Morality and Islam

NATIONALQUALIFICATIONSCURRICULUMSUPPORT

Physics

OurDynamicUniverse

Questions

JamesPage

ArthurBaillie

[HIGHER]

Contents

Problems

Revisionproblems–Speed4

Revisionproblems–Acceleration5

Revisionproblems–Vectors6

Section1:Equationsofmotion

Equationsofmotion8

Motion–timegraphs10

Section2:Forces,energyandpower

Balancedandunbalancedforces19

Resolutionofforces24

Workdone,kineticandpotentialenergy27

Section3:Collisionsandexplosions29

Section4:Gravitation

Projectiles35

Gravityandmass38

Section5:Specialrelativity

Relativity–Fundamentalprinciples40

Relativity–Timedilation42

Relativity–Lengthcontraction44

Relativityquestions45

Section6:Theexpandinguniverse

TheDopplereffectandredshiftofgalaxies48

Hubble’sLaw52

Section7:BigBangtheory56

OUR DYNAMIC UNIVERSE (H, PHYSICS)1

OUR DYNAMIC UNIVERSE: PROBLEMS

Problems

Revisionproblems–Speed

1.TheworlddownhillskiingspeedtrialtakesplaceatLesArcseveryyear.Describeamethodthatcouldbeusedtofindtheaveragespeedoftheskieroverthe1kmrun.Yourdescriptionshouldinclude:

(a)anyapparatusrequired

(b)detailsofwhatmeasurementsneedtobetaken

(c)anexplanationofhowyouwouldusethemeasurementstocarryoutthecalculations.

2.Anathleterunsa1500mraceinatimeof3min40s.Calculatehisaveragespeedfortherace.

3.Ittakeslight8·0minutestotravelfromtheSuntotheEarth.HowfarawayistheSunfromtheEarth?

(speedoflight=3·0×108m s1).

4.ThedistancebetweenLondonandNewYorkis4800km.AplanetravelsatanaveragespeedofMach1·3betweenLondonandNewYork.

Calculatethetime,tothenearestminute,forthisjourney.(Mach1isthespeedofsound.Takethespeedofsoundtobe340m s1).

5.Thegraphshowshowthespeedofagirlvarieswithtimefromtheinstantshestartstorunforabus.

ShestartsfromstandstillatOandjumpsonthebusatQ.

Find:

(a)thesteadyspeedatwhichsheruns

(b)thedistancesheruns

(c)theincreaseinthespeedofthebuswhilethegirlisonit

(d)howfarthebustravelsduringQR

(e)howfarthegirltravelsduringOR.

6.Aground-to-airguidedmissilestartsfromrestandacceleratesat150ms2for5s.Whatisthespeedofthemissile5safterlaunching?

7.AnAstonMartinhasanaccelerationof6ms2fromrest.Whattimedoesittaketoreachaspeedof30ms1?

8.Acaristravellingataspeedof34ms1.Thedriverappliesthebrakesandthecarslowsdownatarateof15ms2.Whatisthetimetakenforthespeedofthecartoreduceto4ms1?

Revisionproblems–Acceleration

1.Askateboarderstartingfromrestgoesdownauniformslopeandreachesaspeedof8ms1in4s.

(a)Whatistheaccelerationoftheskateboarder?

(b)Calculatethetimetakenfortheskateboardertoreachaspeedof12ms1.

2.IntheTourdeFranceacyclististravellingat16ms1.Whenhereachesadownhillstretchheacceleratestoaspeedof20ms1in2·0s.

(a)Whatistheaccelerationofthecyclistdownthehill?

(b)Thecyclistmaintainsthisconstant acceleration.Whatishisspeedafterafurther2·0s?

(c)Howlongafterhestartstoacceleratedoeshereachaspeedof

28ms1?

3.Astudentsetsuptheapparatusshowntofindtheaccelerationofatrolleydownaslope.

Lengthofcardontrolley=50mm

Timeonclock1=0·10s(timetakenforcardtointerrupttoplightgate)

Timeonclock2=0·05s(timetakenforcardtointerruptbottomlightgate)

Timeonclock3=2·50s(timetakenfortrolleytotravelbetweentopandbottomlightgate)

Usetheseresultstocalculatetheaccelerationofthetrolley.

Revisionproblems–Vectors

1.Acartravels50kmduenorthandthenreturns30kmduesouth.Thewholejourneytakes2hours.

Calculate:

(a)thetotaldistancetravelledbythecar

(b)theaveragespeedofthecar

(c)theresultantdisplacementofthecar

(d)theaveragevelocityofthecar.

2.Agirldeliversnewspaperstothreehouses,X,YandZ,asshowninthediagram.

ShestartsatXandwalksdirectlyfromXtoYandthentoZ.

(a)Calculatethetotaldistancethegirlwalks.

(b)Calculatethegirl’sfinaldisplacementfromX.

(c)Thegirlwalksatasteadyspeedof1ms1.

(i)CalculatethetimeshetakestogetfromXtoZ.

(ii)Calculateherresultantvelocity.

3.Findtheresultantforceinthefollowingexample:

4.Statewhatismeantbyavectorquantityandscalarquantity.

Givetwoexamplesofeach.

5.Anorienteerruns5kmduesouththen4kmduewestandthen2kmduenorth.Thetotaltimetakenforthisis1hours.Calculatetheaveragespeedandaveragevelocityoftheorienteerforthisrun.

6.Afootballiskickedupatanangleof70ºat15ms1.

Calculate:

(a)thehorizontalcomponentofthevelocity

(b)theverticalcomponentofthevelocity.

OUR DYNAMIC UNIVERSE (H, PHYSICS)1

SECTION 1: EQUATIONS OF MOTION

Section1:Equationsofmotion

Equationsofmotion

1.Anobjectistravellingataspeedof8·0ms1.Itthenacceleratesuniformlyat4·0ms2for10s.Howfardoestheobjecttravelinthis

10s?

2.Acaristravellingataspeedof15·0ms1.Itacceleratesuniformlyat6·0ms2andtravelsadistanceof200mwhileaccelerating.Calculatethevelocityofthecarattheendofthe200m.

3.Aballisthrownverticallyupwardstoaheightof40maboveitsstartingpoint.Calculatethespeedatwhichitwasthrown.

4.Acaristravellingataspeedof30·0ms1.Itthenslowsdownat

1·80ms2untilitcomestorest.Ittravelsadistanceof250mwhileslowingdown.Whattimedoesittaketotravelthe250m?

5.Astoneisthrownwithaninitialspeed5·0ms1verticallydownawell.Thestonestrikesthewater60mbelowwhereitwasthrown.

Calculatethetimetakenforthestonetoreachthesurfaceofthewater.

Theeffectsoffrictioncanbeignored.

6.Atennisballlauncheris0·60mlong.Atennisballleavesthelauncherataspeedof30ms1.

(a)Calculatetheaverageaccelerationofthetennisballinthelauncher.

(b)Calculatethetimetheballacceleratesinthelauncher.

7.Inanexperimenttofindgasteelballfallsfromrestthroughadistanceof0·40m.Thetimetakentofallthisdistanceis0·29s.

Whatisthevalueofgcalculatedfromthedataofthisexperiment?

8.Atrolleyacceleratesuniformlydownaslope.Twolightgatesconnectedtoamotioncomputerarespaced0·50mapartontheslope.Thespeedsrecordedasthetrolleypassesthelightgatesare0·20ms1and0·50ms1.

(a)Calculatetheaccelerationofthetrolley.

(b)Whattimedoesthetrolleytaketotravelthe0·5mbetweenthelightgates?

9.Ahelicopterisrisingverticallyataspeedof10·0ms1whenawheelfallsoff.Thewheelhitstheground8·00slater.

Calculatetheheightofthehelicopterabovethegroundwhenthewheelcameoff.

Theeffectsoffrictioncanbeignored.

10.Aballisthrownverticallyupwardsfromtheedgeofacliffasshowninthediagram.

Theeffectsoffrictioncanbeignored.

(a)(i)Whatistheheightoftheballabovesealevel2·0safterbeingthrown?

(ii)Whatisthevelocityoftheball2·0safterbeingthrown?

(b)Whatisthetotaldistancetravelledbytheballfromlaunchtolandinginthesea?

Motion–timegraphs

1.Thegraphshowshowthedisplacementofanobjectvarieswithtime.

(a)Calculatethevelocityoftheobjectbetween0and1s.

(b)Whatisthevelocityoftheobjectbetween2and4sfromthestart?

(c)Drawthecorrespondingdistanceagainsttimegraphforthemovementofthisobject.

(d)Calculatetheaveragespeedoftheobjectforthe8secondsshownonthegraph.

(e)Drawthecorrespondingvelocityagainsttimegraphforthemovementofthisobject.¶

2.Thegraphshowshowthedisplacementofanobjectvarieswithtime.

(a)Calculatethevelocityoftheobjectduringthefirstsecondfromthestart.

(b)Calculatethevelocityoftheobjectbetween1and5sfromthestart.

(c)Drawthecorrespondingdistanceagainsttimegraphforthisobject.

(d)Calculatetheaveragespeedoftheobjectforthe5seconds.

(e)Drawthecorrespondingvelocityagainsttimegraphforthisobject.

(f)Whatarethedisplacementandthevelocityoftheobject0·5secondsafterthestart?

(g)Whatarethedisplacementandthevelocityoftheobject3secondsafterthestart?

3.Thegraphshowsthedisplacementagainsttimegraphforthemovementofanobject.

(a)Calculatethevelocityoftheobjectbetween0and2s.

(b)Calculatethevelocityoftheobjectbetween2and4sfromthestart.

(c)Drawthecorrespondingdistanceagainsttimegraphforthisobject.

(d)Calculatetheaveragespeedoftheobjectforthe4seconds.

