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1ProblemsoftheXIInternationalOlympiad,Moscow,1979ThepublicationhasbeenpreparedbyProf.S.KozelandProf.V.Orlov(MoscowInstituteofPhysicsandTechnology)TheXIInternationalOlympiadinPhysicsforstudentstookplaceinMoscow,USSR,inJuly1979onthebasisofMoscowInstituteofPhysicsandTechnology(MIPT).Teamsfrom11countriesparticipatedinthecompetition,namelyBulgaria,Finland,Germany,Hungary,Poland,Romania,Sweden,Czechoslovakia,theDDR,theSFRYugoslavia,theUSSR.TheproblemsforthetheoreticalcompetitionhavebeenpreparedbyprofessorsofMIPT(V.Belonuchkin,I.Slobodetsky,S.Kozel).TheproblemfortheexperimentalcompetitionhasbeenworkedoutbyO.KabardinfromtheAcademyofPedagogicalSciences.Itispitythatmarkingschemeswerenotpreserved.TheoreticalProblemsProblem1.AspacerocketwithmassM=12tismovingaroundtheMoonalongthecircularorbitattheheightofh=100km.Theengineisactivatedforashorttimetopassatthelunarlandingorbit.Thevelocityoftheejectedgasesu=104m/s.TheMoonradiusRM=1,7·103km,theaccelerationofgravityneartheMoonsurfacegM=1.7m/s2Fig.1Fig.21).WhatamountoffuelshouldbespentsothatwhenactivatingthebrakingengineatpointAofthetrajectory,therocketwouldlandontheMoonatpointB(Fig.1)?2).Inthesecondscenariooflanding,atpointAtherocketisgivenanimpulsedirectedtowardsthecenteroftheMoon,toputtherockettotheorbitmeetingtheMoonsurfaceatpointC(Fig.2).Whatamountoffuelisneededinthiscase?2Problem2.Brassweightsareusedtoweighanaluminum-madesampleonananalyticalbalance.TheweighingisonesindryairandanothertimeinhumidairwiththewatervaporpressurePh=2·103Pa.Thetotalatmosphericpressure(P=105Pa)andthetemperature(t=20°C)arethesameinbothcases.Whatshouldthemassofthesamplebetobeabletotellthedifferenceinthebalancereadingsprovidedtheirsensitivityism0=0.1mg?Aluminumdensityρ1=2700kg/m3,brassdensityρ2=.8500kg/m3.Problem3.DuringtheSoviet-FrenchexperimentontheopticallocationoftheMoonthelightpulseofarubylaser(λ=0,69μm)wasdirectedtotheMoon’ssurfacebythetelescopewithadiameterofthemirrorD=2,6m.ThereflectorontheMoon’ssurfacereflectedthelightbackwardasanidealmirrorwiththediameterd=20cm.Thereflectedlightwasthencollectedbythesametelescopeandfocusedatthephotodetector.1)Whatmusttheaccuracytodirectthetelescopeopticalaxisbeinthisexperiment?2)WhatpartofemittedlaserenergycanbedetectedafterreflectionontheMoon,ifweneglectthelightlosesintheEarth’satmosphere?3)CanweseeareflectedlightpulsewithnakedeyeiftheenergyofsinglelaserpulseE=1Jandthethresholdsensitivityofeyeisequaln=100lightquantum?4)SupposetheMoon’ssurfacereflectsα=10%oftheincidentlightinthespatialangle2πsteradian,estimatetheadvantageofausingreflector.ThedistancefromtheEarthtotheMoonisL=380000km.Thediameterofpupiloftheeyeisdp=5mm.Plankconstantish=6.610-34s.ExperimentalProblemDefinetheelectricalcircuitschemeina“blackbox”anddeterminetheparametersofitselements.Listofinstruments:ADCsourcewithtension4.5V,anACsourcewith50Hzfrequencyandoutputvoltageupto30V,twomultimetersformeasuringAC/DCcurrentandvoltage,variableresistor,connectionwires.3SolutionofProblemsoftheXIInternationalOlympiad,Moscow,1979SolutionofTheoreticalProblemsProblem1.1)Duringtherocketmovingalongthecircularorbititscentripetalaccelerationiscreatedbymoongravityforce:RMvRMMGM202,whereR=RM+histheprimaryorbitradius,v0-therocketvelocityonthecircularorbit:RMGvM0Since2MMMRMGgityieldshRgRRRgvMMMMM20(1)Therocketvelocitywillremainperpendiculartotheradius-vectorOAafterthebrakingenginesendstangentialmomentumtotherocket(Fig.1).TherocketshouldthenmovealongtheellipticaltrajectorywiththefocusintheMoon’scenter.DenotingtherocketvelocityatpointsAandBasvAandvBwecanwritetheequationsforenergyandmomentumconservationasfollows:MMBMARMMGMvRMMGMv2222(2)MvAR=MvBRM(3)Solvingequations(2)and(3)jointlywefind)(2MMMARRRRMGvTaking(1)intoaccount,weget4MMARRRvv20.ThustherocketvelocitychangeΔvatpointAmustbe./2422121000smhRRvRRRvvvvMMMMASincetheengineswitchesonforashorttimethemomentumconservationlowinthesystem“rocket-fuel”canbewrittenintheform(M–m1)Δv=m1uwherem1istheburntfuelmass.Thisyieldsvuvm1AllowforΔvuwefindkg291Muvm2)InthesecondcasethevectorisdirectedperpendiculartothevectorthusgivingBasedontheenergyconservationlawinthiscasetheequationcanbewrittenasMMCMRGMMMvRGMMvvM2222220(4)andfromthemomentumconservationlawMCRMvRMv0.(5)Solvingequations(4)and(5)jointlyandtakingintoaccount(1)wefindm/s9722hRghRRRgvMMMM.Usingthemomentumconservationlawweobtainkg11622Muvm.Problem2.5AsampleandweightsareaffectedbytheArchimede’sbuoyancyforceofeitherdryorhumidairinthefirstandsecondcases,respectively.ThedifferenceinthescaleindicationΔFisdeterminedbythechangeofdifferenceoftheseforces.ThedifferenceofArchimede’sbuoyancyforcesindryair:gVFa'1Whereasinhumidairitis:whereΔV-thedifferenceinvolumesbetweenthesampleandtheweights,anda'anda-densitiesofdryandhumidair,respectively.ThenthedifferenceinthescaleindicationsΔFcouldbewrittenasfollows:'21aaVgFFF(1)Accordingtotheproblemconditionsthisdifferenceshouldbedistinguished,i.e.gmF0or0'mVgaa,wherefrom'0aamV.(2)Thedifferenceinvolumesbetweenthealum
本文标题:国际物理林匹克竞赛试题11th_IPhO_1979
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