AP物理C真題28力學(xué)解答題

AP?PhysicsCMechanicsFILLIN"EnterSubject"SUBJECT1995-2008FreeresponseQuestionsThematerialsincludedinthesefilesareintendedforusebyAPteachersforcourseandexampreparationintheclassroom;permissionforanyotherusemustbesoughtfromtheAdvancedPlacementProgram?.Teachersmayreproducethem,inwholeorinpart,inlimitedquantities,forface-to-faceteachingpurposesbutmaynotmassdistributethematerials,electronicallyorotherwise.Thesematerialsandanycopiesmadeofthemmaynotberesold,andthecopyrightnoticesmustberetainedastheyappearhere.Thispermissiondoesnotapplytoanythird-partycopyrightscontainedherein.ThesematerialswereproducedbyEducationalTestingService?(ETS?),whichdevelopsandadministerstheexaminationsoftheAdvancedPlacement

ProgramfortheCollegeBoard.TheCollegeBoardandEducationalTestingService(ETS)arededicatedtotheprincipleofequalopportunity,andtheir

programs,services,andemploymentpoliciesareguidedbythatprinciple.TheCollegeBoardisanationalnonprofitmembershipassociationdedicatedtopreparing,inspiring,andconnectingstudentstocollegeandopportunity.

Foundedin1900,theassociationiscomposedofmorethan4,200schools,colleges,universities,andothereducationalorganizations.Eachyear,the

CollegeBoardservesoverthreemillionstudentsandtheirparents,22,000highschools,and3,500colleges,throughmajorprogramsandservicesin

collegeadmission,guidance,assessment,financialaid,enrollment,andteachingandlearning.Amongitsbest-knownprogramsaretheSAT?,the

PSAT/NMSQT?,andtheAdvancedPlacementProgram?(AP?).TheCollegeBoardiscommittedtotheprinciplesofequityand

