LabManual
AcceleratedPhysicsVersion3.2
© 2011 eScience Labs, Inc.
All rights reserved
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TableofContents
Introduction
Lab1:TheScientificMethod
Lab2:LabReports
Lab3:Measurements
NewtonianMechanics
Lab4:LinearMotion
Lab5:ProjectileMotion
Lab6:TypesofForces
Lab7:Newton’sLaws
Lab8:Gravity
Lab9:WorkandEnergy
Lab10:SimpleMachines
Lab11:CenterofMass
Lab12:Momentum
Lab13:CircularMotion
Lab14:TorqueandRotation
Lab15:Oscillations
MatterandThermalPhysics
Lab16:ExploringMatter
Lab17:ChangeofPhase
Lab18:PropertiesofSolids
Lab19:FluidMechanics
Lab20:TemperatureandHeat
Lab21:Thermodynamics
Lab22:HeatTransfer
WavesandLight
Lab23:PropertiesofWaves
Lab24:Sound
Lab25:LightandColor
Lab26:GeometricOptics
ElectricityandMagnetism
Lab27:ElectricFields
Lab28:ElectricCurrent
Lab29:TypesofCircuits
Lab30:MagneticFields
Lab31:ElectromagneticInduction
3
GoodLaboratoryPractices
GoodLaboratoryPractices
Sciencelabs,whetheratuniversitiesorinyourhome,areplacesofadventureanddiscovery.Oneofthefirst
thingsscientistslearnishowexcitingexperimentscanbe.However,theymustalsorealizesciencecanbedanͲ
gerouswithoutsomeinstructionongoodlaboratorypractices.
General
x Readtheprotocolthoroughlybeforestartinganynewexperiment.Youshouldbefamiliarwiththe
actionrequiredeverystepoftheway.
x Useeyeprotectionwhenexperimentingwithchemicals,batteries,andprojectiles.
x Keepallworkspacesfreefromclutteranddirtydishes.
x Washyourhandsaftereachexperiment.
x Thoroughlyrinselabware(testtubes,beakers,etc.)betweenchemicalexperiments.Todoso,wash
withasoapandhotwatersolutionusingabottlebrushtoscrub.Rinsecompletelyatleastfourtimes.
Letairdry.
x Donotaimprojectilesorothermovingmaterialsatotherindividuals.
MaterialsandChemicals x Useonlythematerialsneededforeachactivity
x Alwayshandlehotwatercarefullyandwithnecessaryhandandeyeprotection.
x Whenusingknivesorblades,alwayscutawayfromyourself.
x Neverusemorebatteriesthananexperimentspecifies.Donotcreateelectricalcircuitsotherthan
thosespecifiedbythelabmanual.
x Avoidcreating“shortcircuits”withelectricalequipment.Thiscancauseunsafebatterytemperatures.
x Immediatelydryanywetelectronics—especiallyinthecaseofspilledliquids.Makesurematerialsare
completelydrybeforeresumingwork.
x Avoidprolongedexposureofbatteriesandchemicalstodirectsunlightandextremetemperatures.
x Immediatelysecurethelidorsealthepackageofliquids,powders,andothermaterialsafteruse.
4
GoodLaboratoryPractices
x Usetesttubecapsorstopperstocovertesttubeswhenshakingormixing–notyourfingers!
x Useanewpipetteforeachchemicaldispensed.
x Neverreturnexcesschemicalbacktotheoriginalbottle.Thiscancontaminatethechemicalsupply.
x Becarefulnottointerchangelidsbetweendifferentchemicalbottles.
x Wipeupanychemicalspillsimmediately.CheckMSDSsforspecialhandlinginstructions(providedon
www.eScienceLabs.com).
x Readthelabelsonallchemicals,andnotethechemicalsafetyratingoneachcontainer.Readall
MSDS(providedonwww.eScienceLabs.com).
x ReadtheMSDSbeforedisposingofachemicaltoinsureitdoesnotrequireextrameasures.(provided
onwww.eScienceLabs.com)
5
Lab5:ProjectileMotion
Lab5:ProjectileMotion
Conceptstoexplore
x
Scalarsvs.vectors
x Projectiles
x Parabolictrajectory
AsyoulearnedintheLinearMotionLab,aquantitythatconveysinformationaboutmagnitudeonlyiscalledascalar.
