00), To rotal' Ih, two m' .. w. ~ recall that. luU ,ircle ~ 360" .Dd 2.. ",d, To ~ 4CI' 10 r.d;'.." wrile

con,"', ..

-II)'

2,,,00 _ o.70rad.

-

w

, ,

If

I/

.

'"=

",

i /,I0m}'3 ill I"mrs of "nil wclors. Firsl. "'P",impos "nd angkl ollhe "nf' 001 displ"""""'''' """lor :1_ . nd whal ar~ IDO"" ol lh. bom ...,rd ''\'Clor 11_ thai "-,,Iem/re is no d""p'" r son . Wecould.lIlS1e.d. to!>,. Ihe axe. (bul nOlloo vOClor II) Ihrougb ,n 'nglo Ibas in Rg. J.19b. ", "'h ir h case tbe compo"o"t. would ba ve new ' -alues. call1''em and a;" Si""e them arc an illfinit~ "umber of Cboir5 of . Ih...'" are an infinit. number of djff.. ~"t pairs of compo"""'S fo, II. Whirh toon is Ibe rig"' pair of compon~nts"l The an'WIlr is Ihal tooy are aU "'IuaUy v,l,d becallSi' each p,i. (~jlh it' u.s) just g>'"eS u. a diff..ent way 01 ~ scribing too same vexes of ,b. OOOIdinat ys_ 'em rolated 'hroogb aD aIlgle 60.

a - ~d' + a' - ~a"' + a" < , ,

(3 -18)

and

6 - 6' + 1b.

(3 -19)

"

The poi"1 " that we h,v" gr~al f, .... >dom in choosing a eoordinal. 'y'tern. becau", tOO rel"iolls among vOClors do ROt do]X'"d 00 Ih~ loc",io" of 100 origin or 0" the ori~lltatjon of too a ..... "This i. also lru" ollb" rolalions 01 ph)',ics: Ihe}' arc all inoop..'1Idellt 01 the ch and J6O' - lb. Eil"'" can be "",d in Eq. 3-20. I'oecaIlSo' lbcir a,~ the sam . N o{~ lhal {he," a,~ only "",lars 00 Ihe rigbt ~ j"" of Eq. 3-20 (ineiuding Ibe valu" of cos 011). Thus a b on Ibe l"f1 ,ide a ,cala, quantity. B.."'CJu"" of the oOlalion, II b is .110 ~nOl'.. n as Ih~ dot prvda,'1 "nd" .poh" as ". dOl b: ' A dol p.od"e! can N "'g.1.d.."'nd ) - 12 unitt? VecI"',

H Eel( POI NT.

bel",.,..

t

I Problem

Wh" I+ lb~ aogl~ d> bo;>lW""";'~-:;';,ili;'~-:-;',;";l:.:";'~';-:-:-------::_::';";'0;,:.;,:-;';,0;);':_::',:00:'-,--:,~,-,;,;) S 3.ot? " - 2.oi Althougll many of Ihe foUow(C",,,,o~:

iJlg slep' can 00 bypassed ..itb a wClof- is Ih~ ",,,,lla of 1he 1'''-0 angle, b. Th. thunm "nds up in Ih. oppo>ite directioo from p.evlOusl}'. and so it must "" th"?' - - .... Ihat i~

a

IU.... ratioool' .. risb,b>r>d eo. VEflor produ"~ (0) s,."P """or tem is. right -h.:uJded wonlin,t . ):sIem.

usc too.tight-band .ok< for the "'oss (>!oooo ; " j - b';lh trut s)'>1Om. If your fingers "'''''p i (ptions 01 tho l'Nt0l. ''''IuiJ.:m ..t,.=I'wi"ing 01 yow hand

.hif,

fi",

to opp/}' the riy.,_ hand ,uk Sometime.t ,.,t b,W"", ..'he. yOll try tom,l" tb ....... p m ,ally ,,,bu tna. """ oily ">iriS your bmd. (4) Roih".,o wOIk wi,h , ri!,h'-1wlded OOOIdio"e .y.. t.m , .. un. lObe. you illlge' how '0 d",,. ...,b a 'l"""" . Se. Fig, 3_14 iIII ooe l""l""'ive. Pr:rC1ko dn"';"g ",he, p..-spelS.brak siS. or:. compoo'.' indica, ... i" diroc'ioII ,be """"""ed JIll;" Oiven iu I" it and S. A ",.al.,. prodoc1 .. ,he produ;tive dir,"';o", 01 ,b .

Unit_ Vector Notation Unit ""10" i.], ...d ~ b.v. m,gni _

The Ve ctor Product The ' reto. (or """".) pn",dll'" 01 'wo .,II aI_ ~gatOf plt. Figur. J-2J .... OM ... over_ bead view 01 011. p"ttmg ,b.n.nge 01 the team; ODX)'d ...mg aoglnd i" .:ocb have. magni'ude 01 50 IJI . .d tie in ... .T)' pl ..... Th.~ diroctioru ",I., ... '0 ,be posi'i", dir...,iOll ot ,be .T >xi. are 30'. 195' .... d ll~ . 'ively. Wb .. or, la) maE.i,od. and (b ) ,be , ogle 01 ''''' v''''" if + b + 7 ... d ,h. m.gni'ude and (d) ,be msJe 01 iI - + n \>''h .. at. m:ogoi'ode >nod (I) any. ot I"""b """or d.uclJ ,na, (il + b) - (7 + d) _ fJI .....19

,b.

'''pee-

)

,h. (.)

. 1Id "" {bJ d (e) an OIly.. (re1>ti"" to I). Now give b - ;J i. (d) ".it _ veclor ""''';011. and .. Ie) mag_ .irude and (f) an :m~e.

