Download - Kinetic Energy Investigation
University of Arkansas, Fayetteville University of Arkansas, Fayetteville
ScholarWorks@UARK ScholarWorks@UARK
High School Lesson Plans Research Experience for Teachers (RET)
7-2017
Kinetic Energy Investigation Kinetic Energy Investigation
Mike Jackson
Follow this and additional works at: https://scholarworks.uark.edu/poetsrethigh
Part of the Dynamics and Dynamical Systems Commons, Energy Systems Commons, and the Power
and Energy Commons
Citation Citation Jackson, M. (2017). Kinetic Energy Investigation. High School Lesson Plans. Retrieved from https://scholarworks.uark.edu/poetsrethigh/1
This Lesson Plan is brought to you for free and open access by the Research Experience for Teachers (RET) at ScholarWorks@UARK. It has been accepted for inclusion in High School Lesson Plans by an authorized administrator of ScholarWorks@UARK. For more information, please contact [email protected].
Mike Jackson, University of Arkansas POETS, 2017.
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NGSSLESSONPLAN1(POETS)HS-PS3INVESTIGATION
Grade:11-12 Topic:HSKineticEnergyInvestigation Lesson#1(90minutes)inaseriesof__lessons.
BriefLessonDescription:Studentswillbuildamousetrappoweredcarthatconvertselasticpotentialenergycontainedinthetrap’sspringtolinearkineticenergyofthecar.Thereleaseofthisenergyresultsinanetforcewhichleadstolinearacceleration.ThisaccelerationcanbemeasuredwithVernierLoggerPro®,andusingNewton’sSecondLawofMotion,thenetforcecanbecalculated.Finally,usingtheconceptofwork,thefinalkineticenergyofthecarcanbecalculated.Oncestudentsbecomefamiliarwiththecalculationofworkandenergy,theteacherwillchallengethestudentstomodifytheircarstoperformwithinaspecificenergyrange.Thismayinvolvemodifyingmass,wheeldesign,leveraction,etc.TheconceptofworkandenergyisdemonstratedinthislessonthroughtheuseofastudentbuiltcarandVernierLoggerPro®.Thelessonutilizesconceptapplication,datacollection,andgraphicalmodelingtechniquestogivethestudentsanunderstandingofenergytransferbybridgingconceptsofkinematicsanddynamics.Beforeproceedingwiththislesson,theteachershouldfamiliarizehim/herselfwithVernierLoggerPro®:VernierLoggerPro®Overview:https://www.vernier.com/products/software/lp/
PerformanceExpectation(s)/Standards:HS-PS3-1 Createacomputationalmodeltocalculatethechangeintheenergyofonecomponentinasystemwhenthe
changeinenergyoftheothercomponent(s)andenergyflowsinandoutofthesystemareknown.[ClarificationStatement:Emphasisisonexplainingthemeaningofmathematicalexpressionsusedinthemodel.][AssessmentBoundary:Assessmentislimitedtobasicalgebraicexpressionsorcomputations;tosystemsoftwoorthreecomponents;andtothermalenergy,kineticenergy,and/ortheenergiesingravitational,magnetic,orelectricfields.]
HS-PS3-3. Design,build,andrefineadevicethatworkswithingivenconstraintstoconvertoneformofenergyintoanotherformofenergy.*[ClarificationStatement:Emphasisisonbothqualitativeandquantitativeevaluationsofdevices.ExamplesofdevicescouldincludeRubeGoldbergdevices,windturbines,solarcells,solarovens,andgenerators.Examplesofconstraintscouldincludeuseofrenewableenergyformsandefficiency.][AssessmentBoundary:Assessmentforquantitativeevaluationsislimitedtototaloutputforagiveninput.Assessmentislimitedtodevicesconstructedwithmaterialsprovidedtostudents.]
