mastering physics: ch 06

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

/

)

4/9/2014 Ch 06 HW


ANSWER:

Correct

PartC

Findthenetwork doneontheparticlebytheexternalforcesduringtheparticle'smotion.


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

4/9/2014 Ch 06 HW


PartE

Findthenetwork doneontheparticlebytheexternalforcesduringthemotionoftheparticleintermsoftheinitialandfinalkineticenergies.


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

4/9/2014 Ch 06 HW



Hint1.Anintegrationformula

Theformulafor is

.

ANSWER:

CorrectTheexpressionthatyouhavejustobtainedisequivalentto .Notsurprisingly,wearebacktothesameexpressionoftheworkenergytheorem!Letusseehowthetheoremcanbeappliedtoproblemsolving.

PartG

Aparticlemovinginthexdirectionisbeingacteduponbyanetforce ,forsomeconstant .Theparticlemovesfrom to .Whatis ,thechangeinkineticenergyoftheparticleduringthattime?


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

=

4/9/2014 Ch 06 HW


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]

/

/

/

/

]

/

/

4/9/2014 Ch 06 HW


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

4/9/2014 Ch 06 HW


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

]

4/9/2014 Ch 06 HW


ANSWER:

CorrectThisresultisworthremembering!Theworkdonebyaconstantforceofmagnitude ,whichactsatanangleof withrespecttothedirectionofmotionalongastraightpathoflength ,is .Thisequationcorrectlygivesthesigninthisproblem.Since istheanglewithrespecttothepositivexaxis(inradians), hence .

PartB

Nowconsiderthesameforce actingonaparticlethattravelsfrompointAtopointB.ThedisplacementvectornowpointsintheoppositedirectionasitdidinPartA.Findthework doneby inthiscase.


Hint1.Aphysicalargument

Theeasiestargumenttomakeisaphysicalone:IftheparticleweretogostraightfrompointAtopointBandthenbackfrompointBtopointAwiththesameforceacting,thetotalworkdonewouldbezero(i.e.,thegaininenergyonthewaytopointBduetothisforcewouldbelostonthewayback,andviceversa).Thisholdsforallconservativeforces(butdoesnotholdfornonconservativeforces),andaconstantforceisindeedconservative.Therefore,

ANSWER:

Correct

=]R J

=#"

DPTJ

] DPT]

J

] R J DPT] DPTR J DPTJ

"#

J

="#

DPTJ

4/9/2014 Ch 06 HW


Exercise6.4

Afactoryworkerpushesa31.5 crateadistanceof4.2 alongalevelflooratconstantvelocitybypushingdownwardatanangleof29 belowthehorizontal.Thecoefficientofkineticfrictionbetweenthecrateandflooris0.25.

PartA

Whatmagnitudeofforcemusttheworkerapplytomovethecrateatconstantvelocity?

Expressyouranswerusingtwosignificantfigures.

ANSWER:

Correct

PartB

Howmuchworkisdoneonthecratebythisforcewhenthecrateispushedadistanceof4.2 ?


ANSWER:

Correct

PartC

Howmuchworkisdoneonthecratebyfrictionduringthisdisplacement?


ANSWER:

Correct

PartD

Howmuchworkisdonebythenormalforce?

ANSWER:

LH N

= 100 /

N

= 380 +

= 380 "

+

= 0 *"

+

4/9/2014 Ch 06 HW


Correct

PartE

Howmuchworkisdonebygravity?

ANSWER:

Correct

PartF

Whatisthetotalworkdoneonthecrate?

ANSWER:

Correct

Exercise6.6

Twotugboatspulladisabledsupertanker.Eachtugexertsaconstantforceof1.7106 ,oneanangle15 westofnorthandtheotheranangle15 eastofnorth,astheypullthetankeradistance0.86 towardthenorth.

PartA

Whatisthetotalworktheydoonthesupertanker?


ANSWER:

Correct

VerticalSpringGun:SpeedandKineticEnergy

Thefigurerepresentsamultiflashphotographofaballbeingshotstraightupbyaspring.Thespring,withtheballatop,wasinitiallycompressedtothepointmarked andreleased.Thepointmarked isthepointwheretheballwouldremainatrestifitwereplacedgentlyonthespring,andtheballreachesitshighestpointatthepointmarked .

= 0 #

+

= 0 *!0

+

/

LN

= 2.8109 +

CPU

UPQ

4/9/2014 Ch 06 HW


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

4/9/2014 Ch 06 HW


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

4/9/2014 Ch 06 HW


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

4/9/2014 Ch 06 HW


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

4/9/2014 Ch 06 HW


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

4/9/2014 Ch 06 HW


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, .)


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

4/9/2014 Ch 06 HW


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.


ANSWER:

Hint3.Findthechangeinkineticenergyofthehammer

4

J

=4G

= '

2

2

#

2

=

G J

4/9/2014 Ch 06 HW


Whatis ,thechangeinkineticenergyofthehammer?


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

4/9/2014 Ch 06 HW


PartA

Whatisthetotalwork doneontheblockbytheforceoffrictionastheblockmovesadistance uptheincline?

Expresstheworkdonebyfrictionintermsofanyorallofthevariables , , , , ,and .

Hint1.Howtostart

Drawafreebodyforcediagramshowingallrealforcesactingontheblock.

Hint2.Findthemagnitudeofthefrictionforce

Writeanexpressionforthemagnitude ofthefrictionforce.

Expressyouranswerintermsofanyorallofthevariables , , ,and .

Hint1.Findthemagnitudeofthenormalforce

Whatisthemagnitude ofthenormalforce?


ANSWER:

ANSWER:

ANSWER:

GSJD

N ) # J

GSJD

N ) # J

) # J

= )#DPTJ

=GSJD

N)#DPTJ

4/9/2014 Ch 06 HW


Correct

PartB

Whatisthetotalwork doneontheblockbytheappliedforce astheblockmovesadistance uptheincline?

Expressyouranswerintermsofanyorallofthevariables , , , , ,and .

ANSWER:

Correct

Nowtheappliedforceischangedsothatinsteadofpullingtheblockuptheincline,theforcepullstheblockdowntheinclineataconstantspeed.

PartC

Whatisthetotalwork doneontheblockbytheforceoffrictionastheblockmovesadistance downtheincline?


ANSWER:

Correct

=GSJD

)#TJOJ

N ) # J

=

GSJD

N ) # J

=GSJD

)#TJOJ

4/9/2014 Ch 06 HW


PartD

Whatisthetotalwork doneontheboxbytheappledforceinthiscase?


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

4/9/2014 Ch 06 HW


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


ANSWER:

Correct

PartB

Howmuchingivingthewaterthekineticenergyithaswhenejected?

ANSWER:

Correct

PartC

Whatmustbethepoweroutputofthepump?

ANSWER:

Correct

Exercise6.37

A7.0 boxmovingat3.0 onahorizontal,frictionlesssurfacerunsintoalightspringofforceconstant70 .

PartA

Usetheworkenergytheoremtofindthemaximumcompressionofthespring.


ANSWER:

Correct

Problem6.77

= 1.04105 +

= 1.10105 +

= 3570 8

LH NT /DN

= 9.5 4 DN

LH

4/9/2014 Ch 06 HW


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 .


ANSWER:

Correct

PartC

Calculatetheworkdonebytheforce duringthefirsttimeintervalof4.40 ofthemotion.


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


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


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


Correct

ScoreSummary:Yourscoreonthisassignmentis96.5%.Youreceived30.88outofapossibletotalof32points.

mastering physics: ch 06

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