.12 IU ,b. vWon it _ (l.0 m)1 + (4.0 m~ .. d b _ (5.0 m + (- l .Om )l. ~ive it + ri in (.J unitvonor .", .. ioo . }i

.20 (a) Wh" is 'he , um 01 ,be foliowinE lou, """or. i. uni,_ vee'"," nou,i",, 1 For tb. , '1UIl. wha' at. (b) ,be ...yti,.de. (e) ,be >llgIe in d.y.. ~ ""d (d) 'be angle in radi.",?

""S";''''''' ..

-c: 6.(IOm., + O.\lOO ,.d

1", 5.00 m at - 75 .rrR , 600m ot-ZW'

n .Dd

Twovtc!or .. regiv byit _ (4.0 .,)1 - (1.0 .. >1 + (1.0m)t.

b _ (- 1.0m)]

+ (1.0m)) + (4.0m)k. b. >nod (e)

In uni'_ v.nor nOl,,"'" find (.J if + b. (b) if ,hird vector i" ouch if - + i" _ O.

,h.a,

.21 In . !=. ot 1 "'11 ch .. ~ wbere piKe. Ol. mCll'ed , be' .... n ,be cen'm ot squ ..... ,b .. at arb 1.00 m o. edge . knigll1 ~ moved;n 'he foUowi.! w.y: (I) '..-osquart> fo,wrnl. OIl' squ"e Ti!h,..-. rd, (2) squ. "" l.f,wOld. 011 . square lon.-.rd: (3) squat .. 1000Old. on. square l,f,,..,rd \\11., . re (') lb. magnitude :iIId (b) ,h. angle ("I" ... to "Ior_ w>rd-) 01 , ... bUg/I1. overoll dkpl" ",,,,,nt!Of 'he ""'. " 01 ,hr.. mov .. ?

'wo

'wo

Find the (.) x. (b) y ... d (e) , """'poIIe.'" 01 'he >lim 7 01 displ:oc ..... n'" i" . nd d whOSf compoll.nts in met." . Iong ,be ,hr...." or. " _ 1.4" , _ - 1& " _ - 6.1; d, _ 4.4. d, _ - 2.0. J, _ 13.

.14

,b,

.15 An "'. crazed O}' ''''' Sun "" a 00' T ..., of"... ooa. d . n. OVtr >J1 xy pi"". II-0). (b,. - 70.0). ( - 20.0. c,J. ( - &0. - 70.0). Th. over>ll di>pf>et ar. (0) b, >nod (b) e,? Wh" Ole ,h. (e) m' g""oo, and (d) .. gIe ("la'ive '0 ,he popf>ee ... n, 1

22 A. explort< is moving ,,,,ay frOID ,be n." . i, h" '\00 choice. 01 patb r"lw,ing' om.all turn in ito ",,,,I dir'peeltvfty. as ""'''''''00 clock ...... from the pooiIive x ali!. \\'h.a, ... ,be val ... , of (a)

direct.,..,.3.

(.. 0)7 (~) De,.rmi ... ,be o.gI .. ,n. body di. goo'" m.ke ";,h ,boo edS"'" (I) D""min. ,h. kns1b of ,n. body di agon al< io 'erms of a.

31 Diopl""''''''n' J, is in ,n. y. pi... HO" from ,b. posi';ve dir,;oo 01 ,be y ..is. bas . posi';"" ~ oompoo,n'. >lid b .. a m"ll"iHod, 014.50[0. D~l'l:ocem..,' J, i, in ,h. x. plao. 3(1.0' flOm ,he positive Xilisle ~ _ 56.!)" oouot.....cloct_ wi! 'heo j, 11 in uru1-Yenor o"'>!iooifB, - B,1 C 3 The ,br ... vector, in Fog. 3_l'i have JIla!IIirud" _ 3.00 Ill. b _ -I.m m. and , _ lO.O m ",d >ogl' ~ _ JO.O'. lib>! ... ( ' j ,he x rom"""e", and (b) 'be y """pone.' of if: (e) ,boo x com""""" and (d) the Y com_

,

121.

-~- .fiG . J-35 Problem 4J.

,

~ Chap_l I Vectoupont"' of O, ... d (.) ,be Xoompoo,n' >lid (f) ,b. Y componen, 01 n If i" _ pil + qt. ,.h, m the values of (g) P .Dd (h) q1 44 In. """,tio ~ 01 ~. mim.' I goes 'hroug/l a di._ plaoem,n' ilL (4.0m)i + (5.0 1D)j .Dd mime 2 soe. _ through. di,pI:=menl "il, _ ( - 3.0 m); + (4.0 .. ,). Wh., .re (0) ;I, ~;. (b) at' J,. (e) (aL + !I,), II,. ,lid (d) ,b. oompone"' of J, .Ioog ,h. dir.;oo 01 J,7 (H."" fur (d), >t. Eq. 3-20 .Dd Fig .!-20.)Probl.m. Rock faullS or. "'pow.. al oo~ '"toeh """",i'. foee.. 01 rook v, slid pa .orn ",h... I. FIg. 3--"6, poi... A and B ooiDcided ""for. tbe Joct in--ilie for.you"" ,lid down to tb. lith,.The "" di5f>lacem.", AS ~ aloo~ ,be pi.... 01 ,he f.1lIt The oo..izoolal-S"'P""""' 01 Ajj i> ,b. strib..up AC The """'po.,,", 01 AB 10>1 i. dir,('!fd dowo tbe plaD.e of the f, uh .. the Jjp->IiJi.flD. (. j YOb., .. the "",ni,.hp i. 17.0 m l (b) If the plaDe of bull i. ilOdimd "' angl. i.52.11' '0 d hocizOll'al. wb .. to vertical com""" ... ' of AB 145"dd~ional

.....

