1998 Physics B Answer Key

01. B02. c03. E04. c05, c06. E07, AOE. D09. A10. A11. Bt2. A13. At4.E15. A16. E17. C18. D19. c20,D21. A22. A23. A24. C

25.826.827.E28. D29.830. D31. A32.833. D34. B35. A36. A37. A38. D39. E40. B41. A42.843.844. C45. D46. A47. C48. D

49.C50. D51. D52. B53. C54. B55. B56, D57. Cs8. c59. E60. D61. D62. C63. Cff i .865. D66. C67.D68. A69. B70. E

Answers to the 1998 AP Physics B Examination

Section I: Muldple Choicer Blank Answer Sheet

Section II: Free Response

Section l: Multiple Choice

Listed below are the correct answers to the multiple-choice questions and the percentage of AP candidateswho answered each question correctly. A copy of the

blank answer sheet appears on the following pages.

Ansrnrer Key and Percent Ansvvering Correctly

t59 Il l

F-3h-----------l

l. (15 poittrs)Tyo small blocks, cach ot Drss u, rtc conncctcd by a,lring of constrnt bnSlh ai rrd ncglEjbh mr$' Bbck I

i, oi-"a on a smoorh tabbop L ifiown "to*,

ltd tiock I hrngs oer thc cdgc of the tabb' Thc ubbop is r

ff;;il;;rh"ftoo"'B6clt isrhcnrctcascdfromrcsaradismcc i abottthcfloorrttimc I=0-

Expcss afl atgcbnic answcrs in rcrms of h, m, ttd g'

(a) Dcicmirr rhc accclcration of btock I as it &scqds'

Very Good Student Response: 13 points

mg - T= rtto-

7-=na a-2tnq- ta^' n

-g"=2-n-4=n2rt

(b) Block I strikcs thc floor and docs not bouncc. D€tcrminc thc timc rj U which block B Srikcs thc floor'

aY'Vt ' /^( '

'1,= 0- ist '

A' / t t^2L= e'tt'= /T

PhysicsB f!@Answers and Samples

(c) Dcscribc drc motion of block A fmm timc r = 0 !o thc timc whcn btock I srrikcs the lloor.

4loo* 2 vuoa Fove taoa .eF7 fr 4teA/7 a.( -.ve

aazFt<t

oF ,7t fAt.c. 7s .a,catr4.96 ea ttCAE'8"?'A7,o^/ fa^ Szock

I ,uraa 8€ -

€a,ra 2e z€ 246a'/tu'G 4 4e4GZAa.92-/a^J -a.Q

3.o"r< 6. (*).

(d) Dcscribc rhc motion ofblock A from thc timc block I srrikcs thc floor to thc rimc btock Alcavcs rhc tabla

O-"a ororK B sTrtx€s )Fz€' Fcao./ aLacK .1 olt.c

C€.1J,G 7o acc.€i1e,.?/rr7-€. .Zr yy222 ca/Vr/A) 4E J+ 7

t aOivS7A.Vf V€CactTY u4/-t1 ,/r a5rcr!€S 7.f€ €ilO

AF 4e rtralE,

(c) Dcarminc rhe disrance bcrwccn thc landing points of thc two blocks.

at . v

*r,9. u,AY"4t ' ! ' t^

-lA.'/tt 'l l , t 't+ "6

Ax'Yott f nt l

^"'@to)("8)o"=Wax= AA

Excellent Student Response: 15 points

(b) Calculatc the magnirudc of t[:f""It:jI9-3!-tlgb[f tSglrio.n gT. to. Sc chargcd wall' and statc its dircc-

tion rclatiw to thc coordinatc axcs-hown'

Fe5 gE

otLN= (-eo ( r-bl)

E=almule&wol''ot

e

z (out)

ThFlttriifG lttachcd to $smlram-nc oar trutsr xr ertuurvuun' D '

ti"n"i?UAt. Thc clcctric forcs on thc ball has a magnitudc of 0'032 N'r-€<

and tabcl thc forccs *t'n,1ilffi(a) On the diagram bclow' draw

tt* t.4tat7.o'xt 2

PhysicsB !@Answers and Samples

(c) Dctcminc thc Frpcndiolar distare fron thc wall to thc antcr of thc ball.

