tpr science wb 2011

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CAT

Science Workbook

2011

Hyperlearning MCAT Science Workbook

PRP # 11274

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Hyperlearning

MCAT Science Workbook

The Princeton Review is not affiliated with Princeton University. 2010 The Princeton Review, Inc. All rights reserved.

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MCAT Science Workbook Cover 2011.indd 1 10/8/10 9:03 AM

Hyperlearning

MCATScience Workbook

2011 Edition

00 MCAT Sci Wkbk FM.indd 1 10/7/10 2:03 PM

Contributors and AcknowledgmentsOriginal Hyperlearning course materials edited for production by Judene Wright, M.S., M.A.Ed., National Content Director for the TPR MCAT Program, who would like to thank all of the Hyperlearning science developers, including James Patick Abulencia, Ph.D.; Jes Adams, M.S.; John Bahling, M.D.; Bethany Blackwell, M.S.; Kristen Brunson, Ph.D.; Joshua Dilworth, M.D., Ph.D.; William Ewing, M.S.; Jon Fowler, M.A.; Matthew Patterson, M.D.; Chris Pentzell, M.S.; Karen Salazar, Ph.D.; and Carolyn Shiau, M.D.

Special thanks to all former contributors, including Peter J. Alaimo, Ph.D.; Garrett T. Biehle, Ph.D.; Kendra Bowman, Clay Cauthen, M.D.; Glenn E. Croston, Ph.D.; Douglas S. Daniels, Ph.D.; Frank Gibson, Ph.D.; Scott C. Johnson, Najeeb Khan, Matthew D. Kohler, Ph.D.; Stefan Loren, Ph.D.; Allen Nicol, Ph.D.; Daniel J. Pallin, M.D.; Kirk Tanner, and Christopher M. Volpe, Ph.D.

The Princeton Review would also like to thank all of the following:Terese Alban, Kyle Alexander, Trevor Andrews, Hillary Anger, Salman Baig, Donna Barba, Nancy Beth Barr, Tom Barry, Elizabeth Barrekette, Jinhee Bae, John Bergdahl, Steve Borstelman, Jessica Brockington, Kristin Brown, Ian Carleton, Alex Carney, Joe Cavallaro, Cecelia Chao, Mina Chong, Kasia Clark, Peggy Cloutier, Lyndall Culbertson, Patrick Darby, Shannon Daugherty, Joseph Deltoro, Ray Dykeman, Leland Elliot, Fritz Engebrethsen, Alicia Ernst, Jen Ewart, Mary Favier, Alan Feinberg, Julie Fisher, Doug French, Michael Gamerl, Jay Glick, Nell Goddin, Mitchell Golden, Joe Goy, Kalee Gregory, Even Gross, Deborah Guest, Russell Haddock, Michael Haile, Julian Ham, Clayton Harding, Ken Howard, Adam Hurwitz, Sara Hymowitz, Norm Issa, Justin Jackson, Brett Jaffe, Sora Jun, Peter Jung, Andrew Kagan, Sara Kane, Jason Kasin, David Kaufman, Jeff Kelley, Bill Kerr, Meher Khambata, Robert Y. Kim, Julie Lapp, Laura Lee, Warren Leung, Lila Kal, Martha Link, John Litter, Karen Lurie, Illeny Maaza, Lisa Mack, Mark Malanowsky, Tom Meltzer, Andre Manitiu, Steve Menzies, Colin Morley, Elahe Mostaghel, Joe Mrus, Bryan Natinsky, Ray Nazzario, Jeff Newman, Jeff Nichols, Mike Nunley, Orestes OBrien, Richard Onishi, John Orsay, John Pak, Karl Pankratz, Dinica Quesada, Andrea Paykin, Laurice Pearson, Gillian Perrone, Seijen Ra, Josh Rabinovich, Ken Riley, Grace Roegner, Jenny Robbins, Lisa Ruyter, Sharjeel H. Sabir, Eric Schroeder, Christopher D. Scott, Marc Seiden, Nilanjan Sen, Jason Shave, Kelly Shrago, Jonathan Silver, Leonard Silver, Carol Slominski, Kristine Smart, Carrie Smith, Susan Stroud, Michael Stuart, John Sun, Aaron Sylvan, Rob Tallia, Johnny Tang, Linda Tarleton, Chris Thomas, Jeff Thompson, Sam Tomasello, Gary Ulaner, Kirsten Ulve, Ed Urbansky, Todd Weiser, Taylor Weiss, Eric Wertzer, Rick Westreich, Joanna Whiteley, Susan Wilcox, Barry Witner, Rose Wong, David Wright, Gail Zarick, Jordan Zaretsky, and Rob Zopf.

Special thanks to Paul Foglino, Kim Magloire, Paul Maniscalco, and John Mariani.

Original TPR course materials created by Theodore Silver, M.D.

Copyright 2010, 2009, 2008, 2001, 2000, 1999, 1998, 1997 by The Princeton Review, Inc.

All rights reserved.

2011 Edition

This manual is for the exclusive use of Princeton Review course students, and is not legal for resale.

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00 MCAT Sci Wkbk FM.indd 2 10/8/10 9:10 AM

ContentsPeriodic Table of the Elements ...................................................... v

PHYSICSFreestanding Questions ................................................................ 1

Passages .................................................................................... 53Solutions .................................................................................... 133

GENERAL CHEMISTRYFreestanding Questions ................................................................ 261


BIOLOGYFreestanding Questions ................................................................ 499


ORGANIC CHEMISTRYFreestanding Questions ................................................................ 777



The Princeton Review, Inc. | v

1H1.03Li6.9

4Be9.0

11Na23.0

12Mg24.3

19K39.1

20Ca40.1

37Rb85.5

38Sr87.6

55Cs132.9

56Ba137.3

87Fr(223)

88Ra226.0

21Sc45.0

22Ti47.9

39Y88.9

40Zr91.2

57*La138.9

72Hf178.5

89Ac227.0

104Rf(261)

23V50.9

24Cr52.0

41Nb92.9

42Mo95.9

73Ta180.9

74W183.9

105Db(262)

106Sg(266)

25Mn54.9

26Fe55.8

43Tc(98)

44Ru101.1

75Re186.2

76Os190.2

107Bh(264)

108Hs(277)

27Co58.9

28Ni58.7

45Rh102.9

46Pd106.4

77Ir192.2

78Pt195.1

109Mt(268)

110DS(281)

111Uuu(272)

112Uub(285)

114Uuq(289)

116Uuh(289)

29Cu63.5

30Zn65.4

47Ag107.9

48Cd112.4

79Au197.0

80Hg200.6

5B10.813Al27.031Ga69.7

6C12.0

7N14.0

14Si28.1

15P31.0

32Ge72.6

33As74.9

49In114.881Tl204.4

50Sn118.7

51Sb121.8

82Pb207.2

83Bi209.0

8O16.016S32.134Se79.0

9F19.0

10Ne20.2

17Cl35.5

18Ar39.9

35Br79.9

36Kr83.8

52Te127.684Po(209)

53I126.9

54Xe131.3

85At(210)

86Rn(222)

2He4.0

58Ce140.1

90Th232.0

59Pr140.9

60Nd144.2

91Pa(231)

92U238.0

61Pm(145)

62Sm150.4

93Np(237)

94Pu(244)

63Eu152.0

64Gd157.3

95Am(243)

96Cm(247)

65Tb158.9

66Dy162.5

97Bk(247)

98Cr(251)

67Ho164.9

99Es(252)

68Er167.3

69Tm168.9

100Fm(257)

101Md(258)

70Yb173.0

102No(259)

71Lu175.0

103Lr(260)

Periodic Table of the Elements

*Lanthanide Series:

Actinide Series:

Periodic Table of the Elements


MCAT PhysicsPractice Questions and Passages

01a MCAT SW Physics freesta.indd 1 8/21/09 4:19 PM

2 | The Princeton Review, Inc.


Freestanding Questions 1 through 425 are NOT based on a descriptive passage.

1. Expressamassof10kgingrams.

A. 104gB. 102gC. 102gD. 104g

2. Throughfreespace,lighttravelsataspeedof3108m/s.Expressthisspeedinkilometerspermicrosecond.

A. 0.3km/sB. 300km/sC. 3103km/sD. 3105km/s

3. Thelineardensityofacertainhomogeneousmetalbarisfoundtobe105mg/cm.Expressthisdensityinkg/m.

A. 103kg/mB. 102kg/mC. 101kg/mD. 103kg/m

4. Thedensityofaluminumisapproximately2700kgperm3.Whatisthisdensitying/cm3?

A. 0.27g/cm3B. 2.7g/cm3C. 27g/cm3D. 2.7104g/cm3

5. Aspeedof1mi/hisequivalenttoxft/min.Whatisx?(Use1mi=5280ft.)

A. 0.011B. 0.66C. 60D. 88

6. Atypicalspeckofdusthasamassof700ng.Howmanyspecksofdustwouldittaketomake1kg?

A. 1.4106B. 7.0107C. 1.4109D. 7.01010

7. Theworkdoneinpushinganobjectofmassm(inkg)fromresttospeedv(inm/s)isgivenbyW=mv2/2.FindtheSIunitforwork.

A. kgm2/s2B. kg2m2/s2C. kgm/sD. kg2m/s2

8. Aparticlesspeedattimetisgivenbyv=kt2,wherekissomeconstant.Whatarethedimensionsofk?(L=length,T=time)

A. LTB. LT1C. LT2D. LT3

9. Whichoneofthefollowingformulascouldgivethespeedv(inm/s)withwhichsoundtravelsthroughamediumwhosebulkmodulusisB(units:kgm1s2)andwhosemassdensityis(units:kg/m3)?

A. B

B. B /

C. B2

D. B / 2

10. WhichoneofthefollowingformulascouldgivethepressureP[inkg/(ms2)]atdepthh(inm)belowthesurfaceoftheocean,where(thedensityofseawater)hasunitsofkg/m3,andghasunitsofm/s2?

A. P =g/hB. P=h/gC. P =ghD. P=gh/


The Princeton Review, Inc. | 3

Physics

R

QP

11. WhichofthefollowingbestrepresentsthedirectionofthevectorsumP+Q+R?

A.

B.

C.

D.

T

N

12. ThevectorsTandNaboveareperpendiculartoeachother.Thasmagnitude 7,andNhasmagnitude 2.WhichofthefollowingbestdescribesthesumofNandT?

A. magnitude3,direction

B. magnitude3,direction

C. magnitude3,direction

D. magnitude9,direction

13. Aparticletravelstotherightalongahorizontalaxiswithconstantlydecreasingspeed.Whichoneofthefollowingbestdescribesthedirectionoftheparticlesacceleration?

A. B. C. D.

14. Aparticletravelstotheleftalongahorizontalaxiswithconstantlyincreasingspeed.Whichoneofthefollowingbestdescribesthedirectionoftheparticlesacceleration?

A. B. C. D.

15. Calculateyourdisplacementafterwalking3minorth,then6miwest,then5minorth.

A. 6miB. 8miC. 10miD. 14mi

16. Intheprecedingquestion,ifittook1h(=1hour)towalkthe3-misectionand1.5htowalkeachofthelasttwosections,whatwasthemagnitudeofyouraveragevelocity?

