Problems (Special Relativity)

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1、SJPOTrainingMechanicsProblemSetSpecialRelativityTanJingLongSitHanYuJune14,20141GeneralRound1.1RelativisticKinematics1.Acarofrestlength5mpassesthroughagarageofrestlength4m.DuetorelativisticLorentzcontraction,thecarisonly3mlonginthegarage'srestframe.Therearedoorsonbothendsofthegarage,

2、whichopenautomaticallywhenthefrontofthecarreachesthemandcloseautomaticallywhentherearpassesthem.Theopeningorclosingofeachdoorrequiresanegligibleamountoftime.(a)Whichofthefollowingstatementsisthebestresponsetothequestion:Wasthecareverinsideaclosedgarage?"A.No,becausethecarislongerth

3、anthegarageinallreferenceframes.B.No,becausetheLorentzcontractionisnotarealeect.C.Yes,becausethecarisshorterthanthegarageinallreferenceframes.D.Yes,becausetheanswertothequestioninthegaragesframemustapplyinallreferenceframes.E.Thereisnouniqueanswertothequestion,astheorderofdooropeni

4、ngsandclosingsdependsonthereferenceframe.(b)Thevelocityofthecarinthegarage'srestframeisA.0:4cB.0:6cC.0:8cD.GreaterthancE.Notdeterminablefromthedatagiven.2.A30-year-oldwomantakesatriponarocket,leavingher20-year-oldbrotherbehind.Shetravelsataspeedof0:8c,andisgonefor20years,accordingto

5、theyoungerbrother.Whenshereturns,howmanyyearsolder/youngerisshethanherbrother?13.RocketAismovingataconstantspeedof0:40crelativetoEarth.RocketBovertakesrocketAwithaconstantspeedof0:87cseenbyabugonrocketA.WhichofthefollowingistrueabouttheclocksintherocketswithrespecttothebuginrocketA?

6、A.ClocksinrocketAwilltickattwicetherateoftheclocksinrocketB.B.ClocksinrocketAwilltickathalftherateoftheclocksinrocketB.C.ClocksinrocketAwilltickatarateaboutone-fththatoftheclocksinrocketB.D.ClocksinrocketAwilltickataboutthesamerateastheclocksinrocketB.E.Noneoftheabove.4.Whichofthef

7、ollowingisaLorentztransformation?A.x0=4x,y0=y,z0=z,t0=0:25tB.x0=x0:75ct,y0=y,z0=z,t0=tC.x0=1:25x0:75ct,y0=y,z0=z,t0=1:25t0:75x=cD.x0=1:25x0:75ct,y0=y,z0=z,t0=0:75t1:25x=cE.Noneoftheabove.5.AspacetravelerismovingrelativetoEarthat0:8c,asmeauredintheEarth'sframeofreference.Inthefr

8、ameoftheEarth,inone