Table Of ContentMO YNAIO RON 8
How to Use This Book
js book will ech you how to do ply sks problems, ‘The explanation of not anly how wo Yost problet but
why we do ita ceria way teaches you at jas collection of solved problems, buta collection of methods tat
‘canbe used, modificg, and built poa v0 do othcrphysies problems. As rescarchors and teachers, we know that
the hey tossing aew and challenging problems is eonained within the collection of techniques already
learned for solving simpler problems Seeing a problem solved and knowing why it was done in a erin
mane isthe best way o lear how to solve elated, mote diclt problems
This book isnot a presentation of every problem you are going o encounter on ates [tsa presentation ofthe
rethods that we have found to work for large grosps of problems, If you develop the tchnigues we describe
fer solving problems then you will now howto succesfully attack the problems you will encounter on the
tess, This isthe book you should have aa reference when you are doing your homework problems, It ill
show you how wo work te problems and explain why they re being Jone the way they are.
‘Tre tories inthis book are in she order of most physics texts. Lach chapter begins with a theoretical discussion
Problems are mixed ia with the éiseussioa as soon as posible. These problems follow the development ofthe
theory. In this way you donot have to assmilae a large amount of conceptual material Before begining to work
probiems.
‘A*standavd” route is flowed for problems wherever possible. In this way you wil eam hat broad entegories
‘of problems worked in a standard “logical” way always produee eorect solutions. Ouremphass i on logic and
‘onder in solving problems. We avoid methods that may be quick ard have ited sppkeason to problers
solving in favor of possibly longer solutions that have broad applications and always work. We believe that alot
of good physics can be taht in problems so we use problems to Mlstrate and expand a topic and sometimes
introduce new concepts. Fer this eason problems and text ae integrated with a mininiam of arial arviers
betceather.
The book i intended as com plement to cither the calculus based or the non caleuls-based elementary
physics course. It hasbeen au: experience that ealcuus concepts ea be introduced into the Kaditonal Hon
‘calculus couse and used inthe develosment of concepts. Conceptually. calculuss not difficult and when iis
imroduced inthe context of a physics problem it is even easier. We use calcul corce3t to exalain theory, but
‘calculus is rarely sed in problems. Even those students who are taking calculus concurrent with ther ysics
‘course scaly lea calculus coovepts in physies before thy se them in wir ealeuls couse.
Ir those irstanees where caleclus is needed, the problems and paragraphs ace marked with nealeulus icon. Even
the stadent withou:fermal calculus ining should eae these sections. They are often explained ina simple
‘mame sa that the ea‘cnis ces not present prate.
“Thochapters on cloetcity and magnetism are also excellent background charters fr someone taking an
‘undergradure couse in lecscty and Magnetism,
‘We have used two significant Figures forthe physial constants and most ofthe numbersin he probes.
Results are given to two, and occasionally three, significant figures Using two significant figures down on
the cher inthe problems, allowing th technique to receive preater exposure, Do at be concemed in warking
‘rough the problems if your answers dono: agre exactly with ous. This is no doubt due te when, oF i
intermediate calculations were raurded off STunite are sed nearly wniversallythraghont the ok
How to Excel in Your Phys
Com
Most scadert ealsecha pig st stray ue the day hoa she can en hen termi he Hea
miuule i nol ellie, Sere stu Uo Ui ayy, berkne 39 Lie Ley lve gullew ave sili, Pecape
ri, Uke ues suds ya snes canopetes eth fd pa tad kill, Ut mye lle yo
ca FEAT Is ur A :
she Nove Tha yam ar in cafe, Me sims will 96 oie iat a is gsm adeanage taco a
sme uzeonzed wpynoac tu hens puurcaure ta
Suaves'W pele goustlly Fase cre things ie eum, Tacs mike oftve a of Ihe ar ey a asa
ot Unacselves sal Uy lve positive aie, Puyscs a chellenging vu sas os uot seus, wel take
wrellenganized commcenc efortto do well sn thes onus, hutsuecess w 9 Saallenging area ids rvesie ga,
Geweral Approneh for Studying Paice
Many pecsle helievs the following: move wor and mere sudy este higher grace. Thiv is uot aecesarly
so. Yew eonzin'y mast nilig to make a erin commiene af tne nd snoray ay his enare, hate Key
Fa goadenviesasces is carcontating yon! oars 07 he Hight Tings als HghL tims, You way Hays noticed
Tuas Some sur ray Boag Lia he te sae al eg ee a exam. a be meso ty ie
abit "SIsighers” ar the fae are ast abray= se vest of psricttion and a ty ais, even we
leo Hefe ar exam ssh an asl aks clay es ogo771 Pais kine ati, Ry thing
dvariage of Ihe sé tvriqnes ha few you can aces higher glade wi less efor,
“Te nn tise viny of erring Physi aed Isms, plore alvin, seston, nd setomng,
“HPSTERETTY wRIT
T Tapa quigs reagan the pies Rs oe Why IMs eae aending elas Ten OF Hgen WCE
vy fsa ar» hoor Tlne, The june Pee sty eels Faerie use wih cies WP
bediscasee, Versus you sn Westy one 3 ep questa cr hey ports a scan for dursig the cure.
