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2014F=maExam3 3.Anobjectofuniformdensity oatspartiallysubmergedsothat20%oftheobjectisabovethewater.A3Nforcepressesdownonthetopoftheobjectsothattheobjectbecomesfullysubmerged.Whatisthevolumeoftheobject?ThedensityofwaterisH2O=1000kg=m3.(A)Vobject=0:3L(B)Vobject=0:67L(C)Vobject=1:2L(D)Vobject=1:5L CORRECT(E)Vobject=3:0L4.Whatarethecorrectvaluesofthenumbersinthefollowingstatements?Assumetherearenoexternalforces,andtakeN=1tomeanthatthestatementcannotbemadeforanymeaningfulnumberofparticles.IfaparticleatrestexplodesintoN1orfewerparticleswithknownmasses,andthetotalkineticenergyofthenewparticlesisknown,thekineticenergyofeachofthenewparticlesiscompletelydetermined.IfaparticleatrestexplodesintoN2orfewerparticles,thevelocitiesofthenewparticlesmustlieinaline.IfaparticleatrestexplodesintoN3orfewerparticles,thevelocitiesofthenewparticlesmustlieinaplane.(A)N1=2,N2=1,N3=1(B)N1=1,N2=2,N3=3(C)N1=2,N2=2,N3=3 CORRECT(D)N1=3,N2=2,N3=3(E)N1=2,N2=3,N3=45.Aunicyclistgoesaroundacirculartrackofradius30mata(amazinglyfast!)constantspeedof10m=s.Atwhatangletotheleft(orright)ofverticalmusttheunicyclistleantoavoidfalling?Assumethattheheightoftheunicyclistismuchsmallerthantheradiusofthetrack.(A)9:46(B)9:59(C)18:4 CORRECT(D)19:5(E)70:5Copyrightc 2014AmericanAssociationofPhysicsTeachers 2014F=maExam10 18.Considerthefollowingdiagramofaboxandtwoweightscales.ScaleAsupportstheboxviaamasslessrope.Apulleyisattachedtothetopofthebox;asecondmasslessropepassesoverthepulley,oneendisattachedtotheboxandtheotherendtoscaleB.ThetwoscalesreadindicatethetensionsTAandTBintheropes.OriginallyscaleAreads30NewtonsandscaleBreads20Newtons. BoxFramePulleyScaleAScaleBTBTAIfanadditionalforcepullsdownonscaleBsothatthereadingincreasesto30Newtons,whatwillbethenewreadingonscaleA?(A)35Newtons(B)40Newtons CORRECT(C)45Newtons(D)50Newtons(E)60NewtonsAdaptedfromademonstrationbyRichardBerg.Copyrightc 2014AmericanAssociationofPhysicsTeachers 2014F=maExam11 19.Ahelicopteris yinghorizontallyatconstantspeed.Aperfectly exibleuniformcableissuspendedbeneaththehelicopter;airfrictiononthecableisnotnegligible.Whichofthefollowingdiagramsbestshowstheshapeofthecableasthehelicopter iesthroughtheairtotheright? (A) (B) CORRECT (C) (D) (E)20.Acrewofscientistshasbuiltanewspacestation.ThespacestationisshapedlikeawheelofradiusR,withessentiallyallitsmassMattherim.Whenthecrewarrives,thestationwillbesetrotatingataratethatcausesanobjectattherimtohaveradialaccelerationg,therebysimulatingEarth'ssurfacegravity.Thisisaccomplishedbytwosmallrockets,eachwiththrustTnewtons,mountedonthestation'srim.Howlongatimetdoesoneneedtoretherocketstoachievethedesiredcondition?(A)t=p gR3M=(2T)(B)t=p gRM=(2T) CORRECT(C)t=p gRM=T(D)t=p gR=M=T(E)t=p gRM=(T)AdaptedfromaprobleminPhysicsforScientistsandEngineersbyRichardWolfsonCopyrightc 2014AmericanAssociationofPhysicsTeachers 2014F=maExam12 21.Twopulleys(showningure)aremadeofthesamemetalwithdensity.PulleyAisauniformdiskwithradiusR.PulleyBisidenticalexceptacircleofR=2isremovedfromthecenter.WhentwoboxesM= m( �1)areconnectedoverthepulleysthroughamasslessropeandmovewithoutslipping,whatistheratiobetweentheaccelerationsinsystemAandB?ThemassofpulleyAisM+m. mMmMPulleyAPulleyB(A)aA=aB=47=48 CORRECT(B)aA=aB=31=32(C)aA=aB=15=16(D)aA=aB=9=16(E)aA=aB=3=422.AbodyofmassMandabodyofmassm Mareincircularorbitsabouttheircenterofmassunderthein uenceoftheirmutualgravitationalattractiontoeachother.ThedistancebetweenthebodiesisR,whichismuchlargerthanthesizeofeitherbody.Asmallamountofmatterm misremovedfromthebodyofmassmandtransferredtothebodyofmassM.Thetransferisdoneinsuchawaysothattheorbitsofthetwobodiesremaincircular,andremainseparatedbyadistanceR.Whichofthefollowingstatementsiscorrect?(A)Thegravitationalforcebetweenthetwobodiesincreases.(B)Thegravitationalforcebetweenthetwobodiesremainsconstant.(C)Thetotalangularmomentumofthesystemincreases.(D)Thetotalangularmomentumofthesystemremainsconstant.(E)Theperiodoftheorbitoftwobodiesremainsconstant. CORRECTCopyrightc 2014AmericanAssociationofPhysicsTeachers 2014F=maExam13 Thefollowinginformationappliestoquestions23and24A100kgastronautcarriesalauncherloadedwitha10kgbowlingball;thelauncherandtheastronaut'sspacesuithavenegligiblemass.Theastronautdiscoversthatringthelauncherresultsintheballmovingawayfromheratarelativespeedof50m=s.23.Whatistheimpulsedeliveredtotheastronautwhenringthelauncher?(A)455Ns CORRECT(B)500Ns(C)550Ns(D)5000Ns(E)5500Ns24.Theastronautintheprevioussituationisnowmovingat10m=s(asmeasuredinacertainframeofreference).Shewishestorethelaunchersothathervelocityturnsthroughaslargeanangleaspossible(inthisframeofreference).Whatisthismaximumangle?(Hint:adiagrammaybeuseful.)(A)24:4(B)26:6(C)27:0 CORRECT(D)30:0(E)180:025.Ablockwithmassmisreleasedfromrestatthetopofafrictionlessramp.Theblockstartsataheighth1abovethebaseoftheramp,slidesdowntheramp,andthenupasecondramp.Thecoecientofkineticfrictionbetweentheblockandthesecondrampisk.Ifbothrampsmakeanangleofwiththehorizontal,towhatheighth2abovethebaseofthesecondrampwilltheblockrise?(A)h2=(h1sin)=(kcos+sin) CORRECT(B)h2=(h1sin)=(k+sin)(C)h2=(h1sin)=(kcos2+sin)(D)h2=(h1sin)=(kcos2+sin2)(E)h2=(h1cos)=(ksin+cos)Copyrightc 2014AmericanAssociationofPhysicsTeachers