. ' . Sr s .3 nco{2 .2-5) =. o 1 rn

(d) Thc rrrins is now cut. \t

i. Crlculatc the magnirudc of thc rcsulting accclcration of thc ball, and sAtc ia dircction rclaaivc to thccoordinatc axct shom.

lN= Ysino

. Ob?-N"7co sg

$ . lrst'r= ta n e@=12.25o

Fresur4r.{F. tM

, , lN - t2.ZSo

e = flrc ton -;tt* I -

c l . f 12.29" b<' lor ' ' r4r 4'fr\ s

f.F5=9=r - r8ine--o-

' lN-Tsine=o [ 'I

€t t=O --Fe - Tcose=:-^\

olzN-Tcose=o II

F= JnO:.1N= (ot t .d)o

ii. Dcscribs thc rcsulting path of lhc ball.

T[.c bott urou-l-d

t^fit d 12

r|\d-\t(- a-t o "r g o Stra'-g tr

?S. bcto"v 'N a/ t i t

61=lomlSL

s

\ luJ

Excellent Student Reaponse: 1O pointg (c) Thc valucs of M, h, ail c for rhc srudcnt3'

Physics B }@@lAnswerc and Samples

o.lJ,J o," tr[.,

thc valucs,ot t4t l, 8d c for rhc srudcntS' lppaBtus air M = 3.Q lg, i = 2.00 m; andc_= 128 J(kg. K): Thc sodcnts mcasurc thc iniiiirt rqnpersuE of rhc tid bcads urd rhcn clfl) noctitions of thc "clcvatc-md-dnin- nm-ecc Aocii ra.rrd. rT.r .rr ^F rL G'r.-.:^--r

lcad bcads urd thcn conduct

lp:f-dl.::_:l*_:!L?vryTd:dnin: proccss.Agaii, ossumc thu a[.of rn g-iir"ti.,i"l-p.t"i'ri"l::gj-f:y{;"toJh€rmal-

cncrs/ in thc lcad bcads. Catculrrc thc rlror"t? go'urf"d;;;;urcincrrsc aftcr thc 100 rEpctitions.

9.1,62. l r ", -AT- ' - !. A I - r -sT,I lP TL.(,/,TIIh

II

I_l_

HollowTitbc

Valvs

Sphercfrllcd with

g [+*p'+ t), l5 l /2 5 K

AL^^.ro,,. -- dr' l.,o . l si,2.F( ,t0o -lS.1ES n

(d) Suppose that thc cxpcrimcnt wsrc conductcd using smallcr rcscrvoin, so that /l,t was onc_tcnth as largc (butf, was. unchmgcd). woutd vour answcrs to pnrs (q and (c) bc chanjcd? ii;";il ;.;;; aiiwrryr rnot, wby not?. kad Bsads

3. (10 points)- iiud"nrr alc designing m crpcrimcnt io dcmonstntc thc con'rersion of mcchanical cnsrgy into lhcrnrl cnclgy.

ift}-ft"r a*d.d rh-c appriatus shown in thc figura aborc. Small lcad bcads of tonl m.ss M ard spccific

hcat' c fill rhc-lo4r hotiow ephcrc. Thc valws bctwccn the sphcrcs and thc hollow tubc c.n bc opcmd or cbscd

to coritrol thc flow of thc lead bcads. Initially both wlrcs rrc opco'

(a) Thc lou,rr valw is cbscd ard a snrdcnt nrrns ihc appurtus 180' aboui a horizontal rris, so $at th€ filhd' sohcrc is ool on toD. This clcratca thc ccntcr of mass of thc lcad bcads by a vertical distttlcc ,r. v/b!t

rninimum amount oi work mu$ thc studcnt do to accomplish this?

st"Jof ,;urs s;aLre pdcnl;ol "rrr3y.',1,1. P E = Mt t

{t.^'1, Jonr is MSI-

(b) Thc valw is now opcncd ud thc bad bcads turnblc down the hollow tubc into thc othsr hotlor sphcrc. If all

of thc grwitationaLpotcntial cncrgy is comYcrtcd into thcrmd drcrgy in thc lcad bcads, what is the tcmpcra'

turc incrcuc of thc lcad?

0=McaT pE=e | ,*c

arnJ l[ trrJ|o tL,.nff

H.^! *rors{.'

