homework 5 - chapter 15
DESCRIPTION
Mastering Physics Homework PHY2049 Course General Physics 1TRANSCRIPT
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 1/14
Homework5Due:7:30pmonTuesday,June2,2015
Youwillreceivenocreditforitemsyoucompleteaftertheassignmentisdue.GradingPolicy
Exercise9.16
At agrindingwheelhasanangularvelocityof30.0 .Ithasaconstantangularaccelerationof30.0 untilacircuitbreakertripsattime =2.50 .Fromthenon,itturnsthroughanangle433 asitcoaststoastopatconstantangularacceleration.
PartA
Throughwhattotalangledidthewheelturnbetween andthetimeitstopped?
ANSWER:
Correct
PartB
Atwhattimediditstop?
ANSWER:
Correct
PartC
Whatwasitsaccelerationasitsloweddown?
ANSWER:
Correct
Problem9.74
Asphereconsistsofasolidwoodenballofuniformdensity800 andradius0.30 andiscoveredwithathincoatingofleadfoilwithareadensity20 .
PartA
0 SBET SBET
0 T SBE
0
= 602 J SBE
= 10.7 0 T
= 12.7 C SBET
LHN
N
LHN
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 2/14
Calculatethemomentofinertiaofthissphereaboutanaxispassingthroughitscenter.
ANSWER:
Correct
ParallelAxisTheorem
Theparallelaxistheoremrelates ,themomentofinertiaofanobjectaboutanaxispassingthroughitscenterofmass,to ,themomentofinertiaofthesameobjectaboutaparallelaxispassingthroughpointp.Themathematicalstatementofthetheoremis ,where istheperpendiculardistancefromthecenterofmasstotheaxisthatpassesthroughpointp,and isthemassoftheobject.
PartA
Supposeauniformslenderrodhaslength andmass .Themomentofinertiaoftherodaboutaboutanaxisthatisperpendiculartotherodandthatpassesthroughitscenterofmassisgivenby .Find ,themomentofinertiaoftherodwithrespecttoaparallelaxisthroughoneendoftherod.
Express intermsof and .Usefractionsratherthandecimalnumbersinyouranswer.
Hint1.Findthedistancefromtheaxistothecenterofmass
Findthedistance appropriatetothisproblem.Thatis,findtheperpendiculardistancefromthecenterofmassoftherodtotheaxispassingthroughoneendoftherod.
ANSWER:
Correct
ANSWER:
Correct
PartB
Nowconsideracubeofmass withedgesoflength .Themomentofinertia ofthecubeaboutanaxisthroughitscenterofmassandperpendiculartooneofitsfacesisgivenby .Find ,themomentofinertiaaboutanaxispthroughoneoftheedgesofthecube
= 4.61 LH N
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Q
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FOE
FOE
)
=
=FOE
)
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FEHF
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 3/14
Express intermsof and .Usefractionsratherthandecimalnumbersinyouranswer.
Hint1.Findthedistancefromthe axistothe axis
Findtheperpendiculardistance fromthecenterofmassaxistothenewedgeaxis(axislabeledpinthefigure).
ANSWER:
ANSWER:
Correct
KineticEnergyofaDumbbell
Thisproblemillustratesthetwocontributionstothekineticenergyofanextendedobject:rotationalkineticenergyandtranslationalkineticenergy.Youaretofindthetotalkineticenergy ofadumbbellofmass whenitisrotatingwithangularspeed anditscenterofmassismovingtranslationallywithspeed .Denotethedumbbell'smomentofinertiaaboutitscenterofmassby .Notethatifyouapproximatethespheresaspointmassesofmass eachlocatedadistance fromthecenterandignorethemomentofinertiaoftheconnectingrod,thenthemomentofinertiaofthedumbbellisgivenby ,butthisfactwillnotbenecessaryforthisproblem.
FEHF
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+ ,
=
=FEHF
)
UPUBM
)
[ 2
DN
)
.
)
DN
.
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 4/14
PartA
Findthetotalkineticenergy ofthedumbbell.
Expressyouranswerintermsof , , ,and .
Hint1.Howtoapproachtheproblem
Computeseparatelytherotationalandtranslationalkineticenergiesofthedumbbell.Thenaddthetwotofindthetotalkineticenergy.
Hint2.Findtherotationalkineticenergy
Whatisthedumbbell'srotationalkineticenergy ?
Giveyouranswerintermsofsomeorallofthevariables , ,and .
Hint1.Formulaforrotationalkineticenergy
Theformulafortherotationalkineticenergy ofabodywithmomentofinertia aboutsomeaxis,rotatingwithangularvelocity aboutit,is
.
ANSWER:
Hint3.Findthetranslationalkineticenergy
Whatisthedumbbell'stranslationalkineticenergy ?
Giveyouranswerintermsofsomeorallofthevariables , ,and .