A. 2mi/hB. 2 12 mi/hC. 3 49 mi/hD. 3 12 mi/h

17. Acaracceleratesuniformlyfrom0to60mi/hin6seconds.Whatistheacceleration?

A. 10mih1B. 10mis2C. 10mih1s1D. 10mih2

18. Whatfractionofamiledoesthecar(describedintheprecedingquestion)travelduringthose6seconds?

A. 1/720B. 1/200C. 1/120D. 1/20




19. Anobjecttravelsalongthexaxisataconstantspeedof3m/sinthexdirection.Iftheobjectisatx=4matt=0,whereisitattimet=4s?

A. x=16mB. x=12mC. x=8mD. x=4m

20. Aracehorsemakesonelaparounda500-metertrackinatimeof25seconds.Whatwastheracehorsesaveragespeed?

A. 0m/sB. 5m/sC. 10m/sD. 20m/s

21. Aracehorsemakesonelaparounda500-metertrackinatimeof25seconds.Whatwastheracehorsesaveragevelocity?


22. Whichofthefollowingexpressionscouldbeinterpretedasvelocity?

A. 5mB. 5mtothenorthC. 5m/sD. 5m/stothenorth

23. Anobjectwhichisacceleratingmustbe:

A. changingitsdirection.B. travelinginastraightline.C. increasingitsspeed.D. changingitsvelocity.

24. Itiswellknownthattheflashandthesoundofthunderproducedbyalightningboltarenotobservedsimultaneously.Thisisduetothefactthatlightwavestravelsomuchfasterthansoundwaves.Lighttravelssoquicklythatonecanassumethatlightningboltsoccuratthesametimeoneseesthem.Giventhatsoundpropagatesthroughairataspeedof340m/s,howfarawayisalightningboltifthedelaybetweenhearingandseeingitis5sec?

A. 68mB. 1700mC. 4250mD. 6120m

25. Abodyisundergoinguniformlyacceleratedmotionoveraperiodoftime.Whichofthefollowingistrue?

A. Thefinalvelocityoftheobjectisgreaterthanitsaveragevelocity.

B. Thefinalvelocityoftheobjectisequaltoitsaveragevelocity.

C. Thefinalvelocityoftheobjectislessthanitsaveragevelocity.

D. Therelationshipbetweenthefinalvelocityoftheobjectanditsaveragevelocitycannotbedeterminedfromtheinformationgiven.

26. A2-kgrockisthrownverticallyupwardataspeedof3.2m/sfromthesurfaceofthemoon.Ifitreturnstoitsstartingpointin4seconds,whatistheaccelerationduetogravityonthemoon?

A. 0.8m/s2B. 1.6m/s2C. 3.2m/s2D. 6.4m/s2

27. Inaseriesofexperimentaltrials,aprojectileislaunchedwithafixedspeed,butwithvariousanglesofelevation.Astheangleofelevationisincreasedfrom0to90,theverticalcomponentoftheinitialvelocity:

A. increases,whilethehorizontalcomponentremainsconstant.

B. decreases,whilethehorizontalcomponentremainsconstant.

C. increases,whilethehorizontalcomponentdecreases.D. decreases,whilethehorizontalcomponentincreases.



Physics

28. Thehorizontalcomponentoftheinitialvelocityofaprojectileisdirectlyproportionaltothe:

A. angleofelevation.B. sineoftheangleofelevation.C. cosineoftheangleofelevation.D. tangentoftheangleofelevation.

29. Aprojectileislaunchedhorizontallyfromaraisedplatform.Ifairresistanceisignored,thenastheprojectilefallstotheearth,themagnitudeoftheverticalcomponentofthevelocityoftheprojectile:

A. increases,whilethehorizontalcomponentremainsconstant.

B. decreases,whilethehorizontalcomponentremainsconstant.

C. increases,whilethehorizontalcomponentdecreases.D. decreases,whilethehorizontalcomponentincreases.

30. Twoprojectilesarelaunchedfromthesamepoint.ProjectileAhasthegreaterhorizontalvelocity,whileProjectileBhasthegreaterverticalvelocity.Whichprojectilewilltravelthegreaterhorizontaldistance?

A. ProjectileA,becausedistancetraveledisdeterminedbyhorizontalvelocity.

B. ProjectileB,becauseitwillbeintheairformoretime.

C. Bothprojectileswilltravelthesamedistance.D. Cannotbepredictedfromtheinformationgiven

31. Whereinitspathdoesaprojectileinfreefallnearthesurfaceoftheearthexperiencethegreatestacceleration?

A. WhileitisascendingB. WhileitisdescendingC. AtitsgreatestheightD. Accelerationisthesameatallpointsinthepath.

32. Anobjectispresentlytravelingatavelocityof6m/s.Calculateitsvelocity5secondslater,ifitexperiencedauniformaccelerationof2m/s2duringthistimeinterval.

A. 12m/sB. 16m/sC. 20m/sD. 24m/s

33. Aparticlewithaninitialvelocityof4m/smovesalongthex-axisunderconstantacceleration.Threesecondslater,itsvelocityis14m/s.Howfardidittravelduringthosethreeseconds?

A. 21mB. 24mC. 27mD. 30m

34. Anobjectstartingfromrestisaccelerateduniformly(inastraightline)untilitsfinalvelocityisv;ittravelsadistancex.Iftheobjectwereacceleratedatthesameratefromrestuntilitsfinalvelocitywere4v,thenthedistancetraveledwouldhavebeen:

A. 2x.B. 4x.C. 8x.D. 16x.

35. Anobjectdecelerateduniformlyfromaninitialvelocityofv0m/stoafinalvelocityof(1/2)v0m/s.Ifthedistancetraveledwas1/8m,whatwasitsacceleration(inm/s2)?

A. 6v02B. 4v02C. 3v02D. 2v02

36. Acar,originallytravelingat10m/s,acceleratesuniformlyfor4secondsatarateof2m/s2.Howfardoesittravelduringthisperiod?

A. 48mB. 56mC. 72mD. 80m

37. Intheprecedingquestion,whatwasthecarsaveragevelocityduringtheaccelerationperiod?

A. 12m/sB. 14m/sC. 18m/sD. 28m/s




38. Car#1startstoacceleratefromrestjustasCar#2passesit.IfCar#2maintainsaconstantvelocityof20m/s,andCar#1acceleratesuniformlyat5/8m/s2,howlongwillittakeforCar#1toovertakeCar#2?

A. 8secB. 16secC. 32secD. 64sec

39. Aparticlemovingalongthexaxispassesthroughthepointx=0(inthexdirection)ataparticularinstant.Ifitexperiencesaconstantaccelerationof2m/s2,wherecouldtheobjectbethreesecondslater?

A. x=3mB. x=6mC. x=9mD. x=12m

40. Thepositionx(inmeters)ofanobjecttravelingalongastraightaxisisplottedasafunctionoftimet(inseconds)below.Howfardidtheobjecttravelfromt=0tot=5?

2 4 531

12

x (in

m)

t (in s)

A. 2mB. 7mC. 8mD. 9m

41. Thevelocityv(inm/s)ofanobjectmovingalongthex axisisplottedasafunctionoftimet(inseconds)below.LetthemagnitudeoftheaccelerationfromOtoPbedenotedaOP,andletthemagnitudeoftheaccelerationfromPtoQ beaPQ.WhatistheratioofaPQtoaOP?

2 4 531

12

v (in

m)

t (in s)

Q

P

O

A. 1:4B. 1:2C. 2:1D. 4:1

42. Thevelocityv(inm/s)ofanobjectmovingalongthex axisisplottedasafunctionoftimet(inseconds)below.Howfardoestheobjecttravelfromt=0tot =5?

2 4 531

12

v (in

m)

t (in s)

Q

P

A. 4mB. 5mC. 6mD. 8m

43. Thevelocityv(inm/s)ofanobjectmovingalongthex axisisplottedasafunctionoftimet (inseconds)below.Whatistheobjectsaveragespeedbetweent=1andt=5?

2 4 531

12

v (in

m)

t (in s)

A. 0.50m/sB. 0.75m/sC. 1.00m/sD. 1.25m/s



Physics

44. Thevelocityv(inm/s)ofanobjectmovingalongthex axisisplottedasafunctionoftimet(inseconds)below.Whichofthefollowingstatementsis(are)true?

I. Att=5,theobjecthadreturnedtoitsoriginalposition.

II. Theobjectsaveragespeedbetweent=0andt=1wasgreaterthanitsaveragespeedbetweent=1andt=5.

III. Theobjectchangeditsdirectionoftravelatt=1.

2 4 531

12

v (in

m)

t (in s)

A. IandIIonlyB. IandIIIonlyC. IIandIIIonlyD. Noneoftheabove

45. Arockisdroppedfroma128-ftcliff.Howlongdoesittaketoreachtheground?(Ignoreairresistanceandtakeg=32ft/sec2.)

A. 2.0secB. 2.8secC. 4.0secD. 5.6sec

46. Arockisdroppedfroma128-ftcliff;findthespeedoftherockasithitstheground.(Ignoreairresistanceandtakeg=32ft/s2.)

A. 64ft/sB. 80ft/sC. 90ft/sD. 128ft/s

47. Anarrowisshotstraightup,anditeventuallyfallsstraightbackdown.Ignoringairresistance,whichoneofthefollowingstatementsconcerningtheaccelerationaofthearrowiscorrect?

A. aalwayspointsdown.B. aalwayspointsup.C. aalwayspointsinthedirectionofthevelocity.D. aalwaysopposesthevelocity.

48. Anarrowisprojectedstraightupwithaninitialvelocityofv0m/s.Ifgdenotesthemagnitudeofthegravitationalacceleration(inm/s2)andairresistanceisignored,howhighdoesthearrowgo(inm)?

A. v0/2gB. v02/2gC. v0/gD. 2v02/g

49. AnobjectisdroppedfromthetopofameteorcrateronthesurfaceoftheMoon.Howmanytimesfartherdoesitfallduringitssecondsecondofflightthanduringitsfirst?(Note:Inthechoicesbelow,gstandsforthemagnitudeofthefree-fallaccelerationnearthesurfaceoftheMoon.)

A. 2B. 3C. 2gD. 3g

50. Ifanobject(releasedfromrest)takes3secondstofalltotheEarth,fromwhatheightwasitdropped?(Ignoreairresistanceandtakeg=10m/s2.)

A. 15mB. 45mC. 90mD. 180m

51. Ifanobjectwerethrownstraightupwardwithaninitialspeedof8m/s,andittook3secondstostriketheground,fromwhatheightwasitthrown?(Ignoreairresistanceandtakeg=10m/s2.)

A. 21mB. 24mC. 45mD. 69m

52. Ifanobjectisdroppedfromrestoffacliffandstrikesthegroundwithanimpactvelocityof14m/s,fromwhatheightwasitdropped?(Ignoreairresistanceandtakeg=9.8m/s2.)