(e)Drawthecorrespondingvelocityagainsttimegraphforthisobject.

(f)Whatarethedisplacementandthevelocityoftheobject0·5safterthestart?

(g)Whatarethedisplacementandthevelocityoftheobject3secondsafterthestart?

4.Anobjectstartsfromadisplacementof0m.Thegraphshowshowthe
velocityoftheobjectvarieswithtimefromthestart.

(a)Calculatetheaccelerationoftheobjectbetween0and1s.

(b)Whatistheaccelerationoftheobjectbetween2and4sfromthestart?

(c)Calculatethedisplacementoftheobject2secondsafterthestart.

(d)Whatisthedisplacementoftheobject8secondsafterthestart?

(e)Sketchthecorrespondingdisplacementagainsttimegraphforthemovementofthisobject.¶

5.Anobjectstartsfromadisplacementof0m.Thegraphshowshowthevelocityoftheobjectvarieswithtimefromthestart.

(a)Calculatetheaccelerationoftheobjectbetween0and2s.

(b)Calculatetheaccelerationoftheobjectbetween2and4sfromthestart.

(c)Drawthecorrespondingaccelerationagainsttimegraphforthisobject.

(d)Whatarethedisplacementandthevelocityoftheobject3secondsafterthestart?

(e)Whatarethedisplacementandthevelocityoftheobject4secondsafterthestart?

(f)Sketchthecorrespondingdisplacementagainsttimegraphforthemovementofthisobject.

6.Thevelocity-timegraphforanobjectisshownbelow.

Apositivevalueindicatesavelocityduenorthandanegativevalueindicatesavelocityduesouth.Thedisplacementoftheobjectis0atthestartoftiming.

(a)Calculatethedisplacementoftheobject:

(i)3saftertimingstarts

(ii)4saftertimingstarts

(iii)6saftertimingstarts.

(b)Drawthecorrespondingacceleration–timegraph.¶

7.Thegraphshowshowtheaccelerationaofanobject,startingfromrest,varieswithtime.¶

Drawagraphtoshowhowthevelocityoftheobjectvarieswithtimeforthe10secondsofthemotion.

8.Thegraphshowsthevelocityofaballthatisdroppedandbounces onafloor.

Anupwardsdirectionistakenasbeingpositive.

(a)InwhichdirectionistheballtravellingduringsectionOBofthegraph?

(b)DescribethevelocityoftheballasrepresentedbysectionCDofthegraph.

(c)DescribethevelocityoftheballasrepresentedbysectionDEofthegraph.

(d)WhathappenedtotheballatthetimerepresentedbypointBonthegraph?

(e)WhathappenedtotheballatthetimerepresentedbypointConthegraph?

(f)Howdoesthespeedoftheballimmediatelybeforereboundfromthefloorcomparewiththespeedimmediatelyafterrebound?

(g)Sketchagraphofaccelerationagainsttimeforthemovementoftheball.¶

9.Aballisthrownverticallyupwardsandreturnstothethrower3secondslater.Whichvelocity-timegraphrepresentsthemotionoftheball?

10.Aballisdroppedfromaheightandbouncesupanddownonahorizontalsurface.Whichvelocity-timegraphrepresentsthemotionoftheballfromthemomentitisreleased?

11.Describehowyoucouldmeasuretheaccelerationofatrolleythatstartsfromrestandmovesdownaslope.Youareprovidedwithametrestickandastopwatch.Yourdescriptionshouldinclude:

(a)adiagram

(b)alistofthemeasurementstaken

(c)howyouwouldusethesemeasurementstocalculatetheaccelerationofthetrolley

(d)howyouwouldestimatetheuncertaintiesinvolvedintheexperiment.

12.Describeasituationwherearunnerhasadisplacementof100mduenorth,avelocityof3ms1duenorthandanaccelerationof2ms2duesouth.Yourdescriptionshouldincludeadiagram.

13.Isitpossibleforanobjecttobeacceleratingbuthaveaconstantspeed?Youmustjustifyyouranswer.

14.Isitpossibleforanobjecttomovewithaconstantspeedfor5secondsandhaveadisplacementof0m?Youmustjustifyyouranswer.

15Isitpossibleforanobjecttomovewithaconstantvelocityfor5sandhaveadisplacementof0m?Youmustjustifyyouranswer.

OUR DYNAMIC UNIVERSE (H, PHYSICS)1

SECTION 2: FORCES, ENERGY AND POWER

Section2:Forces,energyandpower

Balancedandunbalancedforces

1.StateNewton’s1stLawofMotion.

2.Aliftofmass500kgtravelsupwardsataconstantspeed.

Calculatethetensioninthecablethatpullstheliftupwards.

3.(a)Afullyloadedoiltankerhasamassof2·0×108kg.

Asthespeedofthetankerincreasesfrom 0toasteadymaximumspeedof8.0ms1theforcefromthepropellersremainsconstantat3.0×106N.

(i)Calculatetheaccelerationofthetankerjustasitstartsfromrest.

(ii)Whatisthesizeoftheforceoffrictionactingonthetankerwhenitistravellingatthesteadyspeedof8.0ms1?

(b)Whenitsenginesarestopped,thetankertakes50minutestocometorestfromaspeedof8.0ms1.Calculateitsaveragedeceleration.

4.Thegraphshowshowthespeedofaparachutistvarieswithtimeafterhavingjumpedfromanaeroplane.

WithreferencetotheoriginofthegraphandthelettersA,B,C,DandEexplainthevariationofspeedwithtimeforeachstageoftheparachutist’sfall.

5.Twogirlspushacarofmass2000kg.Eachappliesaforceof50Nandtheforceoffrictionis60N.Calculatetheaccelerationofthecar.

6.Aboyonaskateboardridesupaslope.Thetotalmassoftheboyandtheskateboardis90kg.Hedeceleratesuniformlyfrom12ms1to

2ms1in6seconds.Calculatetheresultantforceactingonhim.

7.Aboxofmass30kgispulledalongaroughsurfacebyaconstantforceof140N.Theaccelerationoftheboxis4·0ms2.

(a)Calculatethemagnitudeoftheunbalancedforcecausingtheacceleration.

(b)Calculatetheforceoffrictionbetweentheboxandthesurface.

8.Acarofmass800kgisacceleratedfromrestto18ms1in12seconds.

(a)Whatisthesizeoftheresultantforceactingonthecar?

(b)Howfardoesthecartravelinthese12seconds?

(c)Attheendofthe12secondsperiodthebrakesareoperatedandthecarcomestorestinadistanceof50m.

Whatisthesizeoftheaveragefrictionalforceactingonthecar?

9.(a)Arocketofmass4·0×104kgislaunchedverticallyupwardsfromthesurfaceoftheEarth.Itsenginesproduceaconstantthrustof7·0×105N.

(i)Drawadiagramshowingalltheforcesactingontherocketjustaftertake-off.

(ii)Calculatetheinitialaccelerationoftherocket.

(b)Astherocketrisesthethrustremainsconstantbuttheaccelerationoftherocketincreases.Givethreereasonsforthisincreaseinacceleration.

(c)ExplainintermsofNewton’slawsofmotionwhyarocketcantravelfromtheEarthtotheMoonandformostofthejourneynotburnupanyfuel.

10.ArockettakesofffromthesurfaceoftheEarthandacceleratesto

90ms1inatimeof4·0s.Theresultantforceactingonitis40kNupwards.

(a)Calculatethemassoftherocket.

(b)Theaverageforceoffrictionis5000N.Calculatethethrustoftherocketengines.

11.Ahelicopterofmass2000kgrisesupwardswithanaccelerationof4·00ms2.Theforceoffrictioncausedbyairresistanceis1000N.Calculatetheupwardsforceproducedbytherotorsofthehelicopter.

12.Acrateofmass200kgisplacedonabalance,calibratedinnewtons,inalift.

(a)Whatisthereadingonthebalancewhentheliftisstationary?

(b)Theliftnowacceleratesupwardsat1·50ms2.Whatisthenewreadingonthebalance?

(c)Theliftthentravelsupwardsataconstantspeedof5·00ms1.Whatisthenewreadingonthebalance?

(d)Forthelaststageofthejourneytheliftdeceleratesat1·50ms2whilegoingup.Calculatethereadingonthebalance.

13.Asmallliftinahotelisfullyloadedandhasatotalmassof250kg.Forsafetyreasonsthetensioninthepullingcablemustneverbegreaterthan3500N.

(a)Whatisthetensioninthecablewhentheliftis:

(i)atrest

(ii)movingupwardsataconstantspeedof1ms1

(iii)movingupwardswithaconstantaccelerationof2ms2

(iv)acceleratingdownwardswithaconstantaccelerationof

2ms2.

(b)Calculatethemaximumpermittedupwardaccelerationofthefullyloadedlift.

(c)Describeasituationwheretheliftcouldhaveanupwardaccelerationgreaterthanthevaluein(b)withoutbreachingsafetyregulations.

14.Apackageofmass4·00kgishungfromaspring(Newton)balanceattachedtotheceilingofalift.

Theliftisacceleratingupwardsat3·00ms2.Whatisthereadingonthespringbalance?

15.Thegraphshowshowthedownwardspeedofaliftvarieswithtime.

(a)Drawthecorrespondingaccelerationagainsttimegraph.

(b)A4.0kgmassissuspendedfromaspringbalanceinsidethelift.Determinethereadingonthebalanceateachstageofthemotion.

16.Twotrolleysjoinedbyastringarepulledalongafrictionlessflatsurfaceasshown.

(a)Calculatetheaccelerationofthetrolleys.

(b)Calculatethetension,T,inthestringjoiningthetrolleys.

