Unit 5 physics

Unit5 –   – Physicsfrom Physicsfrom creationtocollapse Thermalenergy Investigaterecogniseandus Investigate recogniseandusetheexpression etheexpressionE=mcθ E=mcθ Specificheatcapacityisthequantityofenergyneededtoraisethe temperatureofmaterial,perkilogramperdegreerisein temperature.  Specific heat capaci acity can be calc alculate ated using ing this equation 

, Giving the c the units 

Measuringspecificheatcapacity: 1. Weighablockofaluminiumtofinditsmassmandthenplace itinthelagging. 2.  Add a small amount of cooking oil to ensure good thermal contactwhentheheaterandthermometerandinserted 3. Taketheinitialtemperatureoftheblock.Switchonthepower supply and start the stopwatch record the current and potentialdifference 4.  Afterthreeminutesswitchofthepowersupplyandrecordthe higheststeadytemperaturereached. 5. You can than find the specific heat capacity using the equation

Explaintheconceptofinternalenergyastherando Explaintheconceptofinterna lenergyastherandom m distributionofpotentialandk distributionof potentialandkineticenergyamo ineticenergyamongstmolecule ngstmolecules s 

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IngasthemoleculeshaveKineticenergyduetotheirrandom motion.Inadditionmoleculesthataremadefromtwoormore atomshavekineticenergyduetorotationandvibration. Inanidealgastheinternalenergyisentirelytherandomkinetic energyofitsmolecules

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Idealgasassumptions: first need to download it. 1. Theintermolecularforcesarenegligibleexceptincollision 2. Thatthecollisionsbetweenmoleculesandwiththewallare Cancel Download And Print elastic 3. Justbeforeacollisionmoleculeshavekineticenergythe closerthemoleculesgetthelargertherepulsiveforcesoK.E istransferredtopotentialenergyasaresultofworkbeing donetoovercomeresistiveforcesothemoleculeis temporarilystationary 4. Timespentincollisionis0comparedtotimespentoutof collision  Hotbodieshaveahigherconcentrationofinternalenergy comparedtocoldbodies.  Heatistherandominterchangeofenergybetweentwobodiesin thermalcontact.  Energycanbetransferredbetweentwobodiesintheformofwork irrespectiveoftemperaturedifference

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Explaintheconceptofabsolutezeroandhowth Explaintheconceptofabsolu tezeroandhowtheaverage eaverage kineticenergyofmoleculesisrela kineticenerg yofmoleculesisrelatedtotheabso tedtotheabsolute lute temperature  Atemperatureof0Kiscalledabsolutezerobecauseitisthelowest temperaturethatcantheoreticallybereached.  ItsvalueontheCelsiusscaleis-273.15degrees   Attemperaturescloseto0Kmatterexhibitsquantumeffe  Attemperaturescloseto0Kmatterexhibitsquantumeffectssuch ctssuch assuperconductivityandsuperfluidity   Asuperconductorisamaterialthatwillconductwithoutany resistancewhencooledtoacertaintemperature 

Thereisacatchtosuperconductors:alotofenergyisneededto maintainverylowtemperaturesandthisisnotalwaysideal. ForexamplethelargeHadroncolliderneeds96tonnesofliquid heliumtomaintainatemperatureof1.9Kwhichis-271degrees.

Recogniseandusetheexpression½m  Recogniseandusetheexpression½ m =3/2kT 2>=3/2kT 

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< >isth >isthem emean eansqu square aredan dandc dcan ancal calcul culate atedb dbysq ysquari uaring ngall allth the e speedsanddividebythenumberofspeeds. TistemperaturemeasuredinKelvin istheaverageKineticenergyofamolecule

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TheaverageKineticenergyofmoleculesisproportionaltothe first need to download it. absolutetemperatureofthegas Cancel

