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?
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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.
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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 .
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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:
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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 .
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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.
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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:
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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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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:
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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 .
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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:
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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)?
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920 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:
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Fractionofboardinregion1= 4
4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920 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 .
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4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920 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 .
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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
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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
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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 .
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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:
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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
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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
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4 4 / /N4 LH
4
4 N
= 7.622 NT
NQI T
NQI
NQI
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
4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920 23/27
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
4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920 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 +
4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920 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
4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920 26/27
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
4/9/2014 Ch 06 HW
http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=2832920 27/27
Correct
ScoreSummary:Yourscoreonthisassignmentis96.5%.Youreceived30.88outofapossibletotalof32points.