2008年物理机械模拟考试及答案

-i-

AP®PhysicsC:MechanicsDirectionsforAdministration

TheAPPhysicsC:MechanicsExamisoneandone-halfhoursinlengthandconsistsofamultiple-choicesectionandafree-responsesection.

The45-minutemultiple-choicesectioncontains35questionsandaccountsfor50percentofthefinalgrade.

The45-minutefree-responsesectioncontains3questionsandaccountsfor50percentofthefinalgrade.

A10-minutebreakshouldbeprovidedafterMechanicsiscompletedifstudentsaretakingPhysicsC:ElectricityandMagnetismimmediatelyafterMechanics.

TheactualAPPhysicsCExamsareadministeredinonesession,MechanicsfirstfollowedbyElectricityandMagnetism.Studentstakingonlyoneoftheexamswillhavethemostrealisticexperienceifbothsectionsarecompletedinonesession.Similarly,studentstakingbothPhysicsCexamswillhavethemostrealisticexperienceifbothexamsarecompletedinonesessionandacompletemorningorafternoonisavailabletoadministerthem.Ifascheduledoesnotpermitonetimeperiodforadministration,itwouldbeacceptabletoadministerMechanicsononedayandElectricityandMagnetismonasubsequentday,ortofurtherbreakthingsupandadministerSectionIandSectionIIofeachexamonsubsequentdays.

Totalscoresonthemultiple-choicesectionarebasedonlyonthenumberofquestionsansweredcorrectly.Nopointsaredeductedforincorrectanswersandnopointsareawardedforunansweredquestions.

TheuseofcalculatorsispermittedonlyonSectionII.Straightedgesorrulersareallowedonbothpartsoftheexam.

Itissuggestedthatthepracticeexambecompletedusingapenciltosimulateanactualadministration.

Teacherswillneedtoprovidepaperforthestudentstowritetheirfree-responseanswers.Teachersshouldprovidedirectionstothestudentsindicatinghowtheywishtheresponsestobelabeledsotheteacherwillbeabletoassociatethestudent’sresponsewiththequestionthestudentintendedtoanswer.

The2008–2009APPhysicsCtableofinformationisincludedasapartofSectionI.ThetableandtheAPPhysicsCequationlistsareincludedwithSectionII.TheequationlistsarenotallowedforSectionI.IfyouusetheseexamsinsubsequentyearsyoushoulddownloadthenewerversionsofthetableandlistsfromAPCentral.

Rememberthatstudentsarenotallowedtoremoveanymaterials,includingscratchwork,fromthetestingsite.

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SectionIMultiple-ChoiceQuestions

TABLEOFINFORMATIONFOR2008and2009

CONSTANTSANDCONVERSIONFACTORS

Protonmass,mp=1.67¥10-27kgNeutronmass,mn=1.67¥10-27kgElectronmass,me=9.11¥10-31kg

Avogadro’snumber,N0=6.02¥1023mol-1

Universalgasconstant,R=8.31J(moliK)Boltzmann’sconstant,kB=1.38¥10-23JK

Electronchargemagnitude,e=1.60¥10-19C1electronvolt,1eV=1.60¥10-19JSpeedoflight,c=3.00¥108ms