However,whenaquantity,suchasvelocity,conveysinformationaboutmagnitudeanddirection,wecallitavector.
Alongwithcarryingthatextrabitofinformationaboutthepathofmotion,vectorsarealsousefulinphysicsbecausethey
canbeseparatedintocomponents.Infact,anyvectorcanberesolved(brokendownto)anequivalentsetofhorizontal
(xͲdirection)andvertical(yͲdirection)components,whichareatrightanglestoeachother.
A
Ay
Ax
Figure1:ThevectorAcanbebrokenupintohorizontalandverticalcomponents,AxandAy.
Consideravectorarrowdrawnonarectangularcoordinateplane,asvectorApicturedinFigure1(Fordistinction,the
boldedtypesignifiesavector).ThehorizontalcomponentofavectoristhedistancealongthexͲaxisthatthevectorcovͲ
ers,whiletheverticalcomponentisinthedirectionoftheyͲaxis.Iftheanglebetweenthehorizontalcomponentandthe
vectorisɽ,youcanusetrigonometrytofindthemagnitudeofthecomponents:
Ay
A sin T
Ax
A cos T
whereAisthemagnitude,orlength,oftheoriginalvector.UsingthePythagoreanTheorem,themagnitudeofanyvecͲ
torcanbeexpressedintermsofitscomponentsas
A
Ax2 Ay2
55
Lab5:ProjectileMotion
andtheanglefromthehorizontalaxiscanbefoundusing:
tan ș
Ax
Ay
Vectoradditionisdonebyaddinghorizontalandverticalcomponents.Inotherwords,thehoriͲ
zontalcomponentofthenewvector—oftencalledthe“resultant”—issimplythesumofthe
horizontalcomponentsofthetwoaddedvectors.Likewise,theverticalcomponentofthereͲ
sultantisthesumoftheindividualverticalcomponents.Youcanthenfindthemagnitudeand
angleoftheresultantusingthetrigonometricequationsabove.
Figure2:Someexamples
ofprojectilesareacanͲ
nonballfiredfromacanͲ
Aprojectileisanyobjectwhich,onceprojectedataninitialvelocity,continuesinmotionbyits
non,abaseballhitbya
owninertiaandisinfluencedonlybythedownwardforceofgravity.RememberthatNewton’s bat,andballsbeingjugͲ
Lawsdictatethatforcescauseacceleration,notsimplymotion.Therefore,theonlyforceacting gledintheair.Allthese
objectsfollowacurved
onaprojectileinitsFreeBodyDiagramistheforceofgravitydownward.Thismayseem
pathduetotheforceof
counterͲintuitivesincetheobjectmightinitiallybemovinginseveraldirections,bothhorizonͲ
gravity.
tallyandvertically,butgravityactsonlyontheverticalmotionoftheobject.
OneconvenientthingaboutusingvectorstodescribeprojectilemoͲ
tionisthatwecanseparatethevelocityoftheprojectileintohorizonͲ
talandverticalmotion.Theverticalcomponentofthevelocity
changeswithtimeduetogravity,butthehorizontalcomponentreͲ
mainsconstantbecausenohorizontalforceisactingontheobject(air
resistanceaddsquiteabitofcomplicationathighervelocitiesbutwill
beneglectedinthislab).Wecanthusanalyzeeachcomponentofthe
projectile’svelocityseparately.Thecombinationofa(constantly)
changingverticalvelocityandaconstanthorizontalvelocitygivesa
projectile’strajectorytheshapeofaparabola.
Figure3:Whenaprojectile(water,inthiscase)is
launchedupwardtheverticalaccelerationwill
reachzeroatthetopoftheparabola.Asgravity
pullstheobjecttowardtheEarththeobjectaccelͲ
erates.Horizontalvelocityremainsconstant
throughoutthismotion.