17.Acarofmass1200kgtowsacaravanofmass1000kg.Thefrictionalforcesonthecarandcaravanare200Nand500N,respectively.Thecaracceleratesat2.0ms2.

(a)Calculatetheforceexertedbytheengineofthecar.

(b)Whatforcedoesthetowbarexertonthecaravan?

(c)Thecarthentravelsataconstantspeedof10ms1.

Assumingthefrictionalforcestobeunchanged,calculate:

(i)thenewengineforce

(ii)theforceexertedbythetowbaronthecaravan.

(d)Thecarbrakesanddeceleratesat5·0ms2.

Calculatetheforceexertedbythebrakes(assumetheotherfrictionalforcesremainconstant).

18.Alogofmass400kgisstationary.Atractorofmass1200kgpullsthelogwithatowrope.Thetensioninthetowropeis2000Nandthefrictionalforceonthelogis800N.Howfarwillthelogmovein4s?

19.Aforceof60Nisusedtopushthreeblocksasshown.

Eachblockhasamassof8·0kgandtheforceoffrictiononeachblockis4·0N.

(a)Calculate:

(i)theaccelerationoftheblocks

(ii)theforcethatblockAexertsonblockB

(iii)theforceblockBexertsonblockC.

(b)Thepushingforceisthenreduceduntiltheblocksmoveatconstantspeed.

(i)Calculatethevalueofthispushingforce.

(ii)DoestheforcethatblockAexertsonblockBnowequaltheforcethatblockBexertsonblockC?Explain.¶

20.A2·0kgtrolleyisconnectedbystringtoa1·0kgmassasshown.Thebenchandpulleyarefrictionless.

(a)Calculatetheaccelerationofthetrolley.

(b)Calculatethetensioninthestring.

Resolutionofforces

1.Amanpullsagardenrollerwithaforceof50N.¶

(a)Findtheeffectivehorizontalforceappliedtotheroller.

(b)Describeandexplainhowthemancanincreasethiseffectivehorizontalforcewithoutchangingthesizeoftheforceapplied.

2.Abargeisdraggedalongacanalasshownbelow.

Whatisthesizeofthecomponentoftheforceparalleltothecanal?

3.Atoytrainofmass0·20kgisgivenapushof10Nalongtherailsatanangleof30ºabovethehorizontal.

Calculate:

(a)themagnitudeofthecomponentofforcealongtherails

(b)theaccelerationofthetrain.

4.Abargeofmass1000kgispulledbyaropealongacanalasshown.

Theropeappliesaforceof800Natanangleof40ºtothedirectionofthecanal.Theforceoffrictionbetweenthebargeandthewateris

100N.Calculatetheaccelerationofthebarge.

5.Acrateofmass100kgispulledalongaroughsurfacebytworopesattheanglesshown.

(a)Thecrateismovingataconstantspeedof1·0ms1.Whatisthesizeoftheforceoffriction?

(b)Theforcesarenoweachincreasedto140Natthesameangle.Assumingthefrictionforceremainsconstant,calculatetheaccelerationofthecrate.

6.A2·0kgblockofwoodisplacedonaslopeasshown.

Theblockremainsstationary.Whatarethesizeanddirectionofthefrictionalforceontheblock?

7.Arunwayis2·0mlongandraised0·30matoneend.Atrolleyofmass0·50kgisplacedontherunway.Thetrolleymovesdowntherunwaywithconstantspeed.Calculatethemagnitudeoftheforceoffrictionactingonthetrolley.

8.Acarofmass900kgisparkedonahill.Theslopeofthehillis15ºtothehorizontal.Thebrakesonthecarfail.Thecarrunsdownthehillforadistanceof50muntilitcrashesintoahedge.Theaverageforceoffrictiononthecarasitrunsdownthehillis300N.

(a)Calculatethecomponentoftheweightactingdowntheslope.

(b)Findtheaccelerationofthecar.

(c)Calculatethespeedofthecarjustbeforeithitsthehedge.

9.Atrolleyofmass2·0kgisplacedonaslopewhichmakesanangleof60ºtothehorizontal.

(a)Astudentpushesthetrolleyandthenreleasesitsothatitmovesuptheslope.Theforceoffrictiononthetrolleyis1·0N.

(i)Whydoesthetrolleycontinuetomoveuptheslopeafteritisreleased?

(ii)Calculatetheunbalancedforceonthetrolleyasitmovesuptheslope.

(iii)Calculatetherateatwhichthetrolleylosesspeedasitmovesuptheslope.

(b)Thetrolleyeventuallycomestorestthenstartstomovedowntheslope.

(i)Calculatetheunbalancedforceonthetrolleyasitmovesdowntheslope.

(ii)Calculatetheaccelerationofthetrolleydowntheslope.

Workdone,kineticandpotentialenergy

1.Asmallballofmass0·20kgisdroppedfromaheightof4·0mabovetheground.Theballreboundstoaheightof2·0m.

(a)Calculatetotallossinenergyoftheball.

(b)Calculatethespeedoftheballjustbeforeithitstheground.

(c)Calculatethespeedoftheballjustafteritleavestheground.

2.Aboxofmass70kgispulledalongahorizontalsurfacebyahorizontalforceof90N.Theboxispulledadistanceof12m.Thereisafrictionalforceof80Nbetweentheboxandthesurface.

(a)Calculatethetotalworkdonebythepullingforce.

(b)Calculatetheamountofkineticenergygainedbythebox.

3.Aboxofmass2·0kgispulledupafrictionlessslopeasshown.

(a)Calculatethegravitationalpotentialenergygainedbytheboxwhenitispulleduptheslope.

(b)Theblockisnowreleased.

(i)Useconservationofenergytofindthespeedoftheboxatthebottomoftheslope.

(ii)Useanothermethodtoconfirmyouranswerto(i).

4.Awinchdrivenbyamotorisusedtoliftacrateofmass50kgthroughaverticalheightof20m.

(a)Calculatethesizeoftheminimumforcerequiredtoliftthecrate.

(b)Calculatetheminimumamountofworkdonebythewinchwhileliftingthecrate.

(c)Thepowerofthewinchis2·5kW.Calculatetheminimumtimetakentoliftthecratetotherequiredheight.¶

5.Atrainhasaconstantspeedof10ms1overadistanceof2·0km.Thedrivingforceofthetrainengineis3·0×104N.

Whatisthepowerdevelopedbythetrainengine?

6.Anarrowofmass22ghasaspeedof30ms1asitstrikesatarget.Thetipofthearrowgoes3·0×102mintothetarget.

(a)Calculatetheaverageforceofthetargetonthearrow.

(b)Whatisthetimetakenforthearrowtocometorestafterstrikingthetarget,assumingthetargetexertsaconstantforceonthearrow?

OUR DYNAMIC UNIVERSE (H, PHYSICS)1

SECTION 3: COLLISIONS AND EXPLOSIONS

Section3:Collisionsandexplosions

1.Whatisthemomentumoftheobjectineachofthefollowingsituations?

(a)(b)(c)

2.Atrolleyofmass2·0kgistravellingwithaspeedof1·5ms1.Thetrolleycollidesandstickstoastationarytrolleyofmass2·0kg.

(a)Calculatethevelocityofthetrolleysimmediatelyafterthecollision.

(b)Showthatthecollisionisinelastic.

3.Atargetofmass4·0kghangsfromatreebyalongstring.Anarrowofmass100gisfiredatthetargetandembedsitselfinthetarget.Thespeedofthearrowis100ms1justbeforeitstrikesthetarget.Whatisthespeedofthetargetimmediatelyaftertheimpact?

4.Atrolleyofmass2·0kgismovingataconstantspeedwhenitcollidesandstickstoasecondstationarytrolley.Thegraphshowshowthespeedofthe2·0kgtrolleyvarieswithtime.

Determinethemassofthesecondtrolley.

5.Inagameofbowlsabowlofmass1·0kgistravellingataspeedof2·0ms1whenithitsastationaryjack‘straighton’.Thejackhasamassof300g.Thebowlcontinuestomovestraightonwithaspeedof1·2ms1afterthecollision.

(a)Whatisthespeedofthejackimmediatelyafterthecollision?

(b)Howmuchkineticenergyislostduringthecollision?

6.Twospacevehiclesmakeadockingmanoeuvre(joiningtogether)inspace.Onevehiclehasamassof2000kgandistravellingat9·0ms1.Thesecondvehiclehasamassof1500kgandismovingat8·0ms1inthesamedirectionasthefirst.Determinetheircommonvelocityafterdocking.

7.Twocarsaretravellingalongaracetrack.Thecarinfronthasamassof1400kgandismovingat20ms1.Thecarbehindhasamassof1000kgandismovingat30ms1.Thecarscollideandasaresultofthecollisionthecarinfronthasaspeedof25ms1.

(a)Determinethespeedoftherearcarafterthecollision.

(b)Showclearlywhetherthiscollisioniselasticorinelastic.

8.Onevehicleapproachesanotherfrombehindasshown.

Thevehicleattherearismovingfasterthantheoneinfrontandtheycollide.Thiscausesthevehicleinfronttobe‘nudged’forwardwithanincreasedspeed.Determinethespeedoftherearvehicleimmediatelyafterthecollision.

9.Atrolleyofmass0·8kgistravellingataspeed1·5ms1.Itcollideshead-onwithanothervehicleofmass1·2kgtravellingat2·0ms1intheoppositedirection.Thevehicleslocktogetheronimpact.Determinethespeedanddirectionofthevehiclesafterthecollision.

10.Afireworkislaunchedverticallyandwhenitreachesitsmaximumheightitexplodesintotwopieces.Onepiecehasamassof200gandmovesoffwithaspeedof10ms1.Theotherpiecehasamassof

120g.Whatisthevelocityofthesecondpieceofthefirework?

