1

AHL 9.1 Energy transformation 17.1.2018

1.[1mark]

ApendulumoscillatingnearthesurfaceoftheEarthswingswithatimeperiodT.Whatisthetime

periodofthesamependulumnearthesurfaceoftheplanetMercurywherethegravitationalfield

strengthis0.4g?

A.0.4T

B.0.6T

C.1.6T

D.2.5T

Markscheme

C

Examiners report

[N/A]

2.[1mark]

Amassoscillateswithsimpleharmonicmotion(SHM)ofamplitudexo.Itstotalenergyis16J.

Whatisthekineticenergyofthemasswhenitsdisplacementis ?

A.4J

B.8J

C.12J

D.16J

Markscheme

C

Examiners report

[N/A]

2

3.[1mark]

Aparticleisoscillatingwithsimpleharmonicmotion(shm)ofamplitudex0andmaximumkinetic

energyEk.Whatisthepotentialenergyofthesystemwhentheparticleisadistance0.20x0fromits

maximumdisplacement?

A.0.20Ek

B.0.36Ek

C.0.64Ek

D.0.80Ek

Markscheme

C

Examiners report

[N/A]

4.[1mark]

Amassisconnectedtoaspringonafrictionlesshorizontalsurfaceasshown.

Thespringisextendedbeyonditsequilibriumlengthandthemassexecutessimpleharmonicmotion

(SHM).Whichofthefollowingisindependentoftheinitialdisplacementofthespring?

A.Theangularfrequencyoftheoscillation

B.Thetotalenergyofthemass

C.Theaveragespeedofthemass

D.Themaximumkineticenergyofthemass

Markscheme

3

A

Examiners report

[N/A]

5.[1mark]

Theperiodofaparticleundergoingsimpleharmonicmotion(SHM)is .

Theratio isproportionalto

A. .

B. .

C. .

D.

Markscheme

A

Examiners report

[N/A]

6.[1mark]

Aparticleofmass oscillateswithsimpleharmonicmotion(SHM)ofangularfrequency .The

amplitudeoftheSHMis .Whatisthekineticenergyoftheparticlewhenitishalfwaybetweenthe

equilibriumpositionandoneextremeofthemotion?

A.

B.

C.

D.

4

Markscheme

B

Examiners report

[N/A]

7.[1mark]

Thebobofapendulumhasaninitialdisplacement 0totheright.Thebobisreleasedandallowedto

oscillate.Thegraphshowshowthedisplacementvarieswithtime.Atwhichpointisthevelocityofthe

bobatmaximumtowardstheright?

Markscheme

A

Examiners report

[N/A]

8.[1mark]

Aparticleundergoessimpleharmonicmotion(SHM)ofmaximumkineticenergyEmaxandamplitudex0.

Theparticleisreleasedfromrestatitsmaximumdisplacementamplitude.

Whatisthechangeinthekineticenergywhentheparticlehastravelledadistanceof ?

A.

5

B.

C.

D.

Markscheme

C

Examiners report

Thecandidatesfoundthisquestiontobethemostdifficultofthepaper,withthecorrectanswerbeing

theleastoftenselected!Thekeytospottingthecorrectsolutionisasimplediagramshowingthatafter

theparticlehastravelledadistanceofx0/3thenitsdistancetotheequilibriumpositionis2x0/3.

SubstitutingthisvalueintotherelevantequationintheDataBookletgivesresponseCdirectly.

9.[1mark]

Abodymoveswithsimpleharmonicmotion(SHM)withperiodTandtotalenergyET.Whatisthetotal

energywhentheperiodofthemotionischangedto5Tandtheamplitudeofthemotionremains

constant?

A.0.04ET

B.0.2ET

C.5ET

D.25ET

Markscheme

A

Examiners report

[N/A]

10.[1mark]

Asmallpointmassmisplacedatthesamedistancefromtwoidenticalfixedsphericalmassesfarfrom

anyothermasses.

6

Thepointmassisreleasedfromrest.Thepointmasswill

A.moveupwards.

B.staywhereitis.

C.movetowardsPandstopthere.

D.oscillateaboutpointP.

Markscheme

D

Examiners report

11.[1mark]

AparticlePexecutessimpleharmonicmotion(SHM)aboutitsequilibriumpositionY.

TheamplitudeofthemotionisXY.

7

AtwhichofthepositionsshownonthediagramistheaccelerationofPequaltozeroandthekinetic

energyofPequaltozero?

