.34160401.
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AND RSAEXAMINATIONS OXFORDCAMBRIDGE AdvancedGCE
B (ADVANCING PHYSTCS PHYSTCS) Universe RiseandFallof theClockwork Thursday
17 JUNE 2004
Morning
llll llll llill lllil llil ill] llill |ililI 2863/01 t hour 15 minutes
answeron thequestionpaper. Candidates materials: Additional Booklet Data,Formulae and Relationships Electronic calculator
Candidate Name
Centre Number
r I
TIME
Candidate Number
t hour15minutes
TO CANDIDATES INSTRUCTIONS o o o
o o
numberin the boxesabove. Writeyourname,CentrenumberandCandidate Answerall the questions. Writeyouranswersin the spaceson the questionpaper. DO NOTWRITEIN THE DO NOTWRITEIN THEBARCODE. DO NOTANSWERIN PENCIL. THEPAGES. GREYAREASBETWEEN Readeachquestioncarefullyand makesureyou knowwhatyou haveto do beforestartingyour answer. and give answersto only a justifiablenumberof Showclearlythe workingin all calculations figures. significant
FORCANDIDATES INFORMATION . o . o
USE FOREXAMINER'S You are advisedto spendabout20 minuteson SectionA and 55 minuteson SectionB. Mark Section Max. The numberof marksis givenin brackets[ ] at the end of each questionor partquestion. 21 A in for the qualityof writtencommunication Fourmarksare available SectionB. B 49 The valuesof standardphysicalconstantsare give in the Data, 70 TOTAL data requiredare Booklet.Any additional Formulaeand Relationship question. givenin the appropriate This question paperconsists of 16 printed pages. sP MML53953/03574621/6.3 @OCR2004 [Hn00/37091
Registered CharityNumber:1066969
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'34160402'
2 llilililillilililililltillillllllillllllllllllll Answerall the questions.
For Examiner's Use
SectionA Hereis a listof energies. 1O-15J
1O-18J
10-21 J
1O-24J
6-t constant,k = 1.38x 1g-2s.1 the Boltzmann to Choosethe valuefromthe listthat is the bestapproximation T= 300K, (a) the energyof a nitrogenmolecule at roomtemperatur@, ............ J
answer f = 9 x 106K. (b) the energyof a protonin the interiorof a starat temperature, . answer
..........J...
t2l Hydrogenatomscan emit ultravioletlightof wavelength122nm.A spectrumfrom a distant quasarshowsthat this light has been stretchedto a wavelengthof 440nm. This is an redshift. exampleof cosmological (a) Calculatethe factorby whichthe Universehas expandedsincethe lightwas emitted by the quasar.
= .............. factor
............. t2l
(b) Explain redshift. whyobjectsfurtherfromtheEarthshowa greatercosmological
l2l
28ory01Jun04
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'34160403'
|ililil iltil tilil il]t ilil ililt ]]til1il lililil It is suggestedthat the heighth of the foamon the top of atizzy drink (see Fig.3.1) decreasesexponentiallywithtime.The tableshowsdatatakento testthisassumption.
x*,,S
m,s ry
ffi q,g # 3,4.,,9
time/s heightof foam, hlcm
0 6.0
15
30
45
60
4.8
3.8
3.1
2.5
Rffi
ry4 TFS reg 4ffi
ryg 19€ 4 tRe i9s
ry4 :R6
Fig.3.1 (a) Use this data to test if the heightof the foamdecreasesexponentially with time.State
yourconclusion.
teq
rys Eg r@
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ros
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toc pR
(b) Giveanotherphysicalexampleof an exponential decrease.
RC Iog EE RO toq
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FE 8o log FE
2.0molof an idealgasis keptat a pressureof 1.5x 105Pa anda temperature of 310K.
FC ff
Calculate thevolumeoccupiedby the gasundertheseconditions.
E$ nd los
F = 8.3JK-l mol-l
rc
BC toc t
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:
.