SpecificLearningOutcomes/IncludingEvidenceStatements:ObservablefeaturesofthestudentperformanceforstandardHS-PS3-1:
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Representation
a
Studentsidentifyanddescribe*thecomponentstobecomputationallymodeled,including:i.Theboundariesofthesystemandthatthereferencelevelforpotentialenergy=0(thepotentialenergyoftheinitialorfinalstatedoesnothavetobezero);ii.Theinitialenergiesofthesystem’scomponents(e.g.,energyinfields,thermalenergy,kineticenergy,energystoredinsprings—allexpressedasatotalamountofJoulesineachcomponent),includingaquantificationinanalgebraicdescriptiontocalculatethetotalinitialenergyofthesystem;iii.Theenergyflowsinoroutofthesystem,includingaquantificationinanalgebraicdescriptionwithflowintothesystemdefinedaspositive;andiv.Thefinalenergiesofthesystemcomponents,includingaquantificationinanalgebraicdescriptiontocalculatethetotalfinalenergyofthesystem.
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ComputationalModeling
aStudentsusethealgebraicdescriptionsoftheinitialandfinalenergystateofthesystem,alongwiththeenergyflowstocreateacomputationalmodel(e.g.,simplecomputerprogram,spreadsheet,simulationsoftwarepackageapplication)thatisbasedontheprincipleoftheconservationofenergy.
bStudentsusethecomputationalmodeltocalculatechangesintheenergyofonecomponentofthesystemwhenchangesintheenergyoftheothercomponentsandtheenergyflowsareknown.
3 Analysis
aStudentsusethecomputationalmodeltopredictthemaximumpossiblechangeintheenergyofonecomponentofthesystemforagivensetofenergyflows.
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bStudentsidentifyanddescribe*thelimitationsofthecomputationalmodel,basedontheassumptionsthatweremadeincreatingthealgebraicdescriptionsofenergychangesandflowsinthesystem.
ObservablefeaturesofthestudentperformanceforstandardHS-PS3-3:
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UsingscientificknowledgetogeneratethedesignsolutionaStudentsdesignadevicethatconvertsoneformofenergyintoanotherformofenergy.
b
Studentsdevelopaplanforthedeviceinwhichthey:i.Identifywhatscientificprinciplesprovidethebasisfortheenergyconversiondesign;ii.Identifytheformsofenergythatwillbeconvertedfromoneformtoanotherinthedesignedsystem;iii.Identifylossesofenergybythedesignsystemtothesurroundingenvironment;iv.Describe*thescientificrationaleforchoicesofmaterialsandstructureofthedevice,includinghowstudent-generatedevidenceinfluencedthedesign;andv.Describe*thatthisdeviceisanexampleofhowtheapplicationofscientificknowledgeandengineeringdesigncanincreasebenefitsformoderncivilizationwhiledecreasingcostsandrisk.
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Describingcriteriaandconstraints,includingquantificationwhenappropriate
aStudentsdescribe*andquantify(whenappropriate)prioritizedcriteriaandconstraintsforthedesignofthedevice,alongwiththetradeoffsimplicitinthesedesignsolutions.Examplesofconstraintstobeconsideredarecostandefficiencyofenergyconversion.
3EvaluatingpotentialsolutionsaStudentsbuildandtestthedeviceaccordingtotheplan.bStudentssystematicallyandquantitativelyevaluatetheperformanceofthedeviceagainstthecriteriaandconstraints.
4Refiningand/oroptimizingthedesignsolution
aStudentsusetheresultsoftheteststoimprovethedeviceperformancebyincreasingtheefficiencyofenergyconversion,keepinginmindthecriteriaandconstraints,andnotinganymodificationsintradeoffs.
PriorStudentKnowledge:HS-PS2-1. AnalyzedatatosupporttheclaimthatNewton’ssecondlawofmotiondescribesthemathematical
relationshipamongthenetforceonamacroscopicobject,itsmass,anditsacceleration.[ClarificationStatement:Examplesofdatacouldincludetablesorgraphsofpositionorvelocityasafunctionoftimeforobjectssubjecttoanetunbalancedforce,suchasafallingobject,anobjectslidingdownaramp,oramovingobjectbeingpulledbyaconstantforce.][AssessmentBoundary:Assessmentislimitedtoone-dimensionalmotionandtomacroscopicobjectsmovingatnon-relativisticspeeds.]
