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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
1/27
Ch06HWDue:11:59amonSunday,April6,2014
Youwillreceivenocreditforitemsyoucompleteaftertheassignmentisdue.GradingPolicy
TheWorkEnergyTheorem
LearningGoal:
Tounderstandthemeaningandpossibleapplicationsoftheworkenergytheorem.
Inthisproblem,youwilluseyourpriorknowledgetoderiveoneofthemostimportantrelationshipsinmechanics:theworkenergytheorem.Wewillstartwithaspecialcase:aparticleofmass
movinginthexdirectionatconstantacceleration
.Duringacertainintervaloftime,theparticleacceleratesfrom to
,undergoingdisplacementgivenby .
PartA
Findtheacceleration oftheparticle.
Expresstheaccelerationintermsof , ,and .
Hint1.Somehelpfulrelationshipsfromkinematics
Bydefinitionforconstantacceleration,.
Furthermore,theaveragespeedis
,
andthedisplacementis
.Combinetheserelationshipstoeliminate .
ANSWER:
Correct
PartB
Findthenetforce actingontheparticle.
Expressyouranswerintermsof and .
Hint1.UsingNewton'slaws
WhichofNewton'slawsmaybehelpfulhere?
)
2
JOJUJBM
2
GJOBM
/ / 4
GJOBM
4
JOJUJBM
2
JOJUJBM
2
GJOBM
/
2
GJOBM
2
JOJUJBM
0
2
BWH
2
JOJUJBM
2
GJOBM
/ 02
BWH
0
= 2GJOBM
2
JOJUJBM
/
)
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
2/27
ANSWER:
Correct
PartC
Findthenetwork
doneontheparticlebytheexternalforcesduringtheparticle'smotion.
Expressyouranswerintermsof and .
ANSWER:
Correct
PartD
Substitutefor
fromPartBintheexpressionforworkfromPartC.Thensubstitutefor
fromtherelationinPartA.Thiswillyieldanexpressionforthenetwork
doneontheparticlebytheexternalforcesduringtheparticle'smotionintermsofmassandtheinitialandfinalvelocities.Giveanexpressionforthework
intermsofthosequantities.
Expressyouranswerintermsof , ,and .
ANSWER:
CorrectTheexpressionthatyouobtainedcanberearrangedas
Thequantity
hasthesameunitsaswork.Itiscalledthekineticenergyofthemovingparticleandis
denotedby .Therefore,wecanwrite
and .
Notethatlikemomentum,kineticenergydependsonboththemassandthevelocityofthemovingobject.However,themathematicalexpressionsformomentumandkineticenergyaredifferent.Also,unlikemomentum,kineticenergyisascalar.Thatis,itdoesnotdependonthesign(thereforedirection)ofthevelocities.
= )
/
=/
) 2
JOJUJBM
2
GJOBM
=)
2
GJOBM
2
JOJUJBM
) )
2
GJOBM
2
JOJUJBM
)
2
)
JOJUJBM
2
JOJUJBM
)
GJOBM
2
GJOBM
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
3/27
PartE
Findthenetwork
doneontheparticlebytheexternalforcesduringthemotionoftheparticleintermsoftheinitialandfinalkineticenergies.
Expressyouranswerintermsof and .
ANSWER:
CorrectThisresultiscalledtheworkenergytheorem.Itstatesthatthenetworkdoneonaparticleequalsthechangeinkineticenergyofthatparticle.Alsonoticethatif
iszero,thentheworkenergytheoremreducesto
.Inotherwords,kineticenergycanbeunderstoodastheamountofworkthatisdonetoacceleratetheparticlefromresttoitsfinalvelocity.
Theworkenergytheoremcanbemosteasilyusediftheobjectismovinginonedimensionandisbeingacteduponbyaconstantnetforcedirectedalongthedirectionofmotion.However,thetheoremisvalidformoregeneralcasesaswell.
