国际物理林匹克竞赛试题Experiment1and2SolutionSUMMARYSHEET

1SUMMARYSHEETEXPERIMENT11.FORWATERANDREDLIGHTATEXTREMEENDOFSPECTRUMk=1FirstOrderRainbowθ1=129.0°137.0°1=137.0±5.0°k=2SecondOrderRainbowθ2=129.0°2=231.0±3.0°k=5FifthOrderRainbowθ5=126.0°5=486.0±4.0°2.LIQUIDSAANDBUSINGSECONDORDERRAINBOWSForLiquidAθ2=105.0°2=255.0±3.0°ForLiquidBθ2=89.5°2=270.5±3.0°Gradientofgraph=0.84±0.07Extrapolated,n=2,θ2,valueof=304±25oθ2=0.0..o012345500400300200100okkFigureE1.1.2=0.0..oForn=120.60.70.80.91.0Exacttheoryvalue1.00.90.80.71/nFigureE1.23SUMMARYSHEETEXPERIMENT2Isthetotalmomentumconserved?YES/NOAccuracyofcomputercalculation1.00000018.01000.002%0:1(RMSvelocity=0.1)TimeTotalEnergy0-1.614992-1.628864-1.628786-1.6230112-1.6288218-1.6259924-1.6279630-1.6270350-1.6275370-1.6267690-1.62580130-1.62713180-1.62409Doesthesystemconserveenergy?YES/NO(~±1%)EquilibriumvalueofEk*EquilibriumtimeSD(Average24to180)(seeFig.E2.1)=0.534±0.05(10to20)1.0ValueofSrecorded20,e.g.60Valueof(forSD=60)(seeFig.E2.2)=0.503Accuracyof=±0.02Forwhattimenumberrangeisgraph,obtainedusingfirstvalueofSR,linear?SZ=18to244Gradientofthisgraphinlinearregion0.027to0.47Accuracyofgradient=0.002GradientofAVERAGER2inlinearregion=0.035Accuracyofthisgradient=±0.01*deleteasappropriateIsthesystemaliquid/solid?Liquid/Solid*MeanMomentumofthesystematrequestedsteps(S)SVX,1VY,1PXPY00.00000000.00000000.0000000.000000400.00000100.00000160.0000480.000077.p.E.800.00000180.00000010.0000860.0000051200.00000140.00000070.0000670.0000341600.00000160.00000100.0000770.000048-2-3K.E.Energyofthesystematrequestedsteps(S)SVX,2VY,2KE=T*UE=TotalEnergy00.01738740.01428510.760140-4.7502660-1.6149920.01625060.01310250.704474-4.6666675-1.6288640.01249660.00895620.514867-4.2873015-1.62878¢080120time$60.00774050.00391130.279643-3.8053113-1.62301120.01187400.01209590.575278-4.4081878-1.62882FigureE2.1180.00995790.00758540.421039-4.0940627-1.62599240.01085770.01169780.541332-4.3385782-1.62796VariationofK.EandP.E300.0126065010003400.543372-4.3407997-1.62703500.01271380.01033340.553133-4.3613165-1.62753700.00886570.01582920.592678-4.4388669-1.62676900.01077400.00764460.442087-4.1357699-1.625801300.00730080.01774460.601090-4.4564333-1.627131800.00971610.00964260.464609-4.1773882-1.624095Allvaluesareinreducedunits.KEisthemeankineticenergyperatom.U*istwicethepotentialenergy.VX,2andVY,2arethemeanvaluesofthesquaresoftheXandYvelocitycomponents,asdescribedinthequestion.SimilarlyVX,1andVY,1arethemeanvaluesofthevelocitycomponents.PXandPYarethemeanmomentumperparticle.KE(T*)0.80.60.40.20-1.9PE½U-2.0-2.1-2.2-2.3-2.4P.E.K.E.FigureE2.1VariationofK.EandP.E.04080120160MaxwellBoltzmannDistribution-8-6-4-202468(a)NN300020001000V6RzcurvesasafunctionoftimeTYPICALRESULTS:NOTETHELARGEVARIATIONSINTHEVALUESOFR2LnN7.06.05.04.0411Steps0204060VFigureE2.2(b)10-2R2864206121824TimestepsFigureE2,37TimeNumberSZ-S-SRSR=261R2SR=301R2SR=334R2SR=370R2AVERAGER200000020.000880.000670.000910.000790.0008140.002870.002760.003820.002980.0031160.005230.00628.I0.006230.0065880.007970.011010.014490.010390.01097100.011430.016560.020950.015230.01604120.015280.022350.027680.020220.02138140.018740.028450.034530.025640.02684160.021840.035390.041570.031600.03260180.025260.042930.049020.038330.03889200.029790.050800.057180.045320.04577220.035380.059180.066050.05100.05303240.040630.067840.075330.055690.059870.00858