2. Ate Lis al take ots, ALet laf the classes, Some paying fr Ukese eines sy ie LLL! Be
Si Wie We MCT Hy We EO OF PORTE Eo QUEERS IM DRAEAGO P'S OMEN WE
“This i-vary mown, you mae he secna dis ein,” make a special nea this yeurenchnck
5. Review your leete nates, Dan sve tia dep antl aw day <tc te exact mero exert
revit gon ws He i ea ine vir Me sensi an oy ad A a at ese ALA pint oe
algal a dost move dssc€ vending ut ie Wal ho Lan gas 8 yu elie Wake
= TE my be ce MOSER Sep Ue Eee HODES ED OLE DOES HAY HE
survicien safe ext end vex yournoss. bet Pages you must he ale a srr te prahlems. Yor
lca pchlem ving alls bys reading examples nf solid prob ome. yon must dee prehlems
suns ding th homeyenkprublens og aegul"asi sot weil Te ae ii ans Tha yo rod
smue wark on wel in wlvance othe test Phosics psoblemas cou > ilu, Te oes when You se valle
wen rules do ots: youre“ tick of working a cerainnuraber of sens, But EASE: weOUTE cere
5. Cempea oma’ stat aatseare propane a deailec ering. TFs poneal sa:rgy ers that a ranTRS” at
Sho-tespacors is tasagsable pecs af une cows me's eicieaT han ons lang capo’ 41g EeeH
af wag 8s 90 prugiess osu Tae cours, son Bet pet yu iene eta ang Ue
‘eal then aga sn the lect thet. gan wa seco reding and yet sein fa eegamazing sevsea where
a dol tis, Pie dene thirst tn sucess te nh
‘sa tirationspiesinys. Van mai parpactinn Kirihe esa ll 3 ansane fe neers ae prepare on
reo Sm Note we uhugr ssl ae ae ein fr Tex hs sae gsirg eal
erg. That whet you have heen doing You make ap yu oral none ne te, What ja hve sane
(ei this syeemace apmeach sto rptduce the nos nd outing hat hs Instruct ering, Fyne
reawanehy goad a, yan will aes a8 goad 4 some af sam qn eas ihe iat
Tras To Prepare Tora PGRTS TERT
Famine the fae a ary noes eatorng i eee" OF AHINT AEN an yOE wl a Saks wih Se
‘wel ss Tio hg he al Pale Tiger Payor Mi uy Suc wig A,T Paap Tos Woks
nll help sate deve. yous pessoal sure-tkmy progr, Ose commer: ted eal books 9 oat pest
areilar sean sco snow Ze queso in alvurce, Most writers of ese types 9 Soo ate nthe Mesness oe
{nso acop in hc paula sa, s0 thao eloas sede pene eh ar mekkne p= exns. Misa
Thon sea ans of Ist qsston, nt ming Me pein vin aw hee Hs gp ote Fa ney
vwrkoowing se uuswess ahereeny We mike eToys aos
1, Ala sl nutes in plies plane sora utente “a eal a ae wots ar ex
lie hive doue it cass, May tines you may excornter he ste problea iL ere eoabe:s, Ubi mikes
Sten fmpectnt to artend wvery cloak nt to miss the opportunity ta see posable est questions you do
2-Ancthr thaqmsnracex tae far sigh relic hone ORI APPEAT SRE
Sify gimp tha oss knwonk pede ns ngatRsr Thema wali shan evn avy oF aa
dove, Don: wae ay anus ue eas gv ures iis route, Your Ga prepahoes Lora est
shale be doue pneatey 9 Ut you cick waceeate oa Uevelpiga pln for king Ue te
7 Fin ample pipe ara 79am Ry yours Heep FER aS, Ws a pon Ter at MOAT Ae
ves ums fae wae Te nee il Le vey ge Fe ape he mg as