A. 10mB. 20mC. 40mD. 80m




53. Anobjectisdroppedfromaheightof980m.LetTbethetimerequiredtofalltheentiredistanceandlettbethetimerequiredtofallthefirsthalfofthedistance.CalculatetheratioT/t.(Ignoreairresistance.)

A. 1/2B. 2C. 2D. 4

54. Onesecondafterbeingthrownstraightdown,anobjectistravelingataspeedof20m/s.Howfastwillitbetravelingtwosecondslater?(Ignoreairresistance.)

A. 30m/sB. 40m/sC. 50m/sD. 60m/s

55. AnobjectisreleasedfromrestatheighthabovethesurfaceoftheEarth,wherehismuchsmallerthantheradiusoftheEarth.Ittakestsecondstofalltotheground.Atwhatheightshouldthisobjectbereleasedfromrestinordertotake2tsecondstofalltotheground?(Ignoreairresistance;g=magnitudeofgravitationalacceleration.)

A. 2hB. 2ghC. 4hD. 4gh

56. Anobjectisthrownhorizontallywithaninitialspeedof10m/s.Howfarwillitdropin4seconds?(Ignoreairresistanceandtakeg=10m/s2.)

A. 20mB. 40mC. 60mD. 80m

57. Fromaheightof100m,aballisthrownhorizontallywithaninitialspeedof15m/s.Howfardoesittravelhorizontallyinthefirst2seconds?(Ignoreairresistance.)

A. 20mB. 30mC. 40mD. 50m

58. Aballisprojectedhorizontallywithinitialspeed5m/sfromaninitialheightof45m.Whentheballlands,howfarhasittraveledhorizontallyfromitsoriginalposition?(Ignoreairresistance.)

A. 15mB. 20mC. 25mD. 30m

59. Anobjectisprojectedupwardata30anglewiththehorizontalwithaninitialspeedof20m/s.Howlongwillittaketoreachthetopofitstrajectory?(Ignoreairresistance.)


60. Anobjectisprojectedupwardata60anglewiththehorizontalwithaninitialspeedof30m/s.Howfarwillittravelhorizontallyinitsfirstthreesecondsofflight?(Ignoreairresistance.)

A. 45.0mB. 63.0mC. 77.9mD. 90.0m

61. TwobricksarereleasedsimultaneouslyfromthesameheightabovethesurfaceoftheEarth.Brick#1issimplydropped,whileBrick#2isgivenapurelyhorizontalinitialvelocityofmagnitude10m/s.Iftheybothstrikethegroundin3seconds,howfarfromBrick#1willBrick#2land?(Ignoreairresistance.)

A. 15mB. 30mC. 45mD. 60m

62. Anobjectisprojectedupwardata30anglewiththehorizontalwithaninitialspeedof60m/s.Howlongwillittaketoreachthetopofitstrajectory?(Ignoreairresistance.)




Physics

63. Undertheactionofacertainconstantnetforce,anobjectofmass2kgtravelsinastraightlinewithaconstantaccelerationof4m/s2.Ifthissamenetforceisappliedtoanobjectwithfourtimesthemass,theaccelerationwillbe:

A. 0.25m/s2.B. 0.5m/s2.C. 1.0m/s2.D. 2.0m/s2.

64. Aforceof1dynewillcauseanobjectofmass1gramtoaccelerateat1cm/s2;therefore,1dyneisequaltoxnewtons.Whatisx?

A. 105B. 101C. 10D. 105

65. Ahockeypuckslidesonasurfaceoffrictionlessice.Ifthemassofthepuckis250grams,anditmovesinastraightlinewithaconstantvelocityof4m/s,findthenetforceactingonthepuck.

A. 0NB. 1NC. 62.5ND. 1000N

66. Twooppositelydirectedhorizontalforces,F1andF2,actonablock(ofmass3kg)whichcanslideonafrictionlesstable.F1hasmagnitude8N,andF2hasmagnitude20N.Iftheblockstartsfromrest,finditsspeedafter4seconds.


67. AnobjectisacceleratedfromresttoafinalspeedvintsecondsbyaconstantnetforceF.Ifwewishtoacceleratethisobjecttothesamefinalspeedin2tseconds,then:

A. theaccelerationwillbehalved,buttheforceshouldstaythesame.

B. theaccelerationwillbehalved,andthemagnitudeoftheforceshouldalsobehalved.

C. theaccelerationwillremainthesame,buttheforceshouldbehalved.

D. theaccelerationwilldouble,buttheforceshouldbehalved.

68. Anobjectisbeingacteduponbytwo(andonlytwo)externalforces,F1andF2.Iftheobjecthasanonzeroacceleration,whichoneofthefollowingmustbetrue?

A. Theobjectcannotmoveatconstantspeed.B. TheforcesF1andF2havethesamelineofaction.C. ThemagnitudeofF1cantequalthemagnitudeofF2.D. ThesumF1+F2isnotzero.

69. AnobjectismovingonaflatsurfaceandisbeingacteduponbyanetnonzeroforceFparalleltothesurface.Thedirectionoftheobjectsmotionmustbe:

A. thesameasthedirectionofF.B. ata45angletothedirectionofF.C. perpendiculartothedirectionofF.D. Noneoftheaboveisnecessarilytrue.

70. Abookwhosemassis2kgrestsonatable.Findthemagnitudeoftheforcethatthetableexertsonthebook.(Useg=9.8m/s2.)

A. 39.2NB. 19.6NC. 9.8ND. 0N

71. Whatforcemustbeprovidedtoacceleratea64-lbobjectupwardatarateof2ft/s2?(Useg=32ft/s2.)

A. 60lbB. 64lbC. 68lbD. 72lb




72. Findtheforcethatmustbeprovidedtolifta49-Nobjectwithanaccelerationof9.8m/s2(g=9.8m/s2).

A. 9.8NB. 49NC. 98ND. 147N

73. Twobodiesofdifferentmassesaresubjectedtoidenticalforces.Comparedtothebodywithsmallermass,thebodywithgreatermasswillexperience:

A. lessacceleration,becausetheproductofmassandaccelerationwillbesmaller.

B. greateracceleration,becausetheproductofmassandaccelerationwillbegreater.

C. lessacceleration,becausetheratioofforcetomasswillbesmaller.

D. greateracceleration,becausetheratioofforcetomasswillbelarger.

74. Agarmenthangsfromaclotheslineasshownbelow.Thetensionintheclotheslineis10Nontherightsideofthegarmentand10Nontheleftsideofthegarment.Findthemassofthegarment.

30

T1 T2

30

A. 0.5kgB. 1kgC. 2kgD. 10kg

75. Acanofpaintwithamassof10kghangsfromarope.Ifthecanistobepulleduptoarooftopwithaconstantvelocityof0.5m/s,whatmustthetensionintheropebe?

A. 0NB. 50NC. 100ND. 200N

76. Whichofthefollowingbestdescribesthedirectioninwhichtheforceofkineticfrictionactsrelativetotheinterfacebetweentheinteractingbodies?

A. Perpendiculartotheinterfaceandawayfromthemoremassivebody

B. Perpendiculartotheinterfaceandtowardthemoremassivebody

C. Paralleltotheinterfaceandoppositethedirectionoftherelativevelocity

D. Paralleltotheinterfaceandinthesamedirectionastherelativevelocity

77. Whichofthefollowingbestdescribesthemotionofabodyalongasurfacewherefrictionmustbetakenintoaccount?

A. Moreforceisrequiredtostarttheobjectinmotionthantokeepitinmotionatconstantvelocity.

B. Oncetheobjectissetinmotion,noforceisrequiredtokeepitinmotionatconstantvelocity.

C. Lessforceisrequiredtostarttheobjectinmotionthantokeepitinmotionatconstantvelocity.

D. Thesameforceisrequiredtostarttheobjectinmotionastokeepitinmotionatconstantvelocity.

78. A100-Ntrashcanispulledacrossthesidewalkatconstantspeedbyaforceof25Nasshownbelow.Howlargeistheforceoffrictionimpedingthemotionofthetrashcan?

Ff

25 N

A. 0NB. 25NC. 75ND. 125N



Physics

79. Howwillthegravitationalforcebetweentwoobjectschangeifthedistancebetweenthemisdoubled?

A. Itwilldecreasebyafactorof4.B. Itwilldecreasebyafactorof2C. Itwillincreasebyafactorof2.D. Itwillincreasebyafactorof4.

80. LetthemassoftheMoonbeMandletitsradiusbeR.IfasmallobjectofmassmisreleasedafewmetersabovetheMoonssurface,withwhataccelerationwillitfall?(G=universalgravitationalconstant)

A. G mR2

B. G MmR2

C. G MR2

D. G MR

2

2

81. Calculatethetensioninacableusedtopulla1000-kgobjectstraightupwardatanaccelerationof0.7m/s2.(Useg=9.8m/s2.)

A. 700NB. 9100NC. 9800ND. 10,500N

82. Anobjecthasamassof36kgandweighs360NatthesurfaceoftheEarth.IfthisobjectistransportedtoanaltitudeequaltotwicetheEarthsradius,thenatthisnewelevatedpositiontheobjectwillhave:

A. mass4kgandweight40N.B. mass36kgandweight40N.C. mass9kgandweight90N.D. mass36kgandweight90N.

83. An0.2-kgapplerestsonthesurfaceoftheEarth.ApproximatethegravitationalforceexertedbytheappleontheEarth.(Note:Theuniversalgravitationalconstant,G,is6.7 1011N-m2/kg2,themassoftheEarthis6.01024kg,andtheradiusoftheEarthis6.4106m.)

A. 41023NB. 2 1015NC. 4107ND. 2N

84. Duringarainstorm,younoticethattheraindropsarenotalwaysthesamesize:somearesmall,othersarelarger.Raindropsfallwithaconstantvelocity(calledtheirterminal velocity).Giventhattheupwardforceofairresistanceisproportionaltothespeedofthefallingdrop,whichraindropsthesmalleronesorthelargeronesfallwiththegreaterspeed?

A. Thesmallerdrops,sincetheforceofairresistanceonthemissmaller.

B. Thesmallerdrops,sincetheirsmallermassgivesthemgreateracceleration.

C. Thelargerdrops,sincetheyacquiregreaterspeedbeforeairresistanceeventuallybalancesouttheforceofgravity.

D. Neither;eventakingairresistanceintoaccount,theyfallatthesamespeed.

85. Acrateofmass100kgisbeingpushedinastraightlineacrossahorizontalfloorataconstantspeedof4.0m/s.Thecoefficientofkineticfrictionbetweenthecrateandtheflooris0.3.Findthenetforceonthecrate.

A. 0NB. 300NC. 400ND. 1200N

86. A2-kgblockisslidingalongahorizontalsurface,pulledbyaropethatisparalleltothesurface.Ifthetensionintheropeis12N,andthecoefficientofkineticfrictionis0.4,findtheaccelerationoftheblock.

A. 2m/s2B. 4m/s2C. 6m/s2D. 8m/s2

87. Acrateofmass100kgrestsonahorizontalfloor.Thecoefficientofstaticfrictionis0.4.Ifaforceof250N,paralleltothefloor,isappliedtothismass,calculatethemagnitudeoftheforceofstaticfrictiononthecrate.