P E= lt, t,

3h=

No, +[z ^o,^l/

r,o* .1,,*g.

Pol,nl,. l En,d',-.g-1', +* l*'"j'

pF= f'lrx=h.DT= Q Ms\ = N"DT 'I>y

"\,parr cr;[l r,"* <-0C..{ {L .l.rrr] ;^ T,s^p.2{ur"hq,lf c:rtl hot <-{tcei .fla choha ;u T25p.2l6ra(e) lVhcn thc crpcrimcnr is rc.ilL9?TfF

frp"rrrc incrcrsc I lcss Oan catcJlaaa inl* 1"1.'tnvu s& r^Frrurq^'*uuv oorc' rnc Fmlrcfaturc tncrcrsc rs lcss than carcrirscd in p''t (c). Idcndfy aphysicrl cffcct rhrt mighr account for rhis discfopancy md "^pr"i"

*r,y it lowcrs rhe arft.",iri ---

il*. *0,^\JL. jronrl.r,.J. l,o- +L t"od,. .*" l[. +1" ,t,4o lL o,ir. lL-t u;l l t i , Le /o.rf

W)=tLrr cAT :AT=

O-yar<lur ou,l $rort

Excellent'student Response: 1 O point9

4. (10 points) :r--.:-.r ri,hlInthccircui tshomabovc'A'B,C'andDarcidcnt ical l ighlbulbs.Assumcthatthcbaucryrnr inuinsr

-nstst Dotcorial diffcrcnce Uai|n-ir at-i""ft (i.c., thc indmJ rtsisrrnce of thc battcry is assumcd o bc

iliffiff-d rh"-rcsistme of cach lightbulb rimains constant'

(a)Drawadiagramofthccircuitinthcboxbclow,usingthcfollowingsymbolstor€PrcsGntthccomPoncntrin*' i.ui'ai"io?r.Lua rrr","ir-roo-i,- ti, cl, and D-ro rcfcr o thc corcsponding lightbulbs.

IT

Battcry

+/\A- --4AA-- --4/v1r- -'VW-

Rcsistos

Draw your diagram in this box onlY'

PhysicsB l@EAnswers and Samples

@) Ust thc bulbs in order of tlicir brighrresscs, from Uigtrtcst to lcast bright. If my two or morc bulbs havcthc samc brighurcss, statc which oncs. Justify your answcr.

-t A; fr AJfr4 .h^ ,/lr? A @"'+'r'4^"f /4v h"-/' -t

D " r--/4 r-it B u..a;7}J ^4J*tMr.-.,.^e

- ,/*,lr-

^'712*A^ 0 "J L,

^----> D;.e z,-.--l /^4h,r_

0 .J 04c, /--- 0J*

a-w-r?4ua4D, +

!*.t C*i zui, ,- V>-./^,e za q,4tf.*Z^,t*

-- B-l L ^ ft. /---t- / ,2,rr-/_** ,-f*I#.tJt4r. .

(c) Bulb D is thcn rcmovcd from its sockct,

i. Dcscribc thc cbangc in thc brightness, if any, of bulb A whcn bulb D is rcmovcd from its sockclJustify yow mswcr.

A ; /..- /-7 /'-.* ,e ,---j ^.A^+-aAzlilr ra*+ ,t" t4.^/v4d E /'--t.*.

ii. Dcscribc rhc changc in rhc brightness, if any, of butb I when bulb D is rcmovcd from its sockcr.Justify your answcr.

8; /'4'h' /"-* ); -*;;- -*E'J'{" t'--'14/'

a-L JlLe @** rh.,,*/r|- ,e-/, ,x'-

,Student ResPonse: 1O Points

t' [.f#:T],-" srmding mrcs, onc cnd of a string is lnachcd to a runing fork with frcq'ercy t20 Hz' Thc other

end of thc srring passcs o*r "

;;tby;d- is conniad to a suspcndcd miss M as shown in thc figurc abort'

The value of "'

is ,uct rl* u,jlc-#ioili Gtlan"tn rtos-fori 'toops.' Thc lcngth of thc string from thc

tunins fork ro thc poinr whcrc ii""i,iilg",*"t; tiiof or rrrc.puttcy is 1.20 m. Thc lincu dcnsity of thc string

i, ' i5 * ibt rs/ri' md rcmains constmt throughort tbc cxpcrimcnt'

