physics as - unit 2 - revision notes
TRANSCRIPT
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PhysicsAS-Unit2-Mechanics,MaterialsandWaves-RevisionNotesMechanics
ScalarandVectorQuantities DefinitionAVectorQuantityhasmagnitudeaswellasdirectionwhileascalar
quantityonlyhadmagnitude
ScalarDistance,Speed,Mass VectorsDisplacement,Velocity,Acceleration
Resultant
Pythagoras- a = b2+ c
2
Note:whenyouknowtheresultantanddrawingthehorizontalandverticalcomponentdraw
bothofthecomponentsfromthesamepointthattheresultantstartsfrom(resultantshouldbe
in-between2components)
ResolutionOfVectors Resolvesvectorintohorizontalandverticalcomponents.
x= acos y = asin
BalancedForces Ifanobjectisinequilibriumthetwoforcesactinguponapointareequalandoppositeto
eachotherandthesumoftheanticlockwisemoments=thesumoftheclockwise
moments.Noresultantforceacting.
Equilibrium3forces2oftheforces(resultant)areequalandoppositetothethirdforce,thereisnoresultantforceacting.Canalsobedrawninaclosedtriangle.
Tocalculateandunknownforceorforcesresolveeachhorizontallyandverticallyandsolve,
ifobjectisinequilibriumthereisnoresultantforce!
a b
a+b
ParallelogramMethod
a
x
y
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Moments DefinitionThemomentofaforceaboutapointisequaltotheforcemultipliedby
theperpendiculardistancebetweenthelineofaction(offorce)andthepivot
(placetakingmomentabout)
Theprincipleofmomentsstatesthatforanobjecttobeinequilibriumthesumoftheanticlockwisemomentsmustequalthesumoftheclockwisemomentsatanypoint.
TwoSupportProblems Ifcenterofmassofbeamismidwaybetweenbothsupportstheforceeachsupport
exertsisequal.
Ifnot:o TakemomentsaboutS1tocalculateS2toworkoutS1orviceversa
Couples DefinitionAcoupleispairofequalandoppositeparallelforcesactingonabody
butnotatthesamepoint.
TheturningeffectofacoupleofequalandoppositeforcesisequaltoOneoftheforcesmultipliedbytheperpendiculardistancebetweenthetwoforces.
MotionAlongaStraightLine
DisplacementTimeGraphs
Gradient=VelocityVelocityTimeGraphs
Gradient=Acceleration AreaUnderneath=Displacement(ifvelocityisalways+)
ConstantAccelerationFormulas
S= ut+ 12
at2
S= 12(u+ v)t
v = u+ at v2 = u2 +2as
WhereV=finalvelocity,S=displacement,U=initialvelocity,T=time
RememberAccelerationisms-2
Whencalculatingdistancecoveredwhensomethingisacceleratingandstartingvelocityisnot0useformulas!!
IFEVERASKSFORDECELERATIONNEVERUSEAMINUSSIGNISITISSLOWINGDOWN!
ProjectileMotion
Accelerationduetogravity=9.81ms-2 Resolvehorizontallyandvertically Gravityonlyeffectstheverticalcomponentofmotion
NewtonsFirstLawOfMotion Objectsstayatrestorremaininuniformmotionunlessacteduponmyanexternal
force
Sobasicallyifanobjectismovingandnothingisactinguponit(e.gairresistance)theobjectwillcarryongoingforever,thishappensinspaceasnoairresistance
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NewtonsSecondLawofMotion Theforceappliestoanobjectisproportionaltothemassandtheaccelerationof
theobjectasaresultofthebeingapplied
F=ma If2forcesareactingupontheobjectitistheresultantforcethatisusedinthisequation-
F1F
2ifF
1isbiggerthanF
2
Witharocketthatistravellingdirectlyupwardstheobjecthastoovercomeitsownweight(mg )inordertoacceleratesoFmg =ma
Withalifto Ifmovingataconstantspeedupwards F=mg o Ifmovingupwardsandaccelerating F=mg+ma >mg o Ifliftmovingupanddecelerating F=mg+ma mg
o Ifmovingdownwardsanddecelerating F=mg+ma
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MeasuredinJoules
KineticEnergy
Ek =1
2mv
2
GravitationalPotentialEnergy
Eg =mgh Asanobjectofmassmisreleasedabovetheground,itgravitationalpotentialenergyis
convertedintokineticenergyastheheightabovegrounddecreasesas Eg =mgh ,inreality
thisisnotstrictlytrueassomegravitationalpotentialisconvertedintoworkagainstAir
resistanceandsomelostasheatandsound.