56
AsshowninFigure4,theprojectilewithhorizontalandverticalmoͲ
tionassumesacharacteristicparabolictrajectoryduetotheeffects
ofgravityontheverticalcomponentofmotion.ThehorizontalmoͲ
tionistheresultofNewton’sFirstLawinaction(youwillleanabout
thisinLab7)–theobject’sinertia!Ifairresistanceisneglected,there
arenohorizontalforcesactinguponprojectile,andthusnohorizontal
acceleration.Itmightseemsurprising,butaprojectilemovesatthe
samehorizontalspeednomatterhowlongitfalls!
Thekinematicequations(Figure5)fromthepreviouslabcandescribe
bothcomponentsofthevelocityseparately.FormosttwoͲ
dimensionalprojectilemotionproblems,thefollowingfourequations
willallowyoutosolvefordifferentaspectsofaprojectile’sflight,as
Lab5:ProjectileMotion
longasyouknowtheinitialpositionandtheinitialvelocity.InthislabyoucanassumethatprojectilesarefiredeithervertiͲ
callyorhorizontally,sothattheinitialvelocitiesineithercasewilleitherbevx = voxorvy = voy.(Thetermvox canberead
as“initialvelocityinthexdirection.”)
Figure4:Asthecannonballintheupperpicturetravelsaparabolicpath,itgainsvelocityduetogravͲ
ity.Youcanseethatthespacebetweensuccessive“snapshots”oftheballgetsgraduallylarger.BeͲ
causegravityonlyacceleratestheballdirectlydownward,onlytheverticalvelocityoftheball
changes.Asyoucanseeinthesecondfigure,theverticalspacingincreasesaccordingtot2,whilethe
horizontalspacingisconstant.Onesurprisingresultoftheindependenceofverticalandhorizontal
motionsisthatiftwoprojectilesarelaunchedatthesametimefromthesameheight,theywillhitthe
groundandthesametime!Theirhorizontalvelocitiesdonotaffecttherateatwhichtheywillfall.
57
Lab5:ProjectileMotion
Inthecasewhereaprojectileisnotlaunchedeitherverticallyorhorizontally,theinitialvelocitycomponentscanbeexͲ
pressedastrigonometricfunctionsofthetotalinitialvelocity,vo:
v ox
vx
v cos T
voy
v sin T
Asyoucansee,forș = 0 (acompletelyhorizontallaunch),thehorizontalvelocityisequaltothetotalinitialvelocityv,while
theverticalvelocityisequaltozero.Meanwhile,forș = 90 (averticallaunch),thehorizontalvelocityiszerowhilethevertiͲ
calvelocityisequaltothetotalinitialvelocity.
UsingthekinematicsequationsofFigure5youcancalculatethe
totaldistanceorrange,R,ofaprojectile.Iftheprojectileisfiredat
anangle,therangeisafunctionoftheinitialangleɽ,theinitialveͲ
locity,andtheforceofgravity.Usingalittlealgebra,youcanderive
thisexpressionusingthekinematicsequationsabove:
v sin( 2T )
g
2
R
Figure5:Fourusefulkinematicequationsfor
projectilemotion:
x
xo v x t
vy
voy gt
y
y o voy t 1 2
gt
2
2 g y yo Thisrangeequationisusefulsolongastheinitialheightandfinal
2
2
heightoftheprojectileareequal.Iftheobjectendsuphigheror
y
oy
lowerthanitstarted,youwillhavetousetheindividualkinematics
equationstosolveforthetotalrange.Itisimportanttoremember
thatinmanycases,airresistanceisnotnegligibleandaffectsboththehorizontalandverticalcomponentsofvelocity.
Whentheeffectofairresistanceissignificant,therangeoftheprojectileisreducedandthepaththeprojectilefollowsis
notatrueparabola.
v
58
v
Lab5:ProjectileMotion
Figure6:Thepathofaprojectileintheabsenceofairresistanceisaperfectparabola(top);however,with
airresistancetheprojectileexperiencesadeceleratingforceintheoppositedirectionofitsmotion.The
resultistheshortenedcurveshown(bottom).