A. 0NB. 150NC. 250ND. 400N




88. A50Nhorizontalforceisappliedtoa5kgcrate,anditslidesalongahorizontalfloorwithanaccelerationof8m/s2.Whatisthemagnitudeoftheforceofkineticfrictionactingonthecrate?

A. 0NB. 5NC. 10ND. Cannotbedeterminedsincemisnotgiven

89. ApersonappliesahorizontalforceFonablockofmassmrestingagainstaverticalwall.Iftheblockslidesverticallydownthewallataconstantspeed,whatmustbetrueaboutthecoefficientofkineticfriction,,betweentheblockandthewall?(g=magnitudeofgravitationalacceleration)

A. =mg/FB. =F/(mg)C. =1D. =g

90. Ablockofmassmbeginstoslidedownaverticalwall.Ifthewallisfrictionless,whatminimumhorizontalforceFmustbeappliedtotheblocktokeepitfromslidinganyfurther?(g=magnitudeofgravitationalacceleration)

A. F=mgB. F=2mgC. F=3mgD. Nohorizontalforce,howeverstrong,cankeepthe

blockfromslidingdownthewall.

91. Acrateofmass100kgrestsonahorizontalfloor.Thecoefficientofstaticfrictionbetweenthefloorandthecrateis0.4.Letfdenotethemaximumstaticfrictionforcethatthefloorcanexertonthecrate.Whathappenstofifachildofmass20kgsitsontopofthecrate?

A. fincreasesby8N.B. fincreasesby20N.C. fincreasesby80N.D. fwillnotchange.

92. Ablockweighing40Nisheldincontactwiththeceilingofaroombyaupwardforceof50N.Whatisthemagnitudeofthenormalforceexertedbytheceilingontheblock?

A. 0NB. 10NC. 50ND. 90N

93. A25-kgblockispushedinastraightlineacrossahorizontalsurface.Ifaconstantforceof49Nmustbeappliedtotheblockinordertomaintainaconstantvelocityof2m/s,whatisthecoefficientofkineticfrictionbetweentheblockandthesurface?

A. 0.1B. 0.2C. 0.4D. 0.5

94. Whathorizontalforcemustbeappliedtoanobjectwithaweightof98Ninordertogiveitahorizontalaccelerationof10m/s2?(Neglecttheforcesoffriction.)

A. 9.8NB. 100.0NC. 490.0ND. 980.0N

95. Anobjectwithamassof50kgmovesacrossalevelsurfacewithaconstantspeedof15m/s.Ifthecoefficientofkineticfrictionis0.7,whichofthefollowingmustbetrueabouttheforcesactingontheobject?

A. Theforceexertedontheobjectbykineticfrictionisnegligible.

B. Theremustbesomeotherhorizontalforceactingontheobject.

C. Noforcesaredoingworkontheobject.D. Therearenoverticalforcesactingontheobject.

96. Consideraninclinedplanethatmakesananglewiththehorizontal.Whatistherelationshipbetweenthelengthoftheramp,L,andtheverticalheightoftheramp,h?

A. L=hsinB. L=htanC. h=LsinD. h=Ltan



Physics

97. A40-kgcrateisbeingpulledalongafrictionlesssurfacebyaforceofmagnitude140Nthatmakesanangleof30withthehorizontal.Whatistheaccelerationofthecrate?

A. 1.75m/s2B. 2m/s2C. 2.5m/s2D. 3m/s2

98. Aboxisrestingonaninclinedplaneasshownbelow.WhatisthemagnitudeofF?

10 N30

F

A. 4.3NB. 5.0NC. 8.7ND. 11.5N

99. A50-kgcrateslidesdownarampasshownbelow.Assumingthattherampisfrictionless,findtheaccelerationofthecrate.

60

50 kg

A. 5.0m/s2B. 8.7m/s2C. 10.0m/s2D. 11.3m/s2

100. Theaccelerationexperiencedbyablockmovingdownafrictionlessplaneinclinedata30angle:

A. decreasesastheblockmovesdowntheplane.B. isconstant.C. increasesastheblockmovesdowntheplane.D. dependsontheheightoftheplane.

101. Ablockismovingdowntheslopeofafrictionlessinclinedplane.Theforceparalleltothesurfaceoftheplaneexperiencedbytheblockis:

A. lessthantheweightoftheblock.B. equaltotheweightoftheblock.C. greaterthantheweightoftheblock.D. unrelatedtotheweightoftheblock.

102. Ablockismovingdowntheslopeofaninclinedplaneatconstantvelocity.Thenormalforceexertedbytheplaneontheblock:

A. increaseswithincreasingvelocity.B. decreaseswithincreasingvelocity.C. isindependentofvelocity.D. dependsonthecoefficientofkineticfrictionbetween

theplaneandblock.

103. Ablockissittingmotionlessonthesurfaceofaninclinedplaneastheangleofelevationisgraduallyincreased.Thenormalforceexertedbytheplaneontheblock:

A. increaseswithincreasingangleofelevation.B. decreaseswithincreasingangleofelevation.C. isindependentofangleofelevation.D. dependsonthecoefficientofstaticfrictionbetween

theplaneandblock.

104. Ablockisslidingdownthesurfaceofaninclinedplanewhiletheangleofelevationisgraduallydecreased.Whichofthefollowingistrueabouttheresultsofthisprocess?

A. Theforceduetofrictiondecreases,andtheweightoftheblockremainsconstant.

B. Theforceduetofrictiondecreases,andtheweightoftheblockdecreases.

C. Theforceduetofrictionincreases,andtheweightoftheblockdecreases.

D. Theforceduetofrictionincreases,andtheweightoftheblockremainsconstant.

105. Ablockisbeingpulledbyaropeupthesurfaceofaninclinedplaneatconstantvelocity.WhichofthefollowingistrueofthetensionintheropeT,theforceduetofrictionFf,andthecomponentoftheblocksweightparalleltotheplanewp?

A. wp=T +FfB. T=wp+FfC. Ff =T+wpD. T+Ff +wp=0




106. Ablockslidesdownafrictionlessinclinedplanethatmakesanangle(where0M1),restatthetopofaninclinedplane.Ifthebottomoftheinclineistakentobethezeroofgravitationalpotentialenergy,thentheseobjectshave:

A. thesameinertiaandthesamepotentialenergy.B. thesameinertiabutdifferentpotentialenergies.C. differentinertiasbutthesamepotentialenergy.D. differentinertiasanddifferentpotentialenergies.

155. Adjustmentsaremadetoamachinethatallowittoprovidelessenergyatanygivenmoment,butthatallowittooperateforagreaterlengthoftime.Thepowerofthemachinehasbeen:

A. decreased.B. unchanged.C. increased.D. changedinamannerthatcantbepredicted.

156. Whichofthefollowingsituationsrequiresthegreatestpower?

A. 20Jofworkdonein10minutesB. 100Jofworkdonein20minutesC. 200Jofworkdonein10minutesD. 10Jofworkdonein20minutes

157. Whichofthefollowingexpressionsisequaltoawatt?

A. (kg)(m)/(sec)B. (kg)(m)/(sec)3C. (kg)2(m)2/(sec)2D. (kg)(m)2/(sec)3




158. Anobjectweighing100Nistravelingverticallyupwardfromtheearthintheabsenceofairresistanceataconstantvelocityof5m/s.Whatisthepowerrequiredtokeeptheobjectinmotion?

A. 0WB. 20WC. 200WD. 500W

159. Anobjectweighing100Nistravelinghorizontallywithrespecttothesurfaceoftheearthintheabsenceofairresistanceataconstantvelocityof5m/s.Whatisthepowerrequiredtomaintainthismotion?

A. 0WB. 20WC. 200WD. 500W

160. Anelectriccranehoistsanobjectweighing4000Ntothetopofabuilding.Thecraneraisestheobjectstraightupwardataconstantrate.Ifittakes60secondstoliftthemass300m,atwhatrateisenergyconsumedbytheelectricmotorinthecrane?(Note:Ignoreallforcesoffriction.)

A. 0.8kWB. 2.0kWC. 10.0kWD. 20.0kW

161. Whichofthefollowingquantitiesis(are)conservedwhenafallingobjectstrikestheground?

I. Momentumoftheobject II. Kineticenergyoftheobject III. Totalenergy

A. IonlyB. IIIonlyC. IandIIIonlyD. IIandIIIonly

162. TwometeorscollideandcombineatPointP:

vA vB30

45

P

AB

Ifeachmeteorhasmassm,whatisthemagnitudeoftheverticalcomponentoftheircommonvelocityjustafterthecollision?

A. (vAsin30+vBsin45)/2B. (vAsin30vBsin45)/2C. (vAcos30+vBcos45)/2D. (vAcos30vBcos45)/2

163. TwomovingbodiesAandBareofunequalmass.Theymeethead-onandimmediatelycometorestasaresultofaperfectlyinelasticcollision.Priortothecollision,BodyAwastravelingataspeed10timesthatofBodyB.WhichofthefollowingrepresentstheratioofthemassofAtothemassofB?

A. 1:100B. 1:10C. 10:1D. 100:1

164. Alaborerexpends800Jtoliftablocktoaheighth.Hethenrepeatsthetaskusingasimplenon-motorizedpulleysystemthatreducesbyhalftheinputforcehemustprovide.Withthepulleysysteminoperation,howmuchworkmustthelaborerperforminordertolifttheblocktoheighth?

A. 200JB. 400JC. 800JD. 1600J



Physics

165. Amachinethatconsumes500wattstakes10sectoliftanobjectwithamassof1kgfromthegroundtoahighplatform.Assumethatthemachineisperfectlyefficient.Theobjectisthenpushedofftheplatformandfallsfreelytotheground.Whatisthespeedoftheobjectatthemomentofimpact?

A. 10m/sB. 32m/sC. 50m/sD. 100m/s

166. Aperfectlyinelasticcollisionoccursbetweena2000-kgcarmovingnorthat7m/sanda1600-kgcarmovingsouthat12m/s.Whatisthevelocityofthecarsimmediatelyafterimpact?

A. 1.4m/snorthB. 1.4m/ssouthC. 9.2m/snorthD. 9.2m/ssouth

167. Aftertheirisolatedcollision,twoballsmoveinoppositedirections:Ball#1movesat0.2m/sinthenegativexdirection,andBall#2movesat0.5m/sinthepositivexdirection.Ifthemassofeachballis100grams,determinethetotalmomentumofthissystembeforethecollision.

A. 0.03kgm/sB. 0.07kgm/sC. 0.30kgm/sD. 0.70kgm/s

168. Acueball(mass225g),movingat0.5m/s,strikesthe8-ball(mass200g)originallyatrest.Afterthecollision,thecueballmoveswithavelocityof0.1m/s.Findthevelocityofthe8-ballafterthecollision.

A. 0.23m/sB. 0.45m/sC. 0.68m/sD. 0.90m/s

169. Object#1movestowardObject#2,whosemassistwicethatof#1,whichisatrest.Aftertheirhead-onimpact,theobjectslocktogetherandmovewithwhatfractionoftheObject#1sinitialspeed?

