备考全国高中物理竞赛11thipho1979电子教案.docx

备考全国高中物理竞赛11thipho1979电子教案.docx

《备考全国高中物理竞赛11thipho1979电子教案.docx》由会员分享，可在线阅读，更多相关《备考全国高中物理竞赛11thipho1979电子教案.docx（11页珍藏版）》请在冰豆网上搜索。

备考全国高中物理竞赛11thipho1979电子教案

备考2014年全国高中物理竞赛---11th_IPhO_1979

ProblemsoftheXIInternationalOlympiad,Moscow,1979

ThepublicationhasbeenpreparedbyProf.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.

TheoreticalProblems

Problem1.

AspacerocketwithmassM=12tismovingaroundtheMoonalongthecircularorbitattheheightofh=100km.Theengineisactivatedforashorttimetopassatthelunarlandingorbit.Thevelocityoftheejectedgasesu=104m/s.TheMoonradiusRM=1,7·103km,theaccelerationofgravityneartheMoonsurfacegM=1.7m/s2

Fig.1Fig.2

1）.WhatamountoffuelshouldbespentsothatwhenactivatingthebrakingengineatpointAofthetrajectory,therocketwouldlandontheMoonatpointB（Fig.1）?

2）.Inthesecondscenariooflanding,atpointAtherocketisgivenanimpulsedirectedtowardsthecenteroftheMoon,toputtherockettotheorbitmeetingtheMoonsurfaceatpointC（Fig.2）.Whatamountoffuelisneededinthiscase?

Problem2.

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）Canweseeareflectedlightpulsewithnakedeyeiftheenergyofsinglelaserpulse

E=1Jandthethresholdsensitivityofeyeisequaln=100lightquantum?

4）SupposetheMoon’ssurfacereflectsα=10%oftheincidentlightinthespatialangle2πsteradian,estimatetheadvantageofausingreflector.

ThedistancefromtheEarthtotheMoonisL=380000km.Thediameterofpupiloftheeyeis

dp=5mm.Plankconstantish=6.6ּ10-34Jּs.

ExperimentalProblem

Definetheelectricalcircuitschemeina“blackbox”anddeterminetheparametersofitselements.

Listofinstruments:

ADCsourcewithtension4.5V,anACsourcewith50Hzfrequencyandoutputvoltageupto30V,twomultimetersformeasuringAC/DCcurrentandvoltage,variableresistor,connectionwires.

SolutionofProblemsoftheXIInternationalOlympiad,Moscow,1979

SolutionofTheoreticalProblems

Problem1.

1）Duringtherocketmovingalongthecircularorbititscentripetalaccelerationiscreatedbymoongravityforce:

whereR=RM+histheprimaryorbitradius,v0-therocketvelocityonthecircularorbit:

Sinceityields

（1）

Therocketvelocitywillremainperpendiculartotheradius-vectorOAafterthebrakingenginesendstangentialmomentumtotherocket（Fig.1）.TherocketshouldthenmovealongtheellipticaltrajectorywiththefocusintheMoon’scenter.

DenotingtherocketvelocityatpointsAandBasvAandvBwecanwritetheequationsforenergyandmomentumconservationasfollows:

（2）

MvAR=MvBRM（3）

Solvingequations

（2）and（3）jointlywefind

Taking

（1）intoaccount,weget

.

ThustherocketvelocitychangeΔvatpointAmustbe

Sincetheengineswitchesonforashorttimethemomentumconservationlowinthesystem“rocket-fuel”canbewrittenintheform

（M–m1）Δv=m1u

wherem1istheburntfuelmass.

Thisyields

AllowforΔv<

2）Inthesecondcasethevectorisdirectedperpendiculartothevectorthusgiving

Basedontheenergyconservationlawinthiscasetheequationcanbewrittenas

（4）

andfromthemome