ScienceandEngineeringPracticesDevelopingandUsingModelsModelingin9–12buildsonK–8andprogressestousing,synthesizing,anddevelopingmodelstopredictandshowrelationshipsamongvariablesbetweensystemsandtheircomponentsinthenaturalanddesignedworlds.• Developanduseamodelbasedon
evidencetoillustratetherelationshipsbetweensystemsorbetweencomponentsofasystem.(HS-PS3-2),(HS-PS3-5)
PlanningandCarryingOutInvestigationsPlanningandcarryingoutinvestigationstoanswerquestionsortestsolutionstoproblemsin9–12buildsonK–8experiencesandprogressestoincludeinvestigationsthatprovideevidenceforandtestconceptual,mathematical,physical,andempiricalmodels.• Planandconductaninvestigation
individuallyandcollaborativelytoproducedatatoserveasthebasisforevidence,andinthedesign:decideontypes,howmuch,andaccuracyofdataneededtoproducereliablemeasurementsandconsider
DisciplinaryCoreIdeasPS3.A:DefinitionsofEnergy• Energyisaquantitativepropertyofa
systemthatdependsonthemotionandinteractionsofmatterandradiationwithinthatsystem.Thatthereisasinglequantitycalledenergyisduetothefactthatasystem’stotalenergyisconserved,evenas,withinthesystem,energyiscontinuallytransferredfromoneobjecttoanotherandbetweenitsvariouspossibleforms.(HS-PS3-1),(HS-PS3-2)
• Atthemacroscopicscale,energymanifestsitselfinmultipleways,suchasinmotion,sound,light,andthermalenergy.(HS-PS3-2)(HS-PS3-3)
• Theserelationshipsarebetterunderstoodatthemicroscopicscale,atwhichallofthedifferentmanifestationsofenergycanbemodeledasacombinationofenergyassociatedwiththemotionofparticlesandenergyassociatedwiththeconfiguration(relativepositionoftheparticles).Insomecasestherelativepositionenergycanbethoughtofasstoredinfields(which
CrosscuttingConceptsCauseandEffect• Causeandeffectrelationshipscanbe
suggestedandpredictedforcomplexnaturalandhumandesignedsystemsbyexaminingwhatisknownaboutsmallerscalemechanismswithinthesystem.(HS-PS3-5)
SystemsandSystemModels• Wheninvestigatingordescribingasystem,
theboundariesandinitialconditionsofthesystemneedtobedefinedandtheirinputsandoutputsanalyzedanddescribedusingmodels.(HS-PS3-4)
• Modelscanbeusedtopredictthebehaviorofasystem,butthesepredictionshavelimitedprecisionandreliabilityduetotheassumptionsandapproximationsinherentinmodels.(HS-PS3-1)
EnergyandMatter• Changesofenergyandmatterinasystem
canbedescribedintermsofenergyandmatterflowsinto,outof,andwithinthatsystem.(HS-PS3-3)
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limitationsontheprecisionofthedata(e.g.,numberoftrials,cost,risk,time),andrefinethedesignaccordingly.(HS-PS3-4)
UsingMathematicsandComputationalThinkingMathematicalandcomputationalthinkingatthe9–12levelbuildsonK–8andprogressestousingalgebraicthinkingandanalysis,arangeoflinearandnonlinearfunctionsincludingtrigonometricfunctions,exponentialsandlogarithms,andcomputationaltoolsforstatisticalanalysistoanalyze,represent,andmodeldata.Simplecomputationalsimulationsarecreatedandusedbasedonmathematicalmodelsofbasicassumptions.• Createacomputationalmodelor
simulationofaphenomenon,designeddevice,process,orsystem.(HS-PS3-1)
