Purposeoftheexperiment
1.Useasimplependulumtomeasurethelocalaccelerationofgravity.
2.Studytheperiodofsimplependulumvibration.
3.Practiceusingmeterrulerandstopwatch.
Instruments
Singlependulum,meterruler,stopwatch(ordigitalmillisecondmeter),verniercaliper.
Experimentalprinciple
(Figure1),whereisthelocalgravitationalacceleration,whichisthelinearaccelerationofthehammeratthistime.Supposethelengthofasimplependulumis,thentheangularaccelerationofthependulumisequalto,thatis
(1)Whenthependulumangleisverysmall(usually5°),itcanbeconsideredthatatthistime
(2)Thatis,theangularaccelerationofvibrationisproportionaltotheangulardisplacement.Thenegativesignintheformulameansthatthedirectionsofangularaccelerationandangulardisplacementarealwaysopposite.Atthistime,thevibrationofasimplependulumisasimpleharmonicvibration.Fromtheoreticalanalysis,itisknownthattherelationshipbetweenitsvibrationperiodandtheabove-mentionedproportionalcoefficientis,so
(3)isthependulumlength,thedistancebetweentheweightofthependulumandthesuspensionpoint,andthelocalgravityAcceleration.Transformequation(3)toget
(4)Substitutingthemeasuredpendulumlengthandcorrespondingperiodintotheaboveequationtoobtainthelocalgravityaccelerationvalue.Thisformulacanberewrittenas
(5)Thismeansthatthereisalinearrelationshipbetweenand,andisitsslope.Ifthecorrespondingperiodismeasuredforvariouspendulumlengths,theslopeofthegraphcanbeFindthevalue.Therelationshipbetweentheoscillationperiodofthependulumandtheangleofthependulumcanbederivedtheoreticallytoobtaintheperiodwhenitis0°.Ifyouomitandthefollowingitems,then
(6)Iftheperiodofdifferentswinganglesismeasured,thisformulacanbetestedbydrawingaline.
Experimentalcontent
1.Takeasinglependulumwithapendulumlengthofabout1m,measurethecycloidlengthwithameterruler,andmeasuretheheightofthependulumwithaverniercaliper,twiceeach.Whenmeasuringthelengthwithameterruler,youshouldmakesurethatthemeterrulerisparalleltothemeasuredcycloidandascloseaspossible.Thelineofsightshouldbeperpendiculartothedirectionoftherulerwhenreadingtopreventerrorsduetoparallax.
Useastopwatchtomeasurethetimeofasinglependulumswingingcontinuouslyfor50cycles,measuring6times.Notethattheswingangleshouldbelessthan10°.
Whenusingthestopwatchtomeasurethecycle,youshouldpressthestopwatchandcount"0"whenthependulumpassesthebalanceposition.Whenacycleiscompleted
"1",andthencontinuetoEverytimeacycleiscompleted,count2,3,...,andfinally,stopthewatchwhilecountingthe50th.
2.Shortenthependulumlengthbyabout10cmeachtime,andmeasurethependulumlengthandperiod.
3.Usethedatafromstep1tofinditserror.
4.Usethedatafromsteps1and2toplotthelineandfindtheslopeandvalueoftheline.
5.Usethedatainstep3todrawthegraphline,andfromtheinterceptandslopeofthegraphline,checkwhetherthe
coefficientinequation(6)isequalto.
Mattersneedingattention
1.Tightenthemainspringbeforeusingthestopwatch,butdonotovertightenit,soasnottodamagethemainspring.
2.Donotuseexcessiveforcewhenpressingthetabletopreventdamagetotheparts.
3.Afterreturningtothewatch,ifthestopwatchdoesnotindicatezero,writedownitsvalue(zeropointreading),andsubtractitfromthemeasuredvalueaftertheexperiment
(notethesymbol).
4.Specialattentionshouldbepaidtopreventthestopwatchfrombeingdropped.Whennotinuse,thewatchmustbeplacedintheboxinthecenterofthetestbench.
5.Trytochooseathinnercycloidandlesselasticity.Anditshouldbeaslongaspossible.Thependulumballshouldbelargeinmassandsmallinsize