物理降落伞速率实验报告

MYPScienceClaudiaZhangScience10-AMay14,2015MotionLaboratoryReportBackgroundinformation/Introduction:Theinvestigationistotestwhethertheincreaseofthesurfaceareaofanobjectwouldcauseachangeinthevelocitysincethereismoreairresistanceforalargersurfacearea.Thetheorywillbetestedthroughtheexperimentofdroppingdifferentsizesofparachutesattachingtoajuicebox.Purpose:Toobserveafreefallingobject(withaparachutemadeofplasticbagsattachedtoit),incasethattheinfluentialfactors(thesizeoftheobject,theheightofthereleasingpoint,theverticaldistancebetweentheparachuteandtheobjectetc.)stayconstant,howdoeschangingthesurfaceareaoftheparachuteaffectthevelocityofthefallingobject?Hypothesis:Ifthesurfaceareaoftheparachuteincreases,thenthedownwardaveragevelocityoftheobjectwoulddecreaseduetotheincreasedairresistance.Iftheobjectisfallingdownwiththeforceofgravity,applyingNewton’sSecondlaw:Force=MassxAcceleration,thefallingobjecthas“mass·gravity”offorce.Sincetheearthisnotavacuum,thentherewouldbeairresistanceactingupwardasthemgofforceispullingtheobjectdownward:“Airresistanceisafriction-likeforcethatopposesthemotionofobjectsthatmovethroughtheair…Theamountoftheairresistanceforcedependsonthespeed,size,shape[andcross-sectionalarea]oftheobject”(BCScience,399)and“howthickthefluidisthatisgoingthrough”whichistheairitself.Airresistanceisvelocitydependent,because“airresistanceistheresultofcollisionsoftheobject'sleadingsurfacewithairmolecules”(ThePhysicsClassroom).Iftheobjecthasagreaterspeedofvelocity,theobjectwouldhittheparticlesharderandwouldinteractwithmoreparticlesintheairpersecond.Thiscreatesgreaterfrictionsbetweentheobjectandtheairandthuscreatingmoreairresistancetoslowdownthefallingobject.Inaddition,theformulaforcalculatingtheforceofairresistanceis“Fair=(1/2)CρSV2”(Baidu)whereCrepresentsdragcoefficient,prepresentsairdensity,Srepresentsthesurfacearea,andVrepresentsvelocity.Inthecaseoftheinvestigation,wherethedragcoefficient,andtheairdensityareconstant,therelationshipbetweentheforceofairresistanceandvelocitycanapproximatelybewrittenas“Fair=S·V2”.TheVintheinvestigationisalwaysnegativebecausetheobjectisfallingdownward.Therefore,fromtheequation,itcanbepredictedthatFairisdirectlyproportionaltoS,andtothesquareofV.However,sinceVisnegative,asthenumberdecreases(whichmeansthereisgreatervelocitydownwards),thesquareofitwillstillbepositive,thereforeitwouldincreaseFair.“Eventually,theforceofairresistancebecomeslargeenoughtobalancetheforceofgravity·mass.Atthisinstantintime,thenetforceiszeroNewton;theobjectwillstopaccelerating”(ThePhysicsclassroom),andreachtoterminalvelocity.Becausethelargersurfaceareaofaparachutewouldincreasetheamountofairresistance,whichmeansthatitwouldreachterminalvelocityinashorteramountoftime,thusdecreasingtheaveragevelocityofthefallingobject.Therefore,itisassumedthatifthesurfaceareaoftheparachuteincreases,itwouldcreatemoreforceofairresistance,reachingtoterminalvelocityinashortertimeperiod,andthusdecreasestheaveragedownwardvelocity.Variable:IndependentSurfaceareaofthegarbage-bagparachutes30cmx30cm;40cmx40cm;50cmx50cm;60cmx60cm,70cmx70cmDependentVelocityofthefallingobjects(cm/s)ConstantSizeoftheobject(acut-openjuiceboxwith4.7cminlength,3.8cminwidth,6cminheight)Heightbetweentheparachuteandtheobject(10cm)Distancebetweenthereleasingpointandthepointwheretheobjecttouchestheground(2.3m)Distancebetweenthefilmingpositionandthedroppingarea(4.5m)Surroundingconditions(sameplacewhendroppingtheobject,sameplacewhenvideotapping)Materials:CapablelaptopcomputerwithLoggerPro3.8.5installedX1PortableCamera/CameraphoneX1Camera/phoneUSBX1Plasticbagscutinsquare-Size30cmx30cmX1-Size40cmx40cmX1-Size50cmx50cmX1-Size60cmx60cmX1-Size70cmx70cmX1Cut-openedemptyJuiceboxX6(withlength4.7cm,width3.8cm,height6cmandweighted4.5g)Strings·20.8cmX4·27.2cmX4·33.9cmX4·40.7cmX4·47.6cmX41mlongrulerX130cmlongrulerX1NeedleX1Diagram:Safety:UsetheneedlecarefullyandmakesureitdoesnotdoharmtopeopleStandonthegroundfirmlyandmakesurepeopledonotfallfromthe2.3mtallplace.Dotheexperimentunderthesupervisionofaninstructor.FollowtheinstructionscarefullyEnvironmentalconcerns:Theprocessofmakingtheparachutesmayresultsinwastingplasticbags.Sinceplasticbagsarenotabletodecomposenaturallyinthesoil,itisneededforthemanualprocessestoeitherburnthem.Theburningplasticbagsreleasedioxingaswhichisacompoundthatis50-100timesmoretoxicthanpotassiumcyanide.Thedioxinwouldentertheecologicalfoodchainfromsoil,pickedupbyplants,furtherconcentratedinprimaryandsecondaryconsumersandeventuallyconsumedbyhumans.Itcanalsoenterthehumanbodydirectlybyhumaninhalingwhichcouldcausecancerandthedamageinskins,immunesystem,reproductivesystemandendocrinesystemetc.Toreducetheuseofplasticbagsintheinvestigation,itispracticaltojustuseonepieceofplasticbagthatis70x70cm.Theotherscalesoftheplasticbagscanbecutfromthe70x70cmscale.Alsoitisessentialtoputtheusedplasticbagsintotherecyclebinaftertheinvestigation.Thewastedjuiceboxedwillbeputintotherelevantrecyclebinandotherdisposalwillgointothegarbagecaninordertomaintainacleanandhealthyenvironment.Procedure:ProcedureforExperimentwithparachutesMeasureaplacethatis2.3mhighwiththe1mruler,wherethereisnoobstacleandyoucandroptheobjectfromtheheight.Twopeoplecarrythefourcornersofthe30x30cmparachutewitheachoftheirhands.Onepersonstands4.5metersfarverticallyinfrontofthedroppingarea,facingtowardsthedroppingarea.*Makesurethatthestringsarenottangledup,andthegarbagebagisnotcrumbled;itisthejuiceboxthatisinthe2.3mhighpositioninsteadoftheparachute.Thetwopeopleholdthefourcornersoftheparachute2.3mhigh(asmeasured)fromthegroundwhilethefilmingpersonstandsinplaceandpreparetovideotapetheprocessofdropping.Makesurethecameraisneitherangledupnordown.*becarefulofthesafetyhazardinwhichpeoplemightfallfromthe2.3mhighplace.Thepersonclicksfilmingaboutthreeseconds,andthenthetwopeoplecarefullyreleasetheparachuteatthesametime.(Leavingthreesecondsbeforetheactualdroppingwouldallowaneasiermanipulationandprocessionofthedatalateron)Makeobservationastheobjectgoesdown.Thepersonclicksstopafterthejuiceboxandtheparachutereachtheground.Labelthevideocliponthecamera/phone.Ex:“30x30cmAtpt1”Repeatstep2-6fortentimes.Repeatstep2-7byusing40cmx40cm,50cmx50cm,60cmx60cmand70cmx70cmparachutes.ProcedureforExperimentwithoutParachutesOnepersoncarriesthejuicebox(withouttheparachute)2.3mhighfromthegroundwhiletheotherpersonstandsinplaceandpreparestovideotapetheprocess.Makesurethecameraisneitherangledupnordown.Thepersonclicksfilmingaboutthreeseconds,andthenthepersonholdingthejuiceboxcarefullyreleasethebox.Repeatstep5-7Repeatstep10-12fortenattempts.ManipulationofDataConnectthecamera/thephonewiththelaptopcomputerImportallthevideoclipstakenfortheexperimentintoanewfolder.Makesurethevideoclipsareineither“.mov”,“.mpeg”,“.wav”or“.avi”format.OpenLoggerPro3.8.5Click‘insert’and‘movie’ontheLoggerProprogramanduploadthevideoclipfromthenewfolder.ClickonbuttonClickthisbuttonontherightofthevideotosetthescale.Setthescale:createalineonthevideoverticallyfromthereleasingpointtothepointwheretheparachutefallsonto.Theninsert2.3mfor‘distance’and‘unit’onthepop-upwindow.