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DSHSAP1Mathy FormalLabEnergy Lab#10Work-EnergyTheorem Everyonesays,“Energyisconserved.”Wedecidedearlyonthatourdecisionsaboutthevalidityofeveryhypothesismust, ultimately,appealtoexperiment.Here,then,isyourchancetotakeon“thebigone”:toinvestigatethevalidityofthework-energy theorem. Theory: Ifanamountofwork,W,isdoneonasystem,thenthekineticenergy,K,ofthesystemchanges.Thechangeinthekineticenergyis equaltotheamountofworkdone.Statedquantitatively: W = ΔK = 1 / 2mv 2f −1 / 2mv02 (1) Equation1isastatementofthework-energytheoremandisthefoundationofmuchofourscience.Assuch,questionsofits validityarecertainlyworthyourconsideration. Procedure: TheexperimentalsetupisdepictedinFigure1.Themass/cartsystemhasamassmandahangingmassisdenotedwithanMwhich willprovidetheforcethatdoesworkonthecartsystem.Asbefore,don’tdropthecart(andifitisaccidentallydropped,askyour instructortoinspectitcarefully).Also,adjustthepulleysothatthestringpassingoverthewheelisparalleltoitssurface. Figure1:ExperimentalSetupwithforce-bodydiagram Asapreliminarystep,weneedtodiscusshowtocalculatetheworkdoneonm.Thecalculationissimplestifweensurethatthenet forceactingonthecartisparalleltothedisplacement(that’swhywejustaskedyoutoadjustthepulley). ApplyingNewton'ssecondlawtoeachofthetwomassesanddefiningthemotiontotherightofthefiguretobepositiveyieldsthe followingequations: Fnet=-T1+T1+Mg=(m+M)a Sincethenetforceactingonthecart’smassisF=m+Ma,theworkthisforcedoesindisplacingthemassadistancesis W=(m+M)ad ! Thisistheworkthatthenet,unbalancedforcewillperform.Ifwecannowdetermineaprocedureforcalculatingthechangeinthe kineticenergyofthecart,wecandetermineifthework-energytheoremisvalid.Frompreviouslabs,weknowthattherearea numberofdifferentmethodstomeasurethevelocityofanobject.Onesuchmethodinvolvesusingamotionsensor.Thecart’s velocityismeasuredbyhavingthesensormeasurethecartsvelocityviaaradiosignal.Opendatastudioandselectthevelocityand positionAsalways,ifitispossible,weliketosimplifythingsinphysics.OnewaytosimplifythedeterminationofDKistomakethe initialkineticenergyzero;thechangeinthekineticenergyofthecartwillthenbesimplythekineticenergyofthecartafterithas beendisplacedacertaindistancex.Ifthecartstartsatrest,theinitialvelocityiszero.Byplacingthesensoradistancefromthe cart’sinitialposition,wewillmeasurethevelocityofthecartafterithastraveledadistancex.Knowingthemassofthecart,wecan calculatethechangeinthekineticenergy.Theall-importantcomparisonbetweenWandDKisallthatremains.Wecanthenusethe changeinvelocitypertimeperiodtocalculateacceleration. 1. SetyourapparatusupasshowninFigure1.Choosemassesthatwillaccelerate,butnotTOOFAST!!! 2. Practiceadropwheretheweighthitsthefloor,yetyourcartdoesnothitthepulley.Markyourdisplacementonthetable withtape. 3. Activatethemotionsensorandallowthehangingmasstoaccelerateyourcarfreely.Record: a) theheighttheweightdroppedfrominmeters b) theinitialvelocityandmaximumvelocitiesachievedfromthegraph. c) thexdisplacementbetweenminimumandmaximumvelocities. d) thetimebetweenminimumandmaximumvelocities. 4. Calculatetheaccelerationofyourcartusingyourvelocityandtimevalues. 5. Yourdatacanberecordedbelow. Trial xdisplacement(m) t(s) vf(m/s) a 1 2 Ave 6.Inthetablebelow,calculatetheworkdoneonthecartandthechangeinthecart’skineticenergy.Useyouraveragevaluesand showyourworkinyourlabsheet. Trial W(Nm) K(J) %Difference 1 Questions: 2 1.Inorderforthework-energytheoremtohavemeaning,work(F·d)andkineticenergy(mv /2)shouldhavethesameunits.Show thattheydo. 2.Doesworkceasetobedoneonthecartwhenthesmallmasscomestorestontheground?Explain. 3.Calculatethepowerconsumedinmovingyourcartthroughthesetdistance.Dothisbyusingbothequationsforpower(P=W/t andFv) 4.Howcouldyouverifythevalidityofquestion#3ifyouwereaskedtodosoonlyusingalightbulbasyoursensor? Conclusions: Nowwriteyourconclusion