IntroductoryPhysics
PHYS101
Dr RichardH.Cyburt
AssistantProfessorofPhysics
Myoffice:402cintheScienceBuilding
Myphone:(304)384-6006
Myemail:[email protected]
Inpersonoremailisthebestwaytogetaholdofme.
PHYS101
MyOfficeHours
TRF9:30-11:00am
F12:30-2:00pm
Meetingsmayalsobearrangedatothertimes,byappointment
PHYS101
PHYS101:IntroductoryPhysics
400
Lecture:8:00-9:15am,TRScienceBuilding
Lab1:3:00-4:50pm,FScienceBuilding304
Lab2:1:30-3:20pm,MScienceBuilding304
Lab3:3:30-5:20pm,MScienceBuilding304
Lab20:6:00-7:50pm,MScienceBuilding304
PHYS101
MasteringPhysicsOnline
GotoHYPERLINK"http://www.masteringphysics.com."www.masteringphysics.com.
◦ UnderRegisterNow,selectStudent.
◦ Confirmyouhavetheinformationneeded,thenselectOK!Registernow.
RCYBURTPHYS101),andchooseContinue.
◦ Enteryourinstructor’sCourseID(
◦ EnteryourexistingPearsonaccountusername andpassword andselectSignin.
◦ YouhaveanaccountifyouhaveeverusedaPearsonMyLab &Masteringproduct,suchasMyMathLab,MyITLab,MySpanishLab,or
MasteringChemistry.
◦ Ifyoudon’thaveanaccount,select Create andcompletetherequiredfields.
◦ Selectanaccessoption.
◦ Entertheaccesscodethatcamewithyourtextbookorwaspurchasedseparatelyfromthebookstore.
PHYS101
IntroductoryPhysics
PHYS101
DouglasAdams
Hitchhiker’sGuidetotheGalaxy
PHYS101
You’realreadyknowphysics!
Youjustdon’tnecessarilyknowtheterminologyand
languageweuse!!!
PhysicsofNASCAR
PhysicsofAngerBirds
PHYS101
Inclass!!
PHYS101
Thislecturewillhelpyouunderstand:
DescribingMotion
UniformMotion
InstantaneousVelocity
Acceleration
PHYS101
Chapter2Preview
LookingBack:MotionDiagrams
AsyousawinSection1.5,agoodfirststepinanalyzingmotionistodrawamotiondiagram,
markingthepositionofanobjectinsubsequenttimes.
Inthischapter,you’lllearntocreatemotiondiagramsfordifferenttypesofmotionalongaline.
Drawingpictureslikethisisagoodstaringpointforsolvingproblems.
©2015PearsonEducation,Inc.
Chapter2Preview
StoptoThink
Abicycleismovingtotheleftwithincreasingspeed.Whichofthefollowingmotiondiagrams
illustratesthismotion?
©2015PearsonEducation,Inc.
Section2.1Describing
Motion
©2015PearsonEducation,Inc.
RepresentingPosition
Themotiondiagramofastudentwalkingtoschoolanda
coordinateaxisformakingmeasurements
EverydotinthemotiondiagramofFigure2.2representsthestudent’spositionataparticular
time.
Figure2.3showsthe
student’smotionshows
thestudent’spositionas
agraph ofx versust.
©2015PearsonEducation,Inc.
FromPositiontoVelocity
Onaposition-versus-timegraph,afaster
speedcorrespondstoasteeperslope.
Theslopeofanobject’sposition-versus-time
graphistheobject’svelocityatthatpointin
themotion.
©2015PearsonEducation,Inc.
FromPositiontoVelocity
Text:p.31
©2015PearsonEducation,Inc.
FromPositiontoVelocity
Wecandeducethevelocity-versus-timegraph
fromtheposition-versus-timegraph.
Thevelocity-versus-timegraphisyetanother
waytorepresentanobject’smotion.
©2015PearsonEducation,Inc.
QuickCheck 2.2
Hereisamotiondiagramofacarmovingalongastraightroad:
Whichvelocity-versus-timegraphmatchesthismotiondiagram?
E. None of the above.
©2015PearsonEducation,Inc.
QuickCheck 2.2
Hereisamotiondiagramofacarmovingalongastraightroad:
Whichvelocity-versus-timegraphmatchesthismotiondiagram?
C.
E. None of the above.
©2015PearsonEducation,Inc.
QuickCheck 2.3
Hereisamotiondiagramofacarmovingalongastraightroad:
Whichvelocity-versus-timegraphmatchesthismotiondiagram?
©2015PearsonEducation,Inc.
