Alevelphysics总结计划学习材料A1docWord格式.docx
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Distinctionbetweensystematicerrors(includingzeroerrors)andrandomerrorsandbetweenprecisionandaccuracy:
Randomerror:
isthetypeoferrorwhichcausesreadingstoscatteraboutthetruevalue.
Systematicerror:
isthetypeoferrorwhichcausesreadingstodeviateinonedirectionfromthetruevalue.
Precision:
referstothedegreeofagreement(scatter,spread)ofrepeated
measurementsofthesamequantity.{NB:
regardlessofwhetherornottheyarecorrect.}
Accuracy:
referstothedegreeofagreementbetweentheresultofameasurementandthetruevalueofthequantity.
Assesstheuncertaintyinaderivedquantitybysimpleadditionofactual,fractionalorpercentageuncertainties(arigorousstatisticaltreatmentisnotrequired).
Foraquantityx=(2.0
±
0.1)mm,
Actual/Absoluteuncertainty,
x=
0.1mm
Fractionaluncertainty,
xx=0.05
100%=5%Percentageuncertainty,
xx
Ifp=(2x+y)/3orp=(2x-
y)/3,
p=(2
x+
y)/3
Ifr=2xy3orr=2x/y
3,
r/r=
x/x+3
y/y
Actualerrormustberecordedtoonly
1significantfigure
&
Thenumberofdecimalplacesacalculatedquantityshouldhaveis
determinedbyitsactualerror.
Foreg,supposeghasbeeninitiallycalculatedtobe9.80645ms
-2&
g
hasbeeninitiallycalculatedtobe0.04848ms
-2.Thefinalvalueof
gmust
berecordedas0.05ms
-2
{1sf},andtheappropriaterecordingofgis
(9.81±
0.05)ms-2.
Distinctionbetweenscalarandvectorquantities
Representationofvectorastwoperpendicularcomponents:
Inthediagrambelow,XYrepresentsaflatkiteofweight4.0N.Atacertain
instant,XYisinclinedat30°
tothehorizontalandthewindexertsasteadyforceof6.0NatrightanglestoXYsothatthekitefliesfreely.
Kinematics
Displacement,speed,velocityandacceleration:
Distance:
Totallengthcoveredirrespectiveofthedirectionofmotion.
Displacement:
Distancemovedinacertaindirection.
Speed:
Distancetravelledperunittime.
Velocity:
isdefinedastherateofchangeofdisplacement,or,displacementperunittime
{NOT:
displacementovertime,nor,displacementpersecond,nor,rateofchangeofdisplacementperunittime}
Acceleration:
isdefinedastherateofchangeofvelocity.
Usinggraphstofinddisplacement,velocityandacceleration:
Theareaunderavelocity-timegraphisthechangeindisplacement.
Thegradientofadisplacement-timegraphisthe{instantaneous}velocity.
Thegradientofavelocity-timegraphistheacceleration.
The'
SUVAT'
EquationsofMotion
ThemostimportantwordforthischapterisSUVAT,whichstandsfor:
S(displacement),
U(initialvelocity),
V(finalvelocity),
A(acceleration)and
T(time)
ofaparticlethatisinmotion.
BelowisalistoftheequationsyouMUSTmemorise,eveniftheyareintheformulabook,memorisethemanyway,toensureyoucanimplementthemquickly.
1.v=u+at
2.s=?
(u+v)t
3.v2=u2+2as
4.s=ut+?
at2
derivedfromdefinitionofacceleration:
a=(v–u)/t
derivedfromtheareaunderthev-tgraphderivedfromequations
(1)and
(2)derivedfromequations
(1)and
(2)
Theseequationsapplyonlyifthemotiontakesplacealongastraightlineandtheaccelerationisconstant;
{hence,foreg.,airresistancemustbenegligible.}
Motionofbodiesfallinginauniformgravitationalfieldwithairresistance:
Considerabodymovinginauniformgravitationalfieldunder2differentconditions:
WithoutAirResistance:
Assumingnegligibleairresistance,whetherthebodyismovingup,oratthehighestpointormovingdown,theweightofthebody,W,istheonlyforceactingonit,causingittoexperienceaconstantacceleration.Thus,thegradientofthev-tgraphisconstantthroughoutitsriseandfall.Thebodyissaidtoundergofreefall.
WithAirResistance:
IfairresistanceisNOTnegligible
andifitisprojectedupwardswiththe
sameinitialvelocity,asthebodymovesupwards,bothairresistanceandweightactdownwards.Thusitsspeedwilldecreaseatarategreaterthan
9.81ms-2.Thiscausesthetimetakentoreachitsmaximumheightreachedtobelowerthaninthecasewithnoairresistance.Themaxheightreachedisalsoreduced.
