PHYSICS111SPRING2018

FINALEXAM:April30,2018;4:30pm-6:30pmName(printed):______________________________________________RecitationInstructor:_________________________Section#_______INSTRUCTIONS:Thisexamcontains30multiple-choicequestion,eachworth3points,foranominalmaximumscoreof80pointsplus10extracreditpoints.Chooseoneansweronlyforeachquestion.Choosethebestanswertoeachquestion.Answerallquestions.Allowedmaterial:Beforeturningoverthispage,putawayallmaterialsexceptforpens,pencils,erasers,rulersandyourcalculator.Thereisaformulasheetattachedattheendoftheexam.Othercopiesoftheformulasheetarenotallowed.Calculator:Ingeneral,anycalculator,includingcalculatorsthatperformgraphing,ispermitted.Electronicdevicesthatcanstorelargeamountsoftext,dataorequations(likelaptops,e-bookreaders,smartphones)areNOTpermitted.CalculatorswithWiFitechnologyareNOTpermitted.Ifyouareunsurewhetherornotyourcalculatorisallowedfortheexam,askyourTA.Howtofillinthebubblesheet:

Useanumber2pencil.DoNOTuseink.Ifyoudidnotbringapencil,askforone.YouwillcontinuetousethesamebubblesheetyoualreadyusedforExam1-3.Bubbleanswers64-93onthebubblesheetforthisexam.Only,ifforsomereasonyouarestartinganewbubblesheet,writeandfillinthebubblescorrespondingto:- Yourlastname,middleinitial,andfirstname.- ««YourIDnumber(themiddle9digitsonyourISUcard)««- SpecialcodesKtoLareyourrecitationsection.Alwaysusetwodigits(e.g.01,09,11,13).

Pleaseturnoveryourbubblesheetwhenyouarenotwritingonit.Ifyouneedtochangeanyentry,youmustcompletelyeraseyourpreviousentry.Also,circleyouranswersonthisexam.Beforehandinginyourexam,besurethatyouranswersonyourbubblesheetarewhatyouintendthemtobe.Youmayalsocopydownyouranswersonapieceofpapertotakewithyouandcomparewiththepostedanswers.Youmayusethetableattheendoftheexamforthis.Whenyouarefinishedwiththeexam,placeallexammaterials,includingthebubblesheet,andtheexamitself,inyourfolderandreturnthefoldertoyourrecitationinstructor.Nocellphonecallsallowed.Eitherturnoffyourcellphoneorleaveitathome.Anyoneansweringacellphonemusthandintheirwork;theirexamisover.

Bestofluck,

Dr.SoerenPrell

64. Thetemperatureinyourclassroomisclosestto

A) 295KB) 68KC) 20KD) 68°CE) 295°C

SolutionRoomtemperatureisclosestto295K,whichisabout22°Cor72°F.

65. Alargevatcontains1.000Lofwaterat20°C.Whatvolumewillthiswateroccupywhenitisheatedupto80°C?Waterhasavolumeexpansioncoefficientof210×10-6K-1.

A) 1.013LB) 1.001LC) 1.600LD) 0.987LE) 1.210L

SolutionV0 +ΔV =V0 (1+βΔT )= 1.000 L( ) 1+ 210×10−6 K−1( ) 60 K( )( ) = 1.013 L

66. Howmuchheatisrequiredtoincreasethetemperatureof1.70molesofHeliumgasby23.0Katconstantpressure?(TreatHeliumasanidealmonatomicgas.)

A) 391JB) 812JC) 487JD) 346JE) 751J

Solution

Q = nCPΔT = n52R

⎛

⎝⎜

⎞

⎠⎟ΔT = 1.70 mol( ) 5

2⎛

⎝⎜⎞

⎠⎟ 8.31 J/(mol K)( ) 23.0 K( ) = 812 J

Thenexttwoquestionspertaintothefollowingsituation:Anironmassinitiallyat0.0oCisdroppedintoalargecontainerofliquidnitrogenat77K,causinggaseousnitrogentoemerge.Aftertheironhascooledto77K,theironhastransferred22.0kJofheattothenitrogen.Thespecificheatofironis0.45kJ/(kg·K)andthelatentheatofvaporizationofironis6340kJ/kg.Thelatentheatofvaporizationofnitrogenis200kJ/kg.