4, Sonne pigaes robles inveles mathemalos that can be Sscepesly sap Fer o43 le if yor ACL
lions every the juin ef kgcrdeny or exponerta sane yar pei a nail
operatens an entesing the embers ftp you clvalutor sey seth to tp am gue a; How ote
“Timsng and the Use af he Subeonstons
Have yo over experienced he fran ef ving x ceniocnn with monn and forging “weeny
anes oe Ua i8 sot Fail ue oC? Ey sory afer sesh ay exericnes, “WC AME GALT” COME
I yan sua sac net seams u say ying he weal i, Aru eaioe Fs svn phous isl
ETEOT r i S ret Up i =r
to eep an.” Boch ofthese tutions bave wcnmzion cturuteitic- he ase the soho eu, Uhe ce
that soins a aan presentod ee ws H dhe abso oe nf active war an the probly ar he-noment we ese
Th sina inser arr pa ihe isin wa aval cing Ihe nine ino a‘ a prevding
saluaex, We cll this-anL of le asia subcurscios, ca dus pont ae bnia is very efectve suing
problems
ae ans me tse far RSTVE ora He EON TATE
|. Your satecnaciae will nt sve the irformariny You rast onse'naay sat et asthe Het oF
Informe tare paniew ar prem. I yom ars "avir Aen with pW em tap sai ima ind
wi yo do ns ath the jslee, Then J deine yuan wl ei yea lu sry ae)
wales abou, Ce prob
3 Tulvancunse Tet rt the ebie~ up hoe pairt a colt sen, Ving soap gwd a gc ovr ptr
after this pot and sccocapish ery te, Hs mere etcest ot yout plu your sly ame 80 that you dene
pur sounain astute were yetr aly epi ist erin on pte,
§. Alle you fs done al yo. en consiadly om Use, “Palin te sack ju i.” Dan. es
‘ng chen Fe Ts Pape dar ek ca” par rind we Harp ea accepts Tuer WGN I CoAT
4, Bese yo huvow caine sor the
$5, Wes soluon eve fe ane Uae on yuly so you 2 on a amelie, ates oe
Son the proh'em eel coe" ares “ar mone irene pram oa ail
_manswere, hac wi he sears ta sea. Wher corld hs "s9poning hors at your suheansn sha ena
The plow val wre aerial coe ffm rang aa phim yen Fh
“La study sree tet we ave vallize, vousising of ayular reve of ete notes, Eecuent wea
dusiewuek probes, vad elie epli.es af your sari uses ua vale, mks rai use of sou
‘wheenscions. The pared nae of new maseial and th reqritedennsciaazsviow ares kesp 400
rmheenacionsly analirg. ar teen. Yee infomnernn Fa“ hae 4 Kran yen ae actin Wp
Here snl hoa gcd appraac' 2 pactcing fara Phy ee
ED 4: exauday ums feu Peywe usurp esc Jus yar vile
iss may cous of qeaions fnuca previns exsns greet byte
Fretacr ant vations nf emer arlo-w er apse
Soir m
a the joer iyi ing yu oe
BLY 3: Stuey foryusr fest spleeseun, Gu uver your ates, te. ed
vommewor uate
TD-2: Take yoer fine arople exam. Asscon as posible afer the exam,
sha died wesiew coreg a he weak ras Mek
be leaps ga6m
FD t: take your fra sample wx, pie verve the TC arcs
se ou igh’ seep twig
Lb: Dow kiceweposstble on the diy ule exam, You way wane
sticky ree: your ening oF a couple at dent ns,
‘Yer will pce ha ths Walk adhe work psp Yr aos his ay omelet wing and aking amale
Iss Ths plarned dat stp, One the commen Fags in prepaing fo exams so popaK’ BFE weONe.