11.Twotrolleysinitiallyatrestandincontactmoveapartwhenaplungerononetrolleyisreleased.Onetrolleywithamassof2kgmovesoffwithaspeedof4ms1.Theothermovesoffwithaspeedof2ms1,intheoppositedirection.Calculatethemassofthistrolley.

12.Amanofmass80kgandwomanofmass50kgareskatingonice.Atonepointtheystandnexttoeachotherandthewomanpushestheman.Asaresultofthepushthemanmovesoffataspeedof0·5ms1.Whatisthevelocityofthewomanasaresultofthepush?

13.Twotrolleysinitiallyatrestandincontactflyapartwhenaplungerononeofthemisreleased.Onetrolleyhasamassof2·0kgandmovesoffataspeedof2·0ms1.Thesecondtrolleyhasamassof3·0kg.Calculatethevelocityofthistrolley.

14.Acueexertsanaverageforceof7·00Nonastationarysnookerballofmass200g.Theimpactofthecueontheballlastsfor45·0ms.Whatisthespeedoftheballasitleavesthecue?

15Afootballofmass500gisstationary.Whenagirlkickstheballherfootisincontactwiththeballforatimeof50ms.Asaresultofthekicktheballmovesoffataspeedof10ms1.Calculatetheaverageforceexertedbyherfootontheball.

16.Astationarygolfballofmass100gisstruckbyaclub.Theballmovesoffataspeedof30ms1.Theaverageforceoftheclubontheballis100N.Calculatethetimeofcontactbetweentheclubandtheball.

17.Thegraphshowshowtheforceexertedbyahockeystickonastationaryhockeyballvarieswithtime.

Themassoftheballis150g.

Determinethespeedoftheballasitleavesthestick.

18.Aballofmass100gfallsfromaheightof0·20montoconcrete.Theballreboundstoaheightof0·18m.Thedurationoftheimpactis

25ms.Calculate:

(a)thechangeinmomentumoftheballcausedbythe‘bounce’

(b)theimpulseontheballduringthebounce

(c)theaverageunbalancedforceexertedontheballbytheconcrete

(d)theaverageunbalancedforceoftheconcreteontheball.

(e)Whatisinthetotalaverageupwardsforceontheballduringimpact?

19.Arubberballofmass40·0gisdroppedfromaheightof0·800montothepavement.Theballreboundstoaheightof0·450m.Theaverageforceofcontactbetweenthepavementandtheballis2·80N.

(a)Calculatethevelocityoftheballjustbeforeithitsthegroundandthevelocityjustafterhittingtheground.

(b)Calculatethetimeofcontactbetweentheballandpavement.

20.Aballofmass400gtravelsfallsfromrestandhitstheground.Thevelocity-timegraphrepresentsthemotionoftheballforthefirst1·2safteritstartstofall.

(a)DescribethemotionoftheballduringsectionsAB,BC,CDandDEonthegraph.

(b)Whatisthetimeofcontactoftheballwiththeground?

(c)Calculatetheaverageunbalancedforceofthegroundontheball.

(d)Howmuchenergyislostduetocontactwiththeground?

21.Waterwithaspeedof50ms1isejectedhorizontallyfromafirehoseatarateof25kgs1.Thewaterhitsawallhorizontallyanddoesnotreboundfromthewall.Calculatetheaverageforceexertedonthewallbythewater.

22.Arocketejectsgasatarateof50kgs1,ejectingitwithaconstantspeedof1800ms1.Calculatemagnitudeoftheforceexertedbytheejectedgasontherocket.

23.Describeindetailanexperimentthatyouwoulddotodeterminetheaverageforcebetweenafootballbootandafootballastheballisbeingkicked.Drawadiagramoftheapparatusandincludeallthemeasurementstakenanddetailsofthecalculationscarriedout.

24.A2·0kgtrolleytravellingat6·0ms1collideswithastationary1·0kgtrolley.Thetrolleysremainconnectedafterthecollision.

(a)Calculate:

(i)thevelocityofthetrolleysjustafterthecollision

(ii)themomentumgainedbythe1·0kgtrolley

(iii)themomentumlostbythe2·0kgtrolley.

(b)Thecollisionlastsfor0·50s.Calculatethemagnitudeoftheaverageforceactingoneachtrolley.

25.Inaproblemtwoobjects,havingknownmassesandvelocities,collideandsticktogether.Whydoestheproblemaskforthevelocityimmediatelyaftercollisiontobecalculated?

26.ANewton’scradleapparatusisusedtodemonstrateconservationofmomentum.

Foursteelspheres,eachofmass0.1kg,aresuspendedsothattheyareinastraightline.

Sphere1ispulledtothesideandreleased,asshownindiagramI.

Whensphere1strikessphere2(asshownbythedottedlines)thensphere4movesoffthelineandreachesthepositionshownbythedottedlines.

Thestudentestimatesthatsphere1hasaspeedof2ms1whenitstrikessphere2.Shealsoestimatesthatsphere4leavesthelinewithaninitialspeedof2ms1.Henceconservationofmomentumhasbeendemonstrated.

Asecondstudentsuggeststhatwhenthedemonstrationisrepeatedthereisapossibilitythatspheres3and4,eachwithaspeedof

0·5ms1,couldmoveoffthelineasshownindiagramII.

Useyourknowledgeofphysicstoshowthisisnotpossible.

OUR DYNAMIC UNIVERSE (H, PHYSICS)1

SECTION 4: GRAVITATION

Section4:Gravitation

Projectiles

1.Aplaneistravellingwithahorizontalvelocityof350ms1ataheightof300m.Aboxisdroppedfromtheplane.

Theeffectsoffrictioncanbeignored.

(a)Calculatethetimetakenfortheboxtoreachtheground.

(b)Calculatethehorizontaldistancebetweenthepointwheretheboxisdroppedandthepointwhereithitstheground.

(c)Whatisthepositionoftheplanerelativetotheboxwhentheboxhitstheground?

2.Aprojectileisfiredhorizontallywithaspeedof12·0ms1fromtheedgeofacliff.Theprojectilehitstheseaatapoint60·0mfromthebaseofthecliff.

(a)Calculatethetimeofflightoftheprojectile.

(b)Whatistheheightofthestartingpointoftheprojectileabovesealevel?

Stateanyassumptionsyouhavemade.

3.Aballisthrownhorizontallywithaspeedof15ms1fromthetopofaverticalcliff.Itreachesthehorizontalgroundatadistanceof45mfromthefootofthecliff.

(a)(i)Drawagraphofverticalspeedagainsttimefortheballforthetimefromwhenitisthrownuntilithitstheground.

(ii)Drawagraphofhorizontalspeedagainsttimefortheball.

(b)Calculatethevelocityoftheball2safteritisthrown.

(Magnitudeanddirectionarerequired.)

4.Afootballiskickedupatanangleof70º above the horizontalat

15ms1.Calculate:

(a)thehorizontalcomponentofthevelocity

(b)theverticalcomponentofthevelocity.

5.Aprojectileisfiredacrosslevelgroundandtakes6stotravelfromAtoB.

ThehighestpointreachedisC.Airresistanceisnegligible.

Velocity-timegraphsfortheflightareshownbelow.VHisthehorizontalvelocityandVVistheverticalvelocity.

(a)Describe:

(i)thehorizontalmotionoftheprojectile

(ii)theverticalmotionoftheprojectile.

(b)UseavectordiagramtofindthespeedandangleatwhichtheprojectilewasfiredfrompointA.

(c)FindthespeedatpositionC.Explainwhythisisthesmallestspeedoftheprojectile.

(d)CalculatetheheightabovethegroundofpointC.

(e)Findthehorizontalrangeoftheprojectile.

6.Aballofmass5·0kgisthrownwithavelocityof40ms1atanangleof30ºtothehorizontal.

Calculate:

(a)theverticalcomponentoftheinitialvelocityoftheball

(b)themaximumverticalheightreachedbythebal

(c)thetimeofflightforthewholetrajectory

(d)thehorizontalrangeoftheball.

7.Alauncherisusedtofireaballwithavelocityof100ms1atanangleof60ºtotheground.Theballstrikesatargetonahillasshown.

(a)Calculatethetimetakenfortheballtoreachthetarget.

(b)Whatistheheightofthetargetabovethelauncher?

8.Astuntdriverattemptstojumpacrossacanalofwidth10m.

Theverticaldroptotheothersideis2masshown.

(a)Calculatetheminimumhorizontalspeedrequiredsothatthecarreachestheotherside.

(b)Explainwhyyouranswerto(a)istheminimumhorizontalspeedrequired.

(c)Stateanyassumptionsyouhavemade.

9.Aballisthrownhorizontallyfromacliff.Theeffectoffrictioncanbeignored.

(a)Isthereanytimewhenthevelocityoftheballisparalleltoitsacceleration?Justifyyouranswer.

(b)Isthereanytimewhenthevelocityoftheballisperpendiculartoitsacceleration?Justifyyouranswer.

10.Aballisthrownatanangleof45ºtothehorizontal.Theeffectoffrictioncanbeignored.

(a)Isthereanytimewhenthevelocityoftheballisparalleltoitsacceleration?Justifyyouranswer.

(b)Isthereanytimewhenthevelocityoftheballisperpendiculartoitsacceleration?Justifyyouranswer.

11.Asmallballofmass0·3kgisprojectedatanangleof60ºtothehorizontal.Theinitialspeedoftheballis20ms1.

Showthatthemaximumgaininpotentialenergyoftheballis45J.

12.Aballisthrownhorizontallywithaspeedof20ms1fromacliff.Theeffectsofairresistancecanbeignored.Howlongafterbeingthrownwillthevelocityoftheballbeatanangleof45ºtothehorizontal?