(a) Dctcrminc thc wawlcngth o! thc standing mw'

r I0PTS-A = Wwutq

r )=

A-- ,6 m(b) Dctcrminc thc spccrt of trurswrsc warrcs along thc string'

y= z(

- [' ut(ta"o)--il.,*le"

t , l rn

a

r-_il

physicsB !!@Answers and Samples

(c) Thc spccd of wavcs along thc string increascs with incrcasing tcnsion in thc sring. Indicate whcthcr thevatuc of l/ should bc incrcased or dccrcascd in ordcr !o doublc thc numbcr of loops in thc standing wavcpattcrn. Justi$ your mswd.

Lf IA h /t-tue/ t trln fD re&/ fh R q,,1/brtn,

, ftr'6W wnuL fucrvue -', fr /aarWe /h Wns/>n: t r l l0I l f 'v 'vv\ v-

dncrUre ne f Nel tr W vwq c.'r 6dilt/ aa/ 6tuoi- E )n"7& waM ltu{n tNou// ltorva5s , +:; ;^;b'1, w)t 'h4;€ toofvs Fn t'A'rt or .fr'

(d) If_a point on thc string at an antinodc moves a total vcnical distancc of 4 cm during onc complctc cyclc,what is thc mplitudc of tha stmding wave?

knl I2cqlt lvt ; 4Crr1

Very Good Student Response: 9 points

6. (lopoingA hcrvy ball swings at thc cnd of r string as shown abovc, with ncgligiblc air rcsistrncc. Point P is thc lowcstpoint rcachcd by thc ball in its motion, snd point O ir onc of rhs two highcsr poinrs.

(a) On thc following diagrams dnw rnd labcl vcctors that could rtprcscnt thc vclocity rnd accclcration of thcball at points P nd Q. If a vcctor is zcro, explicitly stslc this fact. Thc drhcd lincs indicatc horizontaland vcrtical dircctions.

i. Poinr P

ii. Point e

V=o

Tloo-l

FnvsrcsB f!!s@Answerc and Samples

O) ftlcr yvcr.lt swings, rhc srrirg brcakl Th9 ma9 of rhc string and air rcsisrancc are ncgligiblc. on rhcfollowingdiagrams,skctchthc.pathofthcbatlifthcbrcakoccurswhenthcballisatfrin-t P orpoint 0,In cach casc, bricfly dcscribc thc motion of thc ball aftcr thc brcak.

i. Point P

Tt L^tl urovld ac* ^J

,{ t wc_re tl^o*^rrg|rt o* a certa,^ velo<.r\ r^ *L+_fto ,n,tr. l vol "c' ' l / . Jt*

] - e\,r.X dtr<-l- o-t , b uJ'

A-aur>.\ / 0r-^*.- ,J0, *'J, tt 't accqfer<h* (s V, Lu<

ii. Point 0

Tk !"^il. t*.,-.LJ !il!*i" F-,.f & u"!<lr:&'

-o"ly +6 3-u4. v

PhysicsB f@Answers and Samples

Excellent Student ResPonse: 1O pointa(b) Accordiog to thc Bohr modcl, thc cncrgy lcvcls of thc hy&ogcn rtom, lrc givcn by En = -13.6 cylnz

whcrc rl is an intcgcr labcling thc lcvch. Thc rcd linc is a rrsrsition to a inal tevcl with n = 2. Uscthc Bohr modd io dctcrminc thc vduc of a for thc initial tcvcl of thc cansition.

i l '=o

Hydogcn Dischargc Tltbc

It)=

' l3,6eU+--

4Lt't3,6e-U

no

)

't,l;-'r;:f:'r!, #)G) Q{t1ltlv-cty agscribc how thc tocation of thc first-ordcr nd linc would changc if a diffrrction grating

with 800 lircs/mm werc uscd insrcad of onc with 600 lincVmn.