Thing, Me sada wil prs Fora Physics cnn yang Fe ea ae Lp -oaing ay cir pales,
Pryce exam, hexeve, i eaten enc hut weit axe problnc-solsingexcm, Lou Fae 08
ie en 1 clams. you hse i zr
he wooed aeseiage to aking sample tens echanit ie'saes sour sd ie writing a tiers to types a
ohlone rata sly to Been the ret Thi wl a ewe pa more tira ding to eat spond on apex
armnve hyableaane pli sis,
Suwategies to Tse TH
ng Physics Te
‘Yor 6 now anbing W691 ra, Nam ane ws uegen in aby aie we, on Faw eng 6°17 and
snow wal w expect or the exam. Yuu-tive goles youl ung’ sleep the rig beforeuchestens heals
bell hat wll poole su with he energy ned Te wd euncen salon, Yi ve a ave tke, AL
this point aorging slr Foe yna wil Ann th exam inwelose, Smdy Se i oxsr. Yeu nase
soncealcs n= esis fat wil eo yes highsat pees ates the ee, Hevea sem angerinn
TT ally 9 oe eo se we or os Le oT Tee Ts vera Te qe
Loakterths rp ef ewes cha: ye exsoetoe 3 Rus raced co thos fn. Save the sandese
queso fr lat. tec he we Pureating 0 by ere rime eek on questinn #1 enly tsa dar em
Tide even gel ere eal quests Ut es nc ai
2 Hawa eagh ie of he rash Hin yom shea apening.| each questi, Somalis concn qneaas
ie poi thera tors pide thi
$y, ge inal mais eb ot Roun ys enya fs Ihe ie a Ua ean Ct x
vite dave afew uf ke nor carpeted ues ue tv problews ict xieube dase fouls sou ee
lasing overt tos. Later during the tet, your ind ay be cluttere with emmulas end crea be hae t>
‘server teal ere af re more eon picated anes.
Tho nists ae inching arts, This fs nea to mos aT physio owes
5. Wits yorr werk clear orton you sre saeing a plea It i cass" er ts pressor ave gr. pial
‘cir Fe ene slear yao dan yn A Ze valent sorely ah jast made ino semytasior a rm
f.Thnkechevt yaw anewarin x fohlem. Drs “s ane” mae sense? For scares i gon. solving fOr te
serecler har Use ypu cause Lis vere ingens. ty be le lo Uso lke Lis op atest. Lis wel lp you ty can
acer istaes he rang re gn,
Lofuraoately some nbuuctes ove less state ech Jong or giver pero ol ine. see suey
{pene nara ir easurng how ja yeu can deat ee tam Foxe wal you zan dhe. Thy fin nut
inadiarce nf tow if your profoar"s ees ae kets (Feo sor an A inal 79% ines oF
TS FU HET Te ew NTS TFET TOF FOR ATG AP TRE TST
Tecuncnes th at a oe fe wut “or pti i haga gre, Oe Sac ki kets a ey
portant to seep yor col un ry 3 ge us zany int you ns. ea, Say Tlie al he way to
tel oe it your Bese she
Make wars you now he rorogseennev radian eds and degree GF Frarsolrlatr When king @
Iss tha ingles Vigorameuy (See the Matter atical Fackganrd Sooo
9. Ace -swelongeaanrzet wiih her snrats imersdlatslyhetore fs excn. Mang tira Perera ener
Fate, defect, a pels war in ritine ex weve iy fellow sles ce haw ye
pafernaice
TO) Mite Clie Tost Find oot TRS ey pou Fora wrong aw Theda eis a ATO
lanmcered, Fi. ut there fan anil cred: tor shew yous woe ea separtesaeet 3 pape. One hing
‘o think aut or multip chee arts how the poco is erating the ska che ean fe cost
srveaor Hove ane came Igpeal wrong ehnigss ora no shay Physi tn
Tan Te ARTES TE ATTY TATE TRE PRAT TET 8 ERT TP
‘he vous lf hy a fact of 10,
1 fort require shy np a sw ean, Ditonto is gan the bn The arog ansoet sah 4
fico ot 30,
L.A qvestivy ls“ veloc, lvoe is 10 Myth the erect gabe, late wramg ris
‘CEonos Drm 10 ales pr Uo, Ube coxec iswer. Tie lsu heres fo Took flys. Ue oie.