Markscheme

A

Examiners report

[N/A]

12.[1mark]

Whichgraphshowshowvelocityvvarieswithdisplacementxofasystemmovingwithsimple

harmonicmotion?

Markscheme

A

Examiners report

8

Thisquestionwasverypoorlyanswered.Therearemanygraphsassociatedwithsimpleharmonic

motion(SHM)whicharesinusoidal,butthesearethegraphswithtimeonthehorizontalaxis.Having

displacementontheaxis,though,willproducedifferentgraphsandcandidatesshouldbeequally

familiarwiththese.InthiscaseitshouldhavebeenclearthatattheextremitiesofSHMvelocitywillbe

zero,whileattheequilibriumpointitwillbemaximum.SotheonlypossibleanswerisA,showinghalfa

cycleofSHM.

13.[1mark]

Anobjectundergoessimpleharmonicmotion.Whichgraphshowstherelationshipbetweenthe

accelerationaandthedisplacementxfromtheequilibriumposition?

Markscheme

A

Examiners report

[N/A]

14.[1mark]

Anobjectundergoessimpleharmonicmotion(SHM).Thetotalenergyoftheobjectisproportionalto

A.theamplitudeoftheoscillations.

B.thetimeperiodoftheoscillations.

C.thefrequencyoftheoscillations.

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D.themassoftheobject.

Markscheme

D

Examiners report

[N/A]

15.[1mark]

Aparticleisundergoingsimpleharmonicmotion(SHM)inahorizontalplane.Thetotalmechanical

energyofthesystemisE.Whichofthefollowingcorrectlygivesthekineticenergyoftheparticleatthe

positionsofmaximumdisplacementandequilibrium?

Markscheme

B

Examiners report

16.[1mark]

Theequationforthevelocityofanobjectperformingsimpleharmonicmotionis .Which

ofthefollowingisacorrectalternativeformoftheequation?

A.

B.

10

C.

D.

Markscheme

A

Examiners report

[N/A]

17a.[2marks]

Thisquestionisaboutsimpleharmonicmotion(SHM).

Thegraphshowsthevariationwithtime oftheacceleration ofanobjectXundergoingsimple

harmonicmotion(SHM).

Definesimpleharmonicmotion(SHM).

11

Markscheme

force/accelerationproportionaltothedisplacement/distancefroma(fixed/equilibrium)point/mean

position;

directedtowardsthis(equilibrium)point/inoppositedirectiontodisplacement/distance;

Allowalgebraonlyifsymbolsarefullyexplained.

Examiners report

Agooddefinitionofsimpleharmonicmotionmustfocusontheproportionalitybetweenacceleration

anddisplacementfromsomefixedpointandonthedirectionalrelationshipbetweenaccelerationand

displacement.Manyfailedtoemphasisethefixed-pointaspectofthedefinition.Attemptsmadeto

definesimpleharmonicmotioninalgebraictermsnormallyomittedaclearstatementofthesymbols

andthemeaningofthenegativesign.

17b.[1mark]

Xhasamassof0.28kg.CalculatethemaximumforceactingonX.

12

Markscheme

0.73(N);(allowanswerinrangeof0.71to0.75(N))

Examiners report

Thiswasalmostuniversallywelldone.

17c.[4marks]

DeterminethemaximumdisplacementofX.Giveyouranswertoanappropriatenumberofsignificant

figures.

Markscheme

useof ;

or or ;}(allowanswersintherangeofT=7.8to8.0(s)or =

0.785to0.805(rads–1))

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;(allowanswersintherangeof4.0to4.25(m))

twosignificantfiguresinfinalanswerwhateverthevalue;

Award[4]forabaldcorrectanswer.

Examiners report

Similarly,thiswaswelldone.Mostappreciatedtheneedtotruncatethefinalanswertoasensible

numberofsignificantdigits(twointhiscase).

17d.[2marks]

AsecondobjectYoscillateswiththesamefrequencyasXbutwithaphasedifferenceof .Sketch,

usingthegraphopposite,howtheaccelerationofobjectYvarieswith .

Markscheme

shapecorrect,constantamplitudefornewcurve,minimumof10sshown;}(theremustbesome

consistentleadorlagandnochangeinT)

lead/lagof1s(towithinhalfasquarebyeye);

Examiners report

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Alargenumberofcandidatescouldnottranslatea phasechangeintothecorrecttimeleadorlag.

Mostusedtheanswerfor andlostamarkinconsequence.Mostfree-handsketchesofsinecurves

wereacceptable.

