Download PHYS101

IntroductoryPhysics
PHYS101
Dr RichardH.CyburtOfficeHours
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byappointment
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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
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PHYS101
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PHYS101
IntroductoryPhysics
PHYS101
DouglasAdams
Hitchhiker’sGuidetotheGalaxy
PHYS101
You’realreadyknowphysics!
Youjustdon’tnecessarilyknowtheterminologyand
languageweuse!!!
PhysicsofNASCAR
PhysicsofAngerBirds
PHYS101
ThankstomywifeandtheOED
plusquamperfection, n.
[‘ Utterperfection.’]
Pronunciation: Brit. /ˌplʌskwampəˈfɛkʃn/, U.S. /ˈˌpləsˌkwæmpərˈfɛkʃ(ə)n/
Origin:A borrowingfromLatin.Etymon:Latin plūs quam.
Etymology: < German Plusquamperfektion (1603as plusquamperfection inthepassagetranslatedinquot. 1670)< classicalLatin plūs
quam morethan(see plusquam- comb.form)+German Perfektion perfection n. Comparepost-classicalLatin plusquam perfectio(1687in
thepassagetranslatedinquot. 1688;8thcent.inaBritishsourceingrammaticalsense).
Alchemy.Now hist. and rare. Utterperfection.1657 tr. B.Valentinus LastWill&Test. iii. 117 Thisliquoristhetrueprimamateria,and
firstseedofMetalsandMinerals,whichbyVulcansArtisbroughttoaplusquam perfection[Ger. plusquamperfection],intoa
transcendentfix'd Medicine,outofwhichisgeneratedthetruePhilosophick stone.
1670 D.Cable tr. B.Valentinus OfNat.&Supernat.Things iii.57 Ifit..be broughttoaperfectripeness,untothePlusquam perfection
[Ger. plusquamperfection],nothingmaycomparetherewith.
1688 C.Packe tr. F.M.vanHelmont 153Chymical Aphorisms 22Aph.135 Whereforethisoughttobedonetothematterofour
Menstruum,foritscompleat Depuration,equallyastoGold,forits plusquam perfection[L. adejus plusquam pefectionem].
1713 RosieCrucianSecrets(MSHarl.6485)f.268, Itisaheavenlybalsambecauseitsfirstprinciplesandoriginalcomethfromheaven,
madeformalinearthorunderground,andisafterwards,beingexactlyprepared,broughtintoaplusquam perfection.
PHYS101
Inclass!!
PHYS101
Thislecturewillhelpyouunderstand:
TheBasicEnergyModel
Work
KineticEnergy
PotentialEnergy
PHYS101
Section10.1TheBasic
EnergyModel
©2015PearsonEducation,Inc.
TheBasicEnergyModel
Everysysteminnaturehasaquantitywecallitstotal energy E.
©2015PearsonEducation,Inc.
FormsofEnergy
Someimportantformsofenergyare
◦ KineticenergyK:energyofmotion.
◦ GravitationalpotentialenergyUg:storedenergyassociatedwithanobject’sheightabovetheground.
◦ Elasticorspringpotentialenergy Us:energystoredwhenaspringorotherelasticobjectisstretched.
◦ ThermalenergyEth:thesumofthekineticandpotentialenergiesofallthemoleculesinanobject.
◦ ChemicalenergyEchem:energystoredinthebondsbetweenmolecules.
◦ NuclearenergyEnuclear:energystoredinthemassofthenucleusofanatom.
©2015PearsonEducation,Inc.
EnergyTransformations
Energyofonekindcanbetransformed intoenergyofanotherkindwithinasystem.
©2015PearsonEducation,Inc.
EnergyTransformations
Theweightlifterconverts
chemicalenergyinherbody
intogravitationalpotential
energyofthebarbell.
©2015PearsonEducation,Inc.
Elasticpotentialenergyofthe
springboardisconvertedinto
kineticenergy.Asthediverrises
intotheair,thiskineticenergyis
transformedintogravitational
potentialenergy.