01 the p. nide lor 'be rh,ee """",i"" w.pI:ocem'"t~ Wb, . re (l) tbe x""",,,,,,,e.,. (h) tbe y""",,,,,,,e". (i) tb. magni_ tude ... d (j) ,.e direlly d,,6.00 D1 in direte (e) ,b. x component ond (I) rhe y com"""e", 01 d,? Ne ... ooruideo- tbe"'tdi>p""" ... n'

,gni'udoe ond (j) dir1iono/J, ~ (d,l4)1

)

a ,

(m

57

He" are tb:r.., ", "",,;tiv.?

(,.( A whed wil"' r>diuo of 45.0"", ,oil, withoU' oIjpp"'S . IonE bOO""'tal ftoor (Fig. 3.39). At lime ',. ,be dot P palo"d on .be ,im 01 ,Ire ,.1",,1;' " tb. point of Iem. Ako. !! _ (11.0 + (8,0) OIl tb" ..... ~"e 'Y"om. We .""""'a" tire 'l"'om oountercloct ....... boo. the orig.. by 2OJ)",0Iorm ""x'y' ,y5t ..... O.thi ..... . )'Stem. wb .. ore(. ) A .oo(b) 11.blioo?

mp

'")1

&0 A ve .orth. "'b>l .r< (a) th. m".!."i,ude .nd (0) ,h. diroctioa of ~.011 "'b>l are (eJ tire Mog.o"ude .. d (d) tlr. dir.. n","e .. ;1S posihon veCio. ch.nge, in ,uch ..... )' Ih.! 1110 '-ocl", poi'" (the origin). lillie pos~ always eXlond, 10 100 pa.!iclo 110m lhe lion v"""o, changos-sa)'. 1.001 7 , 10 7, dlUing " ""flain Ii",,, i"I""'"I- tbon Ibe par uc],,', d;; p ~......,m.. ' fJ.7 during Ihat lime inw,,.1 is

.eI",""""

,

fJ.--; - 7, - --;,.

(~-2)

Using Itie UID1 -verl'" nolaloon 01 Eq, 4- 1. ".~ can " ..-.ilO this displace"'""l as fJ.--; -

(x,; +

y,j +

z,k) - (x,; + y,j + z,k)(4-3)

"'00" OOO1it's posilion as func ';011' of li""" (So'rond.) are b)'

..,

gi'"'"

- O.Jlt' + 7.1, + 28 Y - 0.22,' - 9.1, + 30..< -

( ~5)

(H)

o

'"

"" "

"' ,

tim'

(aJ AI , - 15 So what is t"" rabbi!", position 'eClor 7 in "nit vectOf nOlalion "od in magnilllooangje oot.Hon? The ... and y cootdi".h. 01 the rat>bil"s ... position. as given by Eq~ 4 5 and 4.0. are Ihe scalar compon"nlS oIlh. rabbll, posilion VOClOl 7 .

,.,

:~-------~~1im)

-~

(

; t~j

ulculalions: We ""n ,,,,il0

"('l - .r~ + J('Jl.

(~ . 7)

(W~ ,,.ile 7(/) .alh., Ihan " b..'C:l"SI' Ih" ronl(Xln""iS a f"OClion, 01 I."nd Ihll"S 7 is also.) AI I - 15 . Ihe "".Ia, coOJ(Xln~"1S are x - (- O.3I){IS)' + (7.2)(15) + 18 - 66 OJ

"

and

J-

(0.22)(15)' - (9.1)(15) + :JO - - 57 OJ. " - (66 m~ - (57 m)j. (A n' ..... )

"hien i. dra ..... in Fig. 4:\'. To gbit", ",,"ilion _ tOf 7 .. time t _ t5 The ""al.. of7Ole oIoog tbe un (b) The.-.b. tm , p"b arid its positioo ., fiv. vol ... of ,

comP"""."

'"

,bow.

" l

t

Avo'''9''VoIocity

~

C".cI 01, i"d"'~le Ihal 100 desi,e_ Th, ... Oim1 ,bat in.... t if it;' t"'v_ ling (.J clock",i....d (b) """" terdockwi", around the cio-clt1 For boob ""' ... dnwl' "" the tiS"'''

.bow,.

,--++-1.

I ProblemF01 III< .. Dbil in S,ml''" P,OOlomaI"nli'-l - 15~ ~ -1

find IIhl .... krily

v

, ("'I

- -

"~ - 12 to

w~ b.' is .unning 8' t - 15"

AI t - 15 '.Ibis gi"" \'y y;" lds

- 2~

m/" Equ,lion 4- 11 Ihen

To gN ,he magllltu oo and angle of v .ci'he, we usc a \'OC!o,-capablc calculator or foUo" Eq. 3-6!O wri,e

'c.

" - ~"; + "; - ~( 1.1 mk)' + ( 2.5m /s ), (An,we'l - 3.3 ml'

'""

6-

ta" - ' ~ I',

'.

tan - '

(-105ml') 2.1 ml'(An """,)1.lO" + 180" - SO"?

- tan - ' 1.19 - - 130'.

0I1Idr: Is too angle. - I J(f Of

-

4-4 IAverage Acceleration and Instantaneous AccelerationWhen" ",'l ic"" wlocily changes from v ,!O V, in a t;m e inwrval fJ.1. its ~wr:,~. """",Ier.llion Q, .. du,ing fJ.1is

awrage _ccele",ion~,

change in "clocity tinw in,orval"j~-.

.. - v, -

~

."",n,o "., ... ...

If we sh,in ~.lt ' 0 zero insun'. ,hen in ", I ",.,iol (0' ...wier. ,i un) g a!

,00"' SO"'"

" 'h" lim;,

(4-15)Q,.. app'oacoos 'he

'h" ;nSl,", ; Ihal is.