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For Examinels Use
'34160404'
lllll llillillllillilllll ilill lllll |ililil lllil of A massof 0.40kg is hungfroma spring.The springextendsby 22mm.The extension to the forceapplied. the springis directlyproportional constantof thespring,is about180N m-1' (a) Showthat& the stiffness g=9.8Nkg-t
l2l (b) The mass is pulleddowna smalldistancefurtherand then released.This sets the massoscillating. of theoscillation' thefrequency Calculate
= .............. fr equency
......Hz [3 ]
at a speedof 7.3ms-1.The A circusclownfiresa watergun thatejectswaterhorizontally waterleavesthe gun at a rateof 2.7kg5-t.
Fig.6.1 (a) Showthat the rate of changeof momentumol the wateron leavingthe gun is about 20 kgm s-2.
2863i/01 Jun04
For Examiner's Use
.34160405'
llillilllil lilll lllil lllil llill lllil Iltilil lilil a backwardforce of about20 N. (b) Explainwhythe clownholdingthe gun experiences
tzl (c) The waterstrikesa secondclownat the samevelocityas it leftthe gun. Thewaterbouncesoff the clown. a forcegreaterthan 20 N fromthe wateriet. Explainwhythisclowncouldexperience
t2l [SectionA Total:21]
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6 Section B
forthe qualityof writtencommunication. In thissection,fourmarksareavailable Thisquestionis aboutusinga capacitorto storeenergy. Peoplesufferingfrom heartproblemscan be fittedwith implantabledefibrillatorswhich candeliveran electricshockto 'kickstart'theheart. capacitance
200pF
p.d.acrossfullychargedcapacitor 390V discharge time
1 0m s defibrillator heart
Fig.7.1defibrillatorin position Thissystemusescapacitorsto storeenergy. defibrillator. Thetableshowssomedataabouta capacitorusedin an implantable (a)
(i) Calculatethe energystoredin the fullychargedcapacitor.
ener gy
......J[2]
(ii) Calculatethe averagerate of energytransferto the heartwhen the capacitor discharges.
average rateof energytransfer 28@01 Jun04
W l2l .....................
For Examiner's Use
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|ffi1il iltil ililr ilililil ililt il]t ilil1 ltil ilil (iii) Explainwhythevaluecalculated in (a)(ii)is an averagevalue. For Examinefs Use
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l2l (b) The dischargetimeof 10ms corresponds to aboutfivetimeconstants(5 FC). Calculatethe resistanceof the capacitordischargecircuit.
rcs :nq tog )cE RO
r esistance= .............
loq ER RE
roe )cE
tro pq
)c&
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(c) In fact,the energyrequiredfrom the capacitorin this defibrillator is abouttwiceas muchas calculated in (a)(i).Onesolutionto thisproblemis to increasethe p.d.across the capacitor. Calculatethe factorby whichthe p.d.mustbe increasedto doublethe energystored in the capacitor.
BO pq fcff
no tog lcs fog EE i r :
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BC
pg
c,* Rg | ::::
(d) Tostorethe energyrequired,defibrillators actuallyusetwo capacitors, eachat a p.d.of 390V.
pe
br RA
oq
Suggestand explainone reasonwhy this methodis chosenrathertnan usingone capacitor at a higherp.d.
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lo tc
286il01 Jun04
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'34160408'
llll ilil llillillllilllil il|il lllll lllil |illil testingof a satellite. Thisquestionis aboutthevibrational simulatethe shakingthe satellitewouldundergoduringlaunch.Assumethe The vibrations aresimpleharmonic. vibrations of of 10Hz,the amplitude at a frequency kg oscillates (a) Whena satelliteof mass1OOOO is 35mm. the oscillation (i) Explainwhatis meantby the termamplitude.
l2l is 2.2ms-1. duringthisoscillation (ii) The maximumspeedof thesatellite speedoccurs. at whichthismaximum of thesatellite Statethe displacement
displacement.............
......m m [1]
(iii) Statethe acceleration of the satelliteat the instantthat maximumspeedoccurs.
.............. acceler ation
.. ms- 2 [t]
dueto thisoscillation. of a satellite (iv) Calculate the maximumacceleration
.............. maximum acceleration
2863/01Jun04
...m s-2 121
For Examinels Use
.34160409'
il|| ilil ]ilt il1il ]]tililt ltil ilil |iltilt ililr forcesfar greaterthan (v) Showthat the satellitewill experienceaccelerating weight.