Letusnowconsiderasituationinwhichtheparticleisstillmovingalongthexaxis,butthenetforce,whichisstilldirectedalongthexaxis,isnolongerconstant.Let'sseehowourearlierdefinitionofwork,
needstobemodifiedbybeingreplacedbyanintegral.Ifthepathoftheparticleisdividedintoverysmalldisplacements,wecanassumethatovereachofthesesmalldisplacementintervals,thenetforceremainsessentiallyconstant
andthework donetomovetheparticlefrom to is
,where
isthexcomponentofthenetforce(whichremainsvirtuallyconstantforthesmalldisplacementfrom
to
).Thenetwork doneontheparticleisthengivenby
.Now,using
and
,itcanbeshownthat
.
PartF
Evaluatetheintegral .
JOJUJBM
GJOBM
= JOJUJBM
GJOBM
JOJUJBM
GJOBM
/
4
4 4 4
4
4
4 4
4
4
GJOBM
4
JOJUJBM
4
GJOBM
4
JOJUJBM
)
2
2
0
2
4
4
0
2
4
)2 2
2
GJOBM
2
JOJUJBM
)2 2
2
GJOBM
2
JOJUJBM
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
4/27
Expressyouranswerintermsof , ,and .
Hint1.Anintegrationformula
Theformulafor is
.
ANSWER:
CorrectTheexpressionthatyouhavejustobtainedisequivalentto
.Notsurprisingly,wearebacktothesameexpressionoftheworkenergytheorem!Letusseehowthetheoremcanbeappliedtoproblemsolving.
PartG
Aparticlemovinginthexdirectionisbeingacteduponbyanetforce
,forsomeconstant .Theparticlemovesfrom to .Whatis
,thechangeinkineticenergyoftheparticleduringthattime?
Expressyouranswerintermsof and .
Hint1.Findingthework
Integrate tocalculatetheworkdoneontheparticle.
Hint2.Anintegrationformula
Theformulafor is
.
ANSWER:
) 2
JOJUJBM
2
GJOBM
0 0
0 0
=)
2
GJOBM
2
JOJUJBM
GJOBM
JOJUJBM
4 4
4
JOJUJBM
4
GJOBM
4 4
1
1
1
1
=
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
5/27
CorrectItcanalsobeshownthattheworkenergytheoremisvalidfortwoandthreedimensionalmotionandforavaryingnetforcethatisnotnecessarilydirectedalongtheinstantaneousdirectionofmotionoftheparticle.Inthatcase,theworkdonebythenetforceisgivenbythelineintegral
where and aretheinitialandthefinalpositionsoftheparticle,
isthevectorrepresentinga
smalldisplacement,and isthenetforceactingontheparticle.
WhenPushComestoShove
Twoforces,ofmagnitudes and
,actinoppositedirectionsonablock,whichsitsatopafrictionlesssurface.Initially,thecenteroftheblockisatposition
.Atsomelatertime,theblockhasmovedtotheright,sothatitscenterisatposition
,where .
PartA
Findthework doneontheblockbytheforceofmagnitude
astheblockmovesfrom to .
Expressyouranswerintermsofsomeorallofthevariablesgivenintheproblemintroduction.
Hint1.Formulafortheworkdonebyaforce
Thework donebyaforce inproducingadisplacement isgivenby
,
where and arethemagnitudesof and respectively,and
isthesmalleranglebetweenthetwo
vectors.
Thescalarthatresultsfromtheoperation
iscalledthescalarproduct,ordotproduct,ofthevectorsand .
GJOBM
JOJUJBM
JOJUJBM
GJOBM
4
J
4
G
4
G
4
J
4
J
4
G
/
DPT]
/
/
/
/
]
/
/
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
6/27
ANSWER:
Correct
PartB
Findthework donebytheforceofmagnitude astheblockmovesfrom to
.
Expressyouranswerintermsofsomeorallofthevariablesgivenintheproblemintroduction.
Hint1.Istheworkpositiveornegative?
Theforceofmagnitude
actsintheoppositedirectiontothatofthemotionoftheblock.Therefore,theworkdonebythatforcemustbenegative.