(4-16) II ,be wlocil)' ch,nge, i" eilhu magn"udcm"OCeIe,.,,,,. oompoo'o"

cllic motion of a ball . nd nloc h 0110.1 i. Sl"'"! In Irying 10 ooouolibol motion fo. '" a1b oc..rd, ODd" is i. mOl", pe>'

>c"COmll,. - 0;" Eqs. 4-21 and 422. '.,~,,'ety Iw.:.. .... ,. II". I nd I. gr.

constants. Eq 425 .. ollh~ lorm, _ ..... + Iu', ,n " 'hoch Q and h a COOSIaott. TbIS IS tile equ31 ..... of a p.rnbola_'" lbe Pllh .. panol>olic,

flG . .a.U Tbe .. """"",,,",ponIN by I..... tl>odo 01' dlioobopon-. Sec TobI... , for "",wI"""'">! JIimlUll fOJ "'~lICb "'ste 01' 45' .Ilowe'cr...hen tbe la"ncb and land log beiShlS diIIC'. ". '" . hol put, h.m""". throw.ud b.l,kclbaU,a laun"" nngle ol 45' d 1o find x ..i! n Eq. 4-21 :

,"1',d ~

Figure 4-16 ,h~~ a pirale sbip 560 m from a lorl delo"mng a harbor ""Uanc;o. A ddens.> CaU"OD. Iocaled al Si" le-vel,fir'" baH... 1inilial s!",oo I'. - 82 ml~

(a) AI "hal a"gle a, f",m lile firM lohil Ih. ship?

~OrilOl\lal

must a baU be

(I) A fired Inno"ball is a projoc1U,,- W~ '.-aul 0" equalio" Ihal r"L:H~s Ib~ lau"m anglo a, '" lile ball's horiT,OIliol displ""",,","1 os il m"".s 1'001 "",,"on 10 shIP. (2) B.Ius.> Ihe ",,"non and 100 ship a,e al 100 same heigh!.lh. horizoolal di'l'I"""",,,nl is 100 range.Cakcations: We can ",Iale IIIder file.

(b) Wbal is Ihe """,imum range of Ine cannonballs?

Il" _ J.. "n-' .f!!:... _ J.. sio- ' (9.8 mls')(S60 on) 2 I't 2 (82 misT- 2 Sln - 'O.816.

,

ulculations: We bave "'." Ihal maximum ,ang. conesponrn !O . u " le-valio" anglo a, 01 45 '. TIt""'- -

(4-31)

,j " (8:' OIls)' . (1 ,_, Sln_lI", !IO\"X .~ ) S 9.8 onls' -686m _ 690m . (Answer)

000 ",IUlio" 01 sin - ' (54.7' ) is displayM by a caleula lot: w" sublrOC1 il lrom l&l" 10 g"l Ihc olher sol Ulion (125.3"j. ThUs. Eq .4- 31 gi\'Cs us

""'

a, - 63".

(An,,,,,r)

As Ibo pira!~ ship sailyco,d Ihal distaIloCe IllbalJ ban"r B hils a high Oy ball 10!1Ie oUlfield. di,ecUy 10ward au ou!field..'1 F and "';Ib a lau"eb spM_ Th , ... OimsI ,IU!O ""n Eq. 4-21 (x - -'0 - (I'G cos 80)/). Sl'nin8 ... - O. Thus, uSlIIg I', - -10 and /10 - 35 ' . w~ ""'. , (-10 sin 3Yj, - 4.9,' (4-33) - 1"0- 153.42 (4000.35,, "

153.42 m - 6.0", - lHA2 m. Regr.ph,ng Ih . [UllCtion

"li,

gi"" th. "Too dOSi''' plot in Fig. 4-17/>. No ... lb "" -alio" ""S'" of the ball "pidly iocr~aS Ih~ di'{JUCIl of 153.42 m in Eq. 4-33 ,,-jIb 159.42 m. Thi! ""ulling plot i, laN-l.d "Too fa,- in th o fig"r~: Tho angkl fim anJ Ihoo rap>r to ,lOy p"LfIln toward ,II bane . or bad: 'W")' from In" b.II",.

Graphing Ih" function V"tsU' I gin', !be middl" plol in Fig. 4-17b. W~ """ Ibal 100 ball'. 'ngl~ in III~ oU lfield .. , ,io ... iOC1c","" a! .n ,101051 steady rale !itroughoulloo ftiglll. ]{ 100 oUlfidrlor i, 6.001 100 doso. 10 Iho ball .. , we I~place lhi>. di'l.n"" of 15:JA1 m in Eq. 4-33 "';111

ilK""..",

AI IUnc I - O. a golf boU is ;/JOI from ground levd jnw lhi>. air. as indicaled in Fig. 4- 1&,. Th nglo 6 Nlw""n lhi>. boll's dir""1Ioo of lra",,1 and Ih. posi!i'" dir.Clion ollh .< is given in Hg. ~- I8b as a IUnClio" 01 lim" I. Tho balllanJs al I - 6.00 s Wh,l is Ihe magnilUrlo "0 01 lhi>. b.Ws laullch "'loci I}". al .. h.1 h.,ghl (y - )'.) aoo", 1hi>.launch lowl doos Ih. ltaU land. and "'hal is 100 b,U', dileelion of Ifavd jusl as ill,ods?