PendulumBob
ifreleasedfromheight hithenatanypointwheretheheightish
vthespeedofthebob
issuchthatKineticenergyatthatpoint=lossingravitationalpotential(ignoringalloverexternalforces)
1
2mv
2=mg(hi hf )
Power PowerRateoftransferofenergymeasuredinWatts
p =E
tp =
W
tp = fv
WhereE=Energy,W=Workandt=time Power=forcexvelocityasitstherateworkisdonepersecondasitsforcemultipliedby
distancemovedeachsecond
Efficiency
=
=
Sobasicallyefficiencyisoutputpoweroverinputpower
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Materials
Density DensityAmaterialsmassperunitvolume
p =m
v
Massofalloy,m = pava + pbvb andthedensityofthatalloy p = mv=
pava + pbvb
m
Springs
HookesLaw
HookesLawTheextensionofaspringisproportionaltotheforceappliedtoitaslongasthelimitofproportionalityisnotexceeded
F= kl (wherekisthespringconstant)
ElasticLimitMaximumstressthatcanbeappliedtoamaterialwithoutelasticbehavioroccurringdeformation
Note:ElasticlimitmaybedifferenttoLimitofProportionality
YieldPointApointisreachedatwhichnoticeablylargerchangeinlengthduetoforce BreakingStress/UltimateTensileStress moststressamaterialcanwithhold
withoutbreaking
BrittlenessMaterialsthatcantextendwithoutbreakingaresaidtobebrittlehoweverbrittlematerialsarestrongincompressionandusedinbuildingwherecompressionis
constant.
Springsinparallel- K= K1 +K2 wherekistheeffectivespringconstant Springsinseries- 1
K=
1
K1
+
1
K2
Inordertocompare2differentmaterialselasticpropertiesuseyoungsmodulus
YoungsModulus
YoungsModulusStiffnessconstantofmaterial TensileStress=forceperunitarea= f
ameasuredinNm-2
TensileStrain=ratiooforiginallengthandextension= LL
NOUNITS
ThisisdeltaLasinchangeinLsofinal-initial E=
=
Stress
StrainYoungsmodulushasunitsNm-2orPascal(Pa)
E=FL
AL
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ExperimentaldeterminationofYoungsModulusOfaMaterial
Twoidenticalwiresarefixedinparallel Bothwiresinitiallyloadedtoremovekinks/strengthenknots Micrometeradjustedtomakespritlevelhorizontal Initialmicrometerreadingtaken Meterrulermeasureoriginallengthofwirel(oneunder
test) Secondmicrometerusedtomeasurediameterofwirein
severalplacestoimproveaccuracy
Calculateareabyusing r2 (halfdtogiver) Testwireloadedwithmassandmicrometeradjustedtolevel
spritlevel
Micrometerreadingtakenandextensioncalculatedbyfinalmicrometerinitial
Furtherloadsareaddedandrepeateduntilrangeobtained Unloadsecondset Graphofforceagainstextension Gradientcalculatedusingbigtriangle
y2 y
1
x2 x
1
Asgradient= FL
andY =FL
ALYcanbecalculatedbygradientmultipliedby
y =GradientL
A
AccuracyImproved
Longthinwiregiveslargeextensionperunitforcethereforpercentageuncertaintydecreases
Controlwireusedsotemperaturechangesdonotimpactresults Measurediameterinseveralplacestogiveaverage Largetriangle/rangeusedtocalculategradient
LoadingandUnloading
IfelasticlimitisreachedtheunloadingcurvewillnothavesamevalueasloadingcurveatF=0ithasbeenmisshapedmetalextended
= Asloadingarea=workdoneandunloadingarea=energygivenback Rememberwhencountingsquarestocalculateworkdonethateachsquareisworth
whateverthesquarerepresentsverticallymultipliedbywhateveritrepresents
horizontally
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Waves
ProgressiveWavesWaveswhoseoscillationstravelanddonotstayaboutafixedpoint,thistypeofwavestransfersenergy
FrequencyNumberofwavecyclesthatoccurinonesecondmeasuredinHz Amplitude-Maximumdisplacementofavibratingparticlefromequilibrium WavelengthDistancebetween2adjacentpoints/particlesinphaseinawave Periodtimeforonecompletewavetopassafixedpointinspace
P =1
f
TransverseWavesWaveswhoseoscillations/vibrationsareperpendiculartothedirectionoftravel(lightetc.)