ANSWER:
Correct
PartC
Whatisthenetwork doneontheblockbythetwoforces?
ANSWER:
Correct
PartD
Imaginethatthetwoforcesareequalinmagnitude,
,andthattherearenootherhorizontalforcesactingontheblock.Determinethechange
inthekineticenergyoftheblockasitmovesfrom to .
Hint1.Iftheforcesareequal,howcantheblockbemoving?
Althoughthenethorizontalforceactingontheblock(andthereforetheaccelerationoftheblock)iszero,theblockmayhavehadsomeinitialvelocity.
=
4
"
4
%
4
J
4
G
=
4
"
4
%
OFU
=OFU
4
"
4
%
G
J
4
J
4
G
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
7/27
ANSWER:
Correct
WorkfromaConstantForce
LearningGoal:
Tounderstandhowtocomputetheworkdonebyaconstantforceactingonaparticlethatmovesinastraightline.
Inthisproblem,youwillcalculatetheworkdonebyaconstantforce.Aforceisconsideredconstantif
isindependentof
.ThisisthemostfrequentlyencounteredsituationinelementaryNewtonianmechanics.
PartA
ConsideraparticlemovinginastraightlinefrominitialpointBtofinalpointA,acteduponbyaconstantforce
.Inthefiguretheforceisindicatedbyaseriesofidenticalvectorspointingtotheleft,paralleltothehorizontalaxis.Thevectorsareallidenticaltoreflecttheideathattheforceisconstanteverywherealongthepath.Themagnitudeoftheforceis
,andthedisplacementvectorfrompointBtopointAis (ofmagnitude
,makinganangle (radians)withthepositivexaxis).Find ,the
workthattheforce
performsontheparticleasitmovesfrompointBtopointA.
Expresstheworkintermsof , ,and
.Remembertouseradians,notdegrees,foranyanglesthatappearinyouranswer.
Hint1.Formulaforworkdonebyaconstantforce
Foraparticlesubjectedtoaconstantforce
alongastraightpathrepresentedbythedisplacementvector,thenetworkdoneby
is .
Hint2.Findtheanglebetween and
Youneedtofindtheanglebetweenthevector
,whichisdirectedhorizontallytotheleft,andthevectorinthedirectionoftheparticle'smotion(atanangle
(radians)relativetothepositivexaxis).Itmayhelptovisualize
directedalongthenegativexaxisattheorigin.Whatistheangle between and
?
Expressyouranswerinradians,notdegrees.
ANSWER:
= 0G
J
.
.
J
#"
J
J
]
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
8/27
ANSWER:
CorrectThisresultisworthremembering!Theworkdonebyaconstantforceofmagnitude
,whichactsatanangleof
withrespecttothedirectionofmotionalongastraightpathoflength ,is
.Thisequationcorrectlygivesthesigninthisproblem.Since
istheanglewithrespecttothepositivexaxis(inradians), hence .
PartB
Nowconsiderthesameforce
actingonaparticlethattravelsfrompointAtopointB.ThedisplacementvectornowpointsintheoppositedirectionasitdidinPartA.Findthework
doneby inthiscase.
Expressyouranswerintermsof , ,and .
Hint1.Aphysicalargument
Theeasiestargumenttomakeisaphysicalone:IftheparticleweretogostraightfrompointAtopointBandthenbackfrompointBtopointAwiththesameforceacting,thetotalworkdonewouldbezero(i.e.,thegaininenergyonthewaytopointBduetothisforcewouldbelostonthewayback,andviceversa).Thisholdsforallconservativeforces(butdoesnotholdfornonconservativeforces),andaconstantforceisindeedconservative.Therefore,
ANSWER:
Correct
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=#"
DPTJ
] DPT]
J
] R J DPT] DPTR J DPTJ
"#
J
="#
DPTJ
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
9/27
Exercise6.4
Afactoryworkerpushesa31.5 crateadistanceof4.2
alongalevelflooratconstantvelocitybypushingdownwardatanangleof29
belowthehorizontal.Thecoefficientofkineticfrictionbetweenthecrateandflooris0.25.