.xi,

".101

, ",-,- \:- , ;- 0 1--",, ('1 (' )

d

(I) Th" b,ll is [l1oj ,hown U\ Fig. 4-2Oc: !an d> - - ' d,a

- (," I'j,;n8 - !an 8. ("'1 ) = 8 ,FIG. 4-20 p,.,;de r """''' i. COWI_ .. l . w ~ I" ~ ~ Ih~ lime do,'valive of Eq . ~- ~ I:

Bfe"oo I hal mow al ooos,""1 volocily ,,,Iali,,, 10 eocb """"""0 100 "'m~ CCo:lJ.:>1alio" 10' a moving pa'lido.olb~,

",II

I" Fig. ""2 3. a plane n'OW5 due casl whilo Ih. pUOI POUIiS Iho pIa .... """"",,hi ""ulb 01 erd i. ,aken I" be poo~I"" dirertiOll.) If,,;' exp, .... d '"' , m.gni,ude (,t..'f"""d y,) and aD aog.le", (....... "d fTOm the bOfizootol ). 'he par'icle', "Iu>1l"", "fIJlOl;oo oI011S bori_ . 011'" X aID .Dd .",ic.,. i1S "'~r"gt 1',loeigh'. is

diII """"1,, ..100 of ""'_ .. ,., .,.gnitucle

a

'0

which can be , . ..Titt.n in o''' _ vector """,,ioo ..

1' -

y,1 + I.,l + Y,k.

(4_1l)

' - -.' . ,a ;, .. a;.

(4_ ) .4

...htl. I', _ . Tid,. ", _ dyid, ..d I', _ d,Id, The ta... "'" veloci'y ,of, .,."icle ;, ~')" dir!ag0 prC;KIile. ye""" fiI>I. , NgU,. 4_ sk"", thr .. situ.,,,,,,. in ",hkb ide"'",,,!,,"_ 26 jed >Jlgle~ Th. projin. h"""", ... R ..... ,be OOCOIding '0 ,b. fin al speods of,b. proj1~ ... ju" before they 1 >Dd l'"'''' fir ...

flG. 4-27 Ooe""",6.

'1

7 Figw _ 1.8

>I>oIn

poi."

,od". -m

pa,h.la- a football tickod I,om yomid level, I~ 'he .1_ 10(," of air. nnt 'be p"h> """",ding '0 (a) rime of Aigh (b) ini,ial ve:rtical v,loci')' d i.. """," ,a'io. """or during !liSI... (0) \>''bicb of ,Ite Ie" .. ed poi"" 011 . hal co",. rone_ spaIe '0 roplac,,,,,,,, .:.7._ 2.!Ii;10; + HIk. e"din! ..-ito !be posi'ioo YOC'OI -; _ J.Oj - 4.ot.i

,,1f,. Wh" was ,h. positron', ini,iaI posi';011 YKlor1

.2 A ,.." orm.IOII OffOSlo "I,,;,.., '0 'he """itiv. direc'ioo 01 ,.e x:OOo. (d) Sbtcb ,..., """or 00 rigb,_b.ndtd coordinat. ')'''TTII_ If ,he ...,d ;, mvI '0 ,I\< xY' COOIdin"es p.OO m. 0 m. 0 mi. wb" ;, i" eIi.pl"""."., (e) in ".i'_""" 01 n",,,ion.ad as (I) rn.!";_ t.d. aDd (V an ang" .. I.,iv. 'h, """;,;",, .lid .. (e) m' gni_ ,ud. and (d) .. >ogle ",I"iv. '0 ,b. """i'iv. directioo 01 'bex

6.01

(.)

~,

.7 A traiD ot COlI".'" 60.0 tOllh move> .a>1 fOI -10.0 min.. ,b in, diTII< ,able edge. (.) H ow I"", i.,boo ball i. Ih

floor" .

air? (b) Wh' il it> opHd at ,b,

u. ....., i, ... "'" ,he 100l.?

" ""bes

"h,.

,. A mod",~,. wind "",," ,o'es 0 I"'bbl, 0 .. ' bOfizp. ,al Xl plaooo ";!h ""nllan' i _ (S.oomJ"" oj-

1>< rim. ven K-ally bel"", P. O.l~ I..... (. ) Wb .. i, ,h. disI """, PQ? (b) H ow fa. ""f I""" . h. don board ~ Ih d. n ....... dl . 26 I. Fi!- 4.. ..\6, a .. on. iI 1"0;.< opeed oq IIO .. '9 of _8""'Y "" bori.. .... ,alKJ'~ .. p.... by7 _ l< tooiz"." ... ........ , ... ,ho ... ag>II""'" 0( " . (.) I>o

__It

Yooalhrooo.boIl_

__ )0 A ~.~"" "~, IU""" ,I>< ....... of ....... ..dot, Mao. A Iarp .,. "",,1ll plxcd ..... ,lit wall _ .. , .... anow< b.:o!l ,Ie., it 0IId (b) w.... io .... diot .... bt, ...... tboo . .... , of ,lot b.:o!l....a 1M lOp of ,b ,,7 5. _ , ......... ndt anpe "" i, (.) 45.00' ond (b) U OO"? Tho .......... mdicate 'hOI ,t..

,04"

..u ht fi B- 4-11. , ball .. 1000000d .... 'k a ~IoC. poi.' ;, .. 1M _ of , ...... p oi .... izootolle.!'b d, _ '-Ill II """ t..igllt d, _ J.6U ... A pl .... u Io:im,tely fta' . and !be track b:.. a .Iope of 11.3'. Figu .. 4--150 a p"f"mp 'bat oll ..... ,h kin '0 1.00 0fI the ' '''' poniOrl of ,b. ""'per u ,.,k. Figwt 445b a jump " tdfle 01 the u ",k. In Fig. 4450. ,110 ,b., lands" _o,;.,,, . ly the lauocb I. v.l. (. j I" !be I:UldioS. u1\a, is , 110 ... y.." h during the ftish, .... , i, migh' .1>0 be "'ppeill! poci!O'II.II, ond SJ .... no< ....... of

.70 A boot .. tnvtlin! ..... t"'..... ,he ",,","" eli""""", of

' 62 A .ot .... ,

WI """,plett, 1200 .00000;ortf e",'Y tni.ut .. Considoo. II>< tip 01 blod or 0 .On of.., x:ro.. H . ''''' 1e!'illY PO" d.. baU to. ' mm", ,., Ions as d.e balr. velocit), ",I.,,,,. 10 ,be 60id doe. not bav. , pooi';"" x rornpo"'nt, Suppooe .be pIa)'.r ruru ., .pel 4.0 mi. to ,b. bold b. pa< 160 MU'icoi mile. "Pan? (J) ",h" ..iU be ,b. bearing of B (,Joe diriioo of B'. "",,'io. ) rel>!iv, ' oA at,battime1 .."".