A. 1/4B. 1/3C. 1/2D. 2/3

170. Apersonsitsonastationarysled(totalmassofperson+sled=100kg)onapondofsmoothiceandholdsaball.Ifthe2-kgballisthrownataspeedof10m/s,findthespeedwithwhichthepersonandsledmoveafterward.

A. 0m/sB. 0.1m/sC. 0.2m/sD. 0.4m/s

171. Afteracceleratinguniformlyfromrestatarateof2m/s2for4.5seconds,anobjectwithmass2kgcollideshead-onwithanotherobjectofmass1kginitiallyatrest.Afterthecompletelyinelasticcollision,whatisthecommonvelocityofthetwoobjects?


172. Atennisballisdroppedfromaheightof1montoahorizontalsurfaceinalargeevacuatedcontainer.Theballwillnotreboundtoaheightof1mbecause:

A. thefloorexertsnoforceontheballwhenitmakescontact.

B. someoftheballskineticenergyislostwhentheballstrikesthefloor.

C. theballsmomentumisnotchangedasaresultofthecollision.

D. thegravitationalforceisreducedwhenactinginavacuum.

173. A2.5-kgstoneisdroppedfromaheightof4m.Whatisitsmomentumonimpact?(Ignoreairresistance.)

A. 7.5kgm/sB. 11.3kgm/sC. 22.5kgm/sD. 45.0kgm/s

01b MCAT SW Physics freesta.indd 21 8/21/09 4:23 PM



174. AnobjectisreleasedfromrestatheighthabovethesurfaceoftheEarth,wherehismuchsmallerthantheradiusoftheEarth.Itsspeedisvm/sasitstrikestheground.Atwhatheightshouldthisobjectbereleasedfromrestinorderforitsspeedtobe2vwhenitstrikestheground?(Ignoreairresistance;gdenotesthemagnitudeofgravitationalacceleration.)

A. 2hB. 2ghC. 4hD. 4gh

175. Aobjectisraisedtoaheightof16mandreleasedfromrest.Attheinstantthattheobjectis12mabovetheground,whatfractionofitstotalmechanicalenergyisintheformofkineticenergy?(Ignoreairresistance.)

A. 1/4B. 3/8C. 1/2D. 3/4

176. A2-kgobjectisataheightof10mabovethesurfaceoftheEarth.Ifitisthrownstraightdownwardwithaninitialspeedof20m/s,whatwillitskineticenergybeasitstrikestheground?(Ignoreairresistance.)

A. 200JB. 400JC. 600JD. 800J

177. Byapplyingalargehorizontalforce,amanpushesaheavycratealongahorizontalfloor.Whilehepushesthecrateadistanced,thefrictionalforcedoesW1joulesofwork.Asmallchildthensitsontopofthecrate,andthemanpushesthecrate(andchild)adistanced.IfthefrictionalforcedoesW2joulesofworkduringthisseconddisplacement,thenwhichofthefollowingistrue?

A. W1W2D. Cannotbedeterminedfromtheinformationgiven

178. A2-kgblockslidesdowna3-meter-long,frictionless30incline.Howmuchworkdoesgravitydoontheblock?

A. 30JB. 40JC. 50JD. 60J

179. Iftheblockdescribedintheprecedingquestionstartedfromrestatthetopoftheincline,withwhatspeeddoesitreachthebottom?

A. 2.7m/sB. 3.6m/sC. 5.5m/sD. 7.1m/s

180. Whatmagnitudeofworkmustbedonetobringa1000-kgcar,movingat20m/s,torest?

A. 1.0105JB. 2.0105JC. 4.0105JD. 1.8106J

181. Calculatetheaveragepowerneededtostopthecardescribedintheprecedingquestionin4seconds.

A. 5kWB. 50kWC. 500kWD. 5000kW

182. Twohockeypucks,eachwithanonzerovelocity,slidetowardeachotheronasurfaceoffrictionlessiceandcollideheadon.Theningeneral:

A. momentumisnotconservedbutkineticenergyisconserved.

B. momentumisconservedbutkineticenergyisnotconserved.

C. neithermomentumnorkineticenergyisconserved.D. bothmomentumandkineticenergyareconserved.



Physics

183. A2-kgobjectinitiallyatrestisstruckhead-onbya4-kgobjectmovingatavelocityof2m/s.Afterthecollision,thetwoobjectssticktogether.LetKbbethekineticenergyofthesystembeforethecollision,andletK

abethekinetic

energyofthesystemafterthecollision.CalculatetheratioK

a/Kb.

A. 1/3B. 4/9C. 1/2D. 2/3

184. Asacrate(ofmassm)slidesdownafrictionlessincline(withangle),aconstanthorizontalforceF,paralleltothebaseoftheincline,isappliedtothecratesothatthecratesspeeddowntheinclineremainsconstant.FindthemagnitudeofF.

A. F=mgsin2B. F=mgcotC. F=mgtanD. F =mgsincos

185. Iftheverticalriseoftheinclineishmeters,determinetheworkdonebythehorizontalforceF(describedintheprecedingquestion)asthecrateslidesdowntheincline.

A. mghcos2B. mghsincosC. mghsin2D. mgh

186. A1-kgballisdroppedfromaheightof6meters.Asitfalls,itisconstantlyacteduponbyairresistance,whoseaverageforceontheballis3.3N.Takingthisintoaccount,calculatethespeedwithwhichtheballhitstheground.

A. 9.0m/sB. 10.0m/sC. 10.6m/sD. 11.1m/s

187. Anergisaunitofenergyequalto1gcm2/s2.Theconversionbetweenergsandjoulesistherefore1joule=xergs.Whatisx?

A. 107B. 105C. 105D. 107

188. Asacrateslidesdownfromthetopofa2-meter-longinclinedplane,thecoefficientoffrictionis0.4.Calculatetheworkdonebyfrictioniftheangleofinclineis30andthemassofthecrateis10kg.

A. 68JB. 39JC. 34JD. 20J

189. Asa5-kgobjecttravelsdownaramp,gravitydoes60Jofworkandfrictiondoes20J.Iftheobjectstartedfromrest,whatisitsfinalspeed?


190. Anobjectsspeedincreasesfrom0to2m/s,duetoanamountofworkW1,andthenincreasesfrom2m/sto4m/sduetoanamountofworkW2.Whichoneofthefollowingistrue?

A. W1W2D. Cannotbedeterminedfromtheinformationgiven

191. Astoneofmassmisdroppedfromaheighth.Ifairresistanceisnegligible,whichoneofthefollowingstatementsistrueconcerningthestoneasitstrikestheground?

A. Itsspeedisproportionaltoh.B. Itsspeedisproportionaltoh2.C. Itskineticenergyisproportionaltoh.D. Itskineticenergyisproportionaltoh2.

192. Apersonspowerexpenditureisbeingmonitored.Iftheamountofworkisdoubledandthetimerequiredtocompleteitishalved,thenthepoweroutput:

A. remainsconstant.B. decreasesbyafactorof4.C. increasesbyafactorof2.D. increasesbyafactorof4.




193. A2.5-kgmassisprojectedstraightupwardwithaninitialkineticenergyof980J.Ifairresistanceisignored,howmuchkineticenergywillthisprojectilehaveasitstrikestheground?

A. 490JB. 980JC. 1470JD. 1960J

194. An10-kgobjectisdroppedfromaheightof100meters.Howmuchgravitationalpotentialenergyhasitlostwhenitsspeedis30m/s?(Ignoreairresistance.)

A. 2250JB. 4500JC. 5500JD. 7750J

195. A10-kgmassisdroppedfromaheightof125m.Whatisitsspeedatimpactwiththeground?(Ignoreairresistance.)

A. 20m/sB. 50m/sC. 75m/sD. 125m/s

196. Aobjectofmassmisdroppedfromaheightofhmeters;itsspeedatimpactwiththegroundisvm/s.Ifanobjectofmass4mweredroppedfromaheightofhmeters,determineitsspeedatimpact.(Ignoreairresistance.)

A. vB. 2vC. 4vD. 16v

197. A10-kgobjectisprojectedstraightupwardwithaninitialkineticenergyof1000J.Howhighwillitgoaboveitslaunchpoint?(Ignoreairresistance.)

A. 5mB. 10mC. 20mD. 50m

198. A10-kgobjectmovesfromPosition#1toPosition#2closetothesurfaceoftheEarth.Insodoing,itsgravitationalpotentialenergydecreasesby200J.HowmuchworkwasdonebythegravitationalforceonthisobjectasitmovedfromPosition#1toPosition#2?

A. 200JB. 100JC. 100JD. 200J

199. Asmallblockisplacedatthetopoftwoinclinedplanes,andallowedtoslidedowntothebottom.TheinclineangleofIncline2islessthanthatofIncline1,thatis,2 f .D. the relationship between f and f can be any of the

above depending on the specific value of f.

368. A source creates sound waves of wavelength 0.68 m which travel away from the source at a speed of 340 m/s. At any fixed location near the source, what is the time interval between successive pressure compressions due to the passing wave?

A. 0.5 msB. 1.0 msC. 2.0 msD. 4.0 ms

369. Find the period of an acoustical wave traveling through the air at 340 m/s with a frequency of 200 Hz.

A. 0.003 secB. 0.005 secC. 0.017 secD. 0.068 sec

370. A source of sound waves (of wavelength ) is traveling at 1/8 the speed of sound toward a stationary listener. If the wavelength of the sound detected is , then which of the following is true?

A. = 78B. = 89C. = 98D. = 87

371. An airplane is traveling at constant speed in a circular path of radius 400 m parallel to the ground whose center is 300 m above an air traffic control tower. Its engine is the source of audible sound waves of a fixed frequency. To a stationary listener on the tower, how would the detected frequency of the engine differ from the actual source frequency while the plane circled above her?

A. The detected frequency would be higher than the source frequency during one quarter of the orbit, lower during the next quarter, higher during the third, lower during the fourth quarter, and so on.

B. The detected frequency would be higher than the source frequency during half the orbit, lower during the next half, and so on.

C. The detected frequency would be higher than the source frequency during one orbit, lower during the next orbit, and so on.

D. The detected frequency would remain constant and equal to the source frequency.

01c MCAT SW Physics freesta.indd 45 8/21/09 4:24 PM



372.

Q

P

S1

S2 4 meters

1.5 meters

1.5 meters

Two speakers, S1 and S2, are driven by the same amplifier and emit sound waves of fixed wavelength ( = 2 m), radiating equally in all directions. How would AP , the amplitude of the resultant wave at Point P, compare to AQ, the amplitude at Point Q?

A. AP < AQB. AP = AQC. AP > AQD. The amplitudes at P and Q vary with time, so no

single comparison can be made.

373. How far could a wave front of an acoustical wave travel in 0.5 second if its frequency is 700 Hz and its wavelength is 0.5 m?

A. 175 mB. 350 mC. 700 mD. 1400 m

374. Sound waves are sent through a certain material in two separate trials. Some of the results are given below:

frequency (Hz) wavelength (m)Trial #1 100 20Trial #2 400

What is the value of the wavelength in Trial #2?