PartA
Whatmagnitudeofforcemusttheworkerapplytomovethecrateatconstantvelocity?
Expressyouranswerusingtwosignificantfigures.
ANSWER:
Correct
PartB
Howmuchworkisdoneonthecratebythisforcewhenthecrateispushedadistanceof4.2
?
Expressyouranswerusingtwosignificantfigures.
ANSWER:
Correct
PartC
Howmuchworkisdoneonthecratebyfrictionduringthisdisplacement?
Expressyouranswerusingtwosignificantfigures.
ANSWER:
Correct
PartD
Howmuchworkisdonebythenormalforce?
ANSWER:
LH N
= 100 /
N
= 380 +
= 380 "
+
= 0 *"
+
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
10/27
Correct
PartE
Howmuchworkisdonebygravity?
ANSWER:
Correct
PartF
Whatisthetotalworkdoneonthecrate?
ANSWER:
Correct
Exercise6.6
Twotugboatspulladisabledsupertanker.Eachtugexertsaconstantforceof1.7106
,oneanangle15 westofnorthandtheotheranangle15
eastofnorth,astheypullthetankeradistance0.86 towardthenorth.
PartA
Whatisthetotalworktheydoonthesupertanker?
Expressyouranswerusingtwosignificantfigures.
ANSWER:
Correct
VerticalSpringGun:SpeedandKineticEnergy
Thefigurerepresentsamultiflashphotographofaballbeingshotstraightupbyaspring.Thespring,withtheballatop,wasinitiallycompressedtothepointmarked
andreleased.Thepointmarked
isthepointwheretheballwouldremainatrestifitwereplacedgentlyonthespring,andtheballreachesitshighestpointatthepointmarked
.
= 0 #
+
= 0 *!0
+
/
LN
= 2.8109 +
CPU
UPQ
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
11/27
Formostsituations,includingthisproblem,thepoint
maybetakentobeatthetopofthespring,wheretheballlosescontactwiththespring.
PartA
Indicatewhetherthefollowingstatementsaretrueorfalse.Assumethatairresistanceisnegligible.
Thespeedoftheballwasgreatestatpoint
whenitwasstillincontactwiththespring.Thespeedoftheballwasdecreasingonitswayfrompoint
topoint .Thespeedoftheballwaszeroatpoint
.Thespeedoftheballwasthesameforallpointsinitsmotionbetweenpoints
and .
Entertfortrueorfforfalseforeachstatement.Separateyourresponseswithcommas(e.g.,t,f,f,t).
ANSWER:
Correct
PartB
Considerthekineticenergyoftheball.Atwhatpointorpointsistheball'skineticenergygreatest?
Hint1.Whatequationtouse
Thekineticenergyisgivenby ,where isthemassoftheobjectand
isitsspeed.
ANSWER:
UPQ
UPQ
UPQ
t,t,t,f
)2
) 2
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
12/27
Correct
DraggingaBoard
Auniformboardoflength andmass
liesnearaboundarythatseparatestworegions.Inregion1,thecoefficientofkineticfrictionbetweentheboardandthesurfaceis
,andinregion2,thecoefficientis
.Thepositivedirectionisshowninthefigure.
PartA
Findthenetwork
donebyfrictioninpullingtheboarddirectlyfromregion1toregion2.Assumethattheboardmovesatconstantvelocity.
Expressthenetworkintermsof , , , ,and .
Hint1.Thenetforceoffriction
Supposethattherightedgeoftheboardisadistance
fromtheboundary,asshown.Whentheboardisatthisposition,whatisthemagnitudeoftheforceoffriction,
,actingontheboard(assumingthatit'smoving)?
onlyonlyonlyand
andandand and
CPU
UPQ
CPU
UPQ
UPQ
CPU
CPU
UPQ
N
N
# N
N
4
4
OFU
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4/9/2014 Ch 06 HW
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13/27
Expresstheforceactingontheboardintermsof , , , , ,and .