Gravityandmass

Inthefollowingquestions,whenrequired,usethefollowingdata:

Gravitationalconstant=6·67×1011Nm2kg2

1.Statetheinversesquarelawofgravitation.

2.Showthattheforceofattractionbetweentwolargeships,eachofmass5·00×107kgandseparatedbyadistanceof20m,is417N.

3.Calculatethegravitationalforcebetweentwocarsparked0·50mapart.Themassofeachcaris1000kg.

4.Inahydrogenatomanelectronorbitsaprotonwitharadiusof5·30×1011m.Themassofanelectronis9·11×1031kgandthemassofaprotonis1·67×1027kg.Calculatethegravitationalforceofattractionbetweentheprotonandtheelectroninahydrogenatom.

5.ThedistancebetweentheEarthandtheSunis1·50×1011m.ThemassoftheEarthis5·98×1024kgandthemassoftheSunis1·99×1030kg.CalculatethegravitationalforcebetweentheEarthandtheSun.

6.Twoprotonsexertagravitationalforceof1·16×1035Noneachother.Themassofaprotonis1·67×1027kg.Calculatethedistanceseparatingtheprotons.

OUR DYNAMIC UNIVERSE (H, PHYSICS)1

SECTION 5: SPECIAL RELATIVITY

Section5:Specialrelativity

Relativity–Fundamentalprinciples

1.Ariverflowsataconstantspeedof0·5ms1south.Acanoeistisabletorowataconstantspeedof1·5ms1.

(a)Determinethevelocityofthecanoeistrelativetotheriverbankwhenthecanoeistismovingupstream.

(b)Determinethevelocityofthecanoeistrelativetotheriverbankwhenthecanoeistismovingdownstream.

2.Inanairport,passengersuseamovingwalkway.Themovingwalkwayistravellingataconstantspeedof0·8ms1andistravellingeast.

Forthefollowingpeople,determinethevelocityofthepersonrelativetotheground:

(a)awomanstandingatrestonthewalkway

(b)amanwalkingat2·0ms1inthesamedirectionasthewalkwayismoving

(c)aboyrunningwestat3·0ms1.

3.Thestepsofanescalatormoveatasteadyspeedof1·0ms1relativetothestationarysideoftheescalator.

(a)Amanwalksupthestepsoftheescalatorat2·0ms1.Determinethespeedofthemanrelativetothesideoftheescalator.

(b)Aboyrunsdownthestepsoftheescalatorat3·0ms1.Determinethespeedoftheboyrelativetothesideoftheescalator.

4.InthefollowingsentencesthewordsrepresentedbythelettersA,B,C,D,E,FandGaremissing:

In_____A____TheoryofSpecialRelativitythelawsofphysicsarethe_____B____forallobservers,atrestormovingatconstantvelocitywithrespecttoeachotherie_____C____acceleration.Anobserver,atrestormovingatconstant_____D____hastheirownframeofreference.

Inallframesofreferencethe_____E____,c,remainsthesameregardlessofwhetherthesourceorobserverisinmotion.

Einstein’sprinciplesthatthelawsofphysicsandthespeedoflightarethesameforallobserversleadstotheconclusionthatmovingclocksrun_____F____(timedilation)andmovingobjectsare_____G____(lengthcontraction).

Matcheachletterwiththecorrectwordfromthelistbelow:

accelerationdifferentEinstein’sfast

lengthenedNewton’ssameshortened

slowspeedoflightvelocityzero

5.AnobserveratrestontheEarthseesanaeroplaneflyoverheadataconstantspeedof2000kmh1.Atwhatspeed,inkmh1,doesthepilotoftheaeroplaneseetheEarthmoving?

6.Ascientistisinawindowlesslift.Canthescientistdeterminewhethertheliftismovingwitha:

(a)uniformvelocity

(b)uniformacceleration?

7.SpaceshipAismovingataspeedof2·4×108ms1.Itsendsoutalightbeamintheforwardsdirection.MeanwhileanotherspaceshipBismovingtowardsspaceshipAataspeedof2·4×108ms1.AtwhatspeeddoesspaceshipBseethelightbeamfromspaceshipApass?

8.Aspacecraftistravellingataconstantspeedof7·5×107ms1.Itemitsapulseoflightwhenitis3·0×1010mfromtheEarthasmeasuredbyanobserverontheEarth.

CalculatethetimetakenforthepulseoflighttoreachtheEarthaccordingtoaclockontheEarthwhenthespacecraftismoving:

(a)awayfromtheEarth

(b)towardstheEarth.

9.AspaceshipistravellingawayfromtheEarthataconstantspeedof

1·5×108ms1.AlightpulseisemittedbyalampontheEarthandtravelstowardsthespaceship.Findthespeedofthelightpulseaccordingtoanobserveron:

(a)theEarth

(b)thespaceship.

10.Convertthefollowingfractionofthespeedoflightintoavaluein

ms1:

(a)0·1c

(b)0·5c

(d)0·8c

11.Convertthefollowingspeedsintoafractionofthespeedoflight:

(a)3·0×108ms1

(b)2·0×108ms1

(d)1·0×108ms1

Relativity–Timedilation

1.Writedowntherelationshipinvolvingthepropertimetanddilatedtimet’betweentwoeventswhichareobservedintwodifferentframesofreferencemovingataspeed,v,relativetooneanother(wherethepropertimeisthetimemeasuredbyanobserveratrestwithrespecttothetwoeventsandthedilatedtimeisthetimemeasuredbyanotherobservermovingataspeed,v,relativetothetwoevents).

2.Inthetableshown,usetherelativityequationfortimedilationtocalculatethevalueofeachmissingquantity(a)to(f)foranobjectmovingataconstantspeedrelativetotheEarth.

Dilatedtime / Propertime / Speedofobject/m s1
(a) / 20h / 1·00×108
(b) / 10year / 2·25×108
1400s / (c) / 2·00×108
1.40×104s / (d) / 1·00×108
84s / 60s / (e)
21minutes / 20minutes / (f)

3.TwoobserversPandQsynchronisetheirwatchesat11.00amjustasobserverQpassestheEarthataspeedof2×108ms1.

(a)At11.15amaccordingtoobserverP’swatch,observerPlooksatQ’swatchthroughatelescope.Calculatethetime,tothenearestminute,thatobserverPseesonQ’swatch.

(b)At11.15amaccordingtoobserverQ’swatch,observerQlooksatP’swatchthroughatelescope.Calculatethetime,tothenearestminute,thatobserverQseesonP’swatch.

4.Thelifetimeofastaris10billionyearsasmeasuredbyanobserveratrestwithrespecttothestar.ThestarismovingawayfromtheEarthataspeedof0·81c.

CalculatethelifetimeofthestaraccordingtoanobserverontheEarth.

5.Aspacecraftmovingwithaconstantspeedof0·75cpassestheEarth.AnastronautonthespacecraftmeasuresthetimetakenforUsainBolttorun100minthesprintfinalatthe2008OlympicGames.Theastronautmeasuresthistimetobe14·65s.CalculateUsainBolt’swinningtimeasmeasuredontheEarth.

6.Ascientistinthelaboratorymeasuresthetimetakenforanuclearreactiontooccurinanatom.Whentheatomistravellingat

8·0×107ms1thereactiontakes4·0×104s.Calculatethetimeforthereactiontooccurwhentheatomisatrest.

7.Thelightbeamfromalighthousesweepsitsbeamoflightaroundinacircleonceevery10s.ToanastronautonaspacecraftmovingtowardstheEarth,thebeamoflightcompletesonecompletecircleevery14s.CalculatethespeedofthespacecraftrelativetotheEarth.

8.ArocketpassestwobeaconsthatareatrestrelativetotheEarth.Anastronautintherocketmeasuresthetimetakenfortherockettotravelfromthefirstbeacontothesecondbeacontobe10·0s.AnobserveronEarthmeasuresthetimetakenfortherockettotravelfromthefirstbeacontothesecondbeacontobe40·0s.CalculatethespeedoftherocketrelativetotheEarth.

9.AspacecrafttravelstoadistantplanetataconstantspeedrelativetotheEarth.Aclockonthespacecraftrecordsatimeof1yearforthejourneywhileanobserveronEarthmeasuresatimeof2yearsforthejourney.Calculatethespeed,inms1,ofthespacecraftrelativetotheEarth.

Relativity–Lengthcontraction

1.Writedowntherelationshipinvolvingtheproperlengthlandcontractedlengthl’ofamovingobjectobservedintwodifferentframesofreferencemovingataspeed,v,relativetooneanother(wheretheproperlengthisthelengthmeasuredbyanobserveratrestwithrespecttotheobjectandthecontractedlengthisthelengthmeasuredbyanotherobservermovingataspeed,v,relativetotheobject).

2.Inthetableshown,usetherelativityequationforlengthcontractiontocalculatethevalueofeachmissingquantity(a)to(f)foranobjectmovingataconstantspeedrelativetotheEarth.

Contractedlength / Properlength / Speedofobject/m s1
(a) / 5·00m / 1·00×108
(b) / 15.0m / 2·00×108
0·15km / (c) / 2·25×108
150mm / (d) / 1·04×108
30m / 35m / (e)
10m / 11m / (f)

3.Arockethasalengthof20mwhenatrestontheEarth.Anobserver,atrestontheEarth,watchestherocketasitpassesataconstantspeedof1·8×108ms1.Calculatethelengthoftherocketasmeasuredbytheobserver.

4.Apimesonismovingat0·90crelativetoamagnet.Themagnethasalengthof2·00mwhenatresttotheEarth.Calculatethelengthofthemagnetin the reference frame ofthepimeson.