excellence,andthatcommitmentisembodiedinallofitsprograms,services,activities,andconcerns.APIELisatrademarkownedbytheCollegeEntranceExaminationBoard.PSAT/NMSQTisaregisteredtrademarkjointlyownedbytheCollegeEntranceExaminationBoardandtheNationalMeritScholarshipCorporation.EducationalTestingServiceandETSareregisteredtrademarksofEducationalTestingService.1995M1.A5kilogramballinitiallyrestsattheedgeofa2metermeterhighfrictionlesstable,asshownabove.Ahardplasticcubeofmass0.5kilogramslidesacrossthetableataspeedof26meterspersecondandstrikestheball,causingtheballtoleavethetableinthedirectioninwhichthecubewasmoving.Thefigurebelowshowsagraphoftheforceexertedontheballbythecubeasafunctionoftime.a.Determinethetotalimpulsegiventotheball.b.Determinethehorizontalvelocityoftheballimmediatelyafterthecollision.c.Determinethefollowingforthecubeimmediatelyafterthecollision. i.Itsspeed ii.Itsdirectionoftravel(rightorleft),ifmovingd.Determinethekineticenergydissipatedinthecollision.e.Determinethedistancebetweenthetwopointsofimpactoftheobjectswiththefloor.1995M2.AparticleofmassmmovesinaconservativeforcefielddescribedbythepotentialenergyfunctionU(r)=a(r/b+b/r),whereaandbarepositiveconstantsandristhedistancefromtheorigin.ThegraphofU(r)hasthefollowingshape.a.Intermsoftheconstantsaandb,determinethefollowing. i.Thepositionroatwhichthepotentialenergyisaminimum ii.TheminimumpotentialenergyUob.Sketchthenetforceontheparticleasafunctionofronthegraphbelow,consideringaforcedirectedawayfromtheorigintobepositive,andaforcedirectedtowardtheorigintobenegative.Theparticleisreleasedfromrestatr=ro/2c.IntermsofUoandm,determinethespeedoftheparticlewhenitisatr=ro.d.Writetheequationorequationsthatcouldbeusedtodeterminewhere,ifever,theparticlewillagaincometorest.Itisnotnecessarytosolveforthisposition.e.Brieflyandqualitativelydescribethemotionoftheparticleoveralongperiodoftime.1995M3.Twostars,AandB.areincircularorbitsofradiiraandrb,respectively,abouttheircommoncenterofmassatpointP,asshownabove.EachstarhasthesameperiodofrevolutionT.Determineexpressionsforthefollowingthreequantitiesintermsofra,rb,T,andfundamentalconstants.a.ThecentripetalaccelerationofstarAb.ThemassMbofstarBc.ThemassMaofstarADetermineexpressionsforthefollowingtwoquantitiesintermsofMa,Mb,ra,rb,T,andfundamentalconstants.d.Themomentofinertiaofthetwostarsystemaboutitscenterofmass.e.Theangularmomentumofthesystemaboutthecenterofmass.1996M1.Athin,flexiblemetalplateattachedatoneendtoaplatform,asshownabove,canbeusedtomeasuremass.Whenthefreeendoftheplateispulleddownandreleased,itvibratesinsimpleharmonicmotionwithaperiodthatdependsonthemassattachedtotheplate.Tocalibratetheforceconstant,objectsofknownmassareattachedtotheplateandtheplateisvibrated,obtainingthedatashownbelow.a.Fillintheblanksinthedatatable.b.Onthegraphbelow,plotT2versusmass.Drawonthegraphthelinethatisyourestimateofthebeststraightlinefittothedatapoints.c.Anobjectwhosemassisnotknownisvibratedontheplate,andtheaveragetimefortenvibrationsismeasuredtobe16.1s.Fromyourgraph,determinethemassoftheobject.Writeyouranswerwithareasonablenumberofsignificantdigits.d. Explainhowonecoulddeterminetheforceconstantofthemetalplate.e.CanthisdevicebeusedtomeasuremassaboardthespaceshuttleColumbiaasitorbitstheEarth?Explainbriefly.f.IfColumbiaisorbitingat0.3x106mabovetheEarth'ssurface,whatistheaccelerationofColumbiaduetotheEarth'sgravity?(RadiusofEarth=6.4x106m,massofEarth=6.0x1024kg)g. Sincetheanswertopart(f)isnotzero,brieflyexplainwhyobjectsaboardtheorbitingColumbiaseemweightless.1996M2.A300kgboxrestsonaplatformattachedtoaforklift,shownabove.Startingfromrestatat2a. Determinetheupwardforceexertedbythehorizontalplatformontheboxasitislowered.Attimet=0,theforkliftalsobeginstomoveforwardwithanaccelerationof2m/s2whileloweringtheboxasdescribedabove.Theboxdoesnotsliportipover.b. Determinethefrictionalforceonthebox.c. Giventhattheboxdoesnotslip,determinetheminimumpossiblecoefficientoffrictionbetweenthe boxandtheplatform.d. Determineanequationforthepathoftheboxthatexpressesyasafunctionofx(andnotoft), assumingthat,attimet=0,theboxhasahorizontalpositionx=0andaverticalpositiony=2m