Lab 5: Projectile Motion - 21st Century Hands-On Science Kits

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Lab 5: Projectile Motion - 21st Century Hands-On Science Kits

LabManualAcceleratedPhysicsVersion3.2© 2011 eScience Labs, Inc.All rights reservedwww.esciencelabs.com • 888.375.5487


TableofContentsIntroductionLab1:TheScientificMethodLab2:LabReportsLab3:MeasurementsNewtonianMechanicsLab4:LinearMotionLab5:ProjectileMotionLab6:TypesofForcesLab7:Newton’sLawsLab8:GravityLab9:WorkandEnergyLab10:SimpleMachinesLab11:CenterofMassLab12:MomentumLab13:CircularMotionLab14:TorqueandRotationLab15:OscillationsMatterandThermalPhysicsLab16:ExploringMatterLab17:ChangeofPhaseLab18:PropertiesofSolidsLab19:FluidMechanicsLab20:TemperatureandHeatLab21:ThermodynamicsLab22:HeatTransferWavesandLightLab23:PropertiesofWavesLab24:SoundLab25:LightandColorLab26:GeometricOpticsElectricityandMagnetismLab27:ElectricFieldsLab28:ElectricCurrentLab29:TypesofCircuitsLab30:MagneticFieldsLab31:ElectromagneticInduction3


GoodLaboratoryPracticesGoodLaboratoryPracticesSciencelabs,whetheratuniversitiesorinyourhome,areplacesofadventureanddiscovery.Oneofthefirstthingsscientistslearnishowexcitingexperimentscanbe.However,theymustalsorealizesciencecanbedangerouswithoutsomeinstructionongoodlaboratorypractices.GeneralReadtheprotocolthoroughlybeforestartinganynewexperiment.Youshouldbefamiliarwiththeactionrequiredeverystepoftheway.Useeyeprotectionwhenexperimentingwithchemicals,batteries,andprojectiles.Keepallworkspacesfreefromclutteranddirtydishes.Washyourhandsaftereachexperiment.Thoroughlyrinselabware(testtubes,beakers,etc.)betweenchemicalexperiments.Todoso,washwithasoapandhotwatersolutionusingabottlebrushtoscrub.Rinsecompletelyatleastfourtimes.Letairdry.Donotaimprojectilesorothermovingmaterialsatotherindividuals.MaterialsandChemicalsUseonlythematerialsneededforeachactivityAlwayshandlehotwatercarefullyandwithnecessaryhandandeyeprotection.Whenusingknivesorblades,alwayscutawayfromyourself.Neverusemorebatteriesthananexperimentspecifies.Donotcreateelectricalcircuitsotherthanthosespecifiedbythelabmanual.Avoidcreating“shortcircuits”withelectricalequipment.Thiscancauseunsafebatterytemperatures.Immediatelydryanywetelectronics—especiallyinthecaseofspilledliquids.Makesurematerialsarecompletelydrybeforeresumingwork.Avoidprolongedexposureofbatteriesandchemicalstodirectsunlightandextremetemperatures.Immediatelysecurethelidorsealthepackageofliquids,powders,andothermaterialsafteruse.4


GoodLaboratoryPracticesUsetesttubecapsorstopperstocovertesttubeswhenshakingormixing–notyourfingers!Useanewpipetteforeachchemicaldispensed.Neverreturnexcesschemicalbacktotheoriginalbottle.Thiscancontaminatethechemicalsupply.Becarefulnottointerchangelidsbetweendifferentchemicalbottles.Wipeupanychemicalspillsimmediately.CheckMSDSsforspecialhandlinginstructions(providedonwww.eScienceLabs.com).Readthelabelsonallchemicals,andnotethechemicalsafetyratingoneachcontainer.ReadallMSDS(providedonwww.eScienceLabs.com).ReadtheMSDSbeforedisposingofachemicaltoinsureitdoesnotrequireextrameasures.(providedonwww.eScienceLabs.com)5


Lab5:ProjectileMotion


Lab5:ProjectileMotionConceptstoexplore Scalarsvs.vectors Projectiles ParabolictrajectoryAsyoulearnedintheLinearMotionLab,aquantitythatconveysinformationaboutmagnitudeonlyiscalledascalar.However,whenaquantity,suchasvelocity,conveysinformationaboutmagnitudeanddirection,wecallitavector.Alongwithcarryingthatextrabitofinformationaboutthepathofmotion,vectorsarealsousefulinphysicsbecausetheycanbeseparatedintocomponents.Infact,anyvectorcanberesolved(brokendownto)anequivalentsetofhorizontal(xdirection)andvertical(ydirection)components,whichareatrightanglestoeachother.AA yA xFigure1:ThevectorAcanbebrokenupintohorizontalandverticalcomponents,A x andA y .Consideravectorarrowdrawnonarectangularcoordinateplane,asvectorApicturedinFigure1(Fordistinction,theboldedtypesignifiesavector).Thehorizontalcomponentofavectoristhedistancealongthexaxisthatthevectorcovers,whiletheverticalcomponentisinthedirectionoftheyaxis.Iftheanglebetweenthehorizontalcomponentandthevectoris,youcanusetrigonometrytofindthemagnitudeofthecomponents:Ay A sinAx AcoswhereAisthemagnitude,orlength,oftheoriginalvector.UsingthePythagoreanTheorem,themagnitudeofanyvectorcanbeexpressedintermsofitscomponentsasAAA2 2x y55