LongitudinalWaves Waveswhoseoscillations/vibrationareinthesamedirectionoftravel(sound)Note:Soundwavespropagateasaaseriesofcompressionsandrarefactions
WaveSpeedSpeedofthewavesisequaltodistancetraveledbywaveinonecycledividedbytimetakenforonecycle
C=
1f
Therefor c = f
Path/PhaseDifference
2pointsareinphaseiftheyareawholewavelengthapart(maxdisplacementatsametime)-thereoscillationsareintimewitheachother
2PointsareinAntiphaseiftheyarehalfawavelengthapart(onemaxdisplacementwhileotherexperiencesmindisplacement)
PhaseDifference
= 2x1 x
2
"
#$
%
&' (inradians)OR= 360
x1 x
2
"
#$
%
&' indegrees
note:x1-x2isthedistancebetweenthetwopoints
PathDifference
Between2differentsourcesthephasedifferencebetweenthe2wavesthentheyconvergeis:
= 360S1P S
2P
"
#$
%
&'
note:whereS1Pisthedistancefromsource1tothepoint
wherethe2wavesconverge
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Polarization
PolarizationWhenoscillationsoftheelectricfieldofanE.Mwavearerestrictedtoonlyoneplane/directionthewaveissaidtobepolarized
Application Polaroid sunglasses reduce glare from water as the light is partiallypolarizedwhen reflected offwater thus theintensityof the light can bereduced This
reducesglare
Reflection Angleofincidenceisthesameasangleofreflection
i = r
StationaryWaves
Superposition
When2similarwavesofsimilarfrequencymeettheirresultantdependsupontheiramplitudeandtheirrelativephasedifference
o Ifnophasedifferenceanglethenconstructiveinterferenceoccurso If180degreesdifferenceanglethendestructiveinterferenceoccursandwaves
canceloutatthatpoint
PrincipleOfSuperpositionStatesthattheresultantdisplacementcausedby2wavesarrivingatapointisthevectorsumofthe2displacementscausedbyeachwavesatthat
instant
StationaryWavesFormation
Formedwhen2continuouswavestravellinginoppositedirectionsofsamefrequencysuperimposeto
formnodisplacement(nodes-completedestructive)
andpointsofmaxdisplacement(antinodescomplete
constructiveinterference) StationaryWaveFixedpatternofvibrationwhere
noenergyistransferredalongthewave
Nodeparticle/pointwithzerodisplacementnoamplitude
AntinodePoint/particlewithmaxdisplacement/amplitude
Thephasedifferencebetween2particles/pointsonstandingwave(thatisthedifferencewhenoneisat
maxdisplacementandotheronealsois,indegrees)is
zeroifthepoints/particlesarebetweenadjacentnodesorseparatedbyevennumberofnodesor180
degreesiftheyareseparatedbyanoddnumberof
nodes.
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FundamentalFrequencies
Distancebetween2AdjacentNodes= 2
(asfrom
nodetonode=halfawavelengthofoneofthe
continuouswavesthatformedstationarywaveseen
indiagram) Asseenindiagramthefirstfundamentalthatiswhen
thereisonestandingwave(1anti-node1node)the
lengthishalfofthewavelength
= 2L
Using c = f
Wefind: f0=
c
2l
(wherecisspeedofpropagationofwaves)
Henceatthesecondharmonicorfirstovertone := L o Hence: f
1=
c
l
Furthermoreatthethirdharmonicorsecondovertone: = 23L
o Hence: f2=
c
23
l
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Refraction RefractionChangeofdirectionofawavewhenitpropagatesthroughadifferent
medium
Speedoflightinairis3.00106 howeverwhenitentersmoreopticallydensemediumitreducesspeed
Sowhenlightentersamoreopticallydensemediumitsspeeddecreasesanditsdirectionchangesmoretowardsthenormal As c = f andthespeedoflightisreducedinmoreopticallydensemediumthe
wavelengthoflightchanges(makessensereallythefrequencycantsuddenlychange!)AbsoluteRefractiveindex
=
note:asthespeedofdifferentfrequencyoflightisnotthesameinagivenmedium(duetothefactthe
propagationdirectionchangestoadifferentdegreeforeachfrequency)togiveabsoluterefractiveindex
Yellowlightfromasodiumbulbisusedasastandard
SometypicalR.Is
Diamond2.4
Perspex1.5 Air1
Ice1.31
RefractiveIndexbetween2materials
=
!!