ANSWER:
UPU
) 2
DN
[
S
DN
2 [
SPU
[
SPU
[
=S
DN
[
U
) 2 [
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 5/14
ANSWER:
Correct
PartB
Therotationalkineticenergytermisoftencalledthekineticenergyinthecenterofmass,whilethetranslationalkineticenergytermiscalledthekineticenergyofthecenterofmass.
Youfoundthatthetotalkineticenergyisthesumofthekineticenergyinthecenterofmassplusthekineticenergyofthecenterofmass.Asimilardecompositionexistsforangularandlinearmomentum.Therearealsorelateddecompositionsthatworkforsystemsofmasses,notjustrigidbodieslikeadumbbell.
Itisimportanttounderstandtheapplicabilityoftheformula .Whichofthefollowingconditionsarenecessaryfortheformulatobevalid?
Checkallthatapply.
ANSWER:
Correct
Exercise10.3
Asquaremetalplate0.180 oneachsideispivotedaboutanaxisthroughpoint atitscenterandperpendiculartotheplate.
=U
)
2
=UPU
)
2
DN
[
UPU
S
U
Thevelocityvector mustbeperpendiculartotheaxisofrotation.Thevelocityvector mustbeperpendicularorparalleltotheaxisofrotation.Themomentofinertiamustbetakenaboutanaxisthroughthecenterofmass.
2
2
N 0
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 6/14
PartA
Calculatethenettorqueaboutthisaxisduetothethreeforcesshowninthefigureifthemagnitudesoftheforcesare=24.0 , =14.6 ,and =16.7 .Theplateandallforcesareintheplaneofthepage.Takepositive
torquestobecounterclockwise.
ANSWER:
Correct
Exercise10.13
Atextbookofmass1.95 restsonafrictionless,horizontalsurface.Acordattachedtothebookpassesoverapulleywhosediameteris0.160 ,toahangingbookwithmass3.07 .Thesystemisreleasedfromrest,andthebooksareobservedtomoveadistance1.15 overatimeintervalof0.750 .
PartA
Whatisthetensioninthepartofthecordattachedtothetextbook?
ANSWER:
Correct
PartB
Whatisthetensioninthepartofthecordattachedtothebook?
Takethefreefallaccelerationtobe =9.80 .
/
/
/
= 1.28 V / N
LH
N LH
N T
7.97 N
# NT
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 7/14
ANSWER:
Correct
PartC
Whatisthemomentofinertiaofthepulleyaboutitsrotationaxis?
Takethefreefallaccelerationtobe =9.80 .
ANSWER:
Correct
Exercise10.45
Alargewoodenturntableintheshapeofaflatuniformdiskhasaradiusof2.00 andatotalmassof140 .Theturntableisinitiallyrotatingat4.00 aboutaverticalaxisthroughitscenter.Suddenly,a75.0 parachutistmakesasoftlandingontheturntableatapointneartheouteredge.
PartA
Findtheangularspeedoftheturntableaftertheparachutistlands.(Assumethatyoucantreattheparachutistasaparticle.)
ANSWER:
Correct
PartB
Computethekineticenergyofthesystembeforetheparachutistlands.
ANSWER:
Correct
PartC
17.5 N
# NT
1.50102 LH N
N LH
SBET LH
= 1.93 [
SBET
= 2240
+
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 8/14
Computethekineticenergyofthesystemaftertheparachutistlands.
ANSWER:
Correct
PartD
Whyarethesekineticenergiesnotequal?
ANSWER:
Submitted,gradepending
Exercise11.30
Averticalsolidsteelpostofdiameter =25 andlength =2.20 isrequiredtosupportaloadofmass =7500 .Youcanignoretheweightofthepost.Takefreefallaccelerationtobe .
PartA
Whatisthestressinthepost?
Expressyouranswerusingtwosignificantfigures.
ANSWER:
Correct
PartB
Whatisthestraininthepost?
Expressyouranswerusingtwosignificantfigures.
ANSWER:
= 1080
+
3701Character(s)remaining
Frictiondoesnegativeworkinordertokeeptheparachutistontheturntable,whichslowsitdown.
DN N ) LH
# NT
= 1.5106 1B
= 7.5106
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 9/14
Correct
PartC
Whatisthechangeinthepost'slengthwhentheloadisapplied?
Expressyouranswerusingtwosignificantfigures.
ANSWER:
Correct
VideoTutor:Walkingtheplank
First,launchthevideobelow.Youwillbeaskedtouseyourknowledgeofphysicstopredicttheoutcomeofanexperiment.Then,closethevideowindowandanswerthequestionatright.Youcanwatchthevideoagainatanypoint.
PartA
Inthevideo,thetorqueduetothemassoftheplankisusedinthecalculations.Forthisquestion,ignorethemassoftheboard.Rank,fromlargesttosmallest,themass neededtokeeptheboardfromtippingover.