5.Intheyear2050aspacecraftfliesoverabasestationontheEarth.Thespacecrafthasaspeedof0·8c.Thelengthofthemovingspacecraftismeasuredas160mbyapersonontheEarth.Thespacecraftlaterlandsandthesamepersonmeasuresthelengthofthenowstationaryspacecraft.Calculatethelengthofthestationaryspacecraft.

6.Arocketistravellingat0·50crelativetoaspacestation.Astronautsontherocketmeasurethelengthofthespacestationtobe0.80km.

Calculatethelengthofthespacestation according to a technician on the space station.

7.Ametrestickhasalengthof1·00mwhenatrestontheEarth.WheninmotionrelativetoanobserverontheEarththesamemetrestickhasalengthof0·50m.Calculatethespeed,inms1,ofthemetrestick.

8.Aspaceshiphasalengthof220mwhenmeasuredatrestontheEarth.ThespaceshipmovesawayfromtheEarthataconstantspeedandanobserver,ontheEarth,nowmeasuresitslengthtobe150m.

Calculatethespeedofthespaceshipinms1.

9.Thelengthofarocketismeasuredwhenatrestandalsowhenmovingataconstantspeedbyanobserveratrestrelativetotherocket.Theobservedlengthis99·0%ofitslengthwhenatrest.Calculatethespeedoftherocket.

Relativityquestions

1.TwopointsAandBareseparatedby240masmeasuredbymetresticksatrestontheEarth.ArocketpassesalongthelineconnectingAandBataconstantspeed.ThetimetakenfortherockettotravelfromAtoB,asmeasuredbyanobserverontheEarth,is1·00×106s.

(a)ShowthatthespeedoftherocketrelativetotheEarthis

2·40×108ms1.

(b)WhatisthedistancebetweenpointsAandBasmeasuredbymetrestickscarriedbyanobservertravellingintherocket?

2.Aspacecraftistravellingataconstantspeedof0·95c.Thespacecrafttravelsatthisspeedfor1year,asmeasuredbyaclockontheEarth.

(a)Calculatethetimeelapsed,inyears,asmeasuredbyaclockinthespacecraft.

(b)Showthatthedistancetravelledbythespacecraftasmeasuredbyanobserveronthespacecraftis2·8×1015m.

(c)Calculatethedistance,inm,thespacecraftwillhavetravelledasmeasuredbyanobserverontheEarth.

3.Apimesonhasameanlifetimeof2·6×108swhenatrest.Apimesonmoveswithaspeedof0·99ctowardsthesurfaceoftheEarth.

(a)CalculatethemeanlifetimeofthispimesonasmeasuredbyanobserverontheEarth.

(b)CalculatethemeandistancetravelledbythepimesonasmeasuredbytheobserverontheEarth.

4.Aspacecraftmovingat2·4×108ms1passestheEarth.Anastronautonthespacecraftfindsthatittakes5·0×107sforthespacecrafttopassasmallmarkerwhichisatrestontheEarth.

(a)Calculatethelength,inm,ofthespacecraftasmeasuredbytheastronaut.

(b)CalculatethelengthofthespacecraftasmeasuredbyanobserveratrestontheEarth.

5.Aneonsignflasheswithafrequencyof0·2Hz.

(a)Calculatethetimebetweenflashes.

(b)AnastronautonaspacecraftpassestheEarthataspeedof0·84candseestheneonlightflashing.Calculatethetimebetweenflashesasobservedbytheastronautonthespacecraft.

6.Whenatrest,asubatomicparticlehasalifetimeof0·15ns.WheninmotionrelativetotheEarththeparticle’slifetimeismeasuredbyanobserverontheEarthas0·25ns.Calculatethespeedoftheparticle.

7.Amesonis10·0kmabovetheEarth’ssurfaceandismovingtowardstheEarthataspeedof0·999c.

(a)Calculatethedistance,accordingtothemeson,travelledbeforeitstrikestheEarth.

(b)Calculatethetimetaken,accordingtothemeson,forittotraveltothesurfaceoftheEarth.

8.The star AlphaCentauriis4·2lightyearsawayfromtheEarth.AspacecraftissentfromtheEarthtoAlphaCentauri.Thedistancetravelled,asmeasuredbythespacecraft,is3·6lightyears.

(a)CalculatethespeedofthespacecraftrelativetotheEarth.

(b)Calculatethetimetaken,inseconds,forthespacecrafttoreachAlphaCentauriasmeasuredbyanobserverontheEarth.

(c)Calculatethetimetaken,inseconds,forthespacecrafttoreachAlphaCentauriasmeasuredbyaclockonthespacecraft.

9.Muons,whenatrest,haveameanlifetimeof2·60×108s.Muonsareproduced10kmabovetheEarth.Theymovewithaspeedof0·995ctowardsthesurfaceoftheEarth.

(a)CalculatethemeanlifetimeofthemovingmuonsasmeasuredbyanobserverontheEarth.

(b)CalculatethemeandistancetravelledbythemuonsasmeasuredbyanobserverontheEarth.

(c)Calculatethemeandistancetravelledbythemuonsasmeasuredbythemuons.

OUR DYNAMIC UNIVERSE (H, PHYSICS)1

SECTION 6: THE EXPANDING UNIVERSE

Section6:Theexpandinguniverse

TheDopplereffectandredshiftofgalaxies

Inthefollowingquestions,whenrequired,usetheapproximationforspeedofsoundinair=340ms1.

1.InthefollowingsentencesthewordsrepresentedbythelettersA,B,CandDaremissing:

Amovingsourceemitsasoundwithfrequencyfs.Whenthesourceismovingtowardsastationaryobserver,theobserverhearsa____A_____frequencyfo.Whenthesourceismovingawayfromastationaryobserver,theobserverhearsa____B_____frequencyfo.Thisisknownasthe_____C______D_____.

Matcheachletterwiththecorrectwordfromthelistbelow:

Dopplereffecthigherlouderlower

quietersofter

2.Writedowntheexpressionfortheobservedfrequencyfo,detectedwhenasourceofsoundwavesinairoffrequencyfsmoves:

(a)towardsastationaryobserverataconstantspeed,vs

(b)awayfromastationaryobserverataconstantspeed,vs.

3.Inthetableshown,calculatethevalueofeachmissingquantity(a)to(f),forasourceofsoundmovinginairrelativetoastationaryobserver.

Frequencyheardbystationaryobserver/Hz / Frequencyofsource/Hz / Speedofsourcemovingtowardsobserver/m s1 / Speedofsourcemovingawayfromobserver/m s1
(a) / 400 / 10 / –
(b) / 400 / – / 10
850 / (c) / 20 / –
1020 / (d) / – / 5
2125 / 2000 / (e) / –
170 / 200 / – / (f)

4.AgirltriesoutanexperimenttoillustratetheDopplereffectbyspinningabattery-operatedsirenaroundherhead.Thesirenemitssoundwaveswithafrequencyof1200Hz.

Describewhatwouldbeheardbyastationaryobserverstandingafewmetresaway.

5.Apolicecaremitssoundwaveswithafrequencyof1000Hzfromitssiren.Thecaristravellingat20ms1.

(a)Calculatethefrequencyheardbyastationaryobserverasthepolicecarmovestowardsher.

(b)Calculatethefrequencyheardbythesameobserverasthepolicecarmovesawayfromher.

6.Astudentisstandingonastationplatform.Atrainapproachingthestationsoundsitshornasitpassesthroughthestation.Thetrainistravellingataspeedof25ms1.Thehornhasafrequencyof200Hz.

(a)Calculatethefrequencyheardasthetrainisapproachingthestudent.

(b)Calculatethefrequencyheardasthetrainismovingawayfromthestudent.

7.Amanstandingatthesideoftheroadhearsthehornofanapproachingcar.Hehearsafrequencyof470Hz.Thehornonthecarhasafrequencyof450Hz.

Calculatethespeedofthecar.

8.Asourceofsoundemitswavesoffrequency500Hz.Thisisdetectedas540Hzbyastationaryobserverasthesourceofsoundapproaches.

Calculatethefrequencyofthesounddetectedasthesourcemovesawayfromthestationaryobserver.

9.Awhistleoffrequency540vibrationspersecondrotatesinacircleofradius0·75mwithaspeedof10ms1.Calculatethelowestandhighestfrequencyheardbyalistenersomedistanceawayatrestwithrespecttothecentreofthecircle.

10.Awomanisstandingatthesideofaroad.Alorry,movingat20ms1,soundsitshornasitispassingher.Thelorryismovingat20ms1andthehornhasafrequencyof300Hz.

(a)Calculatethewavelengthheardbythewomanwhenthelorryisapproachingher.

(b)Calculatethewavelengthheardbythewomanwhenthelorryismovingawayfromher.

11.Asirenemittingasoundoffrequency1000vibrationspersecondmovesawayfromyoutowardsthe base of a verticalcliffataspeedof10ms1.

(a)Calculatethefrequencyofthesoundyouhearcomingdirectlyfromthesiren.

(b)Calculatethefrequencyofthesoundyouhearreflectedfromthecliff.

12.Asoundsourcemovesawayfromastationarylistener.Thelistenerhearsafrequencythatis10%lowerthanthesourcefrequency.

Calculatethespeedofthesource.

13.Abatfliestowardsatreeataspeedof3·60ms1whileemittingsoundoffrequency350kHz.Amothisrestingonthetreedirectlyinfrontofthebat.

(a)Calculatethefrequencyofsoundheardbythebat.

(b)Thebatdecreasesitsspeedtowardsthetree.Doesthefrequencyofsoundheardbythemothincrease,decreaseorstaysthesame?Justifyyouranswer.

(c)Thebatnowfliesdirectlyawayfromthetreewithaspeedof

4·50ms1whileemittingthesamefrequencyofsound.

Calculatethenewfrequencyofsoundheardbythemoth.