QuickCheck 2.3
Hereisamotiondiagramofacarmovingalongastraightroad:
Whichvelocity-versus-timegraphmatchesthismotiondiagram?
D
.
©2015PearsonEducation,Inc.
QuickCheck 2.4
Agraphofpositionversustimeforabasketballplayermovingdownthecourt
appearsasfollows:
Whichofthefollowingvelocitygraphsmatchesthepositiongraph?
A.
©2015PearsonEducation,Inc.
B.
C.
D.
QuickCheck 2.4
Agraphofpositionversustimeforabasketballplayermovingdownthecourt
appearsasfollows:
Whichofthefollowingvelocitygraphsmatchesthepositiongraph?
C.
A.
©2015PearsonEducation,Inc.
B.
D.
Example2.2Analyzingacar’sposition
graph
FIGURE2.11 givestheposition-versus-timegraphofacar.
a. Drawthecar’svelocityversus-timegraph.
b. Describethecar’smotion
inwords.
PREPARE Figure2.11isagraphicalrepresentationofthemotion.Thecar’s
position-versus-timegraphisasequenceofthreestraightlines.Eachofthese
straightlinesrepresentsuniformmotionataconstantvelocity.Wecan
determinethecar’svelocityduringeachintervaloftimebymeasuringtheslope
oftheline.
©2015PearsonEducation,Inc.
Example2.2Analyzingacar’sposition
graph(cont.)
SOLVE
a.
Fromt=0stot=2s(Δt =2s)thecar’sdisplacementis
Δx =-4m- 0m=-4m.Thevelocityduringthisintervalis
Thecar’spositiondoesnotchange
fromt=2stot=4s(Δx =0m),so
vx =0m/s.Finally,thedisplacement
betweent=4sandt=6s(Δt =2s)is
Δx =10m.Thusthevelocityduring
thisintervalis
ThesevelocitiesarerepresentedgraphicallyinFIGURE 2.12.
©2015PearsonEducation,Inc.
Example2.2Analyzingacar’sposition
graph(cont.)
SOLVE
b. Thevelocity-versus-timegraphof
Figure2.12showsthemotionina
waythatwecandescribeina
straightforwardmanner:Thecar
backsupfor2sat2m/s,sitsat
restfor2s,thendrivesforwardat
5m/sfor2s.
ASSESS Noticethatthevelocitygraphandthepositiongraphlookcompletely
different.Theyshould!Thevalueofthevelocitygraphatanyinstantoftime
equalstheslopeofthepositiongraph.Sincethepositiongraphismadeupof
segmentsofconstantslope,thevelocitygraphshouldbemadeupof
segmentsofconstantvalue,asitis.Thisgivesusconfidencethatthegraph
wehavedrawniscorrect.
©2015PearsonEducation,Inc.
FromVelocitytoPosition
Wecandeducetheposition-versus-timegraph
fromthevelocity-versus-timegraph.
Thesignofthevelocitytellsuswhetherthe
slopeofthepositiongraphispositiveor
negative.
Themagnitudeofthevelocitytellsushow
steeptheslopeis.
©2015PearsonEducation,Inc.
QuickCheck 2.1
Hereisamotiondiagramofacarmovingalongastraightroad:
Whichposition-versus-timegraphmatchesthismotiondiagram?
©2015PearsonEducation,Inc.
QuickCheck 2.1
Hereisamotiondiagramofacarmovingalongastraightroad:
Whichposition-versus-timegraphmatchesthismotiondiagram?
E.
©2015PearsonEducation,Inc.
QuickCheck2.6
Agraphofvelocityversustimeforahockeypuckshotintoagoalappears
asfollows:
Whichofthefollowingpositiongraphsmatchesthevelocitygraph?
A.
©2015PearsonEducation,Inc.
B.
C.
D.
QuickCheck2.6
Agraphofvelocityversustimeforahockeypuckshotintoagoalappears
asfollows:
Whichofthefollowingpositiongraphsmatchesthevelocitygraph?
A.
©2015PearsonEducation,Inc.
B.
C.
D.
(d)
QuickCheck 2.7
Whichvelocity-versus-timegraph
goeswiththispositiongraph?
©2015PearsonEducation,Inc.
QuickCheck 2.7
Whichvelocity-versus-timegraph
goeswiththispositiongraph?
C.
©2015PearsonEducation,Inc.
Section2.2Uniform
Motion
©2015PearsonEducation,Inc.
UniformMotion
Straight-linemotioninwhichequal
displacementsoccurduringany
successiveequal-timeintervalsis
calleduniformmotion orconstantvelocitymotion.
Anobject’smotionisuniformifand
onlyifitsposition-versus-timegraph
isastraightline.