=

can? to) If ,bee"" m.;.,.in their volociti.~ do ,b. on.""'" to (a) and (b) chong< .. ,he can move ...... ,b. inle""",iOll?

"hl].

"'>1iv.

FIG. ' ..9 Problem 79. 80 In the """,bc, d view of Fig. 4-50. Ie.p' P . ad B rare alons "'oiS)" lin..., """"" h' .. "oin .nd p'" .",100",), bol_ der 3u.ro A. R.la,iv. ,be guard.. B traveb '" coruUll' ,.,..d of 2IJ.0 mI~ ., "Y' !I, .lO.r a ."aigh,.I,,,,1 rood ,.,i,b ,pelof 50 kmlb? ....

'''''''lint ""

'0

,b.

Alter fiyio~ 101 15 mi. i IOiM bl""';'g 42 kmlb ., 'Y' of2(l """b of ' '''. >II oirpl:me piio' ;, over a '''''" 'h>1 ;" 55 km _ DOI,h 01 ,b. " .. ,inS poin" Wh>l i. ,b. >peed 01 ,be oirpl .... ,.la,i"" 'o,be air? 76

A , ... in !Javel> _ JOO ,h ", J(I", /s Irt]>'iv, '0 ,b. ground) i. a r';n ,Ila, ~ blown ,,,,,,, .. d the ..,."b by ,be wind. Th. pa,h of " "b ... iodrop m>k .. or> ongle 01 70' wilb ,be .. r_ tical ......"""ed by ... observes "ationaryoa younod.A. oo..rver 00 ,b. mio. bowev ....."''' the drops fall .,.,-fily veni Ioo! .go. ~

,.,old

"""old

II In Fi,,4-5-1o. a >led move> in 'be neg. ';" x directiOll at 00.""" speed I', .. hile boll 01 ice ~ .bot I,om Ibe .ted u-i'b ""Icily Vo _ ,.,I + I~ "I"ive '0 the.ted. V"b"n '"" ball lond, iI. blllizorolol diopl:ocem.n, 1 .lIones"ime?

'ow .

,i"",

90 In Fig 4_ . n
! Frt""h t."",... ,be TOY (T, "" G, .. d. \"t,. ...) bas ",h. dull . ve'''S' .plouO1 ,hat .J>f'I'd IlIId ,b. masnitud. 01 ,be >t .pt! row' 'be go ",ound a CIIrve "';,b 1.00 km r..aim '0 be '" 'be """,leratioo 1imi1?

""ill

">r'"

,mi.

,h.

p..,.n!", 'hrough a lOllS corridor. Larry does.OI ... ,he meNin! sidewalk". b. , .... 1';0 , '0 ,..."lk 'brough ,be .Ik. roven ,be """. dr>1:" 1re in 71h Mre board> ,be oideI.! velo cirrular "",. is IS nd ,be" I,,,, is'" _ - 2.01 + ~.O; + 2.ok , aU in """" .. ,(.) Whal ;, ,h. prOlOO', di,plooement vOClor . ... d (b) '0 ,.hot pi .... " ,h.:i, """or palaU.!1 95 A panicle P , ... vek wi,h CODS'..,' ,p'"b '0 O. lind , .. panicle', pooi'ion ""'. flG. 4-54o Problem 95. ' 01 >< , ... ,iI.... , of (. ) 5.00 ,. (b) 7.';O . . . d ) 10.0 ~

lila!!",''''

mi.'

,b.

6.01

102 FOI .. volleyball ,b. 'OP of the"" i, 2.24 .. boY< ,b. Ooor and tI.. ure. 9.0 m by 9.0 m "" e.cb , ide of ,be ""'. U,i"!. jump .. rv . p1>)"'r " rike> ,h. bon a' 'be m . Dd. horiz"""l di .. ... " 01 oor poi"' ,h .. io3.0 m 8.0 111 Irom ,1>< ""' . If ,be in"ial v.locity 01 ,be ball is borirorr_ '111.(. ) u-hal minirrlUln m.agoi'ude m .. ' i, h.:ive if,bo ban i, '0 de .. the "," and (b) ..-h., maximum mayrnud. """;, h.:i .. if , ... baU is 'o"rike ,be fIoOI irrgn;,ude 0I 7J~1 (bJ H"", lIIany revol.,ion! p"1 in' ... oI. tiad (.) iu , v"'ge veloci'y :md it, v. _ loci'y >! ,b. (f) be~nin! .ad W . 0CCe1 . ... ,ion., lb. ini,i ol "",I. Wh" is , ini,iol , peed"!

'0 , end of ,h.

(dJ For ,b. 5.00 . iolervai f,om ,h nd 01 'he tif,' .. rod

105 (. j What ~ ,lie m. grrnud. 01 'he "'"'ripe,aI """,Ie.-.of on objtlks up , ",ll....I 15_m_long ....,... ,or in '10 ~ Wh,n .... di.g 00 ,h. """,Ia,or. r>OW OleNins.'.e pe"O" i, e.mod op i. 60 L Ho .. mucb ,ime ,...",Id i, uke ,hal '0 walk up ,be moving escal >1or? Doe! , n,,,,,, depe.d o. 'bel,ng,b 01 ,b ocaI>1or?