14.Thesirenonapolicecarhasafrequencyof1500Hz.Thepolicecarismovingataconstantspeedof54kmh1.

(a)Showthatthepolicecarismovingat15ms1.

(b)Calculatethefrequencyheardwhenthecarismovingtowardsastationaryobserver.

(c)Calculatethefrequencyheardwhenthecarismovingawayfromastationaryobserver.

15.Asourceofsoundemitsasignalat600Hz.Thisisobservedas640Hzbyastationaryobserverasthesourceapproaches.

Calculatethespeedofthemovingsource.

16.Abattery-operatedsirenemitsaconstantnoteof2200Hz.Itisrotatedinacircleofradius0·8mat3·0revolutionspersecond.Astationaryobserver,standingsomedistanceaway,listenstothenotemadebythesiren.

(a)Showthatthesirenhasaconstantspeedof15·1ms1.

(b)Calculatetheminimumfrequencyheardbytheobserver.

(c)Calculatethemaximumfrequencyheardbytheobserver.

17.Youarestandingatthesideoftheroad.Anambulanceapproachesyouwithitssirenon.Astheambulanceapproaches,youhearafrequencyof460Hzandastheambulancemovesawayfromyou,afrequencyof

410Hz.Thenearesthospitalis3kmfromwhereyouarestanding.

Estimatethetimefortheambulancetoreachthehospital.Assumethattheambulancemaintainsaconstantspeedduringitsjourneytothehospital.

18.OntheplanetLts,anattramovestowardsastationaryndoat10ms1.Thenattraemitssoundwavesoffrequency1100Hz.Thestationaryndohearsafrequencyof1200Hz.

CalculatethespeedofsoundontheplanetLts.

19.InthefollowingsentencesthewordsrepresentedbythelettersA,B,C,DandEaremissing:

Ahydrogensourceoflightgivesoutanumberofemissionlines.Thewavelengthofoneoftheselinesismeasured.WhenthelightsourceisontheEarth,andatrest,thevalueofthiswavelengthisrest.Whenthesamehydrogenemissionlineisobserved,ontheEarth,inlightcomingfromadistantstarthevalueofthewavelengthisobserved.WhenastarismovingawayfromtheEarthobservedis____A_____thanrest.Thisisknownasthe____B_____shift.

WhenthedistantstarismovingtowardstheEarthobservedis____C_____thanrest.Thisisknownasthe____D_____shift.

Measurementsonmanystarsindicatethatmoststarsaremoving____E_____fromtheEarth.

Matcheachletterwiththecorrectwordfromthelistbelow:

awaybluelongerredshortertowards.

20.Inthetableshown,calculatethevalueofeachmissingquantity.

Fractionalchangeinwavelength,z / WavelengthoflightonEarthrest/nm / Wavelengthoflightobservedfromstar,observed/nm
(a) / 365 / 402
(b) / 434 / 456
8·00×102 / 486 / (c)
4·00×102 / 656 / (d)
5·00×102 / (e) / 456
1·00×101 / (f) / 402

Hubble’slaw

Inthefollowingquestions,whenrequired,usetheapproximationfor

Ho=2·4×1018s1

1.Convertthefollowingdistancesinlightyearsintodistancesinmetres.

(a)1lightyear

(b)50lightyears

(d)16,000,000,000lightyears

2.Convertthefollowingdistancesinmetresintodistancesinlightyears.

(a)ApproximatedistancefromtheEarthtoourSun=1·44×1011m.

(b)ApproximatedistancefromtheEarthtonextneareststarAlphaCentauri=3.97×1016m.

(c)ApproximatedistancefromtheEarthtoagalaxyintheconstellationofVirgo=4·91×1023m.

3.Inthetableshown,calculatethevalueofeachmissingquantity.

SpeedofgalaxyrelativetoEarth/m s1 / ApproximatedistancefromEarthtogalaxy/m / Fractionalchangeinwavelength,z
(a) / 7.10×1022 / (b)
(c) / 1.89×1024 / (d)
1·70×106 / (e) / (f)
2·21×106 / (g) / (h)

4.Lightfromadistantgalaxyisfoundtocontainthespectrallinesofhydrogen.Thelightcausingoneoftheselineshasameasuredwavelengthof466nm.WhenthesamelineisobservedfromahydrogensourceonEarthithasawavelengthof434nm.

(a)CalculatetheDopplershift,z,forthisgalaxy.

(b)CalculatethespeedatwhichthegalaxyismovingrelativetotheEarth.

(c)Inwhichdirection,towardsorawayfromtheEarth,isthegalaxymoving?

5.Lightofwavelength505nmformsalineinthespectrumofanelementonEarth.ThesamespectrumfromlightfromagalaxyinUrsaMajorshowsthislineshiftedtocorrespondtolightofwavelength530nm.

(a)CalculatethespeedthatthegalaxyismovingrelativetotheEarth.

(b)Calculatetheapproximatedistance,inmetres,thegalaxyisfromtheEarth.

6.AgalaxyismovingawayfromtheEarthataspeedof0·074c.

(a)Convert0·074cintoaspeedinms1.

(b)Calculatetheapproximatedistance,inmetres,ofthegalaxyfromtheEarth.

7.AdistantstaristravellingdirectlyawayfromtheEarthataspeedof2·4×107ms1.

(a)Calculatethevalueofzforthisstar.

(b)Ahydrogenlineinthespectrumoflightfromthisstarismeasuredtobe443nm.CalculatethewavelengthofthislinewhenitobservedfromahydrogensourceontheEarth.

8.Alineinthespectrumfromahydrogenatomhasawavelengthof489nmontheEarth.Thesamelineisobservedinthespectrumofadistantstarbutwithalongerwavelengthof538nm.

(a)Calculatethespeed,inms1,atwhichthestarismovingawayfromtheEarth.

(b)Calculatetheapproximatedistance,inmetresandinlightyears,ofthestarfromtheEarth.

9.ThegalaxyCoronaBorealisisapproximately1000millionlightyearsawayfromtheEarth.CalculatethespeedatwhichCoronaBorealisismovingawayfromtheEarth.

10.AgalaxyismovingawayfromtheEarthataspeedof3·0×107ms1.Thefrequencyofanemissionlinecomingfromthegalaxyismeasured.Thelightformingthesameemissionline,fromasourceonEarth,isobservedtohaveafrequencyof5·00×1014Hz.

(a)ShowthatthewavelengthofthelightcorrespondingtotheemissionlinefromthesourceontheEarthis6·00×107m.

(b)Calculatethefrequencyofthelightformingtheemissionlinecomingfromthegalaxy.

11.AdistantquasarismovingawayfromtheEarth.Hydrogenlinesareobservedcomingfromthisquasar.Oneoftheselinesismeasuredtobe20nmlongerthanthesameline,ofwavelength486nmfromasourceonEarth.

(a)CalculatethespeedatwhichthequasarismovingawayfromtheEarth.

(b)Calculatetheapproximatedistance,inmillionsoflightyears,thatthequasarisfromtheEarth.

12.Ahydrogensource,whenviewedontheEarth,emitsaredemissionlineofwavelength656nm.Observations,forthesamelineinthespectrumoflightfromadistantstar,giveawavelengthof660nm.CalculatethespeedofthestarrelativetotheEarth.

13.DuetotherotationoftheSun,lightwavesreceivedfromoppositeendsofadiameterontheSunshowequalbutoppositeDopplershifts.TherelativespeedofrotationofapointontheendofadiameteroftheSunrelativetotheEarthis2kms1.Calculatethewavelengthshiftforahydrogenlineofwavelength486·1nmontheEarth.

OUR DYNAMIC UNIVERSE (H, PHYSICS)1

SECTION 7: BIG BANG THEORY

Section7:BigBangtheory

1.Thegraphsbelowareobtainedbymeasuringtheenergyemittedatdifferentwavelengthsfromanobjectatdifferenttemperatures.

(a)Whichpartofthex-axis,PorQ,correspondstoultravioletradiation?

(b)Whatdothegraphsshowhappenstotheamountofenergyemittedatacertainwavelengthasthetemperatureoftheobjectincreases?

(c)Whatdothegraphsshowhappenstothetotalenergyradiatedbytheobjectasitstemperatureincreases?

(d)Eachgraphshowsthatthereisawavelengthmaxatwhichthemaximumamountofenergyisemitted.

(i)Explainwhythevalueofmaxdecreasesasthetemperatureoftheobjectincreases.

Thetableshowsthevaluesofmaxatdifferenttemperaturesoftheobject.

Temperature/K / max/m
6000 / 4·8×107
5000 / 5·8×107
4000 / 73×107
3000 / 9·7×107

(ii)UsethisdatatodeterminetherelationshipbetweentemperatureTandmax.

(e)Useyouranswerto(d)(ii)tocalculate:

(i)thetemperatureofthestarSiriuswheremaxis2·7×107m

(ii)thevalueofmaxforthestarAlphaCruciswhichhasatemperatureof23,000K

(iii)thetemperatureofthepresentuniversewhenmaxforthecosmicmicrowaveradiationismeasuredas1·1×103m.

(iv)theapproximatewavelengthandtypeoftheradiationemittedbyyourskin,assumedtobeatatemperatureof33oC.