A. 5 mB. 40 mC. 80 mD. It cannot be determined from the information given.

375. At a particular position from a fixed source of sound waves, the intensity of sound Wave #1 is I1 = 2.4 108 W/m2, and the intensity of a different sound wave (Wave #2) is I2 = 2.4 105 W/m2. If the sound level of Wave #1 is 1 decibels, and that of Wave #2 is 2 decibels, whats 2 1? (Note: The decibel level of a sound wave is related to the intensity I of the wave by the equation

= 10log(I/I0), where I0 = 1012 W/m2

A. 30B. 10C. 10D. 30

376. The Doppler effect is also experienced by light waves, but the equation that gives the detected frequency f is

=


Physics

377. If a distant galaxy is moving away from the Earth at 6800 km/sec, how will the frequency and wavelength of the visible light detected on earth compare to the frequency and wavelength of the light emitted by the galaxy?

A. The detected frequency will be higher, and the wavelengths will be shifted toward the blue end of the visible spectrum.

B. The detected frequency will be higher, and the wavelengths will be shifted toward the red end of the visible spectrum.

C. The detected frequency will be lower, and the wavelengths will be shifted toward the blue end of the visible spectrum.

D. The detected frequency will be lower, and the wavelengths will be shifted toward the red end of the visible spectrum.

378. The speed of sound in air, v (in m/s), varies with the air temperature, T (in C), according to the equation

v T= +322 1 273

A tuning fork emits a 440-Hz tone. How will the sound wave change as it travels into a warmer region of air?

A. The frequency of the transmitted wave will be lower, but the wavelength will be greater.

B. The frequency of the transmitted wave will remain the same, but the wavelength will be greater.

C. The frequency of the transmitted wave will remain the same, but the wavelength will be shorter.

D. The frequency of the transmitted wave will be higher, but the wavelength will be shorter.

379. How long does it take for a light wave to travel 1 km through a body of water with a refractive index of 1.33?

A. 2.3 1012 secB. 2.3 109 secC. 4.4 109 secD. 4.4 106 sec

380. Which of the following is true of the properties of a light wave that is traveling in vacuum?

A. Increased frequency results in increased wavelength.B. Increased frequency results in decreased wavelength.C. Increased frequency results in increased speed.D. Increased frequency results in decreased speed.

381. Which of the following is true of the properties of a light wave as it moves from a medium of lower refractive index to a medium of higher refractive index?

A. Frequency will increase.B. Frequency will decrease.C. Speed will increase.D. Speed will decrease.

382. A light wave is passing from a medium of lower refractive index to a medium of higher refractive index. Some of the incident light is refracted, and some is reflected. The angle of refraction will be:

A. greater than the angles of incidence and reflection.B. less than the angles of incidence and reflection.C. greater than the angle of incidence and less than the

angle of reflection.D. less than the angle of incidence and greater than the

angle of reflection.

383. A light ray in air strikes a medium whose index of refraction is 1.5. If the angle of incidence is 60, which one of the following expressions gives the angle of refraction?

A. sin1(0.67 sin 30)B. sin1(1.5 sin 30)C. sin1(0.67 sin 60)D. sin1(1.5 sin 60)

384. A mirror forms an image of an object. If the images distance from the mirror is 5 times greater than the objects distance from the mirror, what is the magnification?

A. 1/10B. 1/5C. 5D. 10

385. At what distance from a concave spherical mirror of focal length 100 cm must a man stand in order to see an upright image of himself that is twice his actual height?

A. 20 cmB. 50 cmC. 100 cmD. 200 cm




386. The image of an object placed outside the focal point of a concave mirror will be:

A. real and inverted.B. real and upright.C. virtual and inverted.D. virtual and upright.

387. The image of an object placed in front of a convex mirror will be:

A. real and inverted.B. real and upright.C. virtual and inverted.D. virtual and upright.

388. If an image appears at the same distance from a mirror as the object, the size of the image will be:

A. larger than the object.B. smaller than the object.C. the same as the object.D. unrelated to the image distance.

389. An image formed by a converging lens is 8 cm tall and located 40 cm from the lens. If the object is located 20 cm from the lens, what is its height?

8 cmImage

Lens 40 cm

A. 2 cmB. 4 cmC. 8 cmD. 16 cm

390. If the image produced by a lens appears very close to its focal point, then the object must be very:

A. close to the lens.B. close to the focal point.C. close to the center of curvature of the lens.D. far from the lens.

391. A lens forms a virtual image of an object. Which of the following must be true of the image?

A. It is upright.B. It is inverted.C. It is smaller than the object.D. It is larger than the object.

392. An object is placed at a great distance from a converging lens and gradually moved toward the focal point of the lens. The image will move:

A. toward the lens and decrease in size.B. toward the lens and increase in size.C. away from the lens and decrease in size.D. away from the lens and increase in size.

393. When two converging lenses of equal focal lengths are used together, the effective focal length of the combination is less than the focal length of either individual lens. The power of the lens combination will be:

A. greater than the power of either individual lens.B. less than the power of either individual lens.C. the same as the power of either individual lens.D. None of the above

394. An object is placed at a distance of 0.5 m from a converging lens with a power of 12 diopters. At what distance from the lens will the image appear?

A. 0.1 mB. 0.5 mC. 0.6 mD. 1.2 m

395. A beam of light incident in glass of refractive index 3/2 passes into water with refractive index 4/3. If 1 is the angle of incidence, and 2 is the angle of refraction, what is the value of (sin 1)/(sin 2)?

A. 1/2B. 8/9C. 9/8D. 2



Physics

396. A ray of light in air strikes the surface of a piece of glass; the angle of incidence is 60. If the reflected ray and the refracted ray are perpendicular to each other, what must be the index of refraction of the glass?

A. 2 3 3/

B. 3

C. 3 3 2/

D. 2 3

397. A light ray incident in a piece of polystyrene (whose index of refraction n = 1.55), strikes the polystyreneair boundary. At what angles of incidence between 0 and 90 will the ray be totally internally reflected?

A. < sin1 (1/n)B. > sin1 (1/n)C. < sin1 nD. > sin1 n

398. An incident ray (in air) makes an angle of 30 with the surface of a medium whose index of refraction is 3. Find the angle that the refracted ray makes with the

surface.

A. sin 1 12 3

B. 30

C. 90 12 3

1

sin

D. 60

399. Let n1 be the index of refraction of the incident medium, and let n2 be the index of refraction of the refracting medium. If the angle that the refracted ray makes with the boundary is less than the angle that the incident ray makes with the boundary, then which of the following must be true?

A. n1 < 1B. n2 < 1C. n1 < n2D. n1 > n2

400. A piece of transparent plastic shaped in a 454590 triangle experiences total internal reflection when an incident beam of light strikes surface AC perpendicularly. What can you say about the refractive index n of this piece of plastic, which is surrounded by air?

A B

C

A. 1 2 1/ <



402. Consider a piece of glass (in between the two heavy lines in each diagram) that is struck by a beam of light from the air (and which enters the air after leaving the glass). Which one of the following diagrams best represents the resulting path of the beam? (Note: In each diagram, the dashed lines are normal to the parallel glass surfaces.)A.

glass

B.

glass

C.

glass

D.

glass

403. The walls of a container are formed by two perpendicular mirrors. The container is filled with a liquid whose index of refraction is greater than 2. A beam of light falls onto the surface of the liquid, perpendicular to it. Which one of the rays A, B, or C best illustrates the resulting ray that emerges from the liquid?

air

liquid

mirror 1 mirror 2

A B

C

A. AB. BC. CD. None of these; the beam experiences total internal

reflection after it travels upward through the liquid.

404. An object is placed along the axis of a concave mirror halfway between its focus and vertex. What is the magnification?

A. 1/2B. 1C. 2D. 3

405. An object is placed along the axis of a concave mirror halfway between its focus and center of curvature. In terms of the focal length f, how far from the mirror is the image?

A. 2 f /3B. 3 f /2C. 2 fD. 3 f

406. At which one of the following positions along the axis of a concave mirror would an object produce a virtual image? (Note: o is the object distance, and f is the focal length.)

A. o < fB. f < o < 3 f /2C. 3 f /2 < o < 2 fD. o > 2 f



Physics

407. In order to use a concave mirror to create an upright image that is 4 times larger than the object, at what distance from the mirror should the object be placed (in terms of focal length f )?

A. f /4B. f /2C. 3 f /4D. 5 f /4

408. An object is placed at the center of curvature of a concave mirror; describe the image.

A. Virtual and uprightB. Virtual and invertedC. Real and uprightD. Real and inverted

409. An object is placed 10 cm from a concave mirror; the image is virtual and three times the size of the object. What is the focal length of the mirror?

A. 7.5 cmB. 15 cmC. 20 cmD. 30 cm

410. An object is placed at distance f from a convex mirror, where f is the magnitude of the mirrors focal length. How far from the mirror is the image?

A. f /2B. fC. 2 fD. The image distance is infinity.

411. In terms of the focal length magnitude f, at what distances d from a convex mirror will an object produce a real image?

A. 0 < d < fB. f < d < 2 fC. d > 2 f D. Convex mirrors cannot form real images.

412. What will be the magnification factor for a convex mirror producing an image of an object placed at a distance of 10 cm from the mirror if the focal length is 20 cm?

A. 1/3B. 2/3C. 1D. 3/2

413. In order to produce an image at the center of curvature of a convex mirror of focal length 3 cm, an object must be placed at what distance from the mirror?

A. 2 cmB. 3 cmC. 6 cmD. A convex mirror cannot produce an image at its

center of curvature.

414. A convex mirror with radius 24 cm produces an image that is half the size of the object. At what distance is the object from the mirror?

A. 4 cmB. 6 cmC. 12 cmD. 36 cm

415. An object is placed at a distance of 40 cm from a converging lens with a focal of length 20 cm. Which one of the following best describes the image?

A. Real and uprightB. Real and invertedC. Virtual and uprightD. Virtual and inverted

416. A convex lens with power 4 D is used to create a real image that is twice the size of the object. Calculate the images distance from the mirror.

A. 6 cmB. 12 cmC. 37.5 cmD. 75 cm




417. To use a converging lens to produce an image that appears at the same position as the object, at what distance from the lens should the object be placed? (Note: f denotes the focal length of the lens.)

A. f /2B. fC. 2fD. A converging lens cannot produce an image at the

objects position.

418. If an object is placed just inside the focus of a convex lens, describe the image produced.

A. Virtual and enlargedB. Virtual and diminishedC. Real and enlargedD. Real and diminished

419. As an object is moved from a great distance toward a converging lens, then the image will move:

A. away from the lens, toward the focus.B. away from the focus, toward the lens.C. toward the focus and toward the lens.D. away from the focus and away from the lens.

420. Let f be the focal length of a diverging lens. At what distance d from the lens should an object be placed to create a real image between the lens and the focal point?

A. 0 < d < f /2B. f /2 < d < fC. f < d < 2 fD. None of the above.

421. When an object is placed 10 cm from a converging lens, the real image formed is twice the size of the object. What is the power of this lens?