67. Whatmassdidtheironhave?

A)0.74kgB)2.3kgC)9.1kgD)1.6kgE)0.25kgSolution

Q = mcΔT ⇒ m =QcΔT

=22.0 kJ( )

0.45 kJ/ kg K( )( ) 273 K − 77 K( )= 0.25 kg

68. Whattotalmassofnitrogenwasvaporized?

A)0.34kgB)0.24kgC)0.81kgD)0.67kgE)0.11kgSolution

Q = mL⇒ m =QL=

22.0 kJ( )200 kJ/kg( )

= 0.11 kg

69. Thermsspeedofacertainsampleofcarbondioxidemolecules,withamolecularweightof44g/mol,is396m/s.Whatisthermsspeedofwatermolecules,withamolecularweightof18g/mol,atthesametemperature?

A) 387m/sB) 506m/sC) 253m/sD) 619m/sE) 421m/s

Solution

vrms =3kTm

=3RTM

∝1M

⇒ vrms H2O( ) = vrms CO2( )M CO2( )M H2O( )

= 396 m/s( ) 4418

= 619 m/s

70. Anidealgashasapressureof2.5atm,avolumeof1.0Latatemperatureof30°C.Howmanymoleculesarethereinthisgas?

A) 6.1×1023B) 2.3×1023C) 2.4×1022D) 6.1×1022E) 3.7×1019Solution

PV = nRT = NkT ⇒

N = PVkT

=2.5 atm( ) 1 L( )

1.38×10−23 J/K( ) 273 K + 30 K( ) =2.5 ×1.01×105 Pa( ) 10−3 m3( )

1.38×10−23 J/K( ) 273 K + 30 K( ) = 6.0×1022

71. Whatisthenameofanideal-gasprocessinwhichnoheatistransferred?

A) reversibleB) isobaricC) isochoricD) isothermalE) adiabatic

SolutionAthermalprocessofanidealgasinwhichnoheatistransferrediscalledadiabatic.

72. Anidealgasinaheatengineexecutesthecycle(ABCD)showninthepressureversusvolumegraph.Thetemperatureofthegasismaximum

A)alongthelineBCB)atpointBC)atpointCD)atpointDE)alongthelineCD

SolutionThetemperatureismaximumatpointC.Foranidealgas,PV=nRT,soTismax,whenPVismax,whichcorrespondstothepointfurthestfromtheorigin.

73. ThefigureshowsaPVdiagramforacycleofa

heatengineforwhichQH=59J.Whatisthethermalefficiencyoftheengine?

A) 17%B) 8.5%C) 14%D) 34%E) 83%

Solution

e = W

QH

=area in PV diagram( )

QH

=0.5 100 cm3( ) 200 kPa( )

59 J= 0.17

74. Thegraphinthefigureshowsthepositionofa

particleasittravelsalongthex-axis.Atwhatvalueoftisthespeedoftheparticleequalto0m/s?

A) 0.0sB) 1.0sC) 2.0sD) 3.0sE) 4.0sSolutionThevelocity(andspeed)isequaltotheslopeofpositionversustimegraph.

V

p

A

B C

D

75. Todeterminetheheightofabridgeabovethewater,apersondropsastoneandmeasuresthetimeittakesforittohitthewater.Ifthetimeis2.3s,whatistheheightofthebridge?Neglectairresistance.

A)26mB)14mC)10mD)32mE)52mSolution

Δy = 12g Δt( )2

→Δt = 12

9.8 m/s2( ) 2.3 s( )2= 26 m

76. WhenJeffranupahillwithaspeedof7.0m/s,thehorizontalcomponentofhisvelocityvectorwas5.1m/s.WhatwastheverticalcomponentofJeff'svelocity?

A)3.8m/sB)3.4m/sC)4.3m/sD)4.8m/sE)Notenoughinformationtosolve.