Universalgravitational G=6.67¥10-11m3kgis2

constant,

Accelerationduetogravity g=9.8ms2atEarth’ssurface,

1unifiedatomicmassunit, 1u=1.66¥10-27kg=931MeVc2

Planck’sconstant, h=6.63¥10-34Jis=4.14¥10-15eVis

hc=1.99¥10-25Jim=1.24¥103eVinmVacuumpermittivity, e0=8.85¥10-12C2Nim2

Coulomb’slawconstant,k=14pe0=9.0¥109Nim2C2Vacuumpermeability, m0=4p¥10-7(Tim)A

Magneticconstant,k¢=m04p=10-7(Tim)A

1atmospherepressure, 1atm=1.0¥105Nm2=1.0¥105Pa

meter,

m

mole,

mol

watt,

W

farad,

F

UNITSYMBOLS

kilogram,second,

ampere,

kgs

A

hertz,newton,pascal,

joule,

HzN

Pa

J

coulomb,volt,

ohm,

CV

W

tesla,degreeCelsius,

electron-volt,

T

∞CeV

kelvin,

K

henry,

H

VALUESOFTRIGONOMETRICFUNCTIONSFORCOMMONANGLES

q

0D

30D

37D

45D

53D

60D

90D

sinq

0

12

3

5

2

2

4

5

32

1

cosq

1

32

4

5

2

2

3

5

12

0

tanq

0

33

3

4

1

4

3

3

•

PREFIXES

Factor

Prefix

Symbol

109

giga

G

106

mega

M

103

kilo

k

centi c

milli m

10-6 micro m

10-9 nano n

10-12 pico p

Thefollowingconventionsareusedinthisexam.

Unlessotherwisestated,theframeofreferenceofanyproblemisassumedtobeinertial.

Thedirectionofanyelectriccurrentisthedirectionofflowofpositivecharge(conventionalcurrent).

Foranyisolatedelectriccharge,theelectricpotentialisdefinedaszeroataninfinitedistancefromthecharge.

PHYSICSC:MECHANICSSECTIONI

Time—45minutes35Questions

Directions:Eachofthequestionsorincompletestatementsbelowisfollowedbyfivesuggestedanswersorcompletions.Selecttheonethatisbestineachcaseandplacetheletterofyourchoiceinthecorrespondingboxonthestudentanswersheet.

Note:Tosimplifycalculations,youmayuseg=10m/s2inallproblems.

Whichofthefollowinggraphsofpositiondversustimetcorrespondstomotionofanobjectinastraightlinewithpositiveacceleration?

(A)

(B)

(C)

(D)

Aballisthrownstraightupfromapoint2mabovetheground.Theballreachesamaximumheightof3maboveitsstartingpointandthenfalls5mtotheground.Whentheballstrikestheground,whatisitsdisplacementfromitsstartingpoint?

Zero

8mbelow

5mbelow

2mbelow

3mabove

Whatdoaccelerationandvelocityhaveincommon?

Botharescalars.

Botharevectors.

Botharemeasuredinunitsofdistancedividedbytime.

Botharemeasuredinunitsofdistancedividedbytimesquared.

Theyaredifferentnamesforthesamequantity.

Twoprojectilesarelaunchedwiththesameinitialspeedfromthesamelocation,oneata30∞angleandtheotherata60∞anglewiththehorizontal.Theylandatthesameheightatwhichtheywerelaunched.Ifairresistanceisnegligible,howdotheprojectiles’respectivemaximumheights,H30

andH60,andtimesintheair,T30

comparewitheachother?

andT60,

MaximumHeight TimeinAir

(E) (A)

(B)

(C)

(D)

(E)

H30H30H30H30H30

>H60

>H60

=H60

<H60

<H60

T30T30T30T30T30

>T60

<T60

=T60

>T60

<T60

Anobjectofmass100kgisinitiallyatrestonahorizontalfrictionlesssurface.Attimet=0,ahorizontalforceof10Nisappliedtotheobjectfor1sandthenremoved.Whichofthefollowingistrueoftheobjectattimet=2sifitisstillonthesurface?

Itisatthesamepositionithadatt=0,sinceaforceof10Nisnotlargeenoughtomovesuchamassiveobject.

Itismovingwithconstantnonzeroacceleration.

Itismovingwithdecreasingacceleration.

Itismovingataconstantspeed.

Ithascometorestsomedistanceawayfromthepositionithadatt=0.

Severalforcesactonanobject,buttheobjectisinequilibrium.Whichofthefollowingstatementsabouttheobjectmustbetrue?

Ithaszeroacceleration.

Thenetforceactingonitiszero.

Itisatrest.

Itismovingwithconstantvelocity.