Atthehighestpoint,thebodyismomentarilyatrest;
airresistancebecomeszeroandhencetheonlyforceactingonitistheweight.Theaccelerationisthus9.81ms-2atthispoint.
Asabodyfalls,airresistanceopposesitsweight.Thedownward
accelerationisthuslessthan9.81ms-2.Asairresistanceincreaseswithspeed,iteventuallyequalsitsweight(butinoppositedirection).Fromthentherewillbenoresultantforceactingonthebodyanditwillfallwitha
constantspeed,calledtheterminalvelocity.
Equationsforthehorizontalandverticalmotion:
ParabolicMotion:
tanθ=yv/vx
θ:
directionoftangentialvelocity{NOT:
tanyθ/s=xs}
Dynamics
Newton'
slawsofmotion:
sFirstLaw
Everybodycontinuesinastateofrestoruniformmotioninastraightlineunlessanet(external)forceactsonit.
sSecondLaw
Therateofchangeofmomentumofabodyisdirectlyproportionaltothenetforceactingonthebody,andthemomentumchangetakesplaceinthedirectionofthenetforce.
sThirdLaw
WhenobjectXexertsaforceonobjectY,objectYexertsaforceofthesametypethatisequalinmagnitudeandoppositeindirectiononobjectX.
ThetwoforcesALWAYSactondifferentobjectsandtheyformanaction-reactionpair.
Linearmomentumanditsconservation:
Mass:
isameasureoftheamountofmatterinabody,&
isthepropertyofabodywhichresistschangeinmotion.
Weight:
istheforceofgravitationalattraction(exertedbytheEarth)onabody.
Linearmomentum:
ofabodyisdefinedastheproductofitsmassandvelocityiep=mv
Impulseofaforce(I):
isdefinedastheproductoftheforceandthetimet
duringwhichitacts
ieI=Fxt{forforcewhichisconstoverthedurationt}
Foravariableforce,theimpulseI=AreaundertheF-tgraph{∫Fdt;
mayneedto“countsquares”}
Impulseisequalinmagnitudetothechangeinmomentumofthebodyactedonbytheforce.
Hencethechangeinmomentumofthebodyisequalinmagtotheareaundera(net)force-timegraph.
{Incorrect
todefine
impulseas
changeinmomentum
}
Force:
isdefinedastherateofchangeofmomentum,ie
F=[m(v-u)]/t=
maorF=vdm/dt
The{one}Newton:
isdefinedastheforceneededtoaccelerateamassof1
kgby1ms-2.
PrincipleofConservationofLinearMomentum:
Whenobjectsofasystem
interact,theirtotalmomentumbeforeandafterinteractionareequalifno
net
(external)forceactsonthesystem.
Thetotalmomentumofan
isolatedsystemisconstant
m1u1+m2u2=m1v1+m2v2ifnetF=0{for
allcollisions}
NB:
Totalmomentum
DURING
theinteraction/collisionisalsoconserved.
(Perfectly)elasticcollision:
Bothmomentum&
kineticenergyofthesystem
areconserved.
Inelasticcollision:
Onlymomentumisconserved,totalkineticenergyisnot
conserved.
Perfectlyinelasticcollision:
Onlymomentumisconserved,andtheparticles
sticktogetheraftercollision.(i.e.movewiththesamevelocity.)
Forallelasticcollisions,u1–u2=v2–v1
ie.relativespeedofapproach=relativespeedofseparation
or,?
m1u1
2+?
m2u2
2=?
m1v1
m2v2
2
Ininelasticcollisions,totalenergyisconservedbutKineticEnergymaybeconvertedintootherformsofenergysuchassoundandheatenergy.
Forces
Hooke'
sLaw:
Withinthelimitofproportionality,theextensionproducedinamaterialisdirectlyproportionaltotheforce/loadapplied
F=kx
Forceconstantk=forceperunitextension(F/x)
Elasticpotentialenergy/strainenergy=AreaundertheF-xgraph{May
needto“countthesquares”}
ForamaterialthatobeysHooke?
slaw,
ElasticPotentialEnergy,E=?
Fx=?
kx2
ForcesonMassesinGravitationalFields:
Aregionofspaceinwhichamassexperiencesan(attractive)forceduetothepresenceofanothermass.
ForcesonChargeinElectricFields:
Aregionofspacewhereachargeexperiencesan(attractiveorrepulsive)
forceduetothepresenceofanothercharge.
HydrostaticPressurep=ρgh
{or,pressuredifferencebetween2pointsseparatedbyaverticaldistanceof
h}
Upthrust:
Anupwardfo
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