abovetheground,withzerovelocity.e. Ontheaxesbelowsketchthepathtakenbythebox1996M3.ConsiderathinuniformrodofmassMandlengthl,asshownabove.a. ShowthattherotationalinertiaoftherodaboutanaxisthroughitscenterandperpendiculartoitslengthisMl2/12.TherodisnowgluedtoathinhoopofmassMandradiusR/2toformarigidassembly,asshownabove.ThecentersoftherodandthehoopcoincideatpointP.TheassemblyismountedonahorizontalaxlethroughpointPandperpendiculartothepage.b. Whatistherotationalinertiaoftherodhoopassemblyabouttheaxle?Severalturnsofstringarewrappedtightlyaroundthecircumferenceofthehoop.Thesystemisatrestwhenacat,alsoofmassM,grabsthefreeendofthestringandhangsverticallyfromitwithoutswingingasitunwinds,causingtherodhoopassemblytorotate.Neglectfrictionandthemassofthestring.c. DeterminethetensionTinthestring.d. Determinetheangularaccelerationaoftherodhoopassembly.e. Determinethelinearaccelerationofthecat.f. AfterdescendingadistanceH=5l/3,thecatletsgoofthestring.Atthatinstant,whatistheangular momentumofthecataboutpointP?1997M1.Anonlinearspringiscompressedhorizontally.ThespringexertsaforcethatobeystheequationF(x)=Ax?,wherexisthedistancefromequilibriumthatthespringiscompressedandAisaconstant.Aphysicsstudentrecordsdataontheforceexertedbythespringasitiscompressedandplotsthetwographsbelow,whichincludethedataandthestudent'sbestfitcurves.a.Fromoneorbothofthegivengraphs,determineA.Besuretoshowyourworkandspecifytheunits.b.i.Determineanexpressionfortheworkdoneincompressingthespringadistancex. ii.Explaininafewsentenceshowyoucoulduseoneorbothofthegraphstoestimateanumericalanswertopart(b)iforagivenvalueofx.c.Thespringismountedhorizontallyonacountertopthatis1.3mhighsothatitsequilibriumpositionisjustattheedgeofthecountertop.Thespringiscompressedsothatitstores0.2Jofenergyandisthenusedtolaunchaballofmass0.10kghorizontallyfromthecountertop.Neglectingfriction,determinethehorizontaldistancedfromtheedgeofthecountertoptothepointwherethehallstrikesthefloor1997M2.Anopentoprailroadcar(initiallyemptyandofmassMo)rollswithnegligiblefrictionalongastraighthorizontaltrackandpassesunderthespoutofasandconveyor.Whenthecarisundertheconveyor,sandisdispensedfromtheconveyorinanarrowstreamatasteadyrateM/t=Candfallsverticallyfromanaverageheighthabovetheflooroftherailroadcar.Thecarhasinitialspeedvoandsandisfillingitfromtimet=0tot=T.Expressyouranswerstothefollowingintermsofthegivenquantitiesandg.a.DeterminethemassMofthecarplusthesandthatitcatchesasafunctionoftimetfor0<t<T.b.Determinethespeedvofthecarasafunctionoftimetfor0<t<T.c.i.DeterminetheinitialkineticenergyKioftheemptycar. ii.DeterminethefinalkineticenergyKfofthecaranditsload. iii.Iskineticenergyconserved?Explainwhyorwhynot.d.Determineexpressionsforthenormalforceexertedonthecarbythetracksatthefollowingtimes. i.Beforet=0 ii.For0<t<T iii.Aftert=T1997M3.AsolidcylinderwithmassM,radiusR,androtationalinertia?MR2rollswithoutslippingdowntheinclinedplaneshownabove.ThecylinderstartsfromrestataheightH.Theinclinedplanemakesananglewiththehorizontal.ExpressallsolutionsintermsofM,R,H,,andg.a.Determinethetranslationalspeedofthecylinderwhenitreachesthebottomoftheinclinedplane.b.Onthefigurebelow,drawandlabeltheforcesactingonthecylinderasitrollsdowntheinclinedplaneYourarrowshouldbeginatthepointofapplicationofeachforce.c.Showthattheaccelerationofthecenterofmassofthecylinderwhileitisrollingdowntheinclinedplaneis(2/3)gsin.d.Determinetheminimumcoefficientoffrictionbetweenthecylinderandtheinclinedplanethatisrequiredforthecylindertorollwithoutslipping.e.Thecoefficientoffrictionisnowmadelessthanthevaluedeterminedinpart(d),sothatthecylinderbothrotatesandslips.i.Indicatewhetherthetranslationalspeedofthecylinderatthebottomoftheinclinedplaneisgreaterthan,lessthan,orequaltothetranslationalspeedcalculatedinpart(a).Justifyyouranswer.ii.Indicatewhetherthetotalkineticenergyofthecylinderatthebottomoftheinclinedplaneisgreaterthan,lessthan,orequaltothetotalkineticenergyforthepreviouscaseofrollingwithoutslipping.Justifyyouranswer.1998M1.Twoglidersmovefreelyonanairtrackwithnegligiblefriction,asshownabove.GliderAhasamassof0.90kgandgliderBhasamassof0.60kg.Initially,gliderAmovestowardgliderB,whichisatrest.AspringofnegligiblemassisattachedtotherightsideofgliderA.StrobephotographyisusedtorecordsuccessivepositionsofgliderAat0.10sintervalsoveratotaltimeof2.00s,duringwhichtimeitcollideswithgliderB.ThefollowingdiagramrepresentsthedataforthemotionofgliderA.PositionsofgliderAattheendofeach0.10sintervalareindicatedbythesymbolAagainstametricruler.Thetotalelapsedtimetaftereach0.50sisalsoindicated.a. DeterminetheaveragespeedofgliderAforthefollowingtimeintervals. i.0.L0sto0.30s ii.0.90sto1.10s iii.1.70sto1.90sb. Ontheaxesbelow,sketchagraph,consistentwiththedataabove,ofthespeedofgliderAasafunctionoftimetforthe2.00sinterval.[Continuedonnextpage]