OUR DYNAMIC UNIVERSE (H, PHYSICS)1

SOLUTIONS

Solutions

Revisionproblems–Speed

2.6·8ms1

3.1·4×1011m

4.181minutes

5.(a)5ms1

(b)35m

(d)100m

(e)135m

6.750ms1

75s

8.2s¶

Revisionproblems–Acceleration

1.(a)2ms2

(b)6s

2.(a)2·0ms2

(b)24ms1

3.0·20ms2

Revisionproblems–Vectors

1.(a)80km

(b)40kmh1

(d)10kmh1north

2.(a)70m

(b)50mbearing037

(c)(i)70s

(ii)0·71 ms1bearing037

3.(a)6·8Nbearing077

(b)11·3Nbearing045

5.Averagespeed=11kmh1

Averagevelocity=5kmh1bearing233

6.(a)5·1ms1

(b)14·1ms1

Section1:Equationsofmotion

Equationsofmotion

1.280m

2.51·2m

3.28ms1

4.16·7s

5.3·0s

6.(a)750ms2

(b)0·04s

7.9·5ms2orNkg1¶

8.(a)0·21ms2

(b)1·4s

9.234m

10.(a)(i)21·4m

(ii)15·6ms1downwards

(b)34·6m¶

Motion–timegraphs

1.(a)2ms1duenorth

(b)0ms1

(d)0·75ms1

2.(a)4ms1duenorth

(b)1·0ms1duesouth

(d)1·6ms1

(f)displacement2mduenorth,velocity4ms1duenorth

(g)displacement2mduenorth,velocity1ms1duesouth¶

3.(a)1ms1duenorth

(b)2ms1duesouth

(d)1ms1

(f)displacement0·5mduenorth,velocity 1ms1duenorth

(g)displacement0,velocity2ms1duesouth

4.(a)2ms2duenorth

(b)0ms2

(d)32mduenorth¶

5.(a)1ms2duenorth

(b)2ms2duesouth

(d)displacement3mduenorth,velocity 0ms1

(e)displacement2mduenorth,velocity 2ms1duesouth

6.(a)(i)17·5mduenorth

(ii)22·5mduenorth

(iii)17·5mduenorth

9.D.Notethatinthisquestion,downwardsistakentobethepositivedirectionforvectors.

10.A.Notethatinthisquestion,upwardsistakentobethepositivedirectionforvectors.

Section2:Forces,energyandpower

Balancedandunbalancedforces

2.4900N

3.(a)(i)1·5×102ms2

(ii)3·0×106N

(b)–2·7×103ms2

5.0·02ms2

6.150N¶

7.(a)120N

(b)20N¶

8.(a)1200N

(b)108m

9.(a)(ii)7·7ms2

10.(a)1·78×103kg

(b)6·24×104N¶

11.2·86×104N

12.(a)1·96×103N

(b)2.26×103N

(d)1.66×103N¶

13.(a)(i)2·45×103N

(ii)2·45×103N

(iii)2·95×103N

(iv)1·95×103N

(b)4·2ms2¶

14.51·2N

15.(b)0·4sreading37·2N

4sto10sreading39·2N

10sto12sreading43·2N

16.(a)8ms2

(b)16N

17.(a)5·1×103N

(b)2·5×103N

(c)(i)700N

(ii)500N

(d)1·03×104N

18.24m

19.(a)(i)2ms2

(ii)40N

(iii)20N

(b)(i)12N¶

20.(a)3·27ms2

(b)6·54N

Resolutionofforces

1.(a)43·3N

2.353·6N

3.(a)8·7N

(b)43·5ms2

4.0·513ms2

5.(a)226N

(b)0·371ms2¶

6.9·8Nuptheslope

7.0·735N

8.(a)2283N

(b)2·2ms2

9.(a)(ii)18Ndowntheslope

(iii)9ms2downtheslope

(b)(i)16Ndowntheslope

(ii)8ms2downtheslope

Workdone,kineticandpotentialenergy

1.(a)3·92J

(b)8·9ms1

2.(a)1080J

(b)120J¶

3.(a)9·8J

(b)(i)3·1ms1

4.(a)490N

(b)9·8×103J

5.3·0×105W¶

6.(a)330N

(b)2·0×103s

Section3:Collisionsandexplosions

1.(a)20kgms1totheright

(b)500kgms1downwards

2.(a)0·75ms1inthedirectioninwhichthefirsttrolleywasmoving

3.2·4ms1

4.3·0kg

5.(a)2·7ms1

(b)0·19J

6.8·6ms1intheoriginaldirectionoftravel

7.(a)23ms1

8.8·7ms1

9.0·6ms1intheoriginaldirectionoftravelofthe1·2kgtrolley¶

10.16·7ms1intheoppositedirectiontothefirstpiece

11.4kg

12.0·8ms1intheoppositedirectiontothevelocityoftheman¶

13.1·3ms1intheoppositedirectiontothevelocityofthefirsttrolley¶

14.1·58ms1

15.100N

16.3·0×102s

17.2·67ms1¶

18(a)+0·39kgms1ifyouhavechosenupwardsdirectionstobepositive; –0·39kgms1ifyouhavechosendownwardsdirectionstobepositive

(b)+0·39Nsifyouhavechosenupwardsdirectionstobepositive

(d)15·6Nupwards

(e)16·6Nupwards¶

19.(a)vbefore=3·96ms1downwards;vafter=2·97ms1upwards

(b)9·9×102s

20.(b)0·2s

(d)4·0J

21.1·25×103Ntowardsthewall¶

22.9·0×104N

24.(a)(i)4·0ms1inthedirectionthe2·0kgtrolleywastravelling

(ii)4·0kgms1inthedirectionthe2·0kgtrolleywastravelling

(iii)4·0kgms1intheoppositedirectionthe2·0kgtrolleywastravelling

(b)8·0N

Section4:Gravitation

Projectiles

1.(a)7·8s

(b)2730m

2.(a)5·0s

(b)123m

3.(b)24·7ms1atanangleof52.6ºbelowthehorizontal

4.(a)vhoriz=5·1ms1,vvert=14·1ms1

5.(b)50ms1at36.9ºabovethehorizontal

(d)45m

(e)240m

6.(a)20ms1

(b)20.4m

(d)142m

7.(a)8s

(b)379m

8.(a)15·6ms1

12.2s

Gravityandmass

1.F=

3.2·67×104N

4.3·61×1047N

5.3·53×1022N

6.4·00×1015m

Section5:Specialrelativity

Relativity–Fundamentalprinciples

1.(a)1·0ms1north

(b)2·0ms1south

2.(a)0·8ms1east

(b)2·8ms1east

3.(a)3·0ms1

(b)2·0ms1

4.A=Einstein’s;B=same;C=zero;D=velocity;E=speedoflight;F=slow;G=shortened

5.2000kmh1

6.(a)No

(b)Yes

7.3×108ms1

8.(a)100s

(b)100s

9.(a)3×108ms1

(b)3×108ms1

10.(a)0·3×108ms1

(b)1·5×108ms1

(d)2·4×108ms1

11.(a)c

(b)0·67c

(d)0·33c

Relativity–Timedilation

2.(a)21·2h

(b)15·1year

(d)1·32×104s

(e)2·10×108ms1

(f)9·15×107ms1

3.(a)11.20am

(b)11.20am

4.17·1billionyears

5.9·69s

6.3·9×104s

7.2·1×108ms1or0·70c

8.2·90108ms1or0·97c

9.2·60×108ms1

Relativity–Lengthcontraction

1.l’=l(1–v2/c2)

2.(a)4·71m

(b)11·2m

(d)160mm

(e)1·55×108ms1

(f)1·25×108ms1

3.16m

4.0·872m

5.267m

6.0·92km

7.2·60×108ms1

8.2·19×108ms1

9.4·23×107ms1or0.14c

Relativityquestions

1.(b)144m

2.(a)0·31ofayear

3.(a)1·84×107s

(b)54·6mor54·7m

4.(a)120m

(b)72m

5.(a)5s

(b)9·22s

6.0·8c

7.(a)447m

(b)1·49×106s

8.(a)0·52c

(b)2·55×108s

9.(a)2·60×107s

(b)77·6m

Section6:Theexpandinguniverse

TheDopplereffectandredshiftofgalaxies

1.A=higher;B=lower;C=Doppler;D=effect

2.(a)

(b)

3.(a)412Hz

(b)389Hz

(d)1035Hz

(e)20ms1

(f)60ms1

5.(a)1063Hz

(b)944Hz

6.(a)216Hz

(b)186Hz

7.14·5ms1

8.466Hz

9.556Hz,525Hz

10.(a)1·07m

(b)1·2m

11.(a)971Hz

(b)1030Hz

12.37·8ms1

13.(a)354kHz

(b)Decrease–denominatorislarger

14.(b)1569Hz

15.21·3ms1

16.(b)2106Hz

17.154s

18.120ms1

19.A=longer;B=red;C=shorter;D=blue;E=away

20.(a)1·01×101

(b)5·07×102

(d)682nm

(e)434nm

(f)365nm

Hubble’slaw

1.(a)9·46×1015m

(b)4·73×1017m

(d)1·51×1026m

2.(a)1·52×105lightyears

(b)4·2lightyears

v/m s1 / d/m / z
1·70×105 / 7·10×1022 / 5·67×104
4·54×106 / 1·89×1024 / 1·51×102
1·70×106 / 7·08×1023 / 5·667×102
2·21×106 / 9·21×1023 / 7·37×103

4.(a)7·37×102

(b)2·21×107ms1

(c)Away

5.(a)1·49×107ms1

(b)6·21×1024m

6.(a)2·22×107ms1

(b)9·25×1024m

7.(a)8×102

(b)410nm

8.(a)3·0×107ms1

(b)1·25×1025m,1·32×109lightyears

9.2·27×107ms1

10.(b)4·55×1014Hz

11.(a)1·23×107ms1

(b)542millionlightyears

12.1·83×106ms1

13.3·24×1012m

Section7:BigBangtheory

1.(a)P

(b)Energyemittedincreases

(c)Increases

(d)(ii)Tmax=2·9×103mK

(e)(i)T=11,000K

(ii)max=1·3×107m

(iii)T=2·6K

(iv)=9·5×106m,infrared

OUR DYNAMIC UNIVERSE (H, PHYSICS)1