Iflightfromonemedium1tomedium2isNthenlightfrom2to1is1/NSnellsLaw
n1sin
1= n
2sin
2
OR
sin1
sin2
=
n2
n1
=
c1
c2
=1
2
Notewherenistheabsoluterefractiveindexofacertainmedium
and1istheangleofincidenceand2istheangleofrefraction
TotalInternalReflection
Ifangleofincidenceissolargeandthelightismovingfromamoredensetolessdensemedium(hencepropagationdirectionchangingawayfromnormal)theangleof
incidencewillbelargerthan90andsubsequentlythelightdoesnotexitbutisreflected
backintomedium
Theanglethatthishappensatthatistheangleatwhichlightisreflectedat90tothenormal(
2=90)iscalledthecriticalangleandusually
denotedby i
sini
sin90=
n1
n2
andassin90=1:sin i =
n2
n1
Thisishowfiberopticcableswork:
CladdingInFiberOpticCables o
Improvetensilestrengthofthecableasthecorehastobeverythin.o Increasethecriticalangleneededfortotalinternalreflection:hencereducing
themultipathdispersion(mergingofsignalsoflightdownacable)
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o Stopscorebeingscratchedasscratchescauselighttobedispersedifithitsthescratch
o Improvessecurityaswithoutcladdinglightwouldbeabletotravelbetweenfibers,aswithcladdingtotalinternalreflectionoccursandlightcannottravelbetweenfibershoweverwithoutcladdinglightwouldbefreetotravelbetween
mediansofsimilaropticaldensity(coretocore)
UsedinInternetbroadbandtodeliverfastinternetconnectiontohouseholds.
Interference When2similarwavesmeetatapoint,bytheprincipleofsuperpositionthecombined
displacementisfoundbythevectorsumofthe2displacementsofeachwaveatthat
point,iftheyarriveexactlyinphasethewaveswillconstructivelyinterferetoforma
doubleheightwave,ifexactlyoutofphase(180degrees)theywilladdtogetherdestructivelyandcancel
Inordertoviewasteadyinterferencepatternthewavesourceshavetobecoherent CoherentConstantphaserelationshipandsamefrequency Thepatternweseewilldependuponthephasedifferenceofthe2sourceswhentheyhit
thatpoint
AbrightfringeWhenthewavesconstructivelyinterfere,occurswhenpathdifference= n
AdarkfringeWhenthewavesdestructivelyinterfere,occurswhenpathdifference= (n+
1
2)asthewaveshavetobe180degreesoutofphase
Two-Slitinterferencepatterns(YoungsSlits)
Singleslitdiffractionspreadsoutonewaveandcausesittoactas2coherentsourcesfor2furtherslits.
Showedevidenceforwavetheoryoflight Lightbandsoccurwheneverthepathdifference
betweenthelightwavesareawholenumberof
wavelengths(anddarkwhenhalfnumber) Thedistancebetweentwosuccessivemaximaw
dependsupon:
o Thedistancebetweenthe2slits;increasingSmakesfringesclosertogether(orwsmaller)
o Thewavelengthoflight,Wissmalleratsmallerwavelengthso DistanceDbetweentheslitsandthescreen,ifDincreaseWincreases.
w =D
s Alsocanuselaser
o Laserlightmonochromatico LaserlightIscoherent(constantphaserelationshipsameHz)o Highlydirectionalverylittledivergence
PatternMaximaSimilarintensityandsamewidthascentralfringe Diffraction
WhenwavespassthroughagaporaroundanobstaclethewavesspreadoutthisiscalledDiffraction
Whentheslitwidthisthesameasthewavelengthperfectdiffractionoccurs Whenslitislargethanwavelengthlessdiffractionoccurs
SingleSlitDiffractionPattern
Centralmaximumistwiceaswideastheothers
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Restofthefringesdecreaseslightlyinintensityaswayfromthemiddle(samewidth)
Maximaoccurswithconstructiveinterferenceandzerointensitywithdestructiveinterference
Ifgapgetssmallerofdistancebetweenscreenandslitincreasessodoeswidthofmaxima
Centralmaximagetslargerifwavelengthislongerorthegapissmaller
DiffractionGrating
Seriesofuniformnarrowslitsinparallel dsin= n
Whered=thedistancefromcentertocenterofadjacentslits(N=1/dtoworkoutdifyouonlyhavenumberofslitsinsayameter) istheangleoftheorderyouaretryingto
calculate,nistheordernumbertryingtocalculate12or3etc.
Fractionsofadegreeusuallyexpressedinminutes Tofindmaxnumberofordersubstitute for90(thereforsin=1)anduseequation Application:Spectrometer
o Usescollimatortoproduceparallellightandthenusesdiffractiongratingtoproducespectrumpattern
o Usesamplelightfromexcitinganatomtoproducepatternandanalysiscanbedoneonthis12
o AlwaysawhitelineattheZeroorderasallwavelengthsarriveinphaseatthispoint
o Theshorterthewavelengththeshortertheangleo Hencepatternscanbecomplicatedfirstorderredlightlinecanbecloseto
secondorderblue