c. i.UsethedatatocalculatethespeedofgliderBimmediatelyafteritseparatesfromthespring. ii.Ontheaxesbelow,sketchagraphofthespeedofgliderBasafunctionoftimet.AgraphofthetotalkineticenergyKforthetwoglidersystemoverthe2.00sintervalhasthefollowingshape.Koisthetotalkineticenergyofthesystemattimet=0.d. i.Isthecollisionelastic?Justifyyouranswer. ii.Brieflyexplainwhythereisaminimuminthekineticenergycurveatt=1.00s.

1998M2.AspaceshuttleastronautinacircularorbitaroundtheEarthhasanassemblyconsistingoftwosmalldensespheres,eachofmassm,whosecentersareconnectedbyarigidrodoflengthlandnegligiblemass.Theastronautalsohasadevicethatwilllaunchasmalllumpofclayofmassmatspeedv0.Expressyouranswersintermsofm,v0l.andfundamentalconstants.a. Initially,theassemblyis"floating"freelyatrestrelativetothecabin,andtheastronautlaunchestheclaylumpsothatitperpendicularlystrikesandstickstothemidpointoftherod,asshownabove.i. Determinethetotalkineticenergyofthesystem(assemblyandclaylump)afterthecollision.ii. Determinethechangeinkineticenergyasaresultofthecollision.b. Theassemblyisbroughttorest,theclaylumpremoved,andtheexperimentisrepeatedasshownabove,withtheclaylumpstrikingperpendiculartotherodbutthistimestickingtooneofthespheresoftheassembly.i. Determinethedistancefromtheleftendoftherodtothecenterofmassofthesystem(assemblyandclaylump)immediatelyafterthecollision.(Assumethattheradiiofthespheresandclaylumparemuchsmallerthantheseparationofthespheres.)ii. Onthefigureabove,indicatethedirectionofthemotionofthecenterofmassimmediatelyafterthe collision.iii. Determinethespeedofthecenterofmassimmediatelyafterthecollision. iv. Determinetheangularspeedofthesystem(assemblyandclaylump)immediatelyafterthecollision. v. Determinethechangeinkineticenergyasaresultofthecollision.1998M3.Block1ofmassm1isplacedonblock2ofmassm2whichisthenplacedonatable.Astringconnectingblock2toahangingmassMpassesoverapulleyattachedtooneendofthetable,asshownabove.Themassandfrictionofthepulleyarenegligible.Thecoefficientsoffrictionbetweenblocks1and2andbetweenblock2andthetabletoparenonzeroandaregiveninthefollowingtable.Expressyouranswersintermsofthemasses,coefficientsoffriction,andg,theaccelerationduetogravity.a. SupposethatthevalueofMissmallenoughthattheblocksremainatrestwhenreleased.Foreachofthefollowingforces,determinethemagnitudeoftheforceanddrawavectorontheblockprovidedtoindicatethedirectionoftheforceifitisnonzero. i.ThenormalforceN1exertedonblock1byblock2 ii.Thefrictionforcef1exertedonblock1byblock2 iii.TheforceTexertedonblock2bythestring iv.ThenormalforceN2exertedonblock2bythetabletop v.Thefrictionforcef2exertedonblock2bythetabletop[Continuednextpage]b.DeterminethelargestvalueofMforwhichtheblockscanremainatrest.c. NowsupposethatMislargeenoughthatthehangingblockdescendswhentheblocksarereleased.Assumethatblocks1and2aremovingasaunit(noslippage).Determinethemagnitudeaoftheiracceleration.d. NowsupposethatMislargeenoughthatasthehangingblockdescends,block1isslippingonblock2.Determineeachofthefollowing. i.Themagnitudea1oftheaccelerationofblock1 