QuickCheck10.1
Achildisonaplaygroundswing,motionlessatthehighest
pointofhisarc.Whatenergytransformationtakesplaceas
heswingsbackdowntothelowestpointofhismotion?
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◦
◦
◦
◦
K® Ug
Ug ® K
Eth ® K
Ug ® Eth
K® Eth
©2015PearsonEducation,Inc.
QuickCheck10.1
Achildisonaplaygroundswing,motionlessatthehighest
pointofhisarc.Whatenergytransformationtakesplaceas
heswingsbackdowntothelowestpointofhismotion?
◦
◦
◦
◦
◦
K® Ug
Ug ® K
Eth ® K
Ug ® Eth
K® Eth
©2015PearsonEducation,Inc.
QuickCheck10.2
Askierisglidingdownagentleslopeataconstantspeed.Whatenergytransformationistaking
place?
◦
◦
◦
◦
◦
K® Ug
Ug ® K
Eth ® K
Ug ® Eth
K® Eth
©2015PearsonEducation,Inc.
QuickCheck10.2
Askierisglidingdownagentleslopeataconstantspeed.Whatenergytransformationistaking
place?
◦
◦
◦
◦
◦
K® Ug
Ug ® K
Eth ® K
Ug ® Eth
K® Eth
©2015PearsonEducation,Inc.
EnergyTransfersandWork
Energycanbetransferred betweenasystemanditsenvironmentthroughwork
andheat.
Work isthemechanical
transferofenergytoorfrom
asystembypushingor
pullingonit.
Heat isthenonmechanical
transferofenergybetween
asystemandthe
environmentduetoa
temperaturedifference
betweenthetwo.
©2015PearsonEducation,Inc.
EnergyTransfersandWork
Theathletedoes
work ontheshot,
givingitkinetic
energy,K.
©2015PearsonEducation,Inc.
Thehanddoes
work onthe
match,givingit
thermalenergy,
Eth.
Theboydoes
work onthe
slingshot,giving
itelastic
potential
energy,Us.
TheWork-EnergyEquation
Workrepresentsenergythatistransferredintooroutofasystem.
Thetotalenergyofasystemchangesbytheamountofworkdoneonit.
Workcanincreaseordecreasetheenergyofasystem.
Ifnoenergyistransferredintooroutofasystem,thatisanisolated system.
©2015PearsonEducation,Inc.
TheLawofConservationofEnergy
Thetotalenergyofanisolatedsystemremainsconstant.
©2015PearsonEducation,Inc.
Section10.2Work
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Work
Workisdoneonasystembyexternal forces:forcesfromoutsidethesystem.
©2015PearsonEducation,Inc.
CalculatingWork
Althoughboththeforceandthedisplacementarevectors,workisascalar.
Theunitofwork(andenergy)is:
1 joule = 1 J = 1 N × m
©2015PearsonEducation,Inc.
Example10.1Workdoneinpushinga
crate
Sarahpushesaheavycrate3.0malongthefloorataconstantspeed.Shepusheswithaconstant
horizontalforceofmagnitude70N.HowmuchworkdoesSarahdoonthecrate?
©2015PearsonEducation,Inc.
Example10.1Workdoneinpushinga
crate(cont.)
PREPARE Webeginwiththebefore-and-aftervisualoverviewinFIGURE10.6.Sarah
pusheswithaconstantforceinthedirectionofthecrate’smotion,sowecanuse
Equation10.5tofindtheworkdone.
SOLVE TheworkdonebySarahis
W = Fd = (70 N)(3.0 m) = 210 J
BypushingonthecrateSarahincreasesitskineticenergy,soitmakessensethatthe
workdoneispositive.
©2015PearsonEducation,Inc.
QuickCheck10.4
Acranelowersagirderintoplaceatconstantspeed.ConsidertheworkWg donebygravityand
theworkWTdonebythetensioninthecable.Whichistrue?