©2015PearsonEducation,Inc.
EquationsofUniformMotion
Thevelocityofanobjectinuniformmotiontellsustheamountbywhichits
positionchangesduringeachsecond.
ThedisplacementΔx isproportionaltothetimeintervalΔt.
©2015PearsonEducation,Inc.
QuickCheck 2.8
Hereisapositiongraph
ofanobject:
Att =1.5s,theobject’s
velocityis
◦ 40m/s
◦ 20m/s
◦ 10m/s
◦ –10m/s
◦ Noneoftheabove
©2015PearsonEducation,Inc.
QuickCheck 2.8
Hereisapositiongraph
ofanobject:
Att =1.5s,theobject’s
velocityis
◦
◦
◦
◦
◦
40m/s
20m/s
10m/s
–10m/s
Noneoftheabove
©2015PearsonEducation,Inc.
Example2.3IfatrainleavesClevelandat
2:00…
Atrainismovingduewestataconstantspeed.
Apassengernotesthatittakes10minutestotravel12km.
Howlongwillittakethetraintotravel60km?
©2015PearsonEducation,Inc.
Example2.3IfatrainleavesClevelandat
2:00…(cont.)
SOLVE Wearecomparingtwocases:thetimetotravel12kmandthetimetotravel60km.
BecauseΔx isproportionaltoΔt,theratioofthetimeswillbeequaltotheratioofthedistances.
Theratioofthedistancesis
Thisisequaltotheratioofthetimes:
Ittakes10minutestotravel12km,soitwilltake50minutes—5timesaslong—totravel60km.
©2015PearsonEducation,Inc.
ExampleProblem
Asoccerplayeris15mfromheropponent’sgoal.
Shekickstheballhard;after0.50s,itfliespastadefenderwho
stands5maway,andcontinuestowardthegoal.
Howmuchtimedoesthegoaliehavetomoveintopositiontoblock
thekickfromthemomenttheballleavesthekicker’sfoot?
©2015PearsonEducation,Inc.
FromVelocitytoPosition,OneMore
Time
ThedisplacementΔx isequaltotheareaunderthevelocitygraphduringthetimeintervalΔt.
©2015PearsonEducation,Inc.
QuickCheck 2.11
Hereisthevelocitygraphofanobjectthatisattheorigin
(x = 0m)att = 0s.
Att = 4.0s,theobject’s
positionis
◦ 20m
◦ 16m
◦ 12m
◦ 8m
◦ 4m
©2015PearsonEducation,Inc.
QuickCheck 2.11
Hereisthevelocitygraphofanobjectthatisattheorigin
(x = 0m)att = 0s.
Att = 4.0s,theobject’s
positionis
◦ 20m
◦ 16m
◦ 12m
◦ 8m
◦ 4m
Displacement = area under the curve
©2015PearsonEducation,Inc.
Section2.3
InstantaneousVelocity
©2015PearsonEducation,Inc.
InstantaneousVelocity
Forone-dimensionalmotion,anobjectchangingitsvelocityiseitherspeeding
uporslowingdown.
Anobject’svelocity—aspeedand adirection—ataspecificinstant oftimet is
calledtheobject’s instantaneousvelocity.
Fromnowon,the
word“velocity”will
alwaysmean
instantaneousvelocity.
©2015PearsonEducation,Inc.
FindingtheInstantaneousVelocity
Ifthevelocitychanges,thepositiongraphisacurvedline.Butwecan
computeaslopeatapointbyconsideringasmallsegmentofthe
graph.Let’slookatthemotioninaverysmalltimeintervalright
aroundt=0.75s.Thisishighlightedwithacircle,andweshowa
closeup inthenextgraph.
©2015PearsonEducation,Inc.
FindingtheInstantaneousVelocity
Inthismagnifiedsegmentofthepositiongraph,thecurveisn’t
apparent.Itappearstobealinesegment.Wecanfindtheslopeby
calculatingtheriseovertherun,justasbefore:
vx =(1.6m)/(0.20s)=8.0m/s
Thisistheslopeatt=0.75sandthusthevelocityatthisinstantoftime.
©2015PearsonEducation,Inc.
FindingtheInstantaneousVelocity
Graphically,theslopeofthe
curveatapointisthesame
astheslopeofastraightline
drawntangent tothecurveat
thatpoint.Calculatingrise
overrunforthetangentline,
weget
vx =(8.0m)/(1.0s)=8.0m/s
Thisisthesamevalueweobtainedfromthecloseup view.Theslopeofthetangentlineisthe
instantaneousvelocityatthatinstantoftime.
©2015PearsonEducation,Inc.