IandII

IandIII

IandIV

IIandIII

IIandIV

Questions7-8

Arockisthrownfromtheedgeofacliffwithaninitialvelocityu0atanangleqwiththehorizontal

asshownabove.PointPisthehighestpointintherock’strajectoryandpointQislevelwiththestartingpoint.Assumeairresistanceisnegligible.

WhichofthefollowingcorrectlydescribesthehorizontalandverticalspeedsandtheaccelerationoftherockatpointP?

HorizontalSpeed

VerticalSpeed

Acceleration

(A)

u0cosq

0

g

(B)

0

0

g

(C)

u0cosq

0

0

(D)

u0cosq

u0sinq

g

(E)

0

u0cosq

0

WhichofthefollowingcorrectlydescribesthehorizontalandverticalspeedsandtheaccelerationoftherockatpointQ?

HorizontalSpeed

Vertical

Speed Acceleration

u0cosq 0 g

0 0 g

u0cosq 0 0

u0cosq u0sinq g

0 u0cosq 0

Asshowninthefigureabove,achildofmass

20kgwhoisrunningataspeedof4.0m/sjumps

Inanexperimentwithasimplependulum,measurementsoftheperiodTofthependulumaremadefordifferentvaluesofitslengthL.Whenplottedonagraph,whichofthefollowingshouldresultinastraight-linefitofthedata?

versusL

TversusL

TversusL2

ontoastationarysledofmass5.0kgonafrozenlake.Thespeedatwhichthechildandsledbegintoslideacrosstheiceismostnearly

0.20m/s

0.80m/s

1.2m/s

3.2m/s

16m/s

Atoyspacecraftislauncheddirectlyupward.Whenthetoyreachesitshighestpoint,aspringisreleasedandthetoysplitsintotwopartswithmassesof0.02kgand0.08kg,respectively.Immediatelyaftertheseparation,the0.02kgpartmoveshorizontallydueeast.Airresistance

T2versusLT2versusL2

Sun

isnegligible.Truestatementsaboutthe0.08kgpartincludewhichofthefollowing?

Itcouldmovenorthimmediatelyafterthespringisreleased.

Ittakeslongertoreachthegroundthandoesthe0.02kgpart.

Itstrikesthegroundfartherfromthelaunchpointthandoesthe0.02kgpart.

None

Ionly

IIIonly

IandIIonly

IIandIIIonly

Astudentinitiallystandsonacircularplatformthatisfreetorotatewithoutfrictionaboutitscenter.Thestudentjumpsofftangentially,settingtheplatformspinning.Quantitiesthatareconservedforthestudent-platformsystemasthestudentjumpsincludewhichofthefollowing?

Angularmomentum

Linearmomentum

Kineticenergy

Ionly

IIonly

IandIIonly

IIandIIIonly

I,II,andIII

AcometmovesintheSun’sgravitationalfield,followingthepathshownabove.WhathappenstoitsangularmomentumasitmovesfrompointXtopointY?

Itincreasessteadily.

Itremainsconstant.

Itdecreasessteadily.

ItincreasesasitapproachestheSunanddecreasesasitmovesawayfromtheSun.

ItdecreasesasitapproachestheSunandincreasesasitmovesawayfromtheSun.

SatelliteXmovesaroundEarthinacircularorbitofradiusR.SatelliteYisalsoinacircularorbitaroundEarth,anditcompletesoneorbitforeveryeightorbitscompletedbysatelliteX.WhatistheorbitalradiusofsatelliteY?

1R

4

1R

2

2R

4R

8R

AnewlydiscoveredplanetisfoundtohavetwicetheradiusandfivetimesthemassofEarth.IftheaccelerationofgravityatthesurfaceofEarthisg,theaccelerationofgravityatthesurfaceofthenewplanetis

5

2g

5

4g

Questions16-17

Atoycarofmass6kg,movinginastraightpath,experiencesanetforcegivenbythefunctionF=-3t.Attimet=0,thecarhasavelocityof4m/sinthepositivedirectionandislocated+8mfromtheorigin.