Solution

v = vx2 + vy

2 → vy = v2 − vx2 = 4.8 m/s

77. Ablockofmass2.36kgslidesdownafrictionlessinclinedrampandexperiencesnosignificantairresistance.Iftherampangleis17.0°abovethehorizontalandthelengthofthesurfaceoftherampis20.0m,findthespeedoftheblockasitreachesthebottomoftheramp,assumingitstartedslidingfromrestatthetop.

A)7.57m/sB)10.7m/sC)114m/sD)19.6m/sE)5.85m/sSolution

h = 20.0 m( )sin 17o( ) = 5.85 m→ mgh = 12mv2 → v = 2gh = 10.7 m

78. Twoblocks,AandB,arebeingpulledtotheright

alongahorizontalsurfacebyahorizontal100-Npull,asshowninthefigure.Bothofthemaremovingtogetherataconstantvelocityof2.0m/stotheright,andbothweighthesame.Whichofthefiguresbelowshowsacorrectfree-bodydiagramofthehorizontalforcesactingontheupperblock,A?

A)

B)

C)

D)

E) SolutionBoxAismovingwithconstantvelocityandthereforethenetforceonboxAiszero.BoxBcanexertatmostonehorizontalforceonboxA,eithertotheleftortotheright.InbothcasesboxAwouldexperienceanetforce.Thus,nohorizontalforceisexertedonboxA.

79. A10,000-kgboxcariscoastingat1.50m/salongahorizontaltrackwhenitsuddenlyhitsandcoupleswithastationary14,000-kgboxcar.Whatisthespeedofthecarsjustafterthecollision?

A) Zero.B) 2.10m/sC) 1.07m/sD) 0.875m/sE) 0.625m/s

Solution

m1v1 = m1 +m2( )v→ v = m1v1

m1 +m2

= 0.625 m/s

80. Inacarnivalride,passengersstandwiththeirbacksagainstthewallofacylinder.Thecylinderissetintorotationandthefloorisloweredawayfromthepassengers,buttheyremainstuckagainstthewallofthecylinder.Foracylinderwitha2.0-mradius,whatistheminimumspeedthatthepassengerscanhavesotheydonotfallifthecoefficientofstaticfrictionbetweenthepassengersandthewallis0.25?

A)3.0m/sB)4.9m/sC)8.9m/sD)2.3m/sE)Itdependsonthemassofthepassengers.Solution

fs = mg = µsN; N =mv2

r→ v = Nr

m=

grµs

= 8.9 m/s

81. Apieceofwoodisfloatinginabathtub.Asecondpieceofwoodsitsontopofthefirstpiece,anddoesnottouchthewater.Ifthetoppieceistakenoffandremoved,whathappenstothewaterlevelinthetub?

A)Itdoesnotchange.B)Itgoesdown.C)Itgoesup.D)Itcannotbedeterminedwithoutknowingthemassesofthetwopiecesofwood.E)Itcannotbedeterminedwithoutknowingthedensitiesofthetwopiecesofwood.

SolutionThebuoyantforceonthetwoblocksisequaltotheweightofthedisplacedwaterandequaltothecombinedweightoftheblocks.Afterthetopblockisremoved,thebuoyantforceonthesingleblockisequaltotheweightofthedisplacedwaterandtotheweightofthesingleblock.Thesingleblockweighslessthanthetwoblocktogether.Therefore,afterthetopblockisremovedlesswaterisdisplacedandthewaterlevelinthebathtubdrops.

82. Thefigureshowsagraphofthepositionxasafunctionoftimetforasystemundergoingsimpleharmonicmotion.Whichoneofthefollowinggraphsrepresentsthevelocityofthissystemasafunctionoftime?

A)graphaB)graphbC)graphcD)graphdE)Noneofthegraphs.

SolutionAtt=0thesystemhasmaximumspeed(largestslopeofthexversustcurve)andpositivevelocity(xisincreasing).

83. ConsiderapipeoflengthLthatisopenatoneendandclosedattheotherend.Whatare

thewavelengthsofthethreelowest-pitchtonesproducedbythispipe?