◦
◦
◦
◦
◦
Wg >0andWT >0
Wg >0andWT <0
Wg <0andWT >0
Wg <0andWT <0
Wg =0andWT =0
©2015PearsonEducation,Inc.
QuickCheck10.4
Acranelowersagirderintoplaceatconstantspeed.ConsidertheworkWg donebygravityand
theworkWTdonebythetensioninthecable.Whichistrue?
◦
◦
◦
◦
◦
Wg >0andWT >0
Wg >0andWT <0
Wg <0andWT >0
Wg <0andWT <0
Wg =0andWT =0
©2015PearsonEducation,Inc.
The downward force of gravity is in the
direction of motion Þ positive work.
The upward tension is in the direction
opposite the motion Þ negative work.
QuickCheck10.5
Robertpushestheboxtotheleftatconstantspeed.Indoingso,Robertdoes______workon
thebox.
◦ positive
◦ negative
◦ zero
©2015PearsonEducation,Inc.
QuickCheck10.5
Robertpushestheboxtotheleftatconstantspeed.Indoingso,Robertdoes______workon
thebox.
◦ positive
◦ negative
◦ zero
Force is in the direction of displacement Þ positive work
©2015PearsonEducation,Inc.
ForceatanAngletotheDisplacement
Onlythecomponentofaforceinthedirectionofdisplacementdoeswork.
Iftheforceisatanangleθ tothedisplacement,thecomponentoftheforce,F,
thatdoesworkisFcosθ.
©2015PearsonEducation,Inc.
ForceatanAngletotheDisplacement
©2015PearsonEducation,Inc.
ForceatanAngletotheDisplacement
©2015PearsonEducation,Inc.
ForceatanAngletotheDisplacement
ThesignofW isdeterminedbytheangleθ betweentheforceandthedisplacement.
©2015PearsonEducation,Inc.
QuickCheck 10.6
Aconstantforcepushesaparticlethroughadisplacement
.Inwhichofthesethreecasesdoestheforcedonegativework?
D.BothAandB.
E.BothAandC.
©2015PearsonEducation,Inc.
QuickCheck 10.6
Aconstantforcepushesaparticlethroughadisplacement
.Inwhichofthesethreecasesdoestheforcedonegativework?
D.BothAandB.
E.BothAandC.
©2015PearsonEducation,Inc.
QuickCheck 10.7
Whichforcebelowdoesthemostwork?Allthreedisplacementsarethesame.
◦
◦
◦
◦
The10Nforce.
The8Nforce
The6Nforce.
Theyalldothesamework.
©2015PearsonEducation,Inc.
sin60° = 0.87
cos60° = 0.50
QuickCheck 10.7
Whichforcebelowdoesthemostwork?Allthreedisplacementsarethesame.
◦
◦
◦
◦
The10Nforce.
The8Nforce
The6Nforce.
Theyalldothesamework.
©2015PearsonEducation,Inc.
sin60° = 0.87
cos60° = 0.50
Example10.2Workdoneinpullinga
suitcase
Astrapinclinedupwardata45° anglepullsasuitcasethroughtheairport.Thetensioninthe
strapis20N.Howmuchworkdoesthetensiondoifthesuitcaseispulled
100mataconstantspeed?
©2015PearsonEducation,Inc.
Example10.2Workdoneinpullinga
suitcase(cont.)
PREPARE FIGURE 10.8 showsavisualoverview.Sincethesuitcase
movesataconstantspeed,theremustbearollingfrictionforce
(notshown)actingtotheleft.
SOLVE WecanuseEquation10.6,withforceF
tensiondoeswork:
= T,tofindthatthe
W = Td cos q = (20 N)(100 m)cos 45° = 1400 J
Thetensionisneededtodoworkonthesuitcaseeventhough
thesuitcaseistravelingataconstantspeedtoovercomefriction.
Soitmakessensethattheworkispositive.Theworkdonegoes
entirelyintoincreasingthethermalenergyofthesuitcaseand
thefloor.
©2015PearsonEducation,Inc.