ii.Themagnitudea2oftheaccelerationofblock21999M1Inalaboratoryexperiment,youwishtodeterminetheinitialspeedofadartjustafteritleavesadartgun.Thedart,ofmassm,isfiredwiththegunveryclosetoawoodenblockofmassM0whichhangsfromacordoflengthlandnegligiblemass,asshownabove.Assumethesizeoftheblockisnegligiblecomparedtol,andthedartismovinghorizontallywhenithitstheleftsideoftheblockatitscenterandbecomesembeddedinit.Theblockswingsuptoamaximumanglefromthevertical.Expressyouranswerstothefollowingintermsofm,M0,l,max,andg.a. Determinethespeedv0ofthedartimmediatelybeforeitstrikestheblock.b. Thedartandblocksubsequentlyswingasapendulum.Determinethetensioninthecordwhenitreturnstothelowestpointoftheswing.c. Atyourlabtableyouhaveonlythefollowingadditionalequipment.Meterstick Stopwatch SetofknownmassesProtractor 5mofstring FivemoreblocksofmassM0SpringWithoutdestroyingordisassemblinganyofthisequipment,designanotherpracticalmethodfordeterminingthespeedofthedartjustafteritleavesthegun.Indicatethemeasurementsyouwouldtake,andhowthespeedcouldbedeterminedfromthesemeasurements.d. Thedartisnowshotintoablockofwoodthatisfixedinplace.TheblockexertsaforceFonthedartthatisproportionaltothedart'svelocityvandintheoppositedirection,thatisF=bv,wherebisaconstant.DeriveanexpressionforthedistanceLthatthedartpenetratesintotheblock,intermsofm,v0,andb.1999M2Aspherical,nonrotatingplanethasaradiusRandauniformdensitythroughoutitsvolume.Supposeanarrowtunnelweredrilledthroughtheplanetalongoneofitsdiameters,asshowninthefigureabove,inwhichasmallballofmassmcouldmovefreelyundertheinfluenceofgravity.Letrbethedistanceoftheballfromthecenteroftheplanet.a. Showthatthemagnitudeoftheforceontheballatadistancer<RfromthecenteroftheplanetisgivenbyF=Cr.whereC=4/3(Gm).b. Ontheaxesbelow,sketchtheforceFontheballasafunctionofdistancerfromthecenteroftheplanet.TheballisdroppedintothetunnelfromrestatpointPattheplanet'ssurface.c. Determinetheworkdonebygravityastheballmovesfromthesurfacetothecenteroftheplanet.d. Determinethespeedoftheballwhenitreachesthecenteroftheplanet.e. Fullydescribethesubsequentmotionoftheballfromthetimeitreachesthecenteroftheplanet.f. WriteanequationthatcouldbeusedtocalculatethetimeittakestheballtomovefrompointPtothecenteroftheplanet.Itisnotnecessarytosolvethisequation.1999M3Asshownabove,auniformdiskismountedtoanaxleandisfreetorotatewithoutfriction.Athinuniformrodisrigidlyattachedtothedisksothatitwillrotatewiththedisk.Ablockisattachedtotheendoftherod.Propertiesofthedisk,rod,andblockareasfollows.Disk: mass=3m,radius=R,momentofinertiaaboutcenterID2Rod: mass=m,length=2R,momentofinertiaaboutoneendIR=4/3(mR2)Block: mass=2mThesystemisheldinequilibriumwiththerodatanangle0tothevertical,asshownabove,byahorizontalstringofnegligiblemasswithoneendattachedtothediskandtheothertoawall.Expressyouranswerstothefollowingintermsofm,R,0,andg.a. Determinethetensioninthestring.Thestringisnowcut,andthediskrodblocksystemisfreetorotate.b. Determinethefollowingfortheinstantimmediatelyafterthestringiscut.i.Themagnitudeoftheangularaccelerationofthediskii.ThemagnitudeofthelinearaccelerationofthemassattheendoftherodAsthediskrotates,therodpassesthehorizontalpositionshownabove.c. Determinethelinearspeedofthemassattheendoftherodfortheinstanttherodisinthehorizontalposition.(2000M1)Youareconductinganexperimenttomeasuretheaccelerationduetogravityguatanunknownlocation.Inthemeasurementapparatus,asimplependulumswingspastaphotogatelocatedatthependulum'slowestpoint,whichrecordsthetimet10forthependulumtoundergo10fulloscillations.Thependulumconsistsofasphereofmassmattheendofastringandhasalengthl.Therearefourversionsofthisapparatus,eachwithadifferentlength.Allfourareattheunknownlocation,andthedatashownbelowaresenttoyouduringtheexperiment.