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UsetheexpressionpV= UsetheexpressionpV =NkT NkTastheequationofstateforan astheequationofstateforan idealgas Nisthenumberofmoleculesofgas  k= InvestigatingtherelationshipbetweenPressureandVolumeforafixed mass:  Thevolumeofafixedmassofairundertestcanbegivenbythe lengthofthetubexthecrosssectionalarea.Thereforeifthetube isuniformthenVisproportionaltoL  Thetotalpressurecanbereadoffthepressuregauge.  Openvalvesoairstartsatatmosphericpressurethenincreasethe pressureusingafootpump.  Recordpressureandvolume.   Allowairtoreachthermalequilibrium  Pisproportionalto1/V  PV=constantisBoyel’slaw InvestigatingtherelationshipbetweenPressureandTemperatureofa fixedmassofgasandaconstantvolume:  Startbyputtingiceinabeakertogetthetemperatureaslowas possible,atthistemperaturemeasurethepressureonthe pressuregaugeandrecordboth.  Increasethetemperatureby10degreeseachtimeandrecordthe correspondingpressureuntilboilingpointisreached.   Allowafewminutesbeforetakingresultstoallowanequilibrium temperaturetobereached. 

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Recallthattheconditionforsimpleharmonicmotioni Recallthattheconditionforsimple harmonicmotionis s F F==-kx  kx , , Cancel Download And Print andhenceidentifysituatio andhenceid entifysituationsinwhichsimp nsinwhichsimpleharmonicmotion leharmonicmotion willoccur Inoscillationthemotionisrepetitiveaboutafixedpositionwiththe objectatrestateitherextremesandhasmaximumspeedat midpoint  Foranoscillationtheforceactingontheoscillatingbodyand thereforeitsaccelerationmustbeproportionaltothedisplacement  Theforceandthereforeaccelerationalwaysactinopposite directionstowardstheequilibriumposition 

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 Anobjectwhosemotionsatisfiestheaboveconditionsissaidto haveSHM

Recogniseandusetheexpressionsa=- Recogniseandusetheexpressionsa =-ω 2x ,a ,a==- Aω 2cos 2cosωt  , v= v = Aωsinωt  , ,x x= = Acos  Acosωtand  T T=1/ =1/f f=2π/ =2π/ωasappliedtoa simpleharmonicoscillator 

Sinceforceisproportionaltoaccelerationwecanexpressionin termsof“a” whe where re is isth the eco cons nsta tan nt

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FindingthespringconstantofaspringfromHooke’slaw:  Suspenda100gmasshangerfromaverticalspring  Useasetsquareagainstameterruletomeasuretheinitialheight   Addextramassesin50gincrementsuntil300g.   Aftereachmassisaddedrecordtheextension  PlotagraphofFagainstXthegraphshouldbeastraightlineand thegradientwillbethespringconstant Findingthespringconstantusingsimpleharmonicmotion  Setupapparatussimilartothatforthepreviousexperiment.

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Thistimemeasurethetimetakenforthemassestomake10 first need to download it. oscillations  Tohelpjudgethestartandstopofanoscillationsputamarkerat Cancel Download And Print thecentreofanoscillation,e.g.apinsecuredtoaverticalruler usingbluetack 

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Plot Plota ag gra raph pho of f

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thi this ssh shou ould ldg giv ive ea ast stra raig ight htl lin ine e

throughtheorigin.Thegradientwillgiveyouthevalueofk Equationsofsimpleharmonicmotion:  Inperfectsimpleharmonicmotionthefrequencyofthe oscillationdoesnotdependontheamplitudeofoscillation  Ift=0atoneendofthemotionxatthattimewillbe=tothe  Amplitude.TheSolutionisequalto  Fortheaboveequationthegraphwillbeacosinegraph (displacement-time)thegradientofthiswillbethevelocity  Thevelocitycanthereforebefoundbydifferentiatingtheabove equation which will give us . This means that the velocitytimegraphlookslikeanegativesinewave 

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Obtainadisplacement –   – timegraphforanoscillatingobjectand timegraphforanoscillatingobjectand recognisethatthegradientat recognisetha tthegradientatapointgivesth apointgivesthevelocityatth evelocityatthat at point.  Acardisattachedtomassestogiveagoodreflectivesurface.  Dataloggersettorecordfor10secondsatasamplingrateof100 persecond.  Computercanbeprogramedtogivegraphsofdisplacement, velocityandaccelerationagainsttime. 