56Lab5:ProjectileMotionandtheanglefromthehorizontalaxiscanbefoundusing:Vectoradditionisdonebyaddinghorizontalandverticalcomponents.Inotherwords,thehorizontalcomponentofthenewvector—oftencalledthe“resultant”—issimplythesumofthehorizontalcomponentsofthetwoaddedvectors.Likewise,theverticalcomponentoftheresultantisthesumoftheindividualverticalcomponents.Youcanthenfindthemagnitudeandangleoftheresultantusingthetrigonometricequationsabove.Aprojectileisanyobjectwhich,onceprojectedataninitialvelocity,continuesinmotionbyitsowninertiaandisinfluencedonlybythedownwardforceofgravity.RememberthatNewton’sLawsdictatethatforcescauseacceleration,notsimplymotion.Therefore,theonlyforceactingonaprojectileinitsFreeBodyDiagramistheforceofgravitydownward.Thismayseemcounterintuitivesincetheobjectmightinitiallybemovinginseveraldirections,bothhorizontallyandvertically,butgravityactsonlyontheverticalmotionoftheobject.Atan AxyFigure2:Someexamplesofprojectilesareacannonballfiredfromacannon,abaseballhitbyabat,andballsbeingjuggledintheair.Alltheseobjectsfollowacurvedpathduetotheforceofgravity.Oneconvenientthingaboutusingvectorstodescribeprojectilemotionisthatwecanseparatethevelocityoftheprojectileintohorizontalandverticalmotion.Theverticalcomponentofthevelocitychangeswithtimeduetogravity,butthehorizontalcomponentremainsconstantbecausenohorizontalforceisactingontheobject(airresistanceaddsquiteabitofcomplicationathighervelocitiesbutwillbeneglectedinthislab).Wecanthusanalyzeeachcomponentoftheprojectile’svelocityseparately.Thecombinationofa(constantly)changingverticalvelocityandaconstanthorizontalvelocitygivesaprojectile’strajectorytheshapeofaparabola.AsshowninFigure4,theprojectilewithhorizontalandverticalmotionassumesacharacteristicparabolictrajectoryduetotheeffectsofgravityontheverticalcomponentofmotion.ThehorizontalmotionistheresultofNewton’sFirstLawinaction(youwillleanaboutthisinLab7)–theobject’sinertia!Ifairresistanceisneglected,therearenohorizontalforcesactinguponprojectile,andthusnohorizontalacceleration.Itmightseemsurprising,butaprojectilemovesatthesamehorizontalspeednomatterhowlongitfalls!Thekinematicequations(Figure5)fromthepreviouslabcandescribebothcomponentsofthevelocityseparately.Formosttwodimensionalprojectilemotionproblems,thefollowingfourequationswillallowyoutosolvefordifferentaspectsofaprojectile’sflight,asFigure3:Whenaprojectile(water,inthiscase)islaunchedupwardtheverticalaccelerationwillreachzeroatthetopoftheparabola.AsgravitypullstheobjecttowardtheEarththeobjectaccelerates.Horizontalvelocityremainsconstantthroughoutthismotion.


Lab5:ProjectileMotionlongasyouknowtheinitialpositionandtheinitialvelocity.Inthislabyoucanassumethatprojectilesarefiredeitherverticallyorhorizontally,sothattheinitialvelocitiesineithercasewilleitherbev x = v ox orv y = v oy .(Thetermv ox canbereadas“initialvelocityinthexdirection.”)Figure4:Asthecannonballintheupperpicturetravelsaparabolicpath,itgainsvelocityduetogravity.Youcanseethatthespacebetweensuccessive“snapshots”oftheballgetsgraduallylarger.Becausegravityonlyacceleratestheballdirectlydownward,onlytheverticalvelocityoftheballchanges.Asyoucanseeinthesecondfigure,theverticalspacingincreasesaccordingtot 2 ,whilethehorizontalspacingisconstant.Onesurprisingresultoftheindependenceofverticalandhorizontalmotionsisthatiftwoprojectilesarelaunchedatthesametimefromthesameheight,theywillhitthegroundandthesametime!Theirhorizontalvelocitiesdonotaffecttherateatwhichtheywillfall.57