‘Your Self Ama us a Student
‘ow Linge extent. cy peop. perma Use level wf Ur uve sel image, One hing to ye sgh i your
tind atte hegivring nf the eurse is ther you cit cope mastering the marerialin you" Physics ere
Some stedenes aevatick fe rade of avrg anreding ka." Farc ways moon a C unde.” There ea
‘ioe Tog eal ana Hl shaw ya a hs Ct i lyse vacation ay sli, ahs
sills belt rem come ta cote intl gelkiug C's secouse of tier wicerecai othe mts, bl bess
tht shew they ee themselves. enawsictsty st anconieivuls In series ne moe ea ve suet
raat orntos comrss, for sxe. ir eWay impossi’c to go trom ane aor ra the nxt. at alane
‘essai of seen aleve aly wk ay era isa pris svat, irk Wc fy ya
al vaune were gut ee avg ts Wa, see caliy ae dive, At sae eu: i Ua ee yo
‘ay bave doug thar you coulda’ undencand cea corseps. By now seu have mastared these ss
Colles Physic isthe sie nay You ae-“emaltcapatle of understand ng snd even mastng asic physi.
[Now itis ute sha den: poaple kaon :€ Toren. apoeds. Yew may asco apond Tse caine a
iysos ur mone Tbely, ake ane aetve ef yoni
XtN's plat yam nos 9 sev a goa “or yours your Physies coats, The fist qpsstion fine maerans is
Phys dean mga lexeuies: Blokus ing Phys ak
ever ecunemnet. then yeur primary goal shold be wo get the best ride Jour Biology eves. wie
‘has Your me}. Ine a your gosle "sin havea WaT CEPA. ther Yau shonld wis far an A av aoe: #
IT yan major i Phys es or Fag'neoing "eyo Sho éaint'y go “aren Aa a ames. Wie Caw yor
uals el c1ech them af a hey are acvuupliser, Your eusls Le: ke fr perl ul 4 Phys wourse cay Wok.
someting ike ts:
vwook 1: satuisha schedule fer roming txt. reviewing motos
Aring hans pasha,
eck 2: iawestyate the pony wgeniny a sa gears
ook 32 ae auf ps era rem thi pine ace wel
ah many pine ile to rake ano de re tat
seek gros and eke sarap acne for Hea te
“ae purpoie of iting coin yor gal i mo eneane mae ks, but keep so oeaed wa the mos
invponan ringsahar yon noel asenilish ee sinter Gregtestes, Pease ns emf aT the sty
Ruy On SPAT PC ASEIBITE TS NAST ACTIN NENT BRE HET OT, THE BRO
boxonve store argued und ocuser ou your ges, ke sooner yo... bop o nelle al vor ce eapable of
‘epee tacemphstitents with w eeasenable amour ot eff
‘Pechops Uhysiesie 4 Cavome cea os aey Uni yu aay wih lo ote se flue or pepe yuu sre
Privatityitorat nthe mast cFF cin ay to mai tho this cures. Wheover fen cho for yom
maj tea of study. ti samerhing you enjay en pursue excellence. ive Iyer hea today anda
among, BS ih 9 SHEE
Preface
“Ts pos: al frie hans 4 Show yew nw physi pines sors Hong’ ap. seon a sores
vo sus anoblens Ik we it sau for esa Ut we ublerst! semen, wht te be Ls
naples ease were peshomencem mewsmed sl exclsvey hy youe shay Wy spb.
“ais book is ova wullectow probes, Neier teal Ls an tem ashe a moe bebe uy
‘ea! poclone soving wt Rev eraphasis on che poke sg. ee its mtn to complemen: sear
‘eavae rev. Gianorations af ahgses ens the aacior neha. hace often lar sted. eaneerng thir
pl sicscunges, “Trad cro ang illo aa het bl Tay glee Py il
Iie ya te pres.