Rotarysensor   Apendulumisconnectedtoarotarysensor.Thismeasuresthe rotationalmotionandinthecaseofapendulumismeasuresthe angulardisplacement.

Recallthatthetotalenergyofanundammedsimp Recallthatthetotalenergy ofanundammedsimpleharmonic leharmonic systemremainsconstantandrecog systemremainscon stantandrecogniseanduseexpre niseanduseexpressions ssions fortotalenergyofanoscillator

 AsthependulumswingsthereisacontinuouschangeofKinetic energytoPotentialenergy.   AteitherextremestheKineticenergyis0andG.P.Eismax 

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Distinguishbetweenfree,dam Distinguish betweenfree,dampedandforced pedandforcedoscillations oscillations  A isonewheretherearenoexternalforcesacting ontheoscillatingsystemapartfromtheforcecausingthe oscillation  Theaboveisrarelyachievablebecausethereisairresistanceand otherfrictionalforces   Anoscillatingsystemdoesworkagainsttheexternalforcesacting onitandsousesupsomeofitsenergy.Thistransferofenergy fromthesystemtotheinternalenergyofthesurroundingsslows theoscillatingobjectdownuntiliteventuallydies.Thisisknownas .  -Whenanobjectisforcetovibratebyanother object,usuallyatthesamefrequencyasthevibratingsource. 

Investigateandrecallhowtheamplitudeofa Investigateandrecallhow theamplitudeofaforcedoscillati forcedoscillation on changesatandaroundthena changesatan daroundthenaturalfrequencyof turalfrequencyofasystemand asystemand describe,qualitatively,how describe,qua litatively,howdampingaffec dampingaffectsresonance tsresonance Investigatingdampedoscillations 

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Setupequipmentlikein diagram. InitiallyfindtheperiodTofthe pendulumwithoutthecupby measuring10oscillations twiceandthenfindingthe average Pullbackthependulumsthat theinitialamplitudeis1.00m Letgoandrecordthe amplitudeateachendofthe swing

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Theheavydensebobispulledbackandreleased Thispendu ndulum lumwi will llosc oscilla illate teat atit itnat natura uralfr lfrequ equenc ency y ,  Thispe determinedbyitslengthandgivenbytheequation 

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 Allotherlightpendulumsarecoupledtothisdiverpendulum byastringsotheywillexperienceaforcedoscillation=in frequencytothatofthedrivingpendulum  Pendulumsclosertothedrivingpendulumabsorbmore energybecausetherenaturalfrequencyisclosertothe naturalfrequencyofthedrivingpendulum.Theywilloscillate withlargeamplitudes  Oscillationsoflargeamplitudesiscalledresonance  Forasystemwilllittleornodampingtheresonantfrequency occursatthenaturalfrequency  Forasystemwhichhasbeendampedtheresonant frequencyislowerthanitsnaturalfrequency 

Explainhowdampingandtheplasticdeformat Explainhowdampingandthepl asticdeformationofductile ionofductile materialsreducetheamplitudeofoscillation 

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Dampingisimportantindesignsofmachinesandbuildingto preventunwantedvibrations Theshapeofthelatheisdesignedsothattheresonantfrequency isnowherenearthefrequencyoftherotationofalathe

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Latesttechnologyistocoatturbinebladeswithductilematerial.(A first need to download it. materialthatcanbeplasticallydeformedwithoutfracture)which meansthatitcanabsorbalotofenergy. Cancel Download And Print  Ifaductilematerialfeelsvibrationsitgoesthroughhysteresisloops eachvibration. 

 Astrophysicsandcosmology  Astrophysicsandcosmology UsetheexpressionF Usetheexpression F= =Gm  Gm 1m 2/r  2/r 2 2 

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Newtonproposedthateveryparticleintheuniverseattractsevery otherparticlewiththeForceF. Gisthegravitationalconstant M1M2istheproductofthemassesofthetwoparticlesandristhe distancebetweenthem

Deriveandusetheexpressiong=Deriveandusetheexpressiong =-Gm  Gm /r 2forthegravitational 2forthegravitational fieldduetoapointmass 

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Recallsimilaritiesanddifferencesbetweene Recallsimilaritiesanddifferen cesbetweenelectricand lectricand gravitationalfields Gravitational effects

Electrostatic effects

Fieldstrength

P.d.