"ill"

po"".

.,.."g.

107 A b...,b>.ll i, bit >< grOWld level Th, baU " ",be> its m"-Umum b.igh' above ground level .1.0 , aft..- being h" .The 25 , after re.rnin3 it! maximum .eigh'. 'he balllw.l)' de, ,, , f . "", ,ha' i, 97.~ m Irom w"'re i, 10"" hi,. ,b. grow>d i, level. (.) WIr., rnaJlimum heigh' above yound level i, ,,,.ogle 01 belolo- tho hOO"""aI ? 100 An ai,poc' 'ermin. l h., moviDg , ide..-. tk '0 opeed

.bov.,be

,h. (.)

.Ixw.

108 n.. ,all.'" of , projeclile depend> 001 only "" II, ""d II;, bu1 . bo 0re. 10 19.16. .!ewe Ow.II> ." , bIj,b,d """ld', '\IJl.OinS broad jump 018.0'1 m.' tb. Olympic Gome, >1 Bo,lin ("' ... " g _ 9.8118 mi.'). A .. umirrg ,h. oame v.rue. 01 'b and ~ 0)' bo..- mocb ..-ould his record b, ,, diI_ f"ed if b. b>d compe,ed in".ad in 19'i6 at M.lbown. (..-b.re g _ 9.7'I9911l1 )7 .:s:;: ,'

,.oont

109 Dwing volc .. ic .ruptions. lid rock can be bI .. ,ed "'" of ,b. volc. nO". ,b..., projwilH are called ,'ok""", bomb. Hsur. 4-58 a "'00' Jfi'1ion of M,. Fuji, in Japan. tal A, ,.,1", initi. 1.f"""d would . bomb b.", '0 be .joct.d. at >ogle 80 _ 35" ,o'too borizOllt>Urorn ,too v.n' . , A i. orderro Iall at ,too loot of 'b.volcano at B. at venkal h _ 3.30 om .. d bor'lOrlta! d"u nceJ _ 9,wtlll? [yror . ["" ,too moment. ,be .11....... of >iI "" ,be bomb', tr.vel. (b) Wha, woWd be ,he ,im< 01 !liS.'? (cj Would ,be .lIed 01 ,h. air incr . . .. Of I,

11&

A,

'O/b"

initial

.petI,.."rd airflow 'bat COIl alf"" . pi.,.. . 'l"'ed rel.,iv. '0 Earth , .wf.,..,. If a pilo! m. in,ain., ce"aln speed ",Iativ. '0 !be air (,be plaD'" ~r,J ) . ,b . 'f"'ed r.Ia,; .. ,o!be ... doc. (!be pi"",,', WJ', yOll ""'" ,0t1>OW 'be width 01 ,ho bo._car ?)

,h.

COIIIJl'l'"

"'''.1Il

lb.

1 its ('J y OOOf! dis ...... i, ' ravek dwing ,hat ,im. ,.IIod ,b. m' gni'ude> 01 ill (C hori"""al and (dJ v.nical velocity oompo",n" .. ;, J from rogior:>. 11.. A Iev.,or wi,b"", ceilin~ i, ascendin~ wi,b COII_ of IOm l~ A boy 011 ,be .I.va,or >hoot. , ball dirKrl y uP""">'d. f,om a beWU 01 2.0 m . bove ,hoe . levat"" floor. iud ,, _ SUO'. ",d ,be ,1>0 I."""bin! poin. 10 tho burnt d.,;08 n.. ftighl. Gnrb 'M ""'t"iludoo , ot II>< poIilion V ,i.e ",ad poe'5 An equal-arm balance. When the device is in balance. the gravitational force F;L on the body being w.. ighed (on the left pan) and the total gravitational force F;R on the reference bodi", (on the right pan) are equaJ.Thus, the mass me of the body !x-ing weighed i, equal to the total mass "'R of the rderenc~ bodies.

The Normal ForceIf you stand on a tnal1ress. Earlh pulls you downward. bUI you remain slalionary. Th e reason is thai Ihe mallress, because il deforms downward due 10 you. pushes up on )'ou. Similarl y. if )'ou sland on a floor. it defo rms (it is compressed. benl. or buckled ever so slightl y) and pushes up on you. Even a seemingl)' rigid concrete floor does Ihis (if it is nol sitling directly on Ihe ground . enough people on the floor could brell k it). The push o n )'ou from the mlll1ress or floor is a lIo rn ml f" r~~ F;,.. The name comes from Ihe mathemalicallerm normal. meaning perpendicu lar: llle force on you from. say. the fl oor is perpendicular 10 Ihe floor.

Scat, m,.,-Ledin dth""i~ht or

, . . When a body presses against 3 surface. the surface (e,e'!.a seemingly rigid one) deform, and pushes on the body with a nonn31 force F.v that is perpendicular to th~ surface. Fi gure 5- 7a shows an example. A block of maSS til presses down on a lable. on Ihe block. Th e deforming il somewhal because of Ihe gravilational force lable pushes up on Ihe block wilh t~rrnal ~rce l1le free-body diagram for Ihe bloc k is given in Fi g.5-7b. Forces F8 and F,. are the onl)' Iwo forces on Ihe block and they are bolh verlical. Thus. for lite block we clln write Newton's second lilw for a posilive-upward y axis (F",==f3-="l

FIG . 5-27 QuesTion 8.

'"

9 A vertical force F is applied 10 a bloc~ of mas> '" that lies on a Hoor. Whal happens to Ihe magnimde of the normal force F.v on the block from the floor as magnitude Fis increas~d from zero ifforce F is (a) downward and (b) up ward?