InstantaneousVelocity
Evenwhenthespeedvarieswecanstillusethevelocity-versus-timegraphtodetermine
displacement.
Theareaunderthecurveinavelocity-versus-timegraphequalsthedisplacementevenfornonuniformmotion.
©2015PearsonEducation,Inc.
QuickCheck 2.5
Theslopeatapointonaposition-versus-timegraphofanobjectis
◦ Theobject’sspeedatthatpoint.
◦ Theobject’svelocityatthatpoint.
◦ Theobject’saccelerationatthatpoint.
◦ Thedistancetraveledbytheobjecttothatpoint.
◦ Iamnotsure.
©2015PearsonEducation,Inc.
QuickCheck 2.5
Theslopeatapointonaposition-versus-timegraphofanobjectis
◦ Theobject’sspeedatthatpoint.
◦ Theobject’svelocityatthatpoint.
◦ Theobject’saccelerationatthatpoint.
◦ Thedistancetraveledbytheobjecttothatpoint.
◦ Iamnotsure.
©2015PearsonEducation,Inc.
QuickCheck2.10
MassesP andQ movewiththepositiongraphsshown.DoP andQ
everhavethesamevelocity?Ifso,atwhattimeortimes?
◦
◦
◦
◦
P andQ havethesamevelocityat2s.
P andQ havethesamevelocityat1sand3s.
P andQ havethesamevelocityat1s,2s,and3s.
P andQ neverhavethesamevelocity.
©2015PearsonEducation,Inc.
QuickCheck2.10
MassesP andQ movewiththepositiongraphsshown.DoP andQ
everhavethesamevelocity?Ifso,atwhattimeortimes?
◦
◦
◦
◦
P andQ havethesamevelocityat2s.
P andQ havethesamevelocityat1sand3s.
P andQ havethesamevelocityat1s,2s,and3s.
P andQ neverhavethesamevelocity.
©2015PearsonEducation,Inc.
QuickCheck2.13
Acarmovesalongastraightstretchofroad.Thefollowinggraphshowsthecar’s
positionasafunctionoftime:
Atwhatpoint(orpoints)dothefollowingconditionsapply?
• Thedisplacementiszero.
• Thespeediszero.
• Thespeedisincreasing.
• Thespeedisdecreasing.
©2015PearsonEducation,Inc.
QuickCheck2.13
Acarmovesalongastraightstretchofroad.Thefollowinggraphshowsthecar’s
positionasafunctionoftime:
Atwhatpoint(orpoints)dothefollowingconditionsapply?
• Thedisplacementiszero.
D
• Thespeediszero.
B,E
• Thespeedisincreasing.
C
• Thespeedisdecreasing.
A
©2015PearsonEducation,Inc.
Section2.4Acceleration
©2015PearsonEducation,Inc.
Acceleration
Wedefineanewmotionconcepttodescribeanobjectwhosevelocityischanging.
◦ TheratioofΔvx/Δt istherateofchangeofvelocity.
◦ TheratioofΔvx/Δt istheslopeofavelocity-versus-timegraph.
©2015PearsonEducation,Inc.
UnitsofAcceleration
InourSIunitofvelocity,60mph=27m/s.
TheCorvettespeedsupto27m/sinΔt=3.6s.
Everysecond,theCorvette’svelocity
changesby7.5m/s.
©2015PearsonEducation,Inc.
Itiscustomarytoabbreviate
theaccelerationunits(m/s)/sasm/s2,which
wesayas“meterspersecond
squared.”
Example2.6Animalacceleration
Lions,likemostpredators,arecapableofveryrapidstarts.Fromrest,alioncansustainan
accelerationof9.5m/s2 foruptoonesecond.Howmuchtimedoesittakealiontogofromrest
toatypicalrecreationalrunner’stopspeedof10mph?
PREPARE WecanstartbyconvertingtoSIunits.Thespeedthelionmustreachis
Thelioncanaccelerateat9.5m/s2,changingitsspeedby9.5m/spersecond,foronly1.0s—long
enoughtoreach9.5m/s.Itwilltakethelionlessthan1.0storeach4.5m/s,sowecanuseax =
9.5m/s2 inoursolution.
©2015PearsonEducation,Inc.
Example2.6Animalacceleration(cont.)
SOLVE Weknowtheaccelerationandthedesiredchangeinvelocity,sowecanrearrangeEquation
2.8tofindthetime:
ASSESS Thelionchangesitsspeedby9.5meterspersecondinonesecond.Soit’sreasonable(ifa
bitintimidating)thatitwillreach4.5m/sinjustunderhalfasecond.
©2015PearsonEducation,Inc.
Inclass!!
PHYS101