A. 6.7 DB. 10 DC. 15 DD. 20 D

422. An object of height 3 m is placed 2 m in front of a diverging lens with focal length 4 m. Describe the image that is formed.

A. Real, with a height of 2 mB. Virtual, with a height of 2 mC. Real, with a height of 6 mD. Virtual, with a height of 6 m

423. A concave lens produces a virtual upright image 10 cm from the lens that is one-half the size of the object. What is the power of this lens?

A. 5 DB. 10 DC. 15 DD. 20 D

424. In terms of the focal length f of a diverging lens, where should a real object be placed to produce a real image?

A. 0 < d < f / 2B. f / 2 < d < fC. f < d < 2 fD. None of the above

425. Two converging lens are placed in contact. If one has a focal length of 10 cm, and the other has a focal length of 20 cm, what is the power of the combination?

A. 10 DB. 15 DC. 20 DD. 30 D



Physics

Passage 1 (Questions 1-7)

A vector is a quantity that incorporates both magnitude and direction. A vector can be pictured as an arrow whose orientation indicates direction and whose length indicates magnitude. A scalar quantity possesses magnitude only.

Vectors can be added (or subtracted) using the tip-to-tail method and resolved into components using trigonometry.

Figure 1 shows three vectors plotted on a pair of x-y coordinate axes. Vectors P and R each have a magnitude of 20 m, and Q has a magnitude of 40 m.

P

Q

R

3030

45x

y

Figure 1

1. What are the horizontal and vertical components, respectively, of Vector P?

A. 20 sin 30 and 20 cos 30B. 20 sin 30 and 20 tan 30C. 20 cos 30 and 20 tan 30D. 20 cos 30 and 20 sin 30

2. Which one of the following is NOT a vector quantity?

A. VelocityB. DisplacementC. SpeedD. Acceleration

3. What is the magnitude of the x-component of Vector P?

A. 6 mB. 10 mC. 17 mD. 20 m

4. What is the magnitude of the y-component of Vector P?

A. 6 mB. 10 mC. 17 mD. 20 m

5. Which of the following vectors best illustrates the direction of the vector R?

A.

B.

C.

D.

6. Which of the following vectors best illustrates the direction of the vector P + R?

A.

B.

C.

D.

7. Which of the following vectors best illustrates the direction of the vector Q P?A.

B.

C.

D.

02a MCAT SW Physics passage.indd 53 8/21/09 4:29 PM




A car travels in a straight line for 30 seconds. The graph below represents the cars velocity as a function of time.

5

10

5 10 15 20 25 30

v (m/sec)

t (sec)0

Figure 1

Since acceleration is defined as change in velocity per interval of time, acceleration at any time equals the slope of the velocity graph at that time. Similarly, since distance traveled is directly proportional to time and speed, the distance the car has traveled at any time equals the area under the velocity graph up to that time. For the first 10 seconds the car traveled at a fixed speed. The slope of the graph in that section is, as expected, zero. Also, the area under the graph between t = 0 and t = 10 sec is 50 m, the expected value.

1. How far does the car travel between times t = 0 and t = 10 sec?

A. 2 mB. 5 mC. 25 mD. 50 m

2. What is the cars acceleration between times t = 10 sec and t = 15 sec?

A. 0.67 m/sec2B. 1.0 m/sec2C. 1.5 m/sec2D. 25.0 m/sec2

3. How far does the car travel between times t = 10 sec and t = 15 sec?

A. 12.5 mB. 25.0 mC. 37.5 mD. 50.0 m

4. What is the cars average speed between times t = 10 sec and t = 15 sec?

A. 5.0 m/secB. 7.5 m/secC. 10.0 m/secD. 12.5 m/sec

5. At time t = 25 sec, the car:

A. slowed down and changed direction.B. slowed down but did not change direction.C. sped up and changed direction.D. sped up but did not change direction.

6. Which of the graphs best represents the cars acceleration, a, between times t = 0 and t = 30 sec?

A.

t

a

B.

t

a

C.

ta

D.

ta

7. Which one of the following graphs best represents the distance traveled by the car as a function of time?

A.

t

d

B.

t

d

C.

t

d

D.

t

d



Physics


A car of mass 1000 kg is tested on a straight, flat track. The graph below illustrates the results of the test. The speed (v) of the car in miles per hour (mph) is plotted against the time (t) in seconds. The graph has been divided into three time periods: I (from t = 0 to t = 6 sec), II (from t = 6 to t = 10 sec), and III (from t = 10 to t = 12 sec). The graph supplies enough information so that the average and instantaneous velocities and accelerations can be calculated for any time period or instant in time. In addition, the distance traveled by the car can be calculated for any time period (t) in which the acceleration is constant by using the equation

x x v t a t = +0 012

2 ( ) ,

where x0 and x are the initial and final positions, respectively, v0 is the initial velocity, and a is the acceleration.

Some of the important forces on the car are the propulsive force provided by the engine (through the force of static friction), the retarding force provided by the brakes (when engaged), and the retarding force due to air resistance. The drag force, resulting from the fact that the car is immersed in a fluid (the air), depends on the density, temperature, and composition of the fluid as well as the shape and velocity of the moving object. The magnitude of the force due to air resistance is approximately proportional to the velocity of the object: F

r bv where the proportionality

constant b > 0 is determined by a combination of the factors discussed above. As fuel economy becomes more important, cars are being designed with shapes that minimize the air resistance proportionality constant b. Finally, it is worthwhile to note that driving with windows closed lowers the value of the constant b, thereby improving gas mileage.

60

10 126

I

II

III

t (in seconds)

v (in

mile

s per

hour)

0

1. What is the average acceleration during time period I?

A. 0 mph/secB. 10 mph/secC. 20 mph/secD. 30 mph/sec

2. During which of the three time periods is the value of the acceleration constant?

A. I and III onlyB. II onlyC. I, II, and IIID. The acceleration is not constant during any of the

three time periods.

3. During which time period does the car travel the farthest?

A. IB. IIC. IIID. Cannot be determined from the information given

4. The magnitude of the net force exerted on the car is:

A. greatest during time period I.B. greatest during time period II.C. greatest during time period III.D. the same during all three time periods.

5. The area of the shaded region in the graph represents:

A. the total distance traveled by the car.B. the total change in momentum of the car.C. the average velocity of the car between times t = 0

and t = 12 sec.D. the average acceleration of the car between times

t = 0 and t = 12 sec.

6. What is the net force on the car during period II?

A. 0 NB. 4.4 103 NC. 8.9 103 ND. 1.3 104 N




7. The average speed of the car during time period III is:

A. 0 mph.B. 10 mph.C. 20 mph.D. 30 mph.

8. If the frictional force on the car due to air resistance, Fr, is

directly proportional to the speed of the car, then which one of the following statements must be true during period I?

A. The force provided by the engine was increasing with time.

B. The force provided by the engine was kept equal to F

r.

C. The force provided by the engine remained constant.D. The same acceleration would have been achieved

regardless of the force provided by the engine.

9. Suppose that at t = 8 sec, the previously closed windows suddenly shatter, thereby causing the proportionality constant b to increase. Which of the following best describes the subsequent behavior of the car?

A. Its speed begins to increase due to the change in Fr.

B. Its speed begins to decrease due to the change in Fr.

C. The momentum of the car compensates for the change in F

r so the speed remains constant.

D. The speed remains temporarily constant but then begins to decrease as the air resistance dissipates.

Questions 10 through 12 refer to the following position vs. time (x vs. t) graphs:

A.

x

t

B.

x

t

C.

x

t

D.

x

t

10. Which one of the graphs above best illustrates the shape of that portion of the cars position vs. time graph for the interval between t1 = 0 sec and t2 = 6 sec (that is, during period I)?

A. Graph AB. Graph BC. Graph CD. Graph D

11. Which one of the graphs above best illustrates the shape of that portion of the cars position vs. time graph for the interval between t1 = 6 sec and t2 = 10 sec (that is, during period II)?


12. Which one of the graphs above best illustrates the shape of that portion of the cars position vs. time graph for the interval between t1 = 10 sec and t2 = 12 sec (that is, during period III)?




Physics


A woman of mass m

= 100 kg is standing on the edge of a rotating platform of radius r = 10 m and mass M

= 1000 kg. The period of rotation of the platform is set so that the woman moves with a constant speed of v = 5 m/s. The coefficient of static friction, , between the soles of the womans shoes and the platform is equal to 0.1. A rope of negligible mass connects the woman to the center of the platform. This situation can be discussed in terms of (i) centripetal forces, (ii) pseudo-forces (sometimes called centrifugal forces), or (iii) angular momentum.

(i) In order to cause the woman standing 10 m from the center of the platform to move in a circle, a centripetal force is needed, of magnitude F

c = mv2/r directed toward the center. In the

above example, Fc is provided by the tension in the rope and the

frictional force. In terms of the rotation period T, the centripetal force on the woman is

Fc = 42mr/T 2

(ii) A pseudo-force is a nonexistent force that is experienced by observers in accelerated reference frames. The accelerated observer accounts for her lack of motion relative to her reference frame by inventing a force that cancels out the real forces. The woman on the rotating platform feels real forces of tension and friction directed toward the center. However, she is at rest relative to the platform despite these forces. She therefore experiences a pseudo-force opposite to the real forces. From her point of view, the pseudo-force and the real force cancel, and this allows her to be at rest in her frame of reference.

(iii) The magnitude of the angular momentum of the woman is LW = mr2, where is the angular velocity of the platform (and the woman) and r is the distance of the woman from the center. For the platform, LP = I, where I = Mr2/2 is the rotational inertia of the platform. In the absence of external torques, total angular momentum is a conserved quantity. This means that the sum LW + LP is a constant as long as the platform rotates freely without friction. Under these conditions, the sum will not change even if the woman changes her distance from the center.

1. What is the tension in the rope?

A. 50 NB. 100 NC. 150 ND. 250 N

2. Approximate T, the period of rotation of the platform.

A. 6 secB. 12 secC. 24 secD. 36 sec

3. Suppose the platform is covered with grease, thereby reducing to zero. Then the rope is cut. What is the direction of the womans subsequent motion?

A. Radially inwardB. Radially outwardC. Inward but not along a radiusD. Tangent to the platform

4. Suppose the platform rotates freely without friction so that angular momentum is conserved. If the woman moves in toward the center, what happens to the period of rotation of the platform?

A. It increases.B. It decreases.C. It remains the same.D. It first decreases then increases.

5. When the woman is standing on the edge of the rotating platform, her (real) acceleration is:

A. directed radially inward.B. directed radially outward.C. tangent to the platform.D. zero.




6. What is the direction of the net pseudo-force felt by the woman?

A. Radially inwardB. Radially outwardC. Tangent to the platformD. Perpendicular to the surface of the platform

7. Suppose the platform is driven by a motor so that it always rotates with constant period T. The rope is shortened to 5 meters in length, the woman moves to a point 5 meters from the center and grasps the rope. Compared to the original tension, the new tension is:

A. greater.B. smaller.C. the same.D. equal in magnitude but opposite in direction.


For an ideal elastic collision between two objects, the sum of their linear momenta, p1 + p2, has the same value after the collision as before. The total kinetic energy of the system is also unchanged, that is, none of the systems kinetic energy is converted into other energy forms.