E e4,"4r,*- "6r- dnL-rr*,/L

P rd l<, qfpL6$ /";n ? c""ed=

' k ),4 &.b-t lrr. rwl /,-^o, r"--l( fu,trafffi;Wtu

f )=o

Eyc

rc+= ?/ \ t

[=-CA=+y, * 42E mn (first'ordcr rcd)

!9q Figurc is rtrtwn to scrlc'

7. (10 PoinB)A urnsmission diffracdon grrang with 5fi) lincJmm i3 ulcd to studv tlrc linc spccm'rm of thc ligbt prcduccd

by r hydrogcn discr,"rg" tuU" itrniil;fi"y";b"l; I|9.frati'nr is 1.0 m from thc rourcc (a holc at thc

ccntcr of thc mctcr sricrl nn otiJcr t-."r'ti" n"i-ota.t r"d lii" "t

i ditt-.c y, = 428 m from $c holc'

(r) Crlcutstc thc wavclcngrh of thc rcd lino in thc hydrogcn ll'cctrum'

J s', n&= n&-.(tf"J;'f ?s)

6,t6, ro-4.

TDiffraction

)oratins

. : , . i : : : .

Excellent Student Response: 1O points

Figurc I

8. (10 poinB)'itciong.itraight wirc shown in Figurc t abovc is in tbc plmc-ofthc pagc and canics I curcnt ,. Point P is

also in ihc plaic of thc pagc and is a pcrpcndicular distmce d from thc wirc. Gravitational cffccts 8r€ ncgliSiblc.

(a) Wirh rcfcrcncc to thc coordinatc systcm in Figurc l, what is the dircclioir of thc magnctic field &t point Pduc to thc currcnt in thc wirc?

Dr,r.a. tb ihs, trurertl tn +\ wlhq, t[!- najneirc fi.etd of

frr-rrt ? m\l 6q 0.1"h\ ihrD 1\0_ papr. tfuF-ha^d flr^leJ

A penictc of mrss z ud positivc chugc A is initially moving prallel to thc wir€ with e spccd u6 whcnit is rt point P, as shown in Figurc 2 bclow.

Figurc l

O) With refcrcncc to thc coordinatc aystcm in Figurc 2, what is thc dircclion of thc magnctic forcc acting on 0icprrticlc at point P ?

,I

II

zd+r(out ofpagc)

P.------------r-It

I

, p_hvsicsB !!!$@

(c) Dciaminc rlc mrgniNdc of lhc mlRqmorq .od fundmot *r*o.'"d" fo* dirs otr .hs puicl€ 4 *,". , ," ,"* ,rlljw€rs

and samples

-T}tl rnagn+z finr Ac{r'g o lk pr+rdt af ?n^f P A Ert"b/o,,cf si,,,o ,fg=$4€:fro

" t

ffi";l'?,T""!T+?_" ,.^l ,f?n Va^d. fl"nl Uo, +t^Llktu",qlh4$Mzlt d-ai.d ,!t- ; ,*.#r";;..r Fq:tl/,8

o^il B-E]"S^gbff i=Hf, :zxa-4" FB= lloB= +U:!:t:'j'- o,lJifi +t

(d) Atr cterric rictd i! *0,,r *" .]*r*]Hl*c pmictc b bc &rc a poinl p.i. Wrh EfG@e !o thc @rdinrac s

tiil could r@mplish lllis? ryslcm in Figurc 2, whil is thc dircrion of thc clatric ti€ld il poinr p

1T1r< d16.+iu. o.t dtcirc F,ed. drl.l/ te to**f"! 6l ro*

tO 4 tl,t F$1, *,tkt trrcjn*rc trce arU etecl_^-c_frcL wa,lA coacel 'orir, ord p; O.* 'Lo

*--ii. Dccmie thc Dlgnisde of thc cl(

- I -

, t- *f" fitld io t-s of ftc drcn qu$dtics rd fundamcnrd consrbb.

Srcq [-"1=lF"l., p.= 2llo'$UoI.--"-

ond.sDcs,* t rc ^= O , o.nd cho"{e

"t ilrga*r-rk a g\ E - 2xl;'$U;f

- ----d

bzx1"14V"l

d-4: 2xlc-'l/.I

- d

m,Q'-T ------------T

Id

III

z+i(out ofPagc)

-Il\ n\qgnrha{ ftree actl^, oA th pr^hth d p",rfpIr trwx*1drw^ te {$-botton 4 +L f*q.. Cqft-fr*,'1

f'.--'l

.'. Tl.l. rno.lnitule "f

ftq de*nt fttd D :rto{yofd