Download W = ΔK =1/2mv2 f −1/2mv0

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