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 scholar@uark.edu.

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