Thecarwillcomeinstantaneouslytorestattimet

equalto

2

3s

4s

3

8s

3

8s

4s

Whichofthefollowingbestshowsagraphofpositiondversustimetforthecar?

(A)

g

4

5g

2

5g

(B)

(C)

(D)

(E)

Questions18-19 Questions20-21

AblockofmassM1onahorizontaltableis

connectedtoahangingblockofmassM2byastringthatpassesoverapulley,asshownabove.Theaccelerationoftheblocksis0.6g.Assumethatfrictionandthemassofthestringarenegligible.

ThetensionTinthestringis

zero

0.4M2g

0.6M2g

1.0M2g

1.6M2g

Inthesystemoftwoblocksandaspringshownabove,blocks1and2areconnectedbyastringthatpassesoverapulley.Theinitiallyunstretchedspringconnectsblock1toarigidwall.Block1isreleasedfromrest,initiallyslidestotheright,andiseventuallybroughttorestbythespringandbyfrictiononthehorizontalsurface.

Whichofthefollowingistrueoftheenergyofthesystemduringthisprocess?

Thetotalmechanicalenergyofthesystemisconserved.

Thetotalmechanicalenergyofthesystemincreases.

Theenergylosttofrictionisequaltothegaininthepotentialenergyofthespring.

Thepotentialenergylostbyblock2islessinmagnitudethanthepotentialenergygainedbythespring.

Thepotentialenergylostbyblock2isgreaterinmagnitudethanthepotentialenergy

TheratioofmassesM2

0.67

1.0

1.4

1.5

1.6

M1is gainedbythespring.

Afterblock1comestorest,theforceexertedonitbythespringmustbeequalinmagnitudeto

zero

thefrictionalforceonblock1

thevectorsumoftheforcesonblock1duetofrictionandtensioninthestring

thesumoftheweightsofthetwoblocks

thedifferenceintheweightsofthetwoblocks

Thegraphaboveshowstheforceactingonanobjectasafunctionoftime.Thechangeinmomentumoftheobjectfromtime0totis

2Ft

Ft

1Ft

2

1Ft

4

zero

Questions23-24

Amoonofmassmorbitsaplanetofmass49minanellipticalorbitasshownabove.WhenthemoonisatpointA,itsdistancefromthecenteroftheplanetisrAanditsspeedisu0.WhenthemoonisatpointB,

itsspeedis5u0.

WhenthemoonisatpointA,thedistancefromthemoontothecenterofmassoftheplanet-moonsystemismostnearly

1r

50A

1r

7A

1r

2A

6r

7A

49r

50A

WhenthemoonisatpointB,thedistancefromthemoontothecenteroftheplanetismostnearly

1r

25A

1r

5A

1r

5A

rA

rA

Questions25-26

Thebarshownaboveispivotedaboutoneendandisinitiallyatrestinaverticalposition.Thebarisdisplacedslightlyandasitfallsitmakesanangleqwiththeverticalatanygiventime,asshownabove.

Whichofthefollowinggraphsbestrepresentsthebar’sangularaccelerationaasafunctionofangleq?

(A)

(B)

(C)

(D)

(E)

Whichofthefollowinggraphsbestrepresentsthebar’sangularvelocitywasafunctionoftime?

(A)

(B)

(C)

(D)

(E)

x(m)

F(N)

0

0

1

1

2

8

3

27

4

64

Astonefallsfromrestfromthetopofabuildingasshownabove.Whichofthefollowinggraphsbestrepresentsthestone’sangularmomentumLaboutthepointPasafunctionoftime?

(A)

(B)

(C)

Aspeciallydesignedspringisstretchedfromequilibriumtothedistancesxgiveninthetableabove,andtherestoringforceFismeasuredandrecordedineachcase.Whatisthepotentialenergyofthespringwhenitisstretched3mfromequilibrium?