Saat ete ee ra am OMT PHN MTT A TH WEP NS TERETE A
Atening. wh usstery Ueraoostra cl by wining, Physi ty zo ke at, Rey se be ced ae Ube se,
bus mastery is demoxsreted by zomg prebleres. Writing comes easy 9 Tes: ease, Working problems in
rath oretica symbols ioe sa caay ra mst. and its et sonrathing we Ae repel. eating. psi
reqs leeming tn nthe pooMoars ys rv Byington hv yeti ang sant
syupolsir Le cane aes
"Tos book wa sale 900d 19RD Thy EVO ag was povided in oi—h Kom is eneeigie Pg ATS
iysios sequence fo Fel Sie cers wets al gio Pepto wre encein wong
‘lems Ihe fvecublevesanie tom those sudeat~arovided reo 0 eons 9 expan archer
nel stew af the pix. 1 TX he prchlsme weve used [hy MOs as am df dhe lemensay physics courses
ho was taking, Sage Pew he solse'97 oF pra ome ad ea hag been espanted by DolhgitFersand fined
Hah Ftc ose hy i aes
Tg hy sin desi ofthe nahurs Ia this bok hulp ys bets wna py cal vnc ane ek the
raseekiel problems, We wo ike lo ack Us coy si lento Eve wale aled Ww Was vars by cag the
mak and nv ir tims. Aste Fe att Mea Hil es ally cur em Arthur
idonnan, hav envied aroatly a7 de lay ot ese
ROBERT M OMAN
STPRTERSEC RG, FIATRI
DANIEL MAN
ORT ANDOFLORIDA,
Introduct
‘Mathematical Background
“The purpose ofthis chapter i to provide you with a review of and seference fur tne mathematical techniques
you will ned i working the physics problems this book. Some topics may be familiar to you while others
‘may not. Depnirg on the matbsnatial level of you physics cours, some topics iy nol be oF inlets 1
‘you. Bach topic is covered in suficiet depts to allow you to perform te mathematical manipulators
soessny fora panicalar problem without getting bogged down in lengthy derivations tis not ou intention to
‘each mathematics, btw show you how to apply specie mathematical procedures to physics problems.
The mest efficent use of his chapters for yor todo a bie review ofthe chapter, spending ine on those
sections tat are unfamiliar to you and that you krow you will ned ir your course, hen refer to specific tepies
as they are encountered in the solution to problems, With this reference yov should beable to pefonm al the
rmathetnatica: operations necessary » cumple th problems in your pysies couse If you nee er desi mere
dpe in a particular topic go to an clgsbra or calalus text.
‘Solving Equations
The simplest equations to solve re the linear equations ofthe frm as + b= 0 which have as solution x = -b/
4. You should be very familiar with these.
The next most complicated equations are the quadrats. The simplest quadratic isthe 1
taking squire roots dcedy,withou: any hee manipulations
at canbe solved by
An example sy? =36, which is first divided hy 4 ta red »? = 9 ane sqpare roots taken t produce x= 43. Both
las and vin values ave legitimate solutions. The tality of the physica! problem proncing the equation may
‘itate that one ofthe solutions be discarded
“Tnenext complication in quadratic equations i the faetoreble equations suchas x°-x- 6=0, which ean he
factored 10 (x- 3)cr+2)=0. The solutions, the vslves of x that make each parentheses equal to 2070 and satisfy
the fctoed equation, ae x= 3 an.
Ifthe quadratic cannet be solved by factoring. the most convenient solution i by qudkatc formula, a general
fermula for solution of any quadratic equation inthe form ax? + bx +=.
“The sfuton acording to the quadratic Formula is
‘See any algebra ook fo a derivation ofthis Formula
‘The physics problems you are deing should not produce square roets of negative numer. I your sluton toa
“quacratic produces ary square roots of negative numbers. you are probably doing something wong inte
problem,
‘Certain cubic equations suchas 1° = 8 ean be solved ditctly producing the single answer x = 2. Cubic
‘equations with quadratic (22) ané linear (x) erms canbe solved by factoring (i pssile) or approximated using
apical echoes. You most kely will ma sneouuter cubic uations in your ely plyses Courses