(cm)t10(s)T(s)T2(s2)121832a. Foreachpendulum,calculatetheperiodTandthesquareoftheperiod.Useareasonablenumberofsignificantfigures.Entertheseresultsinthetableabove.b. Ontheaxesbelow,plotthesquareoftheperiodversusthelengthofthependulum.Drawabestfitstraightlineforthisdata.c. Assumingthateachpendulumundergoessmallamplitudeoscillations,fromyourfitdeterminetheexperimentalvaluegexpoftheaccelerationduetogravityatthisunknownlocation.Justifyyouranswer.d. Ifthemeasurementapparatusallowsadeterminationofguthatisaccuratetowithin4%,isyourexperimentalvalueinagreementwiththevalue9.80m/s2?Justifyyouranswer.e. SomeoneinformsyouthattheexperimentalapparatusisinfactnearEarth'ssurface,butthattheexperimenthasbeenconductedinsideanelevatorwithaconstantaccelerationa.Assumingthatyourexperimentalvaluegisexact,determinethemagnitudeanddirectionoftheelevator'sacceleration.

2000M2.Arubberballofmassmisdroppedfromacliff.Astheballfalls,itissubjecttoairdrag(aresistiveforcecausedbytheair).Thedragforceontheballhasmagnitudebv2,wherebisaconstantdragcoefficientandvistheinstantaneousspeedoftheball.Thedragcoefficientbisdirectlyproportionaltothecrosssectionalareaoftheballandthedensityoftheairanddoesnotdependonthemassoftheball.Astheballfalls,itsspeedapproachesaconstantvaluecalledtheterminalspeed.a. Onthefigurebelow,drawandlabelalltheforcesontheballatsomeinstantbeforeitreachesterminalspeed.b. Statewhetherthemagnitudeoftheaccelerationoftheballofmassmincreases,decreases,orremainsthesameastheballapproachesterminalspeed.Explain.c. Write,butdoNOTsolve,adifferentialequationfortheinstantaneousspeedvoftheballintermsoftimet,thegivenquantities,andfundamentalconstants.d. Determinetheterminalspeedvtintermsofthegivenquantitiesandfundamentalconstants.e. Determinetheenergydissipatedbythedragforceduringthefalliftheballisreleasedatheighthandreachesitsterminalspeedbeforehittingtheground,intermsofthegivenquantitiesandfundamentalconstants.2000M3.ApulleyofradiusR1androtationalinertiaI1ismountedonanaxlewithnegligiblefriction.Alightcordpassingoverthepulleyhastwoblocksofmassmattachedtoeitherend,asshownabove.Assumethatthecorddoesnotsliponthepulley.Determinetheanswerstoparts(a)and(b)intermsofm,R1,I1,andfundamentalconstants.a.DeterminethetensionTinthecord.b.Oneblockisnowremovedfromtherightandhungontheleft.Whenthesystemisreleasedfromrest,thethreeblocksontheleftacceleratedownwardwithanaccelerationg/3.Determinethefollowing.i.ThetensionT3inthesectionofcordsupportingthethreeblocksontheleftii.ThetensionTlinthesectionofcordsupportingthesingleblockontherightiii.TherotationalinertiaI1ofthepulley[Continuedonnextpage]c. Theblocksarenowremovedandthecordistiedintoaloop,whichispassedaroundtheoriginalpulleyandasecondpulleyofradius2R1androtationalinertia16I1.Theaxisoftheoriginalpulleyisattachedtoamotorthatrotatesitatangularspeed1,whichinturncausesthelargerpulleytorotate.Theloopdoesnotsliponthepulleys.DeterminethefollowingintermsofI1,RI,and1.i.Theangularspeed2ofthelargerpulleyii.TheangularmomentumL2ofthelargerpulleyiii.Thetotalkineticenergyofthesystem2001M1.Amotionsensorandaforcesensorrecordthemotionofacartalongatrack,asshownabove.Thecartisgivenapushsothatitmovestowardtheforcesensorandthencollideswithit.Thetwosensorsrecordthevaluesshowninthefollowinggraphs.a.Determinethecart'saverageaccelerationbetweent=0.33sandt=0.37s.b.Determinethemagnitudeofthechangeinthecart'smomentumduringthecollision.c.Determinethemassofthecart.d.Determinetheenergylostinthecollisionbetweentheforcesensorandthecart