A)2L,L,L/2B)4L,2L,LC)2L,L,2L/3D)4L,4L/3,4L/5E)L,L/3,L/5

SolutionThewavelengthcorrespondingtothefundamental(lowest-pitch)frequencyofapipewithoneopenandoneclosedendis4L.Thenextpossibleshorterwavelengthis4L/3.Thegeneralequationforthewavelengthofstandingwavesinapipewithoneopenandoneclosedendisλ=4L/n(n=1,3,5,…).

84. Themobileshowninthefigureisperfectlybalanced,andthehorizontalsupportshaveinsignificantmasses.ThemassoffishDis8.00grams.WhatmustbethemassoffishBtomaintainbalance?

A)46.0gB)64.0gC)82.0gD)98.0gE)108g

Solution

17.5 cm( )mD = 5.00 cm( )mC → mC =17.5 cm( )mD

5.00 cm( )=

17.5 cm( ) 8.00 g( )5.00 cm( )

= 28.0 g

15.0 cm( ) mD +mC( ) = 5.00 cm( )mB → mB =15.0 cm( ) mD +mC( )

5.00 cm( )=

15.0 cm( ) 36.00 g( )5.00 cm( )

= 108 g

85. Whenalaboratorysampleofunknownmassisplacedonaverticalspring-scalehavingaforceconstant(springconstant)of467N/m,thesystemobeystheequationy=(4.4cm)cos(33.3s-1t).Whatisthemassofthislaboratorysample?

A) 60.2kgB) 22.4kgC) 3.87kgD) 0.421kgE) 0.192kgSolution

y = Acos wt( ) = 4.4 cm( )cos 33.3 s−1t( )→w= 33.3 s−1;w=km→ m =

kw2 =

467 N/m33.3 s−1( )2 = 0.421 kg

86. Twosmallballs,AandB,attracteachothergravitationallywithaforceofmagnitudeF.Ifwenowdoublebothmassesandtheseparationoftheballs,whatwillnowbethemagnitudeoftheattractiveforceoneachone?

A)16FB)4FC)2FD)F/4E)F

Solution

F ' =G m1m2

r2=G

2m1,0( ) 2m2,0( )2r0( )2

=G2m1,0( ) 2m2,0( )

2r0( )2=G m1,0m2,0

r02 = F

87. Forgeneralprojectilemotionwithnoairresistance,thehorizontalcomponentofaprojectile'svelocity

A) continuouslyincreases.B) firstdecreasesandthenincreases.C) continuouslydecreases.D) remainszero.E) remainsanon-zeroconstant.

SolutionForgeneralprojectilemotionwithnoairresistance,there’snoaccelerationalongthehorizontalaxis.Thereforethehorizontalcomponentofthevelocityremainsconstant.Forgeneralprojectilemotion,thehorizontalcomponentofthevelocityisnon-zero.

88. Considertwosame-sizecubes.Oneismadeofsolidiron,theotherismadeofsolidwood.

Whenputinwater,theironblocksinkstothegroundwhereasthewoodblockfloats.Whichofthestatementsregardingthebuoyantforcesonthetwoblocksiscorrect.

A) Thebuoyantforceontheironblockislarger.B) Thebuoyantforceonthewoodblockislarger.Thebuoyantforceontheironblockis

zero.C) Thebuoyantforceontheironblockandthebuoyantforceonthewoodblockarethe

sameandnon-zero.D) Thebuoyantforceonthewoodblockislarger.Thebuoyantforceontheironblockis

non-zero.E) Thebuoyantforceontheironblockandthebuoyantforceonthewoodblockareboth

zero.

SolutionThebuoyantforceontheironblockislarger.Sincetheironblockisfullysubmergedtheamountofdisplacedwaterbytheironblockislargerthantheonebythewoodblock.

89. Acargoesaroundacircularcurveonahorizontalroadatconstantspeed.Whatisthedirectionofthefrictionforceonthecarduetotheroad?

