Download Conservation of Mechanical Energy

SP211 Lab: Five  Conservation of Mechanical Energy
Version: October 4, 2014
PHYSICS
LAB 5
SP211
ConservationofMechanicalEnergy
I. Introduction
A. In the absence of dissipative forces (i.e. non-conservative forces that do work,
such as kinetic friction), the mechanical energy of an isolated system is
conserved. This can be written in the form: Kf + Uf = Ki + Ui.Thus the sum of the
kinetic energy and potential energy is constant and K + U = 0.
B. Consequently any change in kinetic energy is compensated for by an equal and
opposite change in potential energy. For example, if the potential energy
decreases, the kinetic energy increases by the same amount.
C. An easy experiment to test this theory is to let the cart run freely down the
inclined plane and measure the change in height and change in speed of the cart.
It would then be straightforward to calculate the decrease in potential energy
and increase in kinetic energy and show that their sum is zero.
Let us carry out that experiment.
II. Objectives
Attheendofthisactivity,youshould:
1.UnderstandandusetheConservationofMechanicalEnergyequation
(Kf + Uf = Ki + Ui) while seeing its limitations.
2.UnderstandthattheWork‐EnergyPrinciple(WEP)alwaysapplies:
Wnet,external+Wnonconservastive,internal=K+U=Emech
3.UnderstandthataplotEmechvsxwillfindtheeffectivefrictionalforce.
Page 1 of 4 SP211 Lab: Five  Conservation of Mechanical Energy
Version: October 4, 2014
III.NeededEquipment
Yourinstructorwillshowyoutheexperimentalsetups,whichconsistsofamotion
sensor(MS),aninclinedplane,andadynamicscart.UseofanExcelSpreadsheetto
graphtheenergiesishelpful.
Ourexperimentalsetupisshowninthediagrambelow.Theangleisshownas6o
becauseitgavegoodresultsinatrialrun.Howeveranyanglebetween5oand10o
shouldalsoyieldgoodresults.
IV. Procedure
A.
Discussion:
IntheHomeworkProblem,wefoundthatiftheramp‐cartsystemis
conservative,thenthetotalmechanicalenergyshouldbeconstant.Howcan
wetakedatatotestwhetherthesystemisconservative?Howshallwe
analyzethisdata?
IfyouplotKE,PEandE,allvst,whatshouldthegraphlooklike?Let’ssketch
itontheblackboard. Whichoftheconstantsxi,vi,anda=gsincanwedetermineapriori?Which
canbedeterminedonlyafterwedotheexperiment? B.
PreliminaryData:
B.1.Setyourtrackatarampangleofabout6˚ (5˚ <  < 10˚ works well.),andthen
measuretheanglecarefullybymakingagraphoftheramp’sheightasa
functionofdistancealongitsedge.UsethefunctioninExcelcalled“Linest”to
findsinanditsuncertainty. B.2.Measureandrecordthemassofthecartalongwithitsuncertainty.
B.3.Rememberthatg=+9.810+/‐0.005m/s2
Page 2 of 4 SP211 Lab: Five  Conservation of Mechanical Energy
Version: October 4, 2014
C.
ConnecttheMStotheLab‐ProandsetupLogger‐Pro
Check that everything is plugged in correctly: the MS into DIG/SONIC2 Recurring steps: Using Logger Pro to program the LabPro: Known as the “Three Steps” D.

Experiment ‐> Set Up Sensors ‐> Show all Interfaces: Make sure all the right sensors show up in all the right holes. 
Experiment ‐> Data Collection: Set the length of time data is to be taken and the rate at which data is to be taken. 
File ‐> Settings for...: Check the checkbox to Show Zero on Toolbar, and make sure number of points for Derivative and Smoothing are both 7. Experiment:PotentialEnergytransferringtoKineticEnergy
D.1.FollowtheThreeStepsinLoggerProtoprogramtheLabPrototakedata
forposition(x)asafunctionoftime(t)appropriatelyforthisexperiment.
D.2.Collectdataofthecartasyouallowittorundowntheramp;usethedata
tocalculatevandh,andthenK,U,andE.UseExcelorLoggerPro.
D.3.Notethatsincethisisuniformlyacceleratedmotion,theexactvelocityat
themid‐pointofanytimeintervalisequaltotheaveragevelocityoverthe
entireinterval.
D.4.Onceyouknowv,calculatingKiseasy.
D.5.Ifyoutakehtobezerowherexiszero,thenyoucancalculateU=mgh,
whereh=‐xsin.Notetheminussign!Asalways,g=+9.810+/‐0.005m/s2.
E.
UseExcelorLoggerProtoplotK,U,andEonasinglegraphas
functionsoft.
F.
DiscussionQuestions:
F1.Doesthesystempassthetestforaconservativesystem?Explain.
F2.Howmuchenergywaslosttofrictionduringyourexperiment?
Howdoesthatcompare(what%)withthekineticenergyattheendofyour
experiment?
Page 3 of 4 SP211 Lab: Five  Conservation of Mechanical Energy
Version: October 4, 2014
G.
Sinceourramp‐cartsystemdidnotpassthetestforaconservative
system,ConservationofMechanicalEnergydoesnotapply,butthe
Work‐EnergyPrinciple(WEP)alwaysapplies:
Wnet,external+Wnonconservastive,internal=K+U=Emech,
sothattheslopeofagraphofEmechvsxwillbetheeffectivefrictional
force.
G.1.PlotEmechvsxandfindtheeffectivefrictionalforce.
G.2.Inafewsentences,explainwhethertoday’sexercisesupports,orfailsto
support,conservationofmechanicalenergyandtheWork‐EnergyPrinciple.
H.
LabReport

Measurementofmassofcartandsineoframpangle.

SpreadsheetfrompartDinsupportofthegraphfrompartE.

GraphfrompartE,properlyannotatedandlabeled.

AnswerstodiscussionquestionsfrompartFonbackofgraphH.3.

GraphfrompartG1withconclusionG2.
V. Clean‐Up
A. EndofLabCheckout:Beforeleavingthelaboratory,pleasetidyuptheequipmentat
theworkstationandquitallrunningsoftware.
B. Thelabstationshouldbeinbetterconditionthanwhenyouarrivedandmore
importantly,shouldbeofanappearancethatyouwouldbePROUDtoshowtoyour
legalguardiansduringa“ParentsWeekend.”
C. Haveyourinstructorinspectyourlabstationandreceivetheirpermissiontoleave
theLabRoom.
D. YouSHALLfollowthisproceduredoingeverylabforBOTHSP211andSP212!
Many thanks to Dr. Huddle for his assistance in producing this Laboratory procedure; specific references can be supplied on request. LCDR Timothy Shivok Page 4 of 4