Lab 7: Projectile Motion
Lab 7: Projectile Motion
Lab 7: Projectile Motion
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IntroductoryPhysicsV1Introduction <strong>Lab</strong>1:TheScientificMethod <strong>Lab</strong>2:<strong>Lab</strong>Reports <strong>Lab</strong>3:MeasurementsNewtonianMechanics <strong>Lab</strong>4:TypesofForce <strong>Lab</strong>5:Newton’sLaws <strong>Lab</strong>6:Linear<strong>Motion</strong> <strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong> <strong>Lab</strong>8:Circular<strong>Motion</strong> <strong>Lab</strong>9:CenterofMass <strong>Lab</strong>10:Gravity <strong>Lab</strong>11:Energy <strong>Lab</strong>12:Momentum <strong>Lab</strong>13:MechanicalAdvantageMatter <strong>Lab</strong>14:ExploringMatter <strong>Lab</strong>15:PropertiesofSolids <strong>Lab</strong>16:PropertiesofFluidsTableofContents3
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>Conceptstoexplore: Scalersvs.vectors<strong>Projectile</strong>sParabolictrajectoryFigure1:Theverticalandhorizontalforcesrequiredtopullagliderintoflightcanbeachievedwithonetowrope.Asyoulearnedpreviously,aquantitythatconveysinformationaboutmagnitudeonlyiscalledascalar.However,whenaquantity,suchasvelocity,conveysinformationaboutmagnitudeanddirection,wecallitavector.Alongwithcarryingthatextrabitofinformationaboutthepathofmotion,vectorsarealsousefulinphysicsbecausetheycanbeseparatedintocomponents.Infact,anyvectorcanberesolved(brokendown)intoanequivalentsetofhorizontal(xdirection)andvertical(ydirection)components,whichareatrightanglestoeachother.Aprojectileisanobjectactedonbygravityalone.Typically,aprojectileisanyobjectwhich,onceprojected,continuesinmotionbyitsowninertiaandisinfluencedonlybythedownwardforceofgravity.RememberthatNewton’sLawsdictatethatforcescauseacceleration,notsimplymotion.Therefore,theonlyforceactingonaprojectileinitsFreeBodyDiagramistheforceofgravitydownward.Thismayseemcounterintuitivesincetheobjectmightinitiallybemovinginseveraldirections,bothhorizontallyandvertically,butgravityactsonlyontheverticalmotionoftheobject.Figure2:Someexamplesofprojectilesareacannonballfiredfromacannon,abaseballhitbyabat,andballsbeingjuggled.79
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>Figure3:Noticehowthehorizontaldistancetheprojectilecoversisconstantregardlessofitsverticalmotion.Thisshowsthataprojectile’shorizontalvelocityisconstant.Ifyoufireaprojectilehorizontallyatthesametimeasdroppingonestraightdown,theywillhitthegroundatthesametime!Evenextremelyfastprojectilessuchasbulletsfallattheratedeterminedbygravity.80
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>Figure4:Whenaprojectile(water,inthiscase)islaunchedupward,theverticalaccelerationwillreachzeroatthetopoftheparabola.AsgravitypullstheobjecttowardtheEarth,theobjectaccelerates.Horizontalvelocityremainsconstantthroughoutthismotion.Figure5:Fourusefulkinematicequationsforprojectilemotion:Oneconvenientthingaboutusingvectorstodescribeprojectilemotionisthatwecanseparatethevelocityoftheprojectileintohorizontalandverticalmotion.Theverticalcomponentofthevelocitychangeswithtimeduetogravity,butthehorizontalcomponentremainsconstantbecausenohorizontalforceisactingontheobject(airresistanceaddsquiteabitofcomplicationathighervelocitiesbutwillbeneglectedinthislab).Sinceprojectilesmoveintwodimensions(verticalandhorizontal),thisallowsforindependentanalysisofeachcomponentoftheobject’smotion.Thecombinationofa(constantly)changingverticalvelocityandaconstanthorizontalvelocitygivesaprojectile’strajectorytheshapeofaparabola.AsshowninFigure3,theprojectilewithhorizontalandverticalmotionassumesacharacteristicparabolictrajectoryduetotheeffectsofgravityontheverticalcomponentofmotion.ThehorizontalmotionistheresultofNewton’sFirstLawinaction–theobject’sinertia!Ifairresistanceisneglected,therearenohorizontalforcesactinguponprojectile,andthusnohorizontalacceleration.Itmightseemsurprising,butaprojectilemovesatthesamehorizontalspeednomatterhowlongitfalls!Thekinematicsfromthepreviouslabcandescribebothcomponentsofthevelocityseparately.Formosttwodimensionalprojectilemotionproblems,thefollowingfourequationswillallowyoutosolvefordifferentaspectsofaprojectile’sflight,aslongasyouknowtheinitialpositionandtheinitialvelocity.Thetwonewequationscanbeobtainedthroughsubstitution.Inthislabyoucanassumethatprojectilesarefiredeitherverticallyorhorizontally,sothattheinitialvelocitiesineithercasewillbeeither:v o =v yo orv o =v xo. Usingtheequationsabove,youcancalculatethetotaldistanceorrange,R,ofaprojectile.Iftheprojectileisfiredatanangle,therangeisafunctionoftheinitialangle,theinitialvelocityandtheforceofgravity.Usingalittlealgebra,youcanderivethisexpressionusingthekinematicsequationsabove:81
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>Figure6:Thepathofaprojectileintheabsenceofairresistanceisaperfectparabola(top);withairresistancethetrajectorylookslikea“squashed”parabola,andtherangeoftheobject’sflightisnoticeablyaffected. R=v 2 sin(2) gItisimportanttorememberthatinmanycases,airresistanceisnotnegligibleandaffectsboththehorizontalandverticalcomponentsofvelocity.Whentheeffectofairresistanceissignificant,therangeoftheprojectileisreducedandthepaththeprojectilefollowsisnotatrueparabola.82
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>Experiment1:CalculatingthedistancetraveledbyaprojectileTheobjectiveofthislabistopredicttherangeofaprojectilesetinmotion.MaterialsRampMarbleCornstarch4sheetsofblackconstructionpaperTapemeasureMonofilamentlineFishingsinkerProcedure11. Placetheramponatableandmarkthelocationatwhichyouwillreleasethemarble.Thiswillensurethemarbleachievesthesamevelocitywitheachtrial.2. CreateaplumblinebyattachingthefishingsinkertotheFigure7:Rampsetupdiagrammonofilamentline.3. Holdthestringtotheedgeoftheramp,andmarkthespotatwhichtheweighttouchestheground.Note:Theplumblinehelpstomeasuretheexactdistancefromtheedgeoftheramptothepositionwherethemarble“lands.”4. Laydownarunwayofconstructionpaper.5. Wetthemarblealloverwithwater,anddropintothecornstarchbagtocoat.Rollonapapertoweltoachieveasmooth,evencoatofcornstarchalloverthemarble(youdonotwantanychunksasitwillaffectthepathofmotion.)Whenthemarblehitstheconstructionpaper,theforcewillcausesomeofthecornstarchtocomeoff,andleaveamarkontheconstructionpapersoyoucanseethepointoffirstcontact!6. Begintheexperimentbyreleasingthemarbleatthemarkedpointontheramp.7. Measurethedistancetraveledtothefirstmarkmadeonthecarbonpaperusingthetapemeasure.RecordthisvalueinTable1onthefollowingpage.8. Repeatsteps57ninemoretimesandrecordyourdatainTable1.9. Next,useyourdatatocalculatethevelocityofthemarbleforeachtrial.Procedure21. Findahighertable,orstacksomebooksunderneaththeramptoincreasetheheight.Measurethestartingheightattheendoftherampasbefore.2. Usingtheaveragevelocityfoundearlier,predicthowfarawaythemarblewilllandusingthekinematicequations.RecordthisdistanceinTable2.(Hint:youcaneitheruseoneequationtofindthetotaltimeintheairusingtheinitialandfinalheights,andanothertofindthehorizontaldistance,oryoucanusetherangeequationwith=0.)3. Measurethisdistanceoutandmarkitbeforeyoureleasethemarble.ReleasethemarblefourtimesandrecordthedistancetraveledinTable2.83
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>Calculations:Table1:Rangeandvelocityofprojectile,Procedure1TableHeight(m) DistanceTraveled AvgDistance AverageVelocityTable2:Rangeofprojectile,Procedure2TableHeight(m) ObservedDistance PredictedDistance ObservedD(avg)84