A) tangenttothecurveoppositetothedirectionofthecar'smotionB) perpendiculartothecurveinwardC) tangenttothecurveintheforwarddirectionD) perpendiculartothecurveoutwardE) Thereisnofrictiononthecarbecauseitsspeedisconstant.SolutionThefrictionbetweenthetiresandtheroadprovidethecentripetalforcethatletsthecarnavigatethecurve.

Laboratoryfinalexam

90. Inthecollisionsexperiment,youobtainedtracesofthemotionofapuckliketheoneshownbelow:Thistraceisproducedbythesparksgeneratedatarateof60sparkspersecond.Thedistancebetweenthefirstandlastpointinthetraceshownaboveismeasuredwithastandardmetricrulerandfoundtobe3.40cm.Duetothelimitationsoftheruler,wecanestimatetheuncertaintyinthereadingtobe±0.5mm.Youmayneglecttheuncertaintyinthesparkgeneratorfrequency.Whatistheuncertaintyinthespeedofthepuck?A. ±0.5mm/sB. ±1mm/sC. ±3mm/sD. ±5mm/sE. ±3cm/sThereare6gapsbetweensparks.Sincetheycomeatarateof60sparkspersecondthetimeintervalbetweenthefirstandthelastsparkis0.1seconds.Thepuckmovesataspeedofv=3.4cm/0.10s=34.0cm/s.Theuncertaintyinthedistancebetweenthefirstandthelastsparkis±0.5mm.Therefore,theuncertaintyinthespeedisgivenbyΔv=±0.5mm/0.10s=±5mm/s.

91. IntheForcesandMotionexperiment,aforceprobeisfixedtoacartthatcanrollwithorwithoutfrictiononatrack.Thewholesystem(probe+cart)ispulledthroughahookscrewedontotheprobebyalightstringthatgoesthroughapulleyandhasacylindricalweightattachedtotheotherend(seefigure).Whichofthefollowingmostaccuratelydescribeswhattheprobemeasures?A. Thenetforceonthecart+probesystemB. ThenetforceontheprobealoneC. ThetensioninthestringD. TheweightofthecylinderthatpullsonthesystemE. Theweightofthecart+probesystemTheprobemeasuresthetensioninthestring.ToseethatA)andB)areincorrect,considerasituationwithalargekineticfrictionforce.Thecartwouldalmostnotmove,buttheprobewouldstillmeasurethetensioninthestring,whichinthiscasewouldbeclosetotheweightofthecylinder.Ontheotherhandtheaccelerationandthusthenetforceonthecartorcart-and-probesystemwouldbealmostzero.Only,ifthecarandprobesystemisnotbeingaccelerated,thetensioninthestringisequaltothemassofthecylinder.So,ingeneralD)isincorrect.Innosituation,doestheprobedirectlymeasuretheweightofthecartandprobesystem.

Motiondetector

Reflectiveplate

Aluminumtrack

PulleyForceprobe

Cart

Weight

q

Dx

v0

92. Aballisthrownacrossayardatdifferentangleswiththehorizontal.Theinitialvelocityv0isexpectedtobethesameforallthrows.Foreachinitialangleq,wemeasurethehorizontaldistanceDxcoveredbytheball.Foraprojectilethatstartsandendsatthesameheight,thetheoreticalrelationbetweenthetwoquantitiesis:

( )2

0 sin 2vx

gq

D =

Asexpected,theplotofDxversus ( )sin 2q islinear,soalinearfitwasperformed.

Whatwastheinitialvelocityoftheballduringthesethrows?

A. 1.2m/sB. 3.7m/sC. 6.8m/sD. 11m/sE. 25m/s

Accordingtothetheoreticalprediction,theslopeofthisgraphshouldbeequalto20vg.Therefore,

( ) ( )( )20 slope 1.38m 9.8m/s 3.7m/sv g= = =

Physics111FinalExam–KEY

64A 74D 84E

65A 75A 85D

66B 76D 86E

67E 77B 87E

68E 78E 88A

69D 79E 89B

70D 80C 90D

71E 81B 91C

72C 82B 92B

73A 83D 93A