Hint1.Fractionofboardinregion2
Considerthepartoftheboardinregion2whentherightedgeoftheboardisadistance
fromtheboundary.Themagnitudeoftheforceoffrictionactingontheboard(onlyconsideringthefrictionfromregion2)willbethecoefficientoffriction,multipliedbythemagnitudeofthenormalforcethatactsontheboard.Sincethegroundishorizontal,andtheboardisnotacceleratingintheverticaldirection,thenormalforceshouldequaltheboard'sweight.But,onlyafractionoftheboard'stotalmassisinregion2.Findthefractionoftheboardinregion2intermsofthegivenlengths
.
ANSWER:
Hint2.Forceoffrictioninregion1
Nowconsiderthatpartoftheboardinregion1.Again,onlyafractionoftheboard'smassisinregion1.Usingthisfact,findthemagnitudeoftheforceoffrictionactingontheboard,justduetofrictioninregion1.
Expressyouranswerintermsof , , , ,and .
Hint1.Fractionoftheboardinregion1
Whentherightedgeoftheboardisadistance
fromtheboundary,whatfractionoftheboardliesinregion1?
.
ANSWER:
# 4 N
N
4
GSBDUJPO PG UIF CPBSE JO SFHJPO
MFOHUI PG UIF CPBSE JO SFHJPO
UPUBM MFOHUI PG UIF CPBSE
Fractionofboardinregion2= 4
# 4 N
4
GSBDUJPO PG UIF CPBSE JO SFHJPO
MFOHUI PG UIF CPBSE JO SFHJPO
UPUBM MFOHUI PG UIF CPBSE
Fractionofboardinregion1= 4
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4/9/2014 Ch 06 HW
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14/27
ANSWER:
ANSWER:
Hint2.Workasintegralofforce
Afteryoufindthenetforceoffriction
thatactsontheboard,asafunctionof
,tofindthenetworkdonebythisforce,youwillneedtoperformtheappropriateworkintegral,
Thelowerlimitofthisintegralwillbeat
.Whatwillbetheupperlimit?
ANSWER:
Hint3.Directionofforceoffriction
Don'tforgetthattheforceoffrictionisdirectedoppositetothedirectionoftheboard'smotion.
Hint4.Formulafor
ANSWER:
CorrectThisanswermakessensebecauseitisasiftheboardspenthalfitstimeinregion1,andhalfinregion2,whichonaverage,itinfactdid.
PartB
Whatisthetotalworkdonebytheexternalforceinpullingtheboardfromregion1toregion2?(Again,assumethattheboardmovesatconstantvelocity.)
Expressyouranswerintermsof , , , ,and .
=SFHJPO
#
4
N
=4OFU
4
4
#
N
N
4 4
4 4
4
Upperlimitat =4
4 4
4 4
=#
N
N
# N
N
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4/9/2014 Ch 06 HW
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15/27
Hint1.Noacceleration
Sincetheboardisnotaccelerating,thesumoftheexternalforcesonitmustbezero.Thereforetheexternalforcemustbeoppositelydirectedtothatoffriction.
ANSWER:
Correct
Exercise6.20
Youthrowa20
rockverticallyintotheairfromgroundlevel.Youobservethatwhenitisaheight14.6
abovetheground,itistravelingataspeedof24.1 upward.
PartA
Usetheworkenergytheoremtofinditsspeedjustasitlefttheground.
ANSWER:
Correct
PartB
Usetheworkenergytheoremtofinditsmaximumheight.
ANSWER:
Correct
WorkDonebyaSpring
Consideraspring,withspringconstant
,oneendofwhichisattachedtoawall.Thespringisinitiallyunstretched,withtheunconstrainedendofthespringatposition
.
=FYU
#
N
N
/ N
NT
= 29.4 2
NT
= 44.2 $ N
'
4
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
16/27
PartA
Thespringisnowcompressedsothattheunconstrainedendmovesfrom to
.Usingtheworkintegral
,
findtheworkdonebythespringasitiscompressed.
Expresstheworkdonebythespringintermsof and .