9J

2

9J

81J

4

27J

81J

2

AnobjectontheendofaspringwithspringconstantkmovesinsimpleharmonicmotionwithamplitudeAandfrequencyf.Whichofthefollowingisapossibleexpressionforthekineticenergyoftheobjectasafunctionoftimet?

(D)

(E)

(A)

(B)

(C)

(D)

(E)

kA2sin2(2pft)

2

1kA2cos2(2pft)

2

1kAsin(2pft)

kAcos(2pft)

kA(sin2pft+cos2pft)

Whenacertainspringisstretchedbyan

amountx,itproducesarestoringforceofF(x)=-ax+bx2,whereaandb

areconstants.Howmuchworkisdoneby

anexternalforceinstretchingthespring

byanamountDfromitsequilibriumlength?

Questions31-32refertothefollowing.

Ladder

q

Floor

Wall

(A)

(B)

(C)

(D)

(E)

-aD+bD2

a-2bD

aD2-1bD3

2 3

-aD2+bD3

-2aD2+3bD3

AuniformladderofweightWleanswithoutslippingagainstawallmakinganangleqwithafloorasshownabove.Thereisfrictionbetweentheladderandthefloor,butthefrictionbetweentheladderandthewallisnegligible.

Themagnitudeofthenormalforceexertedbythefloorontheladderis

W

Wsinq

Wcosq

Wsinq

2

Wcosq2

Themagnitudeofthefrictionforceexertedontheladderbytheflooris

2Wtanq

W

Wcotq

W

2

Wcotq

2

Anidealspringwithspringconstantkiscutinhalf.Whatisthespringconstantofeitheroneofthetwohalfsprings?

(A)k

2

k

(B)

ArockethaslandedonPlanetX,whichhashalftheradiusofEarth.AnastronautonboardtherocketweighstwiceasmuchonPlanetXasonEarth.IftheescapevelocityfortherockettakingofffromEarthisu0,thenitsescapevelocityon

PlanetXis

k

k2

(A)

(B)

(C)

2u0

2u0

u0

2k (D)

(E)

u02

u04

SupposethataholeisdrilledthroughthecenterofEarthtotheothersidealongitsaxis.AsmallobjectofmassmisdroppedfromrestintotheholeatthesurfaceofEarth,asshownabove.

IfEarthisassumedtobeasolidsphereofmassMandradiusRandfrictionisassumedtobenegligible,correctexpressionsforthekineticenergyofthemassasitpassesEarth’scenterincludewhichofthefollowing?

1MgR

2

1mgR

2

GmM

2R

Ionly

IIonly

IIIonly

IandIIIonly

IIandIIIonly

STOP

ENDOFMECHANICSSECTIONI

IFYOUFINISHBEFORETIMEISCALLED,

YOUMAYCHECKYOURWORKONMECHANICSSECTIONIONLY.DONOTTURNTOANYOTHERTESTMATERIALS.

SectionII

Free-Response Questions

TABLEOFINFORMATIONFOR2008and2009

CONSTANTSANDCONVERSIONFACTORS

Protonmass,mp=1.67¥10-27kgNeutronmass,mn=1.67¥10-27kgElectronmass,me=9.11¥10-31kg

Avogadro’snumber,N0=6.02¥1023mol-1

Universalgasconstant,R=8.31J(moliK)Boltzmann’sconstant,kB=1.38¥10-23JK

Electronchargemagnitude,e=1.60¥10-19C1electronvolt,1eV=1.60¥10-19JSpeedoflight,c=3.00¥108ms