ForcesThatDoNoWork
Aforcedoesnoworkonanobjectif
◦ Theobjectundergoesnodisplacement.
◦ Theforceis
perpendiculartothe
displacement.
◦ Thepartoftheobject
onwhichtheforceacts
undergoesno
displacement(evenif
otherpartsoftheobject
domove).
Text:p.291
©2015PearsonEducation,Inc.
QuickCheck 10.8
Iswingaballaroundmyheadatconstantspeedinacirclewithcircumference3m.Whatisthe
workdoneontheballbythe10Ntensionforceinthestringduringonerevolutionoftheball?
◦
◦
◦
◦
30J
20J
10J
0J
©2015PearsonEducation,Inc.
QuickCheck 10.8
Iswingaballaroundmyheadatconstantspeedinacirclewithcircumference3m.Whatisthe
workdoneontheballbythe10Ntensionforceinthestringduringonerevolutionoftheball?
◦
◦
◦
◦
30J
20J
10J
0J
©2015PearsonEducation,Inc.
Section10.3Kinetic
Energy
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KineticEnergy
Kineticenergyisenergyofmotion.
Kineticenergycanbeintwoforms:translational,formotionofanobjectalongapath;and
rotational,forthemotionofanobjectaroundanaxis.
©2015PearsonEducation,Inc.
QuickCheck 10.9
BallAhashalfthemassandeighttimesthekineticenergyofballB.Whatisthespeedratio
vA/vB?
◦
◦
◦
◦
◦
16
4
2
1/4
1/16
©2015PearsonEducation,Inc.
QuickCheck 10.9
BallAhashalfthemassandeighttimesthekineticenergyofballB.Whatisthespeedratio
vA/vB?
◦
◦
◦
◦
◦
16
4
2
1/4
1/16
©2015PearsonEducation,Inc.
RotationalKineticEnergy
Rotationalkineticenergyisawayofexpressingthesumofthekineticenergyofallthepartsofa
rotatingobject.
Inrotationalkineticenergy,
themomentofinertiatakes
theplaceofmassandthe
angularvelocitytakesthe
placeoflinearvelocity.
©2015PearsonEducation,Inc.
Example10.5Speedofabobsledafter
pushing
Atwo-manbobsledhasamassof390kg.Startingfromrest,thetworacerspushthesledforthe
first50mwithanetforceof270N.Neglectingfriction,whatisthesled’sspeedattheendofthe
50m?
©2015PearsonEducation,Inc.
Example10.5Speedofabobsledafter
pushing(cont.)
PREPARE Becausefrictionisnegligible,thereisnochangeinthesled’sthermalenergy.
And,becausethesled’sheightisconstant,itsgravitationalpotentialenergyis
unchangedaswell.Thusthework-energyequationissimplyΔK = W.Wecan
thereforefindthesled’sfinalkineticenergy,andhenceitsspeed,byfindingthework
donebytheracersastheypushonthesled.Thefigureliststheknownquantitiesand
thequantity vf thatwewanttofind.
Theworkdonebythepushersincreasesthesled’skineticenergy.
©2015PearsonEducation,Inc.
Example10.5Speedofabobsledafter
pushing(cont.)
SOLVE Fromthework-energyequation,Equation10.3,thechangeinthesled’s
kineticenergyisΔK = Kf - Ki = W.Thesled’sfinalkineticenergyisthus
Kf = Ki + W
Usingourexpressionsforkineticenergyandwork,weget
Becausevi = 0,thework-energyequationreducesto
Wecansolveforthefinalspeedtoget
©2015PearsonEducation,Inc.
.
QuickCheck 10.10
Alightplasticcartandaheavy
steelcartarebothpushedwith
thesameforceforadistance
of1.0m,startingfromrest.
Aftertheforceisremoved,
thekineticenergyofthelight
plasticcartis________that
oftheheavysteelcart.
◦
◦
◦
◦
greaterthan
equalto
lessthan
Can’tsay.Itdependsonhowbigtheforceis.