59
Lab5:ProjectileMotion
Experiment1:Calculatingthedistancetraveledbyaprojectile
Inthisexperimentyouwillapplywhatyouknowaboutprojectilemotionandusekinematicstopredicthowfaraprojectile
willtravel.
Materials
x
Ramp
x Marble
x Cornstarch
x 4Sheetsofblackconstructionpaper
x Measuringtape
x Monofilamentline
x Washer
x *Papertowel
x *Water
*Youmustprovide Figure7:RampsetupforExperiment1
Procedure1
1. PlacetheramponatableasshowninFigure7(referencethediagramatthebeginningofthemanualforramp
assemblyinstructions).Markthelocationatwhichyouwillreleasethemarble.Thiswillensurethemarble
achievesthesamevelocitywitheachtrial.
2. Createaplumblinebyattachingthewashertothemonofilamentline.
3. Holdthestringtotheedgeofthetableandmarkthespotatwhichtheweighttouchestheground.(Note:The
plumblinehelpstomeasuretheexactdistancefromtheedgeoftheramptothepositionwherethemarble
“lands.”)
4. Laydownarunwayofconstructionpaper.
5. Wetthemarbleallover,anddropintothecornstarchbagtocoat.Rollonapapertoweltoachieveasmoth,
evencoatalloverthemarble(youdonotwantanychunksasitwillaffectthepathofmotion).WhenthemarͲ
blehitstheconstructionpaper,theforcewilltransfersomeofthecornstarchtothepaperandallowyoutopinͲ
pointwherecontactwasfirstmade.
5. Begintheexperimentbyreleasingthemarbleatthemarkedpointontheramp.
6. Measurethedistancetraveledtothefirstmarkmadeontheconstructionpaperusingthemeasuringtape.ReͲ
cordthisvalueinTable1below.
7. RepeatSteps5Ͳ6twomoretimesandfindtheaveragedistance.RecordyourdatainTable1.
8. Next,usethisaveragedistancetocalculatetheaverageinitialvelocityofthemarblewhenleavingthetable.
AverageVelocityCalculation:
60
Lab5:ProjectileMotion
Procedure2
1. Findahighertable,orstacksomebooksunderneaththeramptoincreasetheheight.Measurethestarting
heightattheendoftherampasbefore.
2. Usingtheaveragevelocityfoundearlier,predicthowfarawaythemarblewilllandusingthekinematicequaͲ
tions.RecordthisdistanceinTable2.(Hint:youuseoneequationtofindthetotaltimeintheairusingtheiniͲ
tialandfinalheights,andanothertofindthehorizontaldistance)
3. Measurethisdistanceoutandmarkitbeforeyoureleasethemarble.ReleasethemarblethreetimesandreͲ
cordthedistancetraveledinTable2.
4. Completethetablesbelowusingyourmeasurements.
5. OPTIONALExercise:Setuptheramptoanewheight,andcalculatethepredictedrange.PlaceaStyrofoamcup
withasmallamountofwateratyourpredicteddistance.Releasethemarblefromtheramp,testingyourpreͲ
dictionbywhetherornotitlandsinthecup.
Table1:Projectiledistanceandvelocitydata
Table+Ramp
Height
Distancetraveled
AverageDistance
AverageVelocity
Table2:Projectiledistanceandvelocitydata
Table+Ramp
Height
Calculated
Distance
ActualDistance
ActualDistanceAverͲ
age
61
Lab5:ProjectileMotion
Questions
1. Ifyouweretothrowaballhorizontallyandatthesametimedropanexactcopyoftheballyouthrew,which
ballwouldhitthegroundfirstandwhyisthisso?
2. Whatforcesareactingonthemarblebeforeandafteritleavestheramp?
3. Describetheaccelerationofamarblefortheperiodafteritleavestherampandbeforeithitstheground.
4. DidyourpredictioninProcedure2comeclosetotheactualspot?Findthepercenterrorofyourpredicted
distance(expected)comparedtotheactualaveragedistance(observed).