Lab5:ProjectileMotionInthecasewhereaprojectileisnotlaunchedeitherverticallyorhorizontally,theinitialvelocitycomponentscanbeexpressedastrigonometricfunctionsofthetotalinitialvelocity,v o :voxvxv cos v oy v sin Asyoucansee,for = 0 (acompletelyhorizontallaunch),thehorizontalvelocityisequaltothetotalinitialvelocityv,whiletheverticalvelocityisequaltozero.Meanwhile,for = 90 (averticallaunch),thehorizontalvelocityiszerowhiletheverticalvelocityisequaltothetotalinitialvelocity.UsingthekinematicsequationsofFigure5youcancalculatethetotaldistanceorrange,R,ofaprojectile.Iftheprojectileisfiredatanangle,therangeisafunctionoftheinitialangle,theinitialvelocity,andtheforceofgravity.Usingalittlealgebra,youcanderivethisexpressionusingthekinematicsequationsabove:Rv2sin( 2)Thisrangeequationisusefulsolongastheinitialheightandfinalheightoftheprojectileareequal.Iftheobjectendsuphigherorlowerthanitstarted,youwillhavetousetheindividualkinematicsequationstosolveforthetotalrange.ItisimportanttoremembergFigure5:Fourusefulkinematicequationsforprojectilemotion:xvyvy2yxo vyooy v v2oyx gt vtoyt 2gthatinmanycases,airresistanceisnotnegligibleandaffectsboththehorizontalandverticalcomponentsofvelocity.Whentheeffectofairresistanceissignificant,therangeoftheprojectileisreducedandthepaththeprojectilefollowsisnotatrueparabola.12gty 2yo58


Lab5:ProjectileMotionFigure6:Thepathofaprojectileintheabsenceofairresistanceisaperfectparabola(top);however,withairresistancetheprojectileexperiencesadeceleratingforceintheoppositedirectionofitsmotion.Theresultistheshortenedcurveshown(bottom).59


Lab5:ProjectileMotionExperiment1:CalculatingthedistancetraveledbyaprojectileInthisexperimentyouwillapplywhatyouknowaboutprojectilemotionandusekinematicstopredicthowfaraprojectilewilltravel.MaterialsRampMarbleCornstarch4SheetsofblackconstructionpaperMeasuringtapeMonofilamentlineWasher*Papertowel *Water*YoumustprovideProcedure11. PlacetheramponatableasshowninFigure7(referencethediagramatthebeginningofthemanualforrampassemblyinstructions).Markthelocationatwhichyouwillreleasethemarble.Thiswillensurethemarbleachievesthesamevelocitywitheachtrial.2. Createaplumblinebyattachingthewashertothemonofilamentline.3. Holdthestringtotheedgeofthetableandmarkthespotatwhichtheweighttouchestheground.(Note:Theplumblinehelpstomeasuretheexactdistancefromtheedgeoftheramptothepositionwherethemarble“lands.”)4. Laydownarunwayofconstructionpaper.5. Wetthemarbleallover,anddropintothecornstarchbagtocoat.Rollonapapertoweltoachieveasmoth,evencoatalloverthemarble(youdonotwantanychunksasitwillaffectthepathofmotion).Whenthemarblehitstheconstructionpaper,theforcewilltransfersomeofthecornstarchtothepaperandallowyoutopinpointwherecontactwasfirstmade.5. Begintheexperimentbyreleasingthemarbleatthemarkedpointontheramp.6. Measurethedistancetraveledtothefirstmarkmadeontheconstructionpaperusingthemeasuringtape.RecordthisvalueinTable1below.7. RepeatSteps56twomoretimesandfindtheaveragedistance.RecordyourdatainTable1.8. Next,usethisaveragedistancetocalculatetheaverageinitialvelocityofthemarblewhenleavingthetable.AverageVelocityCalculation:Figure7:RampsetupforExperiment160


Lab5:ProjectileMotionProcedure21. Findahighertable,orstacksomebooksunderneaththeramptoincreasetheheight.Measurethestartingheightattheendoftherampasbefore.2. Usingtheaveragevelocityfoundearlier,predicthowfarawaythemarblewilllandusingthekinematicequations.RecordthisdistanceinTable2.(Hint:youuseoneequationtofindthetotaltimeintheairusingtheinitialandfinalheights,andanothertofindthehorizontaldistance)3. Measurethisdistanceoutandmarkitbeforeyoureleasethemarble.ReleasethemarblethreetimesandrecordthedistancetraveledinTable2.4. Completethetablesbelowusingyourmeasurements.5. OPTIONALExercise:Setuptheramptoanewheight,andcalculatethepredictedrange.PlaceaStyrofoamcupwithasmallamountofwateratyourpredicteddistance.Releasethemarblefromtheramp,testingyourpredictionbywhetherornotitlandsinthecup.Table1:ProjectiledistanceandvelocitydataTable+RampHeightDistancetraveledAverageDistanceAverageVelocityTable2:ProjectiledistanceandvelocitydataTable+RampHeightCalculatedDistanceActualDistanceActualDistanceAverage61