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>Questions1. Ifyouweretothrowaballhorizontallyandatthesametimedropanexactcopyoftheballyouthrew,whichballwouldhitthegroundfirstandwhyisthisso?2. Supposeyoualteredyourexistingrampsothatthemarbleshadtwicetheirinitialvelocityrightbeforeleavingtheramp.Howwouldthischangethetotaldistancetraveledandthetimethatthemarbleswereintheair?3. DrawaFBDforthemarblesbeforeandafteritleavestheramp.4. Describetheaccelerationofthemarblesafteritleavestheramp.5. DidyourpredictioninProcedure2comeclosetotheactualspot?Findthepercenterrorofyourpredicteddistance(expected)comparedtotheactualaveragedistance(observed).Whataresomesourcesoferrorinthisexperiment? %error=observedvalueexpectedvalueX100 expectedvalue 85
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>Experiment2:SqueezeRocketprojectilesTheobjectiveofthislabistoobservethedistanceaprojectilewilltravelwhenthelaunchangleischanged.Materials4SqueezeRockets1SqueezeRocketBulbProtractorTapemeasureStopwatchNOTE:Pleaseexercisegreatcautionwhenfiringtheserockets.Besurethelineoffireisclearofpeopleandbreakableobjectspriortolaunchinganyrocket.Rocketswilloftentakeunpredictableflightpaths.Toensuredataprecision,onlyrecordtrialsinwhichtherockettravelsaparabolicpathandcontactsthegroundwiththefrontendfirst.Procedure1. Markthespotfromwhichtherocketswillbelaunched.2. LoadaSqueezeRocketontothebulb.3. Usingaprotractor,aligntherockettoanangleof90°(vertical).4. Squeezethebulb(youwillneedtoreplicatethesamepressureforeachtrial),andsimultaneouslystartthestopwatchuponlaunch(alternatively,haveapartnerhelpyoukeeptime).Measureandrecordthetotaltimetherocketisintheair.Repeatthisstepthreeormoretimes,andaverageyourresults.RecordyourresultsinTable3. t avg =______________5. Calculatetheinitialvelocityoftherocket(v initial =v oy )usingthekinematicsequations.6. RecordyourcalculationinTable3.(Hint:youcantaketheinitialheightaszero.Theverticalvelocityiszeroatthepeakoftheflight,whenthetimeisequaltot/2.)7. Repeatthistrialtwomoretimes,andrecordthevaluesinTable3.8. Choosefouradditionalanglestofiretherocketfrom.Beforelaunchingtherocket,calculatetheexpectedrangeusingtheverticalvelocityandtheanglefromwhichtherocketswillbefired.Rememberthatyoucanusezeroforanyinitialpositions,andthattheaccelerationduetogravity,g,86
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>is9.8m/s 2 .RecordthesevaluesinTable3.9. Next,aligntherocketwiththefirstanglechoiceandfireitwiththesameforceyouusedinitially.Trytorecordlauncheswheretherockettravelsinaparabolaanddoesnotstallorflutteratthetop.Measurethedistancetraveledwiththetapemeasure.Repeatthisfortwoadditionaltrials,recordingtheactualrangeinTable3.10. RepeatStep7foratleast5additionalanglesandrecordthedatainTable3.11. Recordthepercenterrorbetweenyourcalculatedandactualvaluesinthelastcolumn.Table3:<strong>Projectile</strong>dataforExperiment2InitialVelocity(m/s)InitialAnglePredictedRange(m)ActualRange(m)Average %Error90° 0 *Note:%error=observedvalueexpectedvaluex100 expectedvalueQuestions1. Whatistheanglethatgivesthegreatestrange?Theleast?Basedonyourresults,whichangleshouldgivethegreatestrangeforprojectilemotion?87
<strong>Lab</strong>7:<strong>Projectile</strong><strong>Motion</strong>2. DrawaFBDforarocketlaunchedatanarbitraryangle(assumetherockethasjustonlybarelyleftthelaunchtube,andneglectairresistance).3. Whatroledoesairresistanceplayinaffectingyourdata?4. Discussanyadditionalsourcesoferror,andsuggesthowtheseerrorsmightbereducedifyouweretoredesigntheexperiment.5. Howwouldakickeronafootballteamusehisknowledgeofphysicstobetterhisgame?Listsomeotherexamplesinsportsorotherapplicationswherethisinformationwouldbeimportantoruseful.88
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