UniversalgravitationalG=6.67¥10-11m3kgis2constant,

Accelerationduetogravityg=9.8ms2atEarth’ssurface,

1unifiedatomicmassunit, 1u=1.66¥10-27kg=931MeVc2

Planck’sconstant, h=6.63¥10-34Jis=4.14¥10-15eVis

hc=1.99¥10-25Jim=1.24¥103eVinmVacuumpermittivity, e0=8.85¥10-12C2Nim2

Coulomb’slawconstant,k=14pe0=9.0¥109Nim2C2Vacuumpermeability, m0=4p¥10-7(Tim)A

Magneticconstant,k¢=m04p=10-7(Tim)A

1atmospherepressure, 1atm=1.0¥105Nm2=1.0¥105Pa

meter,

m

mole,

mol

watt,

W

farad,

F

UNITSYMBOLS

kilogram,second,

ampere,

kgs

A

hertz,newton,pascal,

joule,

HzN

Pa

J

coulomb,volt,

ohm,

CV

W

tesla,degreeCelsius,

electron-volt,

T

∞CeV

kelvin,

K

henry,

H

VALUESOFTRIGONOMETRICFUNCTIONSFORCOMMONANGLES

q

0D

30D

37D

45D

53D

60D

90D

sinq

0

12

3

5

2

2

4

5

32

1

cosq

1

32

4

5

2

2

3

5

12

0

tanq

0

33

3

4

1

4

3

3

•

PREFIXES

Factor

Prefix

Symbol

109

giga

G

106

mega

M

103

kilo

k

10-2

centi

c

10-3

milli

m

10-6

micro

m

10-9

nano

n

10-12

pico

p

Thefollowingconventionsareusedinthisexam.

Unlessotherwisestated,theframeofreferenceofanyproblemisassumedtobeinertial.

Thedirectionofanyelectriccurrentisthedirectionofflowofpositivecharge(conventionalcurrent).

Foranyisolatedelectriccharge,theelectricpotentialisdefinedaszeroataninfinitedistancefromthecharge.