12 Figure 530 show. three blocks !!eing pushed ncross a frictionless floor by horizontal force F. What total l11ass is accelerated to the right by (a) force F. (b) force,ch ~nk . UM

, ., , ,AG . ..44 Prablen, 45.

"49 The Zacchln, fantlly was renowned for Iheir humancannonball act to whoch a famdy mc",ber "''''' shot from a cannon using eIther clast'" hands OJ con,pr~ air. In one "crsion of the act. Emanuel lacch'"l W"" shot o.-er t hr~ Ferris ",-hee ls to land til a nel at the .an.., helllht as lhe open end oflhe cannOn and al a range of6Q Ill .He ....s propelled tIIside the barrel for S.2 III and launched at an angle of 53 . If hI S m ass "'as 85 kg and he ulldcr"'cnt constant acceleration inside Ihe barrel . ..-hat was the nlagnitude of the force propel"ng him? (flim: Trea l lhe lnunch a.though it wer .. along a ramp at 53. NeglecI airdmll) ~

-SO Fillure 5-48 sho",s four penlluin. tha I are beinll playfully pulled alollil very shpper)" (froctionleso;) ice by a curator. The mas.e5 of three penguIn' a!>d the Icn.ion In 1 of the: "'0 cords are "'I = 12 kg. m) = IS kg. "" = 20 kg. T, = III N. and T, = 222 N. Find Ihe pc-ngu,n m"",m, th at is not ",en.

--46 In Fig.5-45.e1evator rnbs A and IJ are conocctcd by a .hort ca ble alld call be I)u ll cd upward or lo ....ered by the cable .oo,e Cllb A . Cab A has lIIaSI 1700 kg: cab B has ",aM 1300 kg. A 12.0 kg OOX of calnIp IJC5 on Ihc Roor of cab A. Th e len.ion in Ihe cable connling the cabs IS L91 X 10' N. What" the maptl1tK1e of lhe normal force on the box from lhe ROOf?

FIG.

. .

Proble m SO.

,AG. ..4SI~oblc",

"51 In Fi g. 5-49. Ihree connected blocks arc pulled 10 the righl on a hon zonlal fricl;onle.. !abl~ by a force of n1agn;lude T, = 65.0 No If "'I = 110 kg. m, = 24.0 kg. and "'1 = 31.0 kg. calculale (a) the ma .... ilnd~ of Ihe ,)".tem'5 "cccl~ration.(b) the !ension T"and (c) Ib~ ten,ion h46,

"47 In Fig. 5-46, a blOC"k of ",ass '" = 5.00 kg II pulled along a horizon lal fnct ,onless floor by a cord that eJeTt. a force of mallnilllde F = 12.0N at an anye 8=-25D" . (a) Whm is the mognllude ofthe block', accclcrnllon? (b) Th e force magnitude F i Iowly in_ ere.sed, What i. its value just I} F before the blork IS hfted (cont ple lely) off the Roor? (c) What i, the magnItude of the block', AG. 5-46 l~oblcms 47 acrcleralion JUSI before it " hfted (completely) off the and 62. floor? --48 In earltcrda)'" hOl'CS pulled barges down canals In the nlllnner sho"'11 in Fig. 5-17, SUPIK"'C the: hOrle pulls on

G

T,

GFIG. ~9

r,

.

T,

F.

Problem 51.

-52 I n Fill. 550.,. a coostUllt horizontal forCrechon of FIG. "Sf J'roblem 67. tra,,,1 31' = I! 51S"f~""" 47 ProbLem 9&.Figure 5.68 slIo," a box of dirty n,oney (mass "" = 3.0 k~ ) on a fnctionle .. plane indIlled lit ~ ngle 8:t = JOO. 'll'e bo~ is connected ,",a a cord of n egltgible ma.. 10 8 box of lllundered mo .... y (mass FIG. 568 Problem 99. m, = 2.0 kg) o n a friclion ~ plane i"dmtd at angle tI, = 60". The pulley is fnctlOllle,os and has negligible m:us. What IS Ihe le nsion Illlhe cord'! ss.

92

If Ihe I kg Sland~rd bod) is 1>CUleraled by only r, = (3.0 N)I + (4.0N) and = ( - 2.0N); + (-M N)j. Ihe .. whal is (3) in un,lvector notation and as (b) ~ magnllude and (c) nn angle reial,ve to th .. posi llve.T dlrection7 Wh~1 are th e (d) on~goilude and (eJ angle of a?

r..,

r,

99

93 A nucleus IhM captures a stray n.. U1ron must bring the ""u tron 10 a $lOll ",;th... lhe diameter of the nudeus by means of the Mrottg for. '!bat forne. "hich glues" tI.., nudeus tog;!ther. IS ar>P""'Iimntcly urOOUts"" the nucleus. SUI'~ thai a may neutrOll "'l1h an trllhal speed of 1.4 X lOr rn/s ;. jllSt barely """lUred by a nudeU'S ""th wameter d = In X 10- 1< nL A$WlnU!& tlte Strong force' on Ihe ,..,Ulroo IS IXInstant. find t .... magnllude ofllial force. The neutronsnwu.I.67 X 10-" kg.

A 15000kg heltrnpter lifts a 4500 kg Iruck w,lh an upward i>tCelerallO .. of 1.4 mIs' . Calculate (a ) Ihe nel u",,ard forfe on the helicopter blades from the air and (b) the tension "I Ihe C1lble b-el ..ceo helicopter and truck. 95 A motorcycle and 60.0 kg rider acce lerate at 3.0 m/s 1 up a rDmp inclined 10' Dbo~e Ihe horizontal. What are the IImll"i lude, of (a) 1he nCI force on 1he rider and (b) Ihe force On 1he rider from the mo torcycle ? SSM96 An trltefStellar .hlp has a mas. of 1.20 X 10" kg aod IS 1m nally 81 ft'S1