Hint1.Springforceasafunctionofposition
Thespringforcevector asafunctionofdisplacement
fromthespring'sequilibriumposition,isgivenby
where isthespringconstantand
isaunitvectorinthedirectionofthedisplacementofthespring(inthiscase,towardstheright).
Hint2.Integrandoftheworkintegral
Theworkdonebythespringisgivenbytheintegralofthedotproductofthespringforceandaninfinitesimaldisplacementoftheendofthespring:
,
wheretheinfinitesmaldisplacementvector hasbeenwrittenas .Write
intermsofgiven
quantities,andthencomputethedotproducttofindanexpressionfortheintegrand.(Note,
.)
Expressyouranswerintermsof , ,and .
ANSWER:
Hint3.Upperlimitoftheworkintegral
4 4
4
G
4
J
4
4
'
4
'4
%
?
' %
?
4 4
4
G
4
J
4
4
4
G
4
J
%
?
4
4%
?
4
%
?
%
?
' 4 4
=4 4 %? '4 4
J
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
17/27
Thelowerlimitoftheworkintegralwillbeat
.Whatwillbetheintegral'supperlimit?
ANSWER:
ANSWER:
Correct
HoldingForceofaNail
Ahammerofmass ismovingatspeed
whenitstrikesanailofnegligiblemassthatisstuckinawoodenblock.Thehammerisobservedtodrivethenailadistance
deeperintotheblock.
PartA
Findthemagnitude
oftheforcethatthewoodenblockexertsonthenail,assumingthatthisforceisindependentofthedepthofpenetrationofthenailintothewood.Youmayalsoassumethat
,sothatthechangeinthehammer'sgravitationalpotentialenergy,asitdrivesthenailintotheblock,isinsignificant.
Expressthemagnitudeoftheforceintermsof , ,and .
Hint1.Howtoapproachtheproblem
Onewaytosolvethisproblemistousetheworkenergytheorem.Tostopthehammerfrommoving,thewoodenblocknailsystemmustdoacertainamountofworkonthehammer.Oneexpressionforthisamountofworkinvolves
andthedisplacementofthehammer.Inaddition,theworkenergytheoremimpliesthattheinitialkineticenergyofthehammerplustheworkdoneonthehammermustequalthefinalkineticenergyofthehammer.Thisgivesanotherexpressionfortheworkdonethatinvolvesonlythechangeinkineticenergyofthehammer.Equatethetwoexpressionsfortheworkdoneandsolvefor
.
Hint2.Findtheworkdoneintermsof
Theworkenergytheoremconnectstheworkneededtostopthehammerwiththechangeinthehammer'skineticenergy.Findthework
doneonthehammerbythenail.Don'tforgettoconsiderthesignofyouranswer.
Expressyouranswerintermsof and .
ANSWER:
Hint3.Findthechangeinkineticenergyofthehammer
4
J
=4G
= '
2
2
#
2
=
G J
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
18/27
Whatis ,thechangeinkineticenergyofthehammer?
Expressyouranswerintermsof and .
ANSWER:
ANSWER:
Correct
PartB
Nowevaluatethemagnitudeoftheholdingforceofthewoodenblockonthenailbyassumingthattheforcenecessarytopullthenailoutisthesameasthatneededtodriveitin,whichwejustderived.Assumearelativelyheavy
hammer(about18ounces),movingwithspeed
.(Ifsuchahammerwereswungthishardupwardandreleased,itwouldrise5m).Takethepenetrationdepth
tobe2cm,whichisappropriateforonehitonarelativelyheavyconstructionnail.
Expressyouranswertothenearestpound.(Note: .)
ANSWER:
Correct
PullingaBlockonanInclinewithFriction
Ablockofweight sitsonaninclinedplaneasshown.Aforceofmagnitude
isappliedtopulltheblockuptheinclineatconstantspeed.Thecoefficientofkineticfrictionbetweentheplaneandtheblockis
.