Lab5:ProjectileMotionQuestions1. Ifyouweretothrowaballhorizontallyandatthesametimedropanexactcopyoftheballyouthrew,whichballwouldhitthegroundfirstandwhyisthisso?2. Whatforcesareactingonthemarblebeforeandafteritleavestheramp?3. Describetheaccelerationofamarblefortheperiodafteritleavestherampandbeforeithitstheground.4. DidyourpredictioninProcedure2comeclosetotheactualspot?Findthepercenterrorofyourpredicteddistance(expected)comparedtotheactualaveragedistance(observed).62


Lab5:ProjectileMotion5. Explainsomepossiblesourcesoferrorthatcouldhaveproducedthedeviationabove.63


Lab5:ProjectileMotionExperiment2:SqueezeRocketprojectilesTheobjectiveofthislabistoobservethedistanceaprojectilewilltravelwhenthelaunchangleischanged.Materials4SqueezeRockets1SqueezeRocketBulbProtractorMeasuringtape StopWatch****Pleaseexercisegreatcautionwhenfiringtheserockets.Besurethelineoffireisclearofpeopleandbreakableobjectspriortolaunchinganyrocket.****Procedure1. NOTE:Rocketswilloftentakeunpredictableflightpaths.Toensuredataprecision,onlyrecordtrialsinwhichtherockettravelsaparabolicpathandcontactsthegroundwiththefrontendfirst.2. Markthespotfromwhichtherocketswillbelaunched.3. LoadaSqueezeRocketontothebulb.4. Usingaprotractor,aligntherockettoanangleof90°(vertical).5. Squeezethebulb(youwillneedtoreplicatethisforceforeachtrial),andsimultaneouslystartthestopwatchuponlaunch(alternatively,haveapartnerhelpyoukeeptime).Measureandrecordthetotaltimetherocketisintheair.Repeatthisstepthreeormoretimes,andaverageyourresults.tavg5. Calculatetheinitialvelocityoftherocket(v initial = v oy )usingthekinematicsequationsprovided.RecordyourcalculationinTable3below.(Hint:youcantaketheinitialheightaszero.Theverticalvelocityiszeroatthepeakoftheflight,whenthetimeisequalto.) 6. Repeatthistrialtwomoretimes,andrecordthevaluesinTable3below.7. Choosefouradditionalanglestofiretherocketfrom.Beforelaunchingtherocket,calculatethepredictedrangeusingthekinematicsequationsandtheangleoflaunch.Rememberthatyoucanusezeroforanyinitialpositions,andthattheaccelerationduetogravity,g,is–9.8m/s 2 . RecordthesevaluesinTable3.8. Next,aligntherocketwiththefirstanglechoiceandfireitwiththesameforceyouusedinitially.Trytorecordlauncheswheretherockettravelsinaparabolaanddoesnotstallorflutteratthetop(thismighttakeseveralrepetitions).Measurethedistancetraveledwiththemeasuringtape.Repeatthisfortwoadditionaltrials,recordingtheactualrangeinTable3.64


Lab5:ProjectileMotion9. RepeatStep7fortheremaininganglesandrecordthedatainTable3.Table3:Projectilerangevs.launchangledataInitialVelocity(m/s)InitialAnglePredictedRange(m)ActualRange(m)Average%Error90° 0 Questions1. Drawadiagramshowingarocketflyingatanarbitraryangle.Indicatetheforceduetogravityandforceduetoairresistance.Whydoesthedirectionofthenetforcechangeoverthecourseoftherocket’strajectory?65


Lab5:ProjectileMotion2. Explainhowthelaunchangleaffectsboththetrajectoryandfinalrangeoftherocket.Whatangle(orrangeofangles)appearstoproducethegreatestrange?3. Knowingthekinematicsequations,whatangleshouldyieldthegreatestprojectilerange,disregardingairresistanceandotherfactors?Showallcalculations.4. Howdoesairresistanceaffecttheaccuracyandprecisionofyourrocketdatainthislab?66


Lab5:ProjectileMotion5. Calculatethepercenterrorbetweenyourmeasuredvaluesandthepredictedvalues.Giventhenatureofthesqueezerocketandyourresults,commentonanyothersourcesoferrorthatsignificantlyaffectyourdistancemeasurements.6. Howwouldakickeronafootballteamusehisknowledgeofphysicstobetterhisgame?Listsomeothersportsorinstanceswherethisinformationwouldbeuseful.67


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