Torankitemsasequivalent,overlapthem.
Hint1.Howtoapproachtheproblem
Inequilibrium,thesumoftheclockwisetorquesaboutanaxismustequalthesumofthecounterclockwisetorques.
ANSWER:
= 1.6105 N
N
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 10/14
Correct
PrecariousLunch
Auniformsteelbeamoflength andmass isattachedviaahingetothesideofabuilding.Thebeamissupportedbyasteelcableattachedtotheendofthebeamatanangle ,asshown.Throughthehinge,thewallexertsanunknownforce,
,onthebeam.Aworkmanofmass sitseatinglunchadistance fromthebuilding.
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J
)
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 11/14
PartA
Find ,thetensioninthecable.Remembertoaccountforalltheforcesintheproblem.
Expressyouranswerintermsof , , , , ,and ,themagnitudeoftheaccelerationduetogravity.
Hint1.Pickthebestorigin
Thisisastaticsproblemsothesumoftorquesaboutanyaxisawillbezero.Inordertosolvefor ,youwanttopicktheaxissuchthat willgiveatorque,butasfewaspossibleotherunknownforceswillentertheequations.Sowhereshouldyouplacetheoriginforthepurposeofcalculatingtorques?
ANSWER:
Hint2.Calculatethesumtorques
Nowfindthesumofthetorquesaboutcenterofthehinge.Rememberthatapositivetorquewilltendtorotateobjectscounterclockwisearoundtheorigin.
Answerintermsof , , , , , ,and .
ANSWER:
ANSWER:
Correct
PartB
Find ,the componentoftheforceexertedbythewallonthebeam( ),usingtheaxisshown.Remembertopayattentiontothedirectionthatthewallexertstheforce.
Expressyouranswerintermsof andothergivenquantities.
Hint1.Findthesignoftheforce
Thebeamisnotacceleratinginthe direction,sothesumoftheforcesinthe directioniszero.Usingthegivencoordinatesystem,is goingtohavetobepositiveornegative?
)
)
J #
AtthecenterofthebarAtthehingeAttheconnectionofthecableandthebarWherethemaniseatinglunch
)
)
J #
=0= V
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J
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=#
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TJO
J
4
4
4 4
4
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 12/14
ANSWER:
Correct
PartC
Find ,theycomponentofforcethatthewallexertsonthebeam( ),usingtheaxisshown.Remembertopayattentiontothedirectionthatthewallexertstheforce.
Expressyouranswerintermsof , , , ,and .
ANSWER:
CorrectIfyouuseyourresultfrompart(A)inyourexpressionforpart(C),you'llnoticethattheresultsimplifiessomewhat.Thesimplifiedresultshouldshowthatthefurtherthelunchermovesoutonthebeam,thelowerthemagnitudeoftheupwardforcethewallexertsonthebeam.Doesthisagreewithyourintuition?
Problem11.76
Youaretryingtoraiseabicyclewheelofmass andradius upoveracurbofheight .Todothis,youapplyahorizontalforce .
PartA
Whatistheleastmagnitudeoftheforce thatwillsucceedinraisingthewheelontothecurbwhentheforceisappliedatthecenterofthewheel?
ANSWER:
=4
DPTJ
5
J )
)
#
=5
TJOJ # #)
)
) $
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 13/14
Correct
PartB
Whatistheleastmagnitudeoftheforce thatwillsucceedinraisingthewheelontothecurbwhentheforceisappliedatthetopofthewheel?
ANSWER:
Correct
PartC
Inwhichcaseislessforcerequired?
ANSWER:
Correct
Problem11.83
Agaragedoorismountedonanoverheadrail(thefigure).ThewheelsatAandBhaverustedsothattheydonotroll,butratherslidealongthetrack.Thecoefficientofkineticfrictionis0.52.Thedistancebetweenthewheelsis2.00 ,andeachis0.50 fromtheverticalsidesofthedoor.Thedoorisuniformandweighs871
.Itispushedtotheleftatconstantspeedbyahorizontalforce.
= )# $$
$
= )# $$
caseAcaseB
N N
/
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6/16/2015 Homework5
https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=3636112 14/14
PartA
Ifthedistance is1.41 ,whatistheverticalcomponentoftheforceexertedonthewheelAbythetrack?
ANSWER:
Correct
PartB
Ifthedistance is1.41 ,whatistheverticalcomponentoftheforceexertedonthewheelBbythetrack?
ANSWER:
Correct
PartC
Findthemaximumvalue canhavewithoutcausingonewheeltoleavethetrack.
ANSWER:
Correct
ScoreSummary:Yourscoreonthisassignmentis99.3%.Youreceived22.85outofapossibletotalof23points.
$ N
= 116
/
$ N
= 755
/
$
= 1.92 $NBY
N