大学物理试卷含答案 6页

得分评阅人大学物理试卷一、基础知识题（共4小题，每小题10分，共40分）1.FindtheanglebetweenthetwovectorsA=2i-2^j+3kandB=3i+2j-2kSolutionA-B=ABcos0=ABr+ABv+ABZaayyzzAxBx+AB+AzBz4cos3==——=-0.235AB173=180°-arccos0.235=103.6°2.Supposeyoutrytomoveyourcratefullofequipmentbytyingaropearounditandpullingupwardatanangleabovethehorizontalontherope.Findtheangleatwhichyouneedtheminimumforcetokeepthecratemovingwithconstantvelocity.(“&=0-44)Solutionmg=N+Fsina[Fcosa=NjUk，(cosa+Pksina)=0da,二mg山cosa+]LLksinor,一sina+以cosQ=0tanoc—jUk=0.44,oc—23.7°\n1.ItispossibletobankacurvewithradiusRatjusttherightanglesothatacartravelingatacertainspeedvcansafelymaketheturnevenifthereisnofriction.Atwhatangle0shouldthecurvebebanked?Solutiontan/3=v21gRmgtan0=mv2/RP二arctanv2/gR2.Whatisthethermalefficiencyofanenginethatoperatesbytakingnmolesofadiatomicidealgasthroughthecycleofa—b—>c—a?SolutionQ{=nCv(Tb-TJ=n^R^-T^=^RT07Q2=nCm=n寸・(6T°-2TJ=14冰W=p0V0=nRT°wW2"QhQ+@33\n得分评阅人二、计算题（共2小题，每小题10分，共20分）Aprimitiveyo-yoismadebywrappingastringseveraltimesaroundasolidcylinderwithmassMandradiusR.Youholdtheendofthestringstationarywhilereleasingthecylinderwithnoinitialmotion.Thestringunwindsbutdocsnotsliporstretchasthecylinderdropsandrotates.Findthetensioninthestringandthespeedofthecenterofmassofthesolidcylinderafterithasdroppedadistanceh.Solution=Ra[Mg-T=Macmi=Lmr\TR=la2丁1册2T=~Mg,acm=-g2.A50.0-kgwomanstandsupina60>0-kgcanoeoflength5.00m.ShewalksfromapointLOOmfromoneendtoapoint1.00mfromtheotherend.Ifresistancetomotionofthecanoeinthewatercanbeneglected,howfardoesthecanoemoveduringthisprocess?Solution-3x50.0L—50.0+60.0=136(m)mv=MV，ml=ML50.0x(3.00-L)=60.0xLThecanoemoves1.36metersintheoppositedirection.\n2.A50.0-kgwomanstandsupina60>0-kgcanoeoflength5.00m.ShewalksfromapointLOOmfromoneendtoapoint1.00mfromtheotherend.Ifresistancetomotionofthecanoeinthewatercanbeneglected,howfardoesthecanoemoveduringthisprocess?Solution-3x50.0L—50.0+60.0=136(m)mv=MV，ml=ML50.0x(3.00-L)=60.0xLThecanoemoves1.36metersintheoppositedirection.\n得分评阅人三、叙述题（10分）Ifawomaninatraincouldwalkdowntheaisleat030candthetraincouldmoveat0.90cinthesamedirection,thenwhatwouldbeherspeedrelativetotheground?Isit1.20cor0.94c?ExplainintermsofrangeofvalidityaboutNewtonianmechanics.SolutionItwouldbe0.94C・Becausewhenaspeedapproachesthespeedoflight,thevelocity-additionequationofNewtonianmechanicshastobemodified・Itturnsoutthatthewomanwouldmoveat0.94Cratherthan1.20Crelativetotheground.得分评阅人综合应用题（共2小题,每小题15分,共30分）LInacylinder，anidealmonatomicgasexpandsuntilitsvolumedoubles.Iftheexpansionisa)isothermal;b)adiabatic;c)isobaric.Inwhichcaseistheabsolutevalueofthechangeininternalenergyofthegasgreatest?Least?Why?SolutionInisobaricexpansion,theabsolutevalueofthechangeininternalenergyisthegreatest(isobaricT—2T，adiabatic\nT—0.63T)，whileinisothermalexpansion,theleastCT^T)・2.AblockwithmassMattachedtoahorizontalspringwithforceconstantkismovingwithsimpleharmonicmotionhavingamplitudeA.Attheinstantwhentheblockisatoneendofitspath,alumpofputtywithmassmisdroppedverticallyontotheblockfromaverysmallheightandstickstoit.Findthenewamplitudeandperiod.SolutionT=171