18a.[2marks]

Thisquestionisaboutsimpleharmonicmotion(SHM

Anobjectisplacedonafrictionlesssurface.Theobjectisattachedbyaspringfixedatoneendand

oscillatesattheendofthespringwithsimpleharmonicmotion(SHM).

ThetensionFinthespringisgivenbyF=kxwherexistheextensionofthespringandkisaconstant.

Showthat .

Markscheme

15

ma kx;

;(condonelackofnegativesign)

or

implieduseofdefiningequationforsimpleharmonicmotion ;

so ;

Examiners report

[N/A]

18b.[3marks]

Onecycleofthevariationofdisplacementwithtimeisshownfortwoseparatemass–springsystems,A

andB.

(i)CalculatethefrequencyoftheoscillationofA.

(ii)ThespringsusedinAandBareidentical.ShowthatthemassinAisequaltothemassinB.

16

Markscheme

(i)0.833(Hz);

(ii)frequency/periodisthesamesoωisthesame;

kisthesame(asspringsareidentical);

(somisthesame)

Examiners report

[N/A]

18c.[5marks]

ThegraphshowsthevariationofthepotentialenergyofAwithdisplacement.

17

Ontheaxes,

(i)drawagraphtoshowthevariationofkineticenergywithdisplacementforthemassinA.Labelthis

A.

(ii)sketchagraphtoshowthevariationofkineticenergywithdisplacementforthemassinB.Label

thisB.

Markscheme

18

(ii)enddisplacementscorrect 0.01m;

maximumlowerthan0.16J;

maximumequalto0.04J halfsquare;

Examiners report

[N/A]

19a.[3marks]

Thisquestionisabouttheoscillationofamass.

Amassof0.80kgrestsonafrictionlesssurfaceandisconnectedtotwoidenticalspringsbothofwhich

arefixedattheirotherends.Aforceof0.030Nisrequiredtoextendorcompresseachspringby1.0

mm.Whenthemassisatrestinthecentreofthearrangement,thespringsarenotextended.

Themassisdisplacedtotherightby60mmandreleased.

19

Determinetheaccelerationofthemassatthemomentofrelease.

Markscheme

forceof1.8Nforeachspringsototalforceis3.6N;

acceleration ;(allowECFfromfirstmarkingpoint)

toleft/towardsequilibriumposition/negativesignseeninanswer;

Examiners report

Thisisaslightlydifferentsituation.MostcandidatesatSLdidnotuseFandmtofindacceleration.Very

fewaddedtheforceduetoeachspringandECFwasfrequentlyapplied.

19b.[2marks]

Outlinewhythemasssubsequentlyperformssimpleharmonicmotion(SHM).

20

Markscheme

force/accelerationisinoppositedirectiontodisplacement/towardsequilibriumposition;

andisproportionaltodisplacement;

Examiners report

[N/A]

19c.[2marks]

Calculatetheperiodofoscillationofthemass.

21

Markscheme

;

;

WatchoutforECFfrom(a)(i)egaward[2]for for .

Examiners report

[N/A]

19d.[2marks]

Themotionofanioninacrystallatticecanbemodelledusingthemass–springarrangement.Theinter-

atomicforcesmaybemodelledasforcesduetospringsasinthearrangementshown.

Thefrequencyofvibrationofaparticularionis andthemassoftheionis .

Theamplitudeofvibrationoftheionis .

Estimatethemaximumkineticenergyoftheion.

22

Markscheme

;

;

Allowanswersintherangeof4.8to if2sigfigsormoreareused.

Examiners report

[N/A]

19e.[3marks]

Ontheaxes,drawagraphtoshowthevariationwithtimeofthekineticenergyofmassandtheelastic

potentialenergystoredinthesprings.Youshouldaddappropriatevaluestotheaxes,showingthe

variationoveroneperiod.

Markscheme

23

KEandPEcurveslabelled–veryroughly and shapes;}(allowreversalofcurvelabels)

KEandPEcurvesinanti-phaseandofequalamplitude;

atleastoneperiodshown;

either markedcorrectlyonenergyaxis,or markedcorrectlyontimeaxis;

Examiners report

Carewasneededinshowingtheconstantandequalamplitudes.Manypooranswerswereseen.

19f.[1mark]

Calculatethewavelengthofaninfraredwavewithafrequencyequaltothatofthemodelin(b).

Markscheme

isequivalenttowavelengthof ;

Examiners report

[N/A]

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