ConstructingExplanationsandDesigningSolutionsConstructingexplanationsanddesigningsolutionsin9–12buildsonK–8experiencesandprogressestoexplanationsanddesignsthataresupportedbymultipleandindependentstudent-generatedsourcesofevidenceconsistentwithscientificideas,principles,andtheories.Design,evaluate,and/orrefineasolutiontoacomplexreal-worldproblem,basedonscientificknowledge,student-generatedsourcesofevidence,prioritizedcriteria,andtradeoffconsiderations.(HS-PS3-3)
mediateinteractionsbetweenparticles).Thislastconceptincludesradiation,aphenomenoninwhichenergystoredinfieldsmovesacrossspace.(HS-PS3-2)
PS3.B:ConservationofEnergyandEnergyTransfer• Conservationofenergymeansthatthe
totalchangeofenergyinanysystemisalwaysequaltothetotalenergytransferredintooroutofthesystem.(HS-PS3-1)
• Energycannotbecreatedordestroyed,butitcanbetransportedfromoneplacetoanotherandtransferredbetweensystems.(HS-PS3-1),(HS-PS3-4)
• Mathematicalexpressions,whichquantifyhowthestoredenergyinasystemdependsonitsconfiguration(e.g.relativepositionsofchargedparticles,compressionofaspring)andhowkineticenergydependsonmassandspeed,allowtheconceptofconservationofenergytobeusedtopredictanddescribesystembehavior.(HS-PS3-1)
• Theavailabilityofenergylimitswhatcanoccurinanysystem.(HS-PS3-1)
• Uncontrolledsystemsalwaysevolvetowardmorestablestates—thatis,towardmoreuniformenergydistribution(e.g.,waterflowsdownhill,objectshotterthantheirsurroundingenvironmentcooldown).(HS-PS3-4)
PS3.C:RelationshipBetweenEnergyandForces• Whentwoobjectsinteractingthrougha
fieldchangerelativeposition,theenergystoredinthefieldischanged.(HS-PS3-5)
PS3.D:EnergyinChemicalProcesses• Althoughenergycannotbedestroyed,it
canbeconvertedtolessusefulforms—forexample,tothermalenergyinthesurroundingenvironment.(HS-PS3-3),(HS-PS3-4)
ETS1.A:DefiningandDelimitinganEngineeringProblemCriteriaandconstraintsalsoincludesatisfyinganyrequirementssetbysociety,suchastakingissuesofriskmitigationintoaccount,andtheyshouldbequantifiedtotheextentpossibleandstatedinsuchawaythatonecantellifagivendesignmeetsthem.(secondarytoHS-PS3-3)
• Energycannotbecreatedordestroyed—onlymovesbetweenoneplaceandanotherplace,betweenobjectsand/orfields,orbetweensystems.(HS-PS3-2)
ConnectionstoEngineering,Technology,andApplicationsofScienceInfluenceofScience,EngineeringandTechnologyonSocietyandtheNaturalWorld• Moderncivilizationdependsonmajor
technologicalsystems.Engineerscontinuouslymodifythesetechnologicalsystemsbyapplyingscientificknowledgeandengineeringdesignpracticestoincreasebenefitswhiledecreasingcostsandrisks.(HS-PS3-3)
------------------------------------ConnectionstoNatureofScienceScientificKnowledgeAssumesanOrderandConsistencyinNaturalSystems• Scienceassumestheuniverseisavast
singlesysteminwhichbasiclawsareconsistent.(HS-PS3-1)
PossiblePreconceptions/Misconceptions:Misconception:Somestudentsmaythinkanobjectataconstantvelocityisaccelerating.
• Anobjectataconstantvelocityhaszeroacceleration.• Accelerationisdefinedasachangeinvelocityoverachangeintime.• Ifthereisnochangeinvelocity,theobjectcannotbeaccelerating.• Rollamodelcarequippedwithanaccelerometerataconstantvelocitytodemonstratethisconcept.