2001M2.AnexplorerplansamissiontoplaceasatelliteintoacircularorbitaroundtheplanetJupiter,whichhasmassMJ=1.90x1027kgandradiusRJ=7.14x107m.a.IftheradiusoftheplannedorbitisR,useNewton'slawstoshoweachofthefollowing.i. Theorbitalspeedoftheplannedsatelliteisgivenbyii. Theperiodoftheorbitisgivenbyb.Theexplorerwantsthesatellite'sorbittobesynchronizedwithJupiter'srotation.ThisrequiresanequatorialorbitwhoseperiodequalsJupiter'srotationperiodof9hr51min=3.55x104s.Determinetherequiredorbitalradiusinmeters.c. Supposethattheinjectionofthesatelliteintoorbitislessthanperfect.Foraninjectionvelocitythatdiffersfromthedesiredvalueineachofthefollowingways,sketchtheresultingorbitonthefigure.(JisthecenterofJupiter,thedashedcircleisthedesiredorbit,andPistheinjectionpoint.)Also,describetheresultingorbitqualitativelybutspecifically.i. Whenthesatelliteisatthedesiredaltitudeovertheequator,itsvelocityvectorhasthecorrectdirection,butthespeedisslightlyfasterthanthecorrectspeedforacircularorbitofthatradius.ii. Whenthesatelliteisatthedesiredaltitudeovertheequator,itsvelocityvectorhasthecorrectdirection,butthespeedisslightlyslowerthanthecorrectspeedforacircularorbitofthatradius.2001M3.Alightstringthatisattachedtoalargeblockofmass4mpassesoverapulleywithnegligiblerotationalinertiaandiswrappedaroundaverticalpoleofradiusr,asshowninExperimentAabove.Thesystemisreleasedfromrest,andastheblockdescendsthestringunwindsandtheverticalpolewithitsat