(Thisstepcalibratesthevideo)MovevideountiltheparachuteisjustabouttoleavethehandsUsetoclickonthetopedgeofthejuiceboxframebyframetoplotitsmotion.Clickontheprogramandthenclicktofindthebestfitlinearlineoftheresultinggraph.(ignoretheredlinebecauseitrecordsthehorizontalmotion)Recordtheslope(whichisthevelocitym/sforthefallingobject)ofthelinearlineinexcel.ChangethedatafromVelocitym/stoVelocitycm/s.RepeatStep4-12forallthe60attempts.Recordallthedatainexceltable.Calculatetheaverageforeachoftheattemptsonexcel.Graphthedata.SettingupthejuiceboxandtheparachutesUsingtheneedletopokeasmallholeoneachtopcornerofthecut-openedjuicebox.Threadtheneedlewiththe20.8cmlongstringTaketheneedlewiththestringthroughthesmallholefromoutside.Tiethestring;makesurethestringdoesnotslideaway.Tietheothersideofthestringononecornerofthe30cmx30cmplasticbagbythreadingtheneedlethroughthecornerwiththestring.Repeatstep2-4fortheotherthreestrings.Repeatstep1-5foralltheotherfourscaleswhereusing27.2cmlongstringsfor40cmx40cmplasticbag,33.9cmfor50cmx50cm,40.7cmfor60cmx60cmand47.6cmfor70cmx70cm.DataCollection:RawdataSurfaceArea(cm²)Velocity(-cm/s)Atpt1Atpt2Atpt3Atpt4Atpt5Atpt6Atpt7Atpt8Atpt9Atpt10Average0x0376.2376.6394.9389.3394.9386.1382.7398.3370.8388.7385.8530x3096.74123.9110.2106.3103.7121.890.8692.67109.9126.8108.28740x4089.8472.6078.0795.4276.4684.8674.8892.2986.07111.686.20950x5080.6282.4273.7774.85116.183.9670.8263.9273.8176.3979.66660x6072.7755.0272.8788.2181.2783.0268.5668.9092.5575.3775.85470x7070.8259.5855.1463.7672.8659.4475.0552.1372.0364.2764.508ProcessedDataSurfaceArea(cm²)Velocity(-cm/s)0x0385.8530x30108.28740x4086.20950x5079.66660x6075.85470x7064.508Observations:Theparachutesswingbackandforthastheyfalldown.Thesurfaceoftheplasticbagbecomesasemi-sphereshapeasitfallsdown.Thejuiceboxreachesthegroundfirst.Sometimesthejuiceboxmightflipasitjustreachestheground.Graph:        Sample:Thefirstattemptfortrial40x40cmGraphwithouttheoutlier0x0cm²dataGraphwiththeoutlierAnalysis:      Lengthofthestringtomaketheheightbetweentheparachuteandthejuiceboxtobeconstant:PythagoreanTheorem:a2+b2=c2Ex:30cmx30cmtrial:(eq\f(30-4.7,2))2+(eq\f(30-3.8,2))2=331.6325cm2331.6325+102=431.6325cm2eq\r(431.6325)≈20.8cmAverageVelocityFormulaforcalculatingtheaverage:x=EQ\F(1,n)(x1+x2+.....+xn)→average=EQ\F(1,10)(attempt1+attempt2+…+attempt10)Ex:30cmx30cmtrial:EQ\F(1,10)(96.74+123.9+110.2+106.3+103.7+121.8+90.86+92.67+109.9+126.8)=108.287–cm/sTransformfromVelocitym/stoVelocitycm/sEx:30cmx30cmfirstattempt:1m=100cm0.9674m/sx100=96.74cm/sConclusion&Evaluation: Thedataandgraphscarriedoutfromtheinvestigationsupportthehypothesisthatasthesurfaceareaoftheparachuteincreases,theaveragevelocity–cm/sdecreases.Forexample,thehighestpointonthegraph,ifincludingthe0x0cm2parachuteincrement,isatthex-axisof0x0cm2parachutewithdownwardvelocity385.85cm/s,whichrepresentsthattheincrementhasthehighestaveragevelocityin–cm/s.Ifnotincludingtheoutlierof0x0cm2parachuteincrement,thenthehighestpointisat30x30cm2parachuteincrement,thesmallestsurfaceareaamongalltestedincrements,withdownwardvelocityof108.287cm/s.Thelowestpointonthegraphisatthex-axisof70x70cm2parachutewithdownwardvelocityof64.508cm/s.Thedownwardvelocityforthesurfacearea40x40cm2parachuteis86.209cm/s,for50x50cm2is79.666cm/s,andfor60x60cm/sis75.854cm/srespectively,whichclearlyshowsadecreasingtrendline,andthusshowsthattheamountofdownwardvelocityisdecreasingasthesurfaceareaoftheparachutegetslarger.Theenlargedsurfaceareaoftheparachutecausestheincreasedpossibilityofmoresuccessfulcollisionshappeningbetweentheairmoleculesandthesurfaceareaoftheparachutepersecond.Therefore,ithasagreaterforceofairresistance.Inaddition,theresultingdatacanalsoshowtosupportthehypothesisthatairresistanceisvelocitydependentbyusingtheformulaFair=S·V2extractedfromtheformulaFair=(1/2)CρSV2whichmentionedpreviously.Usingthesamplegraphof40x40cm2parachuteasanexample,thefirstpartofthegraphhasnotreachedterminalvelocityyet,wherethedownwardvelocitycm/sishigherthantheaverage.Supposethedownwardvelocityofthatpartis90cm/s,thensubstitutedintothesimplifiedformula:Fair=(40)(40)·(-90)2,andFairwouldassumetobe12960kunit;thensubstitutetheaveragevelocityin:Fair=(40)(40)·(-86)2,andFairwouldbe11833.6kunit.Fromtheresultofthecalculation,itissupportedthattheforceofairresistanceisdirectlyproportionaltotheobject’svelocity.Additionally,althoughnotshown,thetwoproceedgraphsstillhaveillustratedthatthetrendofthegraphwouldmuchsteeperwiththeoutlier0x0cm2parachuteincrementthanwithoutit.Thedownwardvelocityofthefallingobjectwithoutparachuteisaboutthreetimesgreaterthanthatofthefallingobjectwith30x30cm2parachute,showingthattherewouldbeahugedecreasechangeinvelocitybyincreasingthebaseareaofthe4.7x3.8cm2objectto30x30cm2.However,thedataindetailedisinaccurate,andthiscanbedemonstratedbythedifferencesbetweenthevelocitiesofeachincrement,excludingtheoutlier.Forexample,thedifferencebetweenthedownwardvelocityof30x30cm2and40x40cm2parachuteincrementis108.287-86.209=22.078cm/s.Thenexttwodifferencestendtofollowadecreasingpatternbypresenting6.543cm/sdifferencebetween40x40cm2and50x50cm2incrementand,3.812cm/sdifferencebetween50x50cm2and60x60cm2increment.However,thedifferencebetween60x60cm2and70x70cm2incrementbreaksthepatternbyresultinginadifferenceof11.346cm/s.Itcanalsobeshownbylookingatthegraph,wheretherearedotsgoingaboveandbelowthetrendlinewithoutanyorder.Theresultingdataisreliableinalargerscale,butnotreliableinthepartialdetails.Itisfairlyprecisebecausethemoreattemptsthereare,themoreaccuratelywillthecalculatedaveragebe,andtheinvestigationhastenattemptsforeachincrementinsteadofthreeasusuallyrequired.Howeverinminordetails,therepeatedreadingsforeachtrialarenotveryclose.Forexamplefortrial50x50cm2,withallattempts’dataresultstobearound70cm/sto80cm/s,theeighthtrialreachesonly63.92cm/s.Especiallyforthefifthattemptwhereitreachesto116.1cm/s,itisaresultthatisevenhigherthananyattemptresultofthe30x30cm2increment.Suchwouldleadtothelaterinaccuracyoftheaveragevelocity,thusaffectingvaliditytodrawconclusion.Italsorepresentsthatthedataisnotreliableiftolookintodetails.Thereareseveraluncontrollablefactorsdiscoveredandproblemsoccurredasweprocessedthroughtheinvestigation.Themajoronesthatwillaffectthevalidityaretheconstantvariablescontrol,issuesinindependentvariableanddisadvantaginglocation.Thedisadvantaginglocationwherewedidourinvestigationsetsthedatatobeinaccurate.Duetothelimitedlocationsprovidedinschool,itishardtofindaplacewith2.3mtallwithnoobstaclesandpeoplecanstandonitsafely.Theplacewechoseisthestairsinthelobbywhereithasa“bump”stickoutfromthelateralsurfaceofthestairs.Forseveraltimesthattheparachuteshitthe“bump”asitfallsdown.Forexampleinthemiddle-leftofthesamplegraph,thereisasignificantdifferenceonthedottedtrend,andthatiswhentheparachutehitsthe“bump”.Thiswouldaffecttheaccuracyofthedatagreatlybecausethechangeinthedottedlinewouldfirstaffecttheauto-calculationoftheslope(thevelocityinm/s)intheprogram.Thentheinaccuratevelocitieswouldgointotheattemptsandaffecttheresultofaveragevelocity.However,theten-timesattemptsreducestheeffetenessoftheissuebylittletomaketheresultingdatastillexplainable.Toresolvethisproblem,itisessentialtoattheline“thereisnoobstacleandyoucandroptheobjectfromtheheight”whenfindingthelocationtodotheinvestigation.Withsuchawarenessinmind,thepossibilityoftheoccurredproblemwoulddecrease.Theissueinthex-axisofthegraphhasbeenidentifiedthroughprocessingthedata.Thex-axisofthegraphseemstobeincreasinginaconsistentratebyshowing“30x30,40x40,50x50etc”.However,itisnotconsistentlyincreasingbecauseitisincreasedbycentimetersquareinsteadofcentimeter.Ifcalculated,itwillbe900cm2,1600cm2,2500cm2,3600cm2,4900cm2fortheincreasingindependentvariables.Fromthat,itcantellthattheindependentvariableisnotconstantlyincreasinginalinearratebutinahalf-parabolashape.Thiswouldnotaffecttheresultofthedata,butwillinfluencetheconclusioniftocomparetherelationshipbetweeneachincrementfurtheron.Additionally,thereareseveralconstantvariablesthatcannotbecontrolledwhichwouldaffecttheaccuracyoftheresultingdata.Forexample,theleadingsurfaceareaforeachobjectwithparachutewouldnotbeexactly30cm2becausethereisstillthebasesurfaceareaofthejuiceboxaheadoftheparachuteasitfallsdown.Alsothedistancebetweentheparachuteandthejuiceboxisuncontrollable.Thisisbecausethedistancebetweenthetwoisconstant10cmiftheplasticbagisinaflatform.However,astheobjectfallsdown,theparachuteturnsintoasame-sphereshape,andthedifferentstringlengthswouldmakethefactortobeinconsistent.Theseuncontrollablefactorswouldaffecttheresultingdatabecausetheonlysupposedvariablesthatarechangingisthedependentvariable(velocity–cm/s)andindependentvariable(surfacearea).Therefore,thechanginginconstantvariableswoulddistracttheaccuracyofthedata.Inordertoinvesttheresearchquestionsuccessfullyitisessentialtosolvetheproblemsmentionedabove.Sincetheinvestigationwithparachuteastheobjectwouldinvolvesomuchuncontrollablefactorsandareinevitabletohaveerrorsoccurduringtheexperiment,itwouldbebettertochangeitsimplerobjectthanparachute.Forexample,usingdifferencesizesofballswouldavoidtheproblemsmentionedabove.Forexample,itdoesnotinvolvetheproblemsofobjectchangingshapesasitfallsdown:theballisinasphere-form,whichalsomeansthattherewillbesameamountofsurfaceareawillinteractwiththeairmoleculesforeachsizeoftheball.Alsodoingtheballexperimentdoesnotinvolveindeterminingthingssuchasthelengthsofthestringsforeachparachute,andthuswouldreducethecomplexityoftheprocedure,andmakestheinvestigationmorestraightforward.Howevertherewillbepossibleproblemshappenintheexperimentoffree-fallingballs.Forexample,thedifferentsizeoftheballmaybemadeofdifferentmaterialssuchaswoodorelastic,thesurfaceofdifferentmaterialwouldhavedifferenttexture,andwithdifferenttexturesofthematerial,itmightinterferewiththeaccuracyofvelocityduetothefrictionofairresistance.Theproblemwillbefoundtoresolveinfurtherresearchandexperiments.WorksCited:"FreeFallandAirResistance."FreeFallandAirResistance.Web.15May2015."Newton'sSecondLaw."Newton'sSecondLaw.Web.15May2015."ObjectsFallingwithAirResistance(partI)."YouTube.YouTube.Web.15May2015."牛顿运动定律之降落伞下落的规律."百度文库.Web.15May2015.Translation:patternofafallingparachuteaccordingtoNewton’slaws,BaiduEssays"空气阻力."百度百科.Web.15May2015.Translation:Airresistance,BaiduEncyclopedia"空气阻力和速度的关系."百度知道.Web.15May2015.Translation:Relationshipbetweenairresistanceandspeed,BaiduKnowledge"空气阻力的计算."百度知道.Web.15May2015.Translation:CalculatingAirresistance,BaiduKnowledge"空气阻力计算公式."百度作业帮.Web.15May2015.Translation:AirresistanceFormula,BaiduHomeworkHelp"降落伞动量定理."百度文库.Web.15May2015.Translation:motiontheoremoffallingparachute,BaiduEssay