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LESSONPLAN–5-EModel
ENGAGE:OpeningActivity–AccessPriorLearning/StimulateInterest/GenerateQuestions:Brainstormwithstudentsabouttheconceptofenergy.Probetheclassforadefinitionofenergy.Askforexamples.Peaktheirinterestbysettingarattraponatableandplacingapencilinthetrap.Thiswillloudlyanddramaticallysnapthepencilintopieces.Askthestudentsifthisinvolvedanenergyexchange.Ifso,wheredidtheenergycomefrom?Sinceenergywastransferredfromthespringofthetraptothepencil,couldthatenergybeharnesseddifferently?Coulditbeusedtodosomethinguseful,suchasmoveaminiaturecar?Homeworkproject:Placethestudentsinpairs.Theirtaskistobuildamousetrappoweredcarthatoperateswithinthefollowingparameters:
• Thecarmustrollfreelyonthegroundandmaynotbeattachedtoanything.• Thecarmayoperateundermousetrappoweronly.• Thecarmusttravelandcontinuouslyaccelerateaminimumof3meters(approximatelytenfeet).• Thecarmustberobustlybuilttowithstandseveraltrials.
Whilecraftstoresofferkitstobuildthese,encouragestudentstodoasimpleYouTubesearchfordesignideas.Onespecificdesignlinkcanbefoundat:https://youtu.be/mVNFxlEMWvwHavestudentpairsbrainstormondesigns,whatmaterialstheywillneed,anddivisionoflabor.Theywillneedtobegivenafewdaystocompletetheprojectoutsideofclass.ThisisalsoagreattimetointroducestudentstotheVernierLoggerPro®.Theeasiestmethodofdatacollection,aswellasthemethodoutlinedinthislessonplan,utilizesthevideoanalysisfeatureofLoggerPro.Avideolinkoutliningthevideoanalysisprocessisgivenbelow.AdownloadlinkforVernierLoggerLite®isalsogiven.PleasenotethattheanalysisfeaturesofLoggerLitearelimitedcomparedtothoseofLoggerPro.VideoAnalysiswithVernierLoggerPro:https://www.youtube.com/watch?v=shNPrswj_kADownloadLinkforVernierLoggerLite:https://www.vernier.com/products/software/logger-lite/
EXPLORE:LessonDescription–MaterialsNeeded/ProbingorClarifyingQuestions:Thedatacollectionlessoncanbeginonthedaytheteachermakesthecarsdue.Onthatday,eachstudentpairwillworktogetheratacomputerstation.
1. Today,studentswillmakemotionmeasurementsontheircarsusingVernierLoggerPro®.2. Eachstudentpairwillneedtheirmousetrapcar,asmartphoneordigitalcamera,andacomputerwithVernierLoggerPro®.3. Placethecaronabalancetodetermineitsmass.4. Placethecar(primedformotion)inthevideoframealongwithameterstickforscale.
5. Beginrecording.Besuretosetthecameraasstillaspossible.Captureasmuchofthecar’smotionaspossible.6. SavethevideotothecomputerwithVernierLoggerPro.7. ImportthevideointoLoggerPro.
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8. Analyzethecar’smotiontoobtainavelocity-timegraph.
9. Thegraphshouldbelinearasaresultofthecar’suniformacceleration.Performalinearfitonthegraphtoobtainthecar’sacceleration.
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10. Theareaunderthegraphwilltellushowfarthecarwentinaparticulartimeinterval.Selectdatapointswithinaparticulartime
interval,andperformanintegralfittodeterminethedisplacementofthecar.