The principal condition necessary for a collision to be perfectly elastic is the absence of friction. At atomic and subatomic levels this condition usually exists, and atoms and nuclear particles often undergo ideal elastic collisions. The condition necessary for a perfectly elastic collision is not achievable for macroscopic bodies situated on the earth. All such bodies produce collisions that are, to some extent, inelastic, in which the kinetic energy of each body is therefore converted into other forms of energy.

In order to simulate motion and contact that is free of friction, researchers conduct experiments with miniature carriages that slide along a track and which are supported by air streams projecting from the tracks surface. The air streams allow the carriages to slide almost free of friction.

Researchers conduct an experiment involving the collision of two miniature carriages situated on an air track. Attached to each carriage at the front and back ends are light springs that undergo compression and extension and obey Hookes law. One carriage has a mass of 1 kg and the other a mass of 2 kg. With the air streams turned off, the coefficient of kinetic friction between each carriage and the surface of the track is 0.4. When the air streams are activated, the coefficient of kinetic friction drops to less than 0.01, so frictional effects can be ignored. The carriages are made to slide toward each other, and immediately prior to the collision, the lighter carriage has a speed of 4 m/s, and the heavier carriage has a speed of 2 m/s.

1. Just before the collision, what is the total kinetic energy of the system?

A. 0 JB. 8 JC. 12 JD. 24 J



Physics

2. Which of the following statements applies to a system in which two objects undergo an ideal elastic collision?

I. Kinetic energy is conserved. II. Momentum is conserved. III. The velocity of each object remains unchanged.

A. I onlyB. II onlyC. I and II onlyD. I, II, and III

3. If the carriages were redesigned so that collisions between them were perfectly inelastic, each collision would cause energy dissipation of:

A. 0 J.B. 4 J.C. 8 J.D. 12 J.

4. When the two carriages approach each other, collide, and then separate, their movements are associated with corresponding energy transfers of:

A. kinetic to elastic potential to kinetic.B. elastic potential to kinetic to elastic potential.C. gravitational potential to heat to kinetic.D. heat to kinetic to gravitational potential.

5. If the air streams are deactivated and the carriages are in motion, what is the ratio of the frictional force acting on the heavier carriage to the frictional force acting on the lighter carriage?

A. 1 : 2B. 2 : 1C. 1 : 4D. 4 : 1

6. If the plane on which the carriages are sliding is inclined to an angle of 55 with the horizontal, what is the magnitude of the component of a carriages weight, mg, normal to the plane?

A. mg sin 35B. mg cos 35C. mg sin 55D. None of the above


Figure 1 depicts a dam preventing the flow of water. Using the base of the dam as the pivot line (Line X in Figure 1), we can determine the torque exerted by the water on the dam by using the equation

= gLd3/6

Equation 1

where is the density of the water (1000 kg/m3), g is the acceleration due to gravity, L is the length of the dam, and d is the total depth of the water behind the dam.

Knowing the sheer strength of the dams structure, it can be determined whether the dam can withstand the fluid pressure exerted by the water behind it. The pressure due to the water at depth y below the surface is given by the equation

P = gy

Equation 2

The total pressure at depth y is equal to the pressure exerted by the water plus the atmospheric pressure, which is approximately 105 N/m2.

L

Damwater

d

Line X

reinforcementsection of dam

Figure 1

1. What is the pressure exerted on the dam by the water at a point 5 m below the surface?

A. 4.9 104 N/m2B. 9.8 104 N/m2C. 4.9 105 N/m2D. 9.8 105 N/m2




2. If the area of the dam exposed to water is quadrupled by doubling the length of the dam and doubling the depth of the water retained, then this will cause the torque due to the water to increase by what factor?

A. 2B. 4C. 8D. 16

3. If the dam is 5 m high, approximately how fast (neglecting friction) would water flowing over the top be moving when it struck the river at the base of the dam?

A. 7 m/sB. 10 m/sC. 14 m/sD. 20 m/s

4. Which one of the following graphs best depicts the relationship between the magnitude of the torque, , caused by the water and the depth, d, of the water behind the dam?

A.

d

B.

d

C.

d

D.

d

5. Assume that water has risen to a height d and exerts a torque on the dam. Assume also that a single force F is to be applied at a height d perpendicular to the opposite face of the dam so that the its torque will exactly cancel the torque due to the water. Which one of the following expressions gives the magnitude of F?

A. gLd2/6B. gLd3/6C. gLd4/6D. gLd5/6


A projectile launched near the surface of the Earth is, to a good approximation, influenced only by the gravitational field of the Earth. The acceleration due to gravity near the Earths surface is given by g 10 m/s2. If the y coordinate of the projectile is plotted as a function of time, a parabola is obtained. The graph of the x coordinate vs. time yields a straight line with a positive slope since the horizontal velocity is constant. The trajectory of the projectile (y coordinate plotted as a function of x) is a symmetric parabola in which the maximum y coordinate coincides with the midpoint in the x coordinate.

The horizontal distance traveled by the projectile when the y coordinate has returned to its initial value is called the range. If 0 is the angle above the horizontal at which the projectile is launched, then the range depends on 0, varying from its maximum at 0 = 45 to zero at 0 = 90.

If the projectile is launched in the Earths atmosphere, air resistance will slightly alter the above results. Energy will be carried away from the system, and the range attained by the projectileas well as its time of flightwill be reduced. The trajectory of the projectile (y vs. x) will no longer be parabolic, or even symmetric. The horizontal velocity decreases with time, and the horizontal distance traveled after the high point in the trajectory is less than the horizontal distance traveled before the high point is reached.

Unless otherwise indicated, neglect any aerodynamic forces on the projectile. The projectile has a mass of 2 kg and is launched from ground level; the ground is perfectly flat. The kinetic energy at launch time is E0 = 1000 J. At the top of the trajectory, the kinetic energy is Etop = 600 J.



Physics

1. What is the maximum height above the ground attained by the projectile?

A. 20 mB. 40 mC. 60 mD. 80 m

2. What is the magnitude of its initial horizontal velocity?

A. 15.5 m/sB. 20.0 m/sC. 24.5 m/sD. 32.0 m/s

3. If T denotes the total time of flight of the projectile, which of the following expressions correctly gives the initial vertical velocity, v0y?

A. v0y = gT/2B. v0y = gT sin 45C. v0y = gTD. v0y = 2gT

4. Which of the following best approximates the magnitude of the projectiles initial total velocity?

A. 10 m/sB. 20 m/sC. 24 m/sD. 32 m/s

5. What is the kinetic energy of the projectile when it strikes the ground?

A. 400 JB. 600 JC. 1000 JD. 1600 J

6. Let vx be the projectiles horizontal speed when it is at its

maximum height, and let Vx be the horizontal speed just

before the projectile strikes the ground. Then the ratio vx/V

x :

A. is less than 1.B. is equal to 1.C. is greater than 1.D. depends on the angle at which the projectile is

launched.

7. If T denotes the total flight time of the projectile, and v0x and v0y denote its initial horizontal and initial vertical velocity, respectively, then the range R is given by which one of the following equations?

A. R = v0xT 2/2

B. R v T Tx

= 012

2g

C. R v vx y= ( ) /02 02 2g

D. R = v0xT

8. If air resistance is considered, the ratio Hvac/H

atm of the maximum height attained by a projectile in vacuum to the maximum height that it attains in the atmosphere given the same initial kinetic energy at launch is:

A. less than 1.B. equal to 1.C. greater than 1.D. less than 1 for a spherical object but greater than 1

for an irregularly-shaped object.

9. Let X denote the horizontal distance traveled when a projectile (launched at an angle 0 with 30 < 0 < 60) has attained its maximum height. If the effect of air resistance is taken into account, then which one of the following relations is correct concerning the projectiles range R?

A. R/2 < XB. (R cos 0)/2 > XC. (R sin 0)/2 > XD. R/2 > X





The gravitational attraction between the Earth (mass M) and an object of mass m on its surface is given approximately by the formula Fgrav = GMm/R2, where G is the universal gravitational constant and R is the radius of the Earth. The formula is exact for a uniform perfect sphere. The gravitational acceleration of an object near the surface of a planet is given by g = GM/R2, which is very nearly 10 m/s2 for the Earth.

The above equation for Fgrav may be generalized so that it is valid both near and far from the surface: Fgrav = GMm/r2 where r is now the distance between the object of mass m and the center of the Earth. On the surface, of course, r = R, so the two formulations are consistent.

The potential energy of an object near the surface of the Earth at a height h above the ground is Ep = mgh. The change in potential energy when an object is moved from height h1 to h2 is

Ep = mg(h2 h1). If an object is falling in a vacuum, energy is conserved so Ep + Ek = 0, where Ek is the change in kinetic energy of the object.

If h is larger than about 0.01R, then Ep = mgh is no longer a good approximation since the gravitational acceleration g decreases as one moves away from the Earths surface. To handle problems involving objects far from the surface of the Earth, we use, in analogy with electrostatics, the gravitational potential V = GM/r where r is the distance of the object from the center of the planet. If an object of mass m is moved from a point at r1 to a point at r2, the change in potential energy will be Ep = m(GM/r1 GM/r2).

If r1 = and r2 = R, then Ep applies to an object dropped to the ground from far away (outer space). If the situation is reversed, and r1 = R and r2 = , then Ep applies to an object launched into outer space from the surface of the Earth. In either case, conservation of energy can be used to determine the velocity of the object. The computed velocities will have the same magnitude; one will be an impact velocity and the other will be an escape velocity.

All of the above can be applied to any celestial body as long as one can ignore air resistance. Some convenient approximations for the relevant constants are G = 6.7 1011 Nm2/kg2, M = 6 1024 kg, and R = 6 106 m. The Earth is roughly 100 times more massive than the Moon, and the Earths radius is about 4 times greater. The EarthMoon distance is about 60R, and the EarthSun distance is about 25,000R. The Suns mass is about 300,000M.

1. What would be the acceleration of an object dropped near the surface of the Moon?

A. 0.1 m/s2B. 0.4 m/s2C. 1.6 m/s2D. 2.5 m/s2

2. An object that weighs 15 N near the surface of the Earth is transported to an altitude of 1.2 107 m. Compute its weight at this altitude.

A. 1.67 NB. 3.75 NC. 5.00 ND. 7.50 N

3. Assuming the Moons orbit is a perfect circle, at what speed does it orbit the Earth?

A. 101 m/sB. 103 m/sC. 105 m/sD. 107 m/s

4. Which one of the following expressions correctly gives the minimum speed with which one must launch a rock of mass m in order to ensure that it escapes the Earths gravitational field (air resistance neglected)?

A. 2GM R/

B. 2GMm R/

C. GM R/ 2

D. GMm R/ 2

5. If the gravitational force exerted by the Earth on the Moon is denoted F1, and the gravitational force exerted by the Moon on the Earth is F2, then:

A. F1 = 1600F2B. F1 = 100F2C. F1 = 6.25F2D. F1 = F2


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