国际物理林匹克竞赛试题iphotheoreticalouestions

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1、IPhO1983TheoreticalQuestions1.Mechanics–ProblemI(8points)JumpingparticleAparticlemovesalongthepositiveaxis(one-dimensionalsituation)underaforcethat’sprojectiononisasrepresentedinthefigurebelow(asfunctionof).Attheoriginofaxisisplacedaperfectlyreflectingwal

2、l.Africtionforceofconstantmodulusactsanywheretheparticleissituated.Theparticlestartsfromthepointhavingthekineticenergy.a.Findthelengthofthepathoftheparticlebeforeitcomestoafinalstopb.Sketchthepotentialenergyoftheparticleintheforcefield.c.Drawqualitatively

3、thedependenceoftheparticlespeedasfunctionofhiscoordinate.2.Electricity–ProblemII(8points)DifferentkindofoscillationLet’sconsidertheelectriccircuitinthefigure,forwhich,,,and.Theswitchbeingclosedthecircuitiscoupledwithasourceofalternatingcurrent.Thecurrentf

4、urnishedbythesourcehasconstantintensitywhilethefrequencyofthecurrentmaybevaried.a.Findtheratiooffrequencyforwhichtheactivepowerincircuithasthemaximumvalueandthefrequencydifferenceofthefrequenciesandforwhichtheactivepowerinthecircuitishalfofthemaximumpower

5、.Page4from4IPhO1983TheoreticalQuestionsTheswitchisnowopen.Inthemomentimmediatelyaftertheswitchisopentheintensitiesofthecurrentsinthecoilsandand(thecurrentsflowasinthefigure);atthesamemoment,thepotentialdifferenceonthecapacitorwithcapacityis:a.Calculatethe

6、frequencyofelectromagneticoscillationincircuit;b.Determinetheintensityoftheelectriccurrentintheconductor;c.Calculatetheamplitudeoftheoscillationoftheintensityofelectriccurrentinthecoil.Neglectthemutualinductionofthecoils,andtheelectricresistanceofthecondu

7、ctors.Neglectthefasttransitionphenomenaoccurringwhentheswitchisclosedoropened.1.Optics–ProblemIII(7points)PrismsTwodispersiveprismshavingapexanglesandaregluedasinthefigurebelow().Thedependencesofrefractionindexesoftheprismsonthewavelengtharegivenbytherela

8、tions;werea.Determinethewavelengthoftheincidentradiationthatpassthroughtheprismswithoutrefractiononfaceatanyincidentangle;determinethecorrespondingrefractionindexesoftheprisms.Page4from4IPhO1983TheoreticalQuestionsa