Alevelphysics总结计划学习材料A1docWord格式.docx

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