G J
2
=
G J
2
=
2
LH NT2
MC /
= 281 lb] ]
)#
N
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
19/27
PartA
Whatisthetotalwork
doneontheblockbytheforceoffrictionastheblockmovesadistance
uptheincline?
Expresstheworkdonebyfrictionintermsofanyorallofthevariables , ,
, , ,and .
Hint1.Howtostart
Drawafreebodyforcediagramshowingallrealforcesactingontheblock.
Hint2.Findthemagnitudeofthefrictionforce
Writeanexpressionforthemagnitude ofthefrictionforce.
Expressyouranswerintermsofanyorallofthevariables , , ,and .
Hint1.Findthemagnitudeofthenormalforce
Whatisthemagnitude ofthenormalforce?
Expressyouranswerintermsof , ,and .
ANSWER:
ANSWER:
ANSWER:
GSJD
N ) # J
GSJD
N ) # J
) # J
= )#DPTJ
=GSJD
N)#DPTJ
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
20/27
Correct
PartB
Whatisthetotalwork doneontheblockbytheappliedforce
astheblockmovesadistance uptheincline?
Expressyouranswerintermsofanyorallofthevariables , , , , ,and
.
ANSWER:
Correct
Nowtheappliedforceischangedsothatinsteadofpullingtheblockuptheincline,theforcepullstheblockdowntheinclineataconstantspeed.
PartC
Whatisthetotalwork
doneontheblockbytheforceoffrictionastheblockmovesadistance
downtheincline?
Expressyouranswerintermsofanyorallofthevariables , , , , ,and
.
ANSWER:
Correct
=GSJD
)#TJOJ
N ) # J
=
GSJD
N ) # J
=GSJD
)#TJOJ
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
21/27
PartD
Whatisthetotalwork doneontheboxbytheappledforceinthiscase?
Expressyouranswerintermsofanyorallofthevariables , , , , ,and
.
ANSWER:
Correct
Exercise6.47
Aforceinthe directionwithmagnitude isappliedtoa7.90
boxthatissittingonthehorizontal,frictionlesssurfaceofafrozenlake.
istheonlyhorizontalforceonthebox.
PartA
Iftheboxisinitiallyatrestat
,whatisitsspeedafterithastraveled17.0 ?
Expressyouranswertothreesignificantfiguresandincludetheappropriateunits.
ANSWER:
Correct
ACarwithConstantPower
Theengineinanimaginarysportscarcanprovideconstantpowertothewheelsoverarangeofspeedsfrom0to70milesperhour(mph).Atfullpower,thecarcanacceleratefromzeroto30.0
intime1.20 .
PartA
Atfullpower,howlongwouldittakeforthecartoacceleratefrom0to60.0
?Neglectfrictionandairresistance.
Expressyouranswerinseconds.
Hint1.Energyandpower
Intheabsenceoffriction,theconstantpoweroftheengineimpliesthatthekineticenergyofthecarincreaseslinearlywithtime.
Hint2.Findtheratioofkineticenergies
N ) # J
=
4 4 / /N4 LH
4
4 N
= 7.622 NT
NQI T
NQI
NQI
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
22/27
Findthe(numerical)ratioofthecar'skineticenergy attime60.0 to
,thekineticenergyattime30.0 .
ANSWER:
ANSWER:
CorrectOfcourse,neglectingfriction,especiallyairfriction,iscompletelyunrealisticatsuchspeeds.
PartB
Amorerealisticcarwouldcausethewheelstospininamannerthatwouldresultinthegroundpushingitforwardwithaconstantforce(incontrasttotheconstantpowerinPartA).Ifsuchasportscarwentfromzeroto30.0intime1.20
,howlongwouldittaketogofromzeroto60.0 ?
Expressyouranswernumerically,inseconds.
Hint1.Howtoapproachtheproblem
Constantforcemeansconstantacceleration.Usethisfacttofindhowthespeedincreaseswithtime.
ANSWER:
CorrectThisisprobablythefirstandlasttimeyouwillcomeacrossanimaginarycarthatgoesslowerthantherealone!