©2015PearsonEducation,Inc.
QuickCheck 10.10
Alightplasticcartandaheavy
steelcartarebothpushedwith
thesameforceforadistance
of1.0m,startingfromrest.
Aftertheforceisremoved,
thekineticenergyofthelight
plasticcartis________that
oftheheavysteelcart.
◦
◦
◦
◦
greaterthan
equalto
Same force, same distance Þ same work
lessthan
Same work Þ change of kinetic energy
Can’tsay.Itdependsonhowbigtheforceis.
©2015PearsonEducation,Inc.
done
QuickCheck 10.11
Eachoftheboxesshownispulledfor10macrossalevel,frictionlessfloorbytheforcegiven.
Whichboxexperiencesthegreatestchangeinitskineticenergy?
©2015PearsonEducation,Inc.
QuickCheck 10.11
Eachoftheboxesshownispulledfor10macrossalevel,frictionlessfloorbytheforcegiven.
Whichboxexperiencesthegreatestchangeinitskineticenergy?
D
Work-energy equation: ∆K = W = Fd.
All have same d, so largest work (and
hence largest ∆K) corresponds to
largest force.
©2015PearsonEducation,Inc.
QuickCheck10.12
Eachofthe1.0kgboxesstartsatrestandisthenispulledfor2.0macrossalevel,frictionless
floorbyaropewiththenotedforceatthenotedangle.Whichboxhasthehighestfinalspeed?
°
©2015PearsonEducation,Inc.
°
°
°
°
QuickCheck10.12
Eachofthe1.0kgboxesstartsatrestandisthenispulledfor2.0macrossalevel,frictionless
floorbyaropewiththenotedforceatthenotedangle.Whichboxhasthehighestfinalspeed?
°
°
B
©2015PearsonEducation,Inc.
°
°
°
Section10.4Potential
Energy
©2015PearsonEducation,Inc.
PotentialEnergy
Potentialenergyisstoredenergythatcanbereadilyconvertedtootherformsofenergy,suchas
kineticorthermalenergy.
Forcesthatcanstoreusefulenergyareconservativeforces:
◦ Gravity
◦ Elasticforces
Forcessuchasfrictionthatcannotstoreusefulenergyarenonconservative forces.
©2015PearsonEducation,Inc.
GravitationalPotentialEnergy
Thechangeingravitationalpotential
energyisproportionaltothechangeinits
height.
©2015PearsonEducation,Inc.
GravitationalPotentialEnergy
Wecanchoosethereferencelevelwheregravitationalpotential
energyUg = 0 sinceonlychangesinUg matter.
Becausegravityisaconservativeforce,
gravitationalpotentialenergydepends
onlyontheheightofanobjectand
notonthepaththeobjecttooktoget
tothatheight.
©2015PearsonEducation,Inc.
QuickCheck 10.13
Rankinorder,fromlargesttosmallest,thegravitationalpotentialenergiesoftheballs.
◦
◦
◦
◦
1>2=4>3
1>2>3>4
3>2>4>1
3>2=4>1
©2015PearsonEducation,Inc.
QuickCheck 10.13
Rankinorder,fromlargesttosmallest,thegravitationalpotentialenergiesoftheballs.
◦
◦
◦
◦
1>2=4>3
1>2>3>4
3>2>4>1
3>2=4>1
©2015PearsonEducation,Inc.
QuickCheck 10.14
Startingfromrest,amarblefirstrollsdownasteeperhill,thendownalesssteephillofthesame
height.Forwhichisitgoingfasteratthebottom?
◦
◦
◦
◦
Fasteratthebottomofthesteeperhill.
Fasteratthebottomofthelesssteephill.
Samespeedatthebottomofbothhills.
Can’tsaywithoutknowingthemassofthemarble.
©2015PearsonEducation,Inc.
QuickCheck 10.14
Startingfromrest,amarblefirstrollsdownasteeperhill,thendownalesssteephillofthesame
height.Forwhichisitgoingfasteratthebottom?