ADVANCEDPLACEMENTPHYSICSCEQUATIONSFOR2008and2009

MECHANICS ELECTRICITYANDMAGNETISM

u=u0+at

x=x0+u0t+1at2

a=acceleration

F=force

f=frequency

F= 1 q1q2

4pe0r2

F

A=area

B=magneticfield

C=capacitance

h=height

I=rotationalinertia

E=q

d=distance

E=electricfield

u2=u02+2a(x-x0) J=impulse

e=emf

ÂF=FnetF=dp

dt

=ma

K=kineticenergyk=springconstantA=length

L=angularmomentum

m=mass

vÚE∑dA=e

0

E=-dV

dr

F=force

I=current

J=currentdensity

L=inductance

A=length

J=ÚFdt=Dp

N=normalforce

V= 1 Âqi

n=numberofloopsofwire

p=mv

P=power

p=momentum

r=radiusordistance UE

4pe0

=qV

iri

= 1 q1q2

perunitlength

N=numberofchargecarriers

P=powpeerrunitvolume

Ffric£mN r=positionvector

T=period

4pe0 r Q=charge

W=ÚF

1

∑dr

2

t=time

U=potentialenergy

u=velocityorspeed

C=Q

V

keA

q=pointcharge

R=resistance

r=distance

K= mu

2

P=dW

dt

P=F?v

DUg=mgh

W=workdoneonasystem

x=position

m=coefficientoffriction

q=angle

t=torque

w=angularspeed

a=angularacceleration

C= 0

d

Cp=ÂCi

i

=Â

1 1

Cs iCi

t=time

U=potentialorstoredenergy

V=electricpotentialu=velocityorspeedr=resistivity

fm=magneticflux

k=dielectricconstant

a

2

=u= 2r F=-kx

I=dQ

dt

c r w s

=1QV=1CV2 vÚB∑d,=m0I

Uc

2 2

t=r¥F

U=1kx2

m0Id,¥r

A

s 2

Ât=tnet=Ia

R=rA

dB=4p r3

2 2 T=

2p=1 E

F= Id,¥B

I=Úrdm=Âmr w f

=rJ Ú

rcm=ÂmrÂm T

I=NeudA Bs=m0nI

mk

=2p

u=rw

s

V=IR

fm=ÚB∑dA

L=r¥p=Iw Tp=2pg

Rs=ÂRi

i

df

e=- m

K=1Iw2 F=-Gm1m2rˆ

2

dt

Â

1= 1 dI

R

w=w0+at

G r2

Gm1m2

p i i

F

P=IV

e=-Ldt

1

q=q0+w0t+

1at2

2

UG=-

r M=qv¥B

U = LI2

L

2

xdx=1

sinq=a

cosq=b

tanq=a

Rectangle

A=bh

Triangle

A=1bh

Circle

C=2prParallelepipedV=Awh

Cylinder

V=pr2A

S=2prA+2pr2Sphere

V=4pr3

S=4pr2RightTriangle

ADVANCEDPLACEMENTPHYSICSCEQUATIONSFOR2008and2009

Úcosxdx=sinx

Úsinxdx=-cosx

n+1

n+1

dx

dx

d(sinx)=cosx

dx

d(1nx)=1

dx

d(ex)=ex

dx

dx=dudx

df dfdu

CALCULUS

A=area

C=circumference

V=volume

S=surfacearea

b=baseh=heightA=lengthw=widthr=radius

GEOMETRYANDTRIGONOMETRY

PHYSICSC:MECHANICSSECTIONII

Time—45minutes3Questions

Directions:Answerallthreequestions.Thesuggestedtimeisabout15minutesforansweringeachofthequestions,whichareworth15pointseach.Thepartswithinaquestionmaynothaveequalweight.Allfinalnumericalanswersshouldincludeappropriateunits.Creditdependsonthequalityofyoursolutionsandexplanations,soyoushouldshowyourwork.Creditalsodependsondemonstratingthatyouknowwhichphysicalprincipleswouldbeappropriatetoapplyinaparticularsituation.Therefore,youshouldclearlyindicatewhichpartofaquestionyourworkisfor.

Mech.1.

Achunkofclayofmass0.20kgisthrownfromthegroundwithaninitialspeedof12msatanangleof30∞withthehorizontal,asshownabove.Atthetopofitstrajectory,theclaystrikesasmallblockofmass2.3kgsuspendedfroma3.0mlongstring.Theclaystickstotheblock,whichthenswingsfreely.Neglectairresistance.

CalculatethehorizontaldistanceDbetweenthelaunchingpointoftheclayandapointonthefloordirectlybelowtheinitialpositionoftheblock.

Calculatethespeedoftheblock-claysystemimmediatelyafterthecollisionwiththeclay.

Calculatetheangleqthroughwhichtheblock-claysystemwillrisebeforecomingmomentarilytorest.

Calculatethetimebetweenwhentheblockisstruckandwhenitfirstreturnstoitsoriginalposition.

Theprocedureisrepeatedwithachunkofclayofgreatermass.Indicatewhetherthenewangleqwillbegreaterthan,lessthan,orthesameasthatdeterminedin(c).

Greater Less ThesameJustifyyouranswer.

Mech.2.

Inthelabapparatusabove,aforcesensorattachedtoacartisconnectedbyastringtoablock.Thestringpassesoverapulley.Theblockisallowedtofall,acceleratingthecart.Acomputerattachedtotheforcesensorandamotiondetectordisplaystheposition,thespeed,andtheforceappliedtothecartatfivedifferentlocations,asgiveninthetablebelow.Thesquareofthespeedisalsoprovided.

Position(m)

Speed(ms)

Force(N)

Speed2(m2s2)

0.00

0.55

0.84

0.30

0.10

0.66

0.85

0.44

0.20

0.85

0.84

0.73

0.30

0.94

0.83

0.88

0.40

1.08

0.85

1.17

i.Determinetheaverageforceexertedbythestring.

Estimatetheworkdonebytheaverageforceonthecartduringthetimethatdatawastaken.

i.Ontheaxesbelow,graphthesquareofthespeedversusposition.

Drawabest-fitlinethroughthepoints.

Calculatetheaccelerationofthecartfromthebest-fitline.

Themassofthecartis0.65kg.