Problem6.91
Apumpisrequiredtoliftamassof760
ofwaterperminutefromawellofdepth14.0 andejectitwithaspeedof17.0
.
PartA
Howmuchworkisdoneperminuteinliftingthewater?
NQI
NQI
= 4
4.80 T
NQI
T NQI
2.40 T
LH N
NT
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920
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ANSWER:
Correct
PartB
Howmuchingivingthewaterthekineticenergyithaswhenejected?
ANSWER:
Correct
PartC
Whatmustbethepoweroutputofthepump?
ANSWER:
Correct
Exercise6.37
A7.0 boxmovingat3.0
onahorizontal,frictionlesssurfacerunsintoalightspringofforceconstant70
.
PartA
Usetheworkenergytheoremtofindthemaximumcompressionofthespring.
Expressyouranswerusingtwosignificantfigures.
ANSWER:
Correct
Problem6.77
= 1.04105 +
= 1.10105 +
= 3570 8
LH NT /DN
= 9.5 4 DN
LH
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4/9/2014 Ch 06 HW
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24/27
Ablockoficewithmass6.10
isinitiallyatrestonafrictionless,horizontalsurface.Aworkerthenappliesahorizontalforce
toit.Asaresult,theblockmovesalongthexaxissuchthatitspositionasafunctionoftimeisgivenby
,where =0.190 and =1.95102 .
PartA
Calculatethevelocityoftheobjectattime =4.40 .
Expressyouranswertothreesignificantfigures.
ANSWER:
Correct
PartB
Calculatethemagnitudeof attime =4.40 .
Expressyouranswertothreesignificantfigures.
ANSWER:
Correct
PartC
Calculatetheworkdonebytheforce duringthefirsttimeintervalof4.40
ofthemotion.
Expressyouranswertothreesignificantfigures.
ANSWER:
Allattemptsusedcorrectanswerdisplayed
Exercise6.19
Usetheworkenergytheoremtosolveeachoftheseproblems.YoucanuseNewton'slawstocheckyouranswers.Neglectairresistanceinallcases.
PartA
LH
40 C D0
0
C NT
D NT
0 T
= 2.80 2 NT
0 T
= 5.46 /
T
= 24.0 +
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4/9/2014 Ch 06 HW
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25/27
Abranchfallsfromthetopofa95.0
tallredwoodtree,startingfromrest.Howfastisitmovingwhenitreachestheground?
ANSWER:
Correct
PartB
Avolcanoejectsaboulderdirectlyupward527
intotheair.Howfastwasthebouldermovingjustasitleftthevolcano?
ANSWER:
Correct
PartC
Askiermovingat5.50
encountersalong,roughhorizontalpatchofsnowhavingcoefficientofkineticfriction0.220withherskis.Howfardoesshetravelonthispatchbeforestopping?
ANSWER:
Correct
PartD
SupposetheroughpatchinpartCwasonly2.90
long?Howfastwouldtheskierbemovingwhenshereachedtheendofthepatch?
ANSWER:
Correct
PartE
Atthebaseofafrictionlessicyhillthatrisesat30.0
abovethehorizontal,atobogganhasaspeedof12.0
N
= 43.2 2 NT
N
= 102 2 NT
NT
= 7.02 / N
N
= 4.21 2 NT
NT
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towardthehill.Howhighverticallyabovethebasewillitgobeforestopping?
ANSWER:
Correct
Problem6.85
A5.00 blockismovingat6.00
alongafrictionless,horizontalsurfacetowardaspringwithforceconstant=500
thatisattachedtoawall(thefigure).Thespring
hasnegligiblemass.
PartA
Findthemaximumdistancethespringwillbecompressed.
ANSWER:
Correct
PartB
Ifthespringistocompressbynomorethan0.350
,whatshouldbethemaximumvalueof ?
ANSWER:
= 7.35 $ N
LH NT
' /N
= 0.600 4 N
N 2
= 3.50 2
NT
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Correct
ScoreSummary:Yourscoreonthisassignmentis96.5%.Youreceived30.88outofapossibletotalof32points.