For Examinels Use
g=9.8Nkg-t
l2l (b) The communications aerialon the satelliteis observedto shakeviolentlyat one particularfrequency. Thisis an exampleof resonance. (i) Explainwhythe aerialbehavesin thisway.
tzl (ii) Suggestand explainhow the aerialcould be modifiedin order to reducethe problemof resonance.
t2) 121 lTotal:
286U01Jun04
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'34160410'
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10
Thisquestionis aboutheatingsoupwith microwaves.
For Examine/s Use
E ooeo Fig.9.1 (a) The microwave ovensuppliesenergyto the soupat a rateof 600W. of 20'C. Thesoup,of mass0.40kg,hasan initialtemperature willbe about85"C. Showthatafterthreeminutesof heatingthe maximumtemperature kg-t 6-t specificthermalcapacity= 42OOJ
t3l (b) Use ideasaboutthe Boltzmannfactor,f = s-E/Kr,to explainwhy increasingnumbersof rises. fromthe soupas its temperature moleculesevaporate
t2l
2863/01Jun04
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bc
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H H F F
.34160411.
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(c) Thesoupcontainer hasa tightfittinglid on it. (i) As the temperature rises,the number of moleculesin the vapourincreases. Exp l a i nw h y th e g ro w i n gnumberof moleculesin the vapourincr easesthe pressureof the vapour.
For Examine/s Use
H
H b bcn ho
l2l (ii) As the temperature in the vapourrises. rises,the averagespeedof the molecules Explainwhythisalso increasesthe pressureof the vapour.
tsc DCR
F" ;oc )cR
ho
)oc
F loc
H tsc F Fo lo"
l2l (iii) Explainwhy it is recommended thatyou do not usetightfittinglidson containers usedin microwave cooking.
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10 Thisquestionis aboutthe timeit takesa planetto orbitoncearoundthe Sun.Thisis called the orbitalperiodof the planet. symbolswillbe used. ln thisquestionthe following orbitalperiodf meanradiusof orbitF massof sun M, massof planetMo
Fi9.10.1 (a) In the seventeenth centuryJohannesKepler(Fig.10.1)suggesteda relationship betweenthe orbitalperiodof a planetf and the radiusof its orbit F. This relationship can be writtenas T2cr.R3.'
Datafor fourof the planetsareshownin Fig.10.2.
T2lyear2 2
radius3/A.U.3 Fig.10.2 to H3. Statewhichfeaturesof the graphshowthat f2 is proportional
Jun04 2863Y01
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For Examinels Use
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'34160413'
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( b ) l s a a c Ne w to n(F i g .1 0 .3 )d e velopeda descr iptionof gr avitythat pr ovided backingfor Kepler'swork. mathematical
tr lo tr
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ts Pc F lo
F tr
lo Dc gR
lo
DC CR lo DC CB
Fig.10.3
lo
Pc
F
lo
Pc
(i) Supposethata planettravelsat speedv in a circularorbitof radiusR. Usingthe showthat the centripetalforceon the planet equationfor centripetalacceleration is givenby the expression
FR lo
r
p"
Mr"
t - = - '
R
tr
I,o DC in fo Pc
tr
lo pc FR
lo Pc t8
fo Pc
t1l forceon a (ii) Writedownthe equationthat givesthe magnitudeof the gravitational planetof massModue to the Sunof massM, at distanceF.
FR lo
Pc ER lo bc
CR
lo DC ge lo
oc CR BO DC CR
t1I (iii) Henceshowthat v2 R= G M".
lo pc qR
to oc
c3 lo oq c& RC
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2863Y01 Jun04
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For Examinels Use
'34160414'
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14
(iv) Fora circularorbit,thespeedv is givenby
For Examinefs Use
2nR v=__. Usethis and the resultof (bXiai)to showthat NewtoncouldpredictKepler'slaw in the form (zn)2 R3 - =
12
l - .
GM"
l2l (v) Calculatethe mass of the Sun M" usingthe following datafor the orbitof the planet. G=6.7x10-1tP*z;.n-z R=1.5x1011m T = 3 . 2 x1 0 7 s
m assof Sun= ..............
.......kg[2 ]
(c) TheSunlosesmassat a rateof 6.2x 1011kgs-t. Suggestand explainhowthis masslossmightaffectthe orbitof the planet.
l2l 11] [Total: 4] Communication of Written [Quality [SectionB Total:49] 286301Jun04