62
Lab5:ProjectileMotion
5. Explainsomepossiblesourcesoferrorthatcouldhaveproducedthedeviationabove.
63
Lab5:ProjectileMotion
Experiment2:SqueezeRocketprojectiles
Theobjectiveofthislabistoobservethedistanceaprojectilewilltravelwhenthelaunchangleischanged.
Materials
x
x
x
x
x
4SqueezeRockets
1SqueezeRocketBulb
Protractor
Measuringtape
StopWatch
****Pleaseexercisegreatcautionwhenfiringtheserockets.BesurethelineoffireisclearofpeopleandbreakableobͲ
jectspriortolaunchinganyrocket.****
Procedure
1. NOTE:Rocketswilloftentakeunpredictableflightpaths.Toensuredataprecision,onlyrecordtrialsinwhich
therockettravelsaparabolicpathandcontactsthegroundwiththefrontendfirst.
2. Markthespotfromwhichtherocketswillbelaunched.
3. LoadaSqueezeRocketontothebulb.
4. Usingaprotractor,aligntherockettoanangleof90°(vertical).
5. Squeezethebulb(youwillneedtoreplicatethisforceforeachtrial),andsimultaneouslystartthestopwatch
uponlaunch(alternatively,haveapartnerhelpyoukeeptime).Measureandrecordthetotaltimetherocketis
intheair.Repeatthisstepthreeormoretimes,andaverageyourresults.
t a vg
5. Calculatetheinitialvelocityoftherocket(vinitial = voy )usingthekinematicsequationsprovided.Recordyour
calculationinTable3below.(Hint:youcantaketheinitialheightaszero.Theverticalvelocityiszeroatthe
peakoftheflight,whenthetimeisequalto–Ȁʹ.) 6. Repeatthistrialtwomoretimes,andrecordthevaluesinTable3below.
7. Choosefouradditionalanglestofiretherocketfrom.Beforelaunchingtherocket,calculatethepredicted
rangeusingthekinematicsequationsandtheangleoflaunch.Rememberthatyoucanusezeroforanyinitial
positions,andthattheaccelerationduetogravity,g,is–9.8m/s2.RecordthesevaluesinTable3.
8. Next,aligntherocketwiththefirstanglechoiceandfireitwiththesameforceyouusedinitially.Trytorecord
launcheswheretherockettravelsinaparabolaanddoesnotstallorflutteratthetop(thismighttakeseveral
repetitions).Measurethedistancetraveledwiththemeasuringtape.Repeatthisfortwoadditionaltrials,reͲ
cordingtheactualrangeinTable3.
64
Lab5:ProjectileMotion
9. RepeatStep7fortheremaininganglesandrecordthedatainTable3.
Table3:Projectilerangevs.launchangledata
Initial
Initial
Velocity(m/s) Angle
90°
Predicted
Range(m)
0
ActualRange(m)
Average
%Error
Questions
1. Drawadiagramshowingarocketflyingatanarbitraryangle.Indicatetheforceduetogravityandforcedueto
airresistance.Whydoesthedirectionofthenetforcechangeoverthecourseoftherocket’strajectory?
65
Lab5:ProjectileMotion
2. Explainhowthelaunchangleaffectsboththetrajectoryandfinalrangeoftherocket.Whatangle(orrangeof
angles)appearstoproducethegreatestrange?
3. Knowingthekinematicsequations,whatangleshouldyieldthegreatestprojectilerange,disregardingairresisͲ
tanceandotherfactors?Showallcalculations.
4. Howdoesairresistanceaffecttheaccuracyandprecisionofyourrocketdatainthislab?
66
Lab5:ProjectileMotion
5. Calculatethepercenterrorbetweenyourmeasuredvaluesandthepredictedvalues.Giventhenatureofthe
squeezerocketandyourresults,commentonanyothersourcesoferrorthatsignificantlyaffectyourdisͲ
tancemeasurements.
6. Howwouldakickeronafootballteamusehisknowledgeofphysicstobetterhisgame?Listsomeother
sportsorinstanceswherethisinformationwouldbeuseful.
67
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