Useamethoddifferentfromthatusedin(a)ii.tocalculatetheworkdoneonthecartfromthedatagiven.

Indicatewhetherthevaluesyouobtainedin(a)and(d)areinagreement.Iftheyare,explainwhytheyshouldbe.Iftheyarenot,indicateapossiblecauseofthediscrepancy.

Mech.3.

Astudentholdsoneendofathread,whichiswrappedaroundacylindricalspool,asshownabove.Thestudentthendropsthespoolfromaheighthabovethefloor,andthethreadunwindsasitfalls.ThespoolhasamassMandaradiusR,andthethreadhasnegligiblemass.ThespoolcanbeapproximatedasasolidcylinderofmomentofinertiaI=1MR2.ExpressyouranswersintermsofM,R,h,andfundamentalconstants.

2

Calculatethelinearaccelerationofthespoolasitfalls.

Calculatetheangularvelocityofthespooljustbeforeitstrikesthefloor.

Attimet=0,thespinningspoollandsonthefloorwithoutbouncingandcomesfreefromthethread.Itcontinuestospin,butslipsonthefloor’ssurfacewhiledoingso.Assumeaconstantcoefficientofslidingfrictionm.

Calculatetheangularvelocityofthespoolasafunctionoftimet.

Calculatethehorizontalspeedofthespoolasafunctionoftime,assumingthehorizontalspeediszeroattimet=0.

Atwhattimedoesslippingbetweenthespoolandfloorcease?

STOPENDOFEXAM

Name:

AP®PhysicsC:Mechanics

StudentAnswerSheetforMultiple-ChoiceSection

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AP®PhysicsC:MechanicsMultiple-ChoiceAnswerKey

No.

Correct

Answer No.

CorrectAnswer

1

D

2

D

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B

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E

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D

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A

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AP®PhysicsC:MechanicsFree-ResponseScoringGuidelines

GeneralNotesaboutAPPhysicsPracticeExamScoringGuidelines

Thesolutionscontainacommonmethodofsolvingthefree-responsequestionsandtheallocationofpointsforthesolutions.Somealsocontainacommonalternatesolution.Theyaretypicalofdraftguidelinesdevelopedbeforestudentsolutionsareavailable.Teachersshouldfeelfreetomakemodificationsbasedontheirstudents’responses.

Thescoringguidelinestypicallyshownumericalresultsusingthevalueg=9.8ms2,butuseof

10ms2isofcoursealsoacceptable.Solutionsusuallyshownumericalanswersusingbothvalueswhentheyaresignificantlydifferent.

ThefollowingrulesapplytotheofficialscoringofAPPhysicsExams.

Allcorrectmethodsofsolutionreceiveappropriatecreditforcorrectwork.

Generally,doublepenaltyforerrorsisavoided.Forexample,ifanincorrectanswertopart(a)iscorrectlysubstitutedintoanotherwisecorrectsolutiontopart(b),fullcreditwillusuallybeawarded.Oneexceptiontothismaybecaseswhenthenumericalanswertoalaterpartshouldbeeasilyrecognizedaswrong,e.g.,aspeedfasterthanthespeedoflightinvacuum.

Implicitstatementsofconceptsnormallyreceivecredit.Forexample,ifuseoftheequationexpressingaparticularconceptisworth1point,andastudent’ssolutioncontainstheapplicationofthatequationtotheproblembutthestudentdoesnotwritethebasicequation,thepointisstillawarded.However,whenstudentsareaskedtoderiveanexpression,itisnormallyexpectedthattheywillbeginbywritingoneormorefundamentalequations,suchasthosegivenontheAPPhysicsExamequationsheet.Foradescriptionoftheuseofsuchtermsas“derive”and“calculate”ontheexams,andwhatisexpectedforeach,see“TheFree-ResponseSections StudentPresentation”intheAPPhysicsCourseDescription.

Strictrulesregardingsignificantdigitsareusuallynotappliedtonumericalanswers.However,insome