11. asdf
Materials:
• 1-ComputerequippedwithVernierLoggerPro®pergroup• 1-Cameraorsmartphone(broughtbystudent)• 1-Mousetrappoweredcar(studentbuilt)pergroup• 1-Meterstickforscaleinvideo
EXPLAIN:ConceptsExplainedandVocabularyDefined:ForStudentsaftertheactivity:1.Whattrendsdoyouseeinyourdata?2.Shareyourdatawithothergroups.3.Asaclass,doyouseethesametrends?Sinceaccelerationisconstantforaspecificamountoftime,thefinalvelocitycanbedeterminedbycalculatingv=at.Askstudentswhatwecanlearnaboutthecar’smotionfromthegraphasamodelofmotion.Doestheslopetellusanything?Sinceslopeisdefinedastheriseofthelineovertherunoftheline,theslopeistheratioofthechangeinvelocityoverchangeintime.Theslopeistheaccelerationthatwasmeasuredwiththeaccelerationvtimegraph.Doestheareaunderthelinetellusanything?Sincethelineisangled,wehaveatriangularareaunderthegraph.Theareaofatriangleisdefinedas½(base)(height),whichtranslatesto½(time)(velocity).Dimensionally,multiplyingvelocitybetimegivesdisplacement.Theareaisthedisplacementofthecarduringthetimeinterval.Usingtheserelationshipsandthepreviouslylearneddefinitionofworkbeingtheproductofforcetimesdisplacement,wecandeterminetheamountofworkthetrapdidtomovethecar:
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Inordertodowork,anobjectmusthaveenergy.Thisenergyisdisplayedintheformofmotion,sothisiskineticenergy.Nowchallengestudentstobrainstormonmodificationsontheircarstoincreasekineticenergyoutputby25%(oranyamountofchangedirectedbytheteacher).Havethestudentsmodifythecars,returnthem,andtesttodetermineiftheenergyoutputhaschanged.Vocabulary:Displacement:achangeinpositionVelocity:achangeinpositionasafunctionoftimeAcceleration:achangeinvelocityasafunctionoftimeMass:thequantityofmatterinanobjectNetForce:anunbalancedpushorpullonanobjectthatresultsinanaccelerationWork:forceappliedoveracertaindisplacementEnergy:workdone(orabilitytodowork)onorbyanobject
ELABORATE:ApplicationsandExtensions:TheconceptofworkandenergydemonstratedinthislessoncanbefurtherinvestigatedbyusingaTexasInstruments®SensorTag.TheSensorTagisacompactsensorarraythatconnectswirelesslytomobiledevicesviaBluetooth.Beforeproceedingwiththisextension,theteachershouldfamiliarizehim/herselfwiththeTexasInstruments®SensorTagandtheirsmartphone/tabletapplicationsforbasicfunctionality:SensorTagOverview:https://www.youtube.com/watch?v=UhMKG761l78iOSApplication:https://itunes.apple.com/us/app/ti-sensortag/id552918064?mt=8AndroidApplication:https://play.google.com/store/apps/details?id=com.ti.ble.sensortagTheteachershouldalsofamiliarizehim/herselfwithusingtheTexasInstruments®SensorTagwiththeN-spireCalculatorandiPadapplication:http://compasstech.com.au/SensorTag/index.htmlEnergycalculationsareextremelyimportantintheautomotiveindustry.Automanufacturersareconstantlylookingforwaystomakeenginesmorepowerfulandefficient.Asademonstration,enlisttheassistanceofafellowteacherandhis/herautomobile.AttachaSensorTagintotheenginecompartmentandclosethehood.OnetheiPadapplication,select“IRTemperature”asasensortodisplaydata.Astheengineruns,studentswillnoticethattheengineisproducingalargeamountofheat.Whatisheat?Heatisenergythatiscausingairmoleculestomove.Wheredoesthisheatcomefrom?Theheatissimplywastedenergyfromtheengine.Challengethestudentstodeterminewaysofharnessingthiswastedenergy.Thislessoncanleadintoafurtherinvestigationinvolvingthermoelectricgeneratorsthatcanconvertheatenergytoelectricalenergy.
EVALUATE:FormativeMonitoring(Questioning/Discussion):
1. Whydoesthecarmoveinthefirstplace?Whatiscausingittomove?2. Whattrendsdoyouseeinyourdataofaccelerationvtime?3. Canyoutranslatetheaccelerationvtimegraphintoavelocityvtimegraphwiththegiveninformation?4. Usingthestatedrelationships,canyouderivethekineticenergyequation?
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SummativeAssessment(ProjectExtension):1. Didyoudetermineplausiblemodificationstoyourcartoincreaseitsenergyoutput?2. Doesyourenergyoutputconformtothestatedguidelines?
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MaterialsRequiredforThisLesson/Activity
Quantity Description PotentialSupplier(item#) EstimatedPrice
1pergroup Smartphoneorcameraforrecording Broughtbystudent
1perdistrict VernierLoggerPro VernierScienceandTechnology $250sitelicense
1perdistrict VernierLoggerLite(limited,butfree,alternativetoLoggerPro) VernierScienceandTechnology Free