Energyconservation

ForceLaws

RadialFields

Differences: 

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Gravitationalforceaffectsallparticleswithamass,but electrostaticforceonlyaffectsparticlewithcharge Gravitationalforceisalwaysattractivewhereaselectrostaticforce canbeattractiveorrepulsive Itisnotpossibletoshieldmassfromgravitationalfieldbutitis possibletoshieldachargefromanelectrostaticfield

Recogniseandusetheexpressionrelatingflux,l Recogniseandusetheexp ressionrelatingflux,luminosityand uminosityand distanceF distance F= =L L/4π /4πd  d 2applicationtostandardcandles 2applicationtostandardcandles 

Ilightyearisthedistancetravelledbylightinoneyear

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Luminosity,Lisusedtodescribethetotaloutputpowerofastar, unitsW Cancel Download And Print  Theelectromagneticwaveenergypersecondperunitareafroma starreachingusonearthiscalledtheradiationflux,F  Radiationfluxisalsoknownaslightintensity  FandLarelinkedbytheinversesquarelaw 

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Standardcandles  The problem with using

to measure the distance between

earthandastaristhatitistoofarsoitwon’texhibitparallax.   ACepheidstarchangeluminositywithtime  ThemaximumluminosityLofCepheidstarisrelatedtotheperiod Tofitsluminosityvariation  Supernovaexplosionscanbeusedasstandardcandlestofindthe distancetoevenmoredistantgalaxies

RecogniseanduseasimpleHertzsprung-Russelldi Recogniseanduseasimple Hertzsprung-Russelldiagramto agramto relateluminosityandtemperature relateluminos ityandtemperature.Usethisdiagramt .Usethisdiagramtoexplain oexplain thelifecycleofstars. 

TheHertzsprung-Russelldiagramisaplotofstellarluminosityand surfacetemperature

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Lifecycleofthestar

Onthehorizontal axisthe temperaturegoes fromHigh temperatureson thelefttolow temperatureson 

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Onceastarisformeditadoptsapositiononthemainsequence andspendsmostofitslifeatafairlyconstantsurfacetemperature Cancel Download And Print andluminosity  Moremassivestarsspendashortertimeonthemainsequence comparedtolessmassivestars 1. Itwasformedfromacloudofhydrogenandhelium 2. Itjoinedthemainsequenceabout5billionyearsagoanditwill leavethemainsequence5billionyearfromnow 3.  Afterleavingthemainsequenceitswillexpandandbecomea redgiantandafterlosingabout50%ofitsmassitwillbecomea whitedwarf 4. Itwillcoolslowlyforbillionsofyearsandeffectivelydie 

Massive stars

Supergiant

Supernova

Neutrino star or black hole

Birth of  stars in a dark cloud

Stars like our sun

Red Giant

White dwarf  Planetary nebula

Recogniseandusetheexpression:λmaxT Recogniseandusetheexpression:λ maxT=2.898x10-3mK =2.898x10-3mK (Wien’slaw)forblackbodyradiators Thesunisayellowstarbutstarsthatarehotterthanthesun appearwhite Wien’slawλmaxT=2.898x10-3mKtellsusthatλ λmaxandTare  Wien’slawλmaxT=2.898x10-3mKtellsusthat inverselyproportional  Onlyappliestoblackbodyradiators   Allstarsactasblackbodyradiatorswhichmeanstheyabsorbany electromagneticradiationfallingonthem 

Recogniseandusetheexpressionsz=Δλ/  λ≈Δ λ≈Δf   f  /f f≈ ≈v  v /c cforasourceofelectromagneticradiation forasourceofelectromagneticradiation   forobjectsatcosmologicaldistances movingrelativetoanobserverandv= v=H  H o odforobjectsatcosmologicaldistances d