◦
◦
◦
◦
Fasteratthebottomofthesteeperhill.
Fasteratthebottomofthelesssteephill.
Samespeedatthebottomofbothhills.
Can’tsaywithoutknowingthemassofthemarble.
©2015PearsonEducation,Inc.
QuickCheck10.15
AsmallchildslidesdownthefourfrictionlessslidesA–D.Rankinorder,fromlargesttosmallest,
herspeedsatthebottom.
◦
◦
◦
◦
vD >vA >vB >vC
vD >vA =vB >vC
vC >vA >vB >vD
vA =vB =vC =vD
©2015PearsonEducation,Inc.
QuickCheck10.15
AsmallchildslidesdownthefourfrictionlessslidesA–D.Rankinorder,fromlargesttosmallest,
herspeedsatthebottom.
◦
◦
◦
◦
vD >vA >vB >vC
vD >vA =vB >vC
vC >vA >vB >vD
vA =vB =vC =vD
©2015PearsonEducation,Inc.
ElasticPotentialEnergy
Elastic(orspring)potentialenergyis
storedwhenaforcecompressesaspring.
Hooke’slawdescribestheforcerequired
tocompressaspring.
©2015PearsonEducation,Inc.
ElasticPotentialEnergy
Theelasticpotentialenergystoredinaspringisdeterminedbytheaverageforcerequiredto
compressthespringfromitsequilibriumlength.
©2015PearsonEducation,Inc.
QuickCheck 10.16
Threeballsarethrownfromacliffwiththesamespeedbutatdifferentangles.Whichballhas
thegreatestspeedjustbeforeithitstheground?
◦
◦
◦
◦
BallA.
BallB.
BallC.
Allballshavethesamespeed.
©2015PearsonEducation,Inc.
QuickCheck 10.16
Threeballsarethrownfromacliffwiththesamespeedbutatdifferentangles.Whichballhas
thegreatestspeedjustbeforeithitstheground?
◦
◦
◦
◦
BallA.
BallB.
BallC.
Allballshavethesamespeed.
©2015PearsonEducation,Inc.
QuickCheck 10.17
Ahockeypuckslidingonsmoothiceat4m/scomestoa
1-m-highhill.Willitmakeittothetopofthehill?
◦
◦
◦
◦
Yes.
No.
Can’tanswerwithoutknowingthemassofthepuck.
Can’tsaywithoutknowingtheangleofthehill.
©2015PearsonEducation,Inc.
QuickCheck 10.17
Ahockeypuckslidingonsmoothiceat4m/scomestoa
1-m-highhill.Willitmakeittothetopofthehill?
◦
◦
◦
◦
Yes.
No.
Can’tanswerwithoutknowingthemassofthepuck.
Can’tsaywithoutknowingtheangleofthehill.
©2015PearsonEducation,Inc.
Example10.8Pullingbackonabow
Anarcherpullsbackthestringonherbowtoadistanceof70cmfromitsequilibriumposition.To
holdthestringatthispositiontakesaforceof140N.Howmuchelasticpotentialenergyisstored
inthebow?
= -kx,wherex
isthedistancethestringispulledback.Wecanusetheforcerequiredtoholdthestring,andthe
distanceitispulledback,tofindthebow’sspringconstantk.ThenwecanuseEquation10.15to
findtheelasticpotentialenergy.
PREPARE Abowisanelasticmaterial,sowewillmodelitasobeyingHooke’slaw,Fs
©2015PearsonEducation,Inc.
Example10.8Pullingbackonabow
(cont.)
SOLVE FromHooke’slaw,thespringconstantis
Thentheelasticpotentialenergyoftheflexedbowis
ASSESS Whenthearrowisreleased,thiselasticpotentialenergywillbe
transformedintothekineticenergyofthearrow.AccordingtoTable10.1,the
kineticenergyofa100mphfastballisabout150J,so49Jofkineticenergyfora
fast-movingarrowseemsreasonable.
©2015PearsonEducation,Inc.