MODREN PHYSICS Chapter 1A Review.docx
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MODREN PHYSICS Chapter 1A Review.docx
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MODRENPHYSICSChapter1AReview
ModernPhysics
Fengyibing
Contents:
Chapter1AReview
Chapter2WavesAsParticlesandParticlesAsWaves
Chapter3AtomsandtheBohrModel
Chapter4TheSchrödingerEquation
Chapter5WavePacketsandtheUncertaintyPrinciple
Chapter6BarriersandWell
Chapter7AngularMomentumandtheHydrogenAtom
Chapter8ManyParticles
Chapter9ComplexAtomsandMolecules
Chapter10StatisticalPhysics
Chapter11Decays,RadiationfromAtoms,andLasers
Chapter12Conductors,Semiconductors,Superconductors
Chapter13TheAtomicNucleus
Chapter14ElementaryParticlePhysics
Chapter1AReview
§1-1Newton’sLaws
IsaacNewton(a17thcenturyscientist)createdtheoreticalphysics-theideaofdescribingnatureintermsofequations.
Inordertosolvetheproblemofuniversalgravitation,Newtoninventedthedifferentialandintegralcalculusandintroducedthethreebasiclawsofmechanicswhichexplainwhyobjectsmove(ordon'tmove)astheydoandthesethreelawshavebecomeknownasNewton'sthreelawsofmotion.
Part1Inertialframesofreference
Theseareframesofreferencethatmoveatconstantvelocitywithrespectto(相关)oneanother.
Universalframeofreference
Part2Newton’sFirstLawofmotion
Newton'sfirstlawofmotion–sometimesreferredtoasthe"lawofinertia."
1.Newton'sfirstlawofmotionisoftenstatedas:
Anobjectatresttendstostayatrestandanobjectinmotiontendstostayinmotionwiththesamespeedandinthesamedirectionunlessacteduponbyanunbalancedforce.
任何物体都保持静止或匀速直线运动的状态,直到受到其它物体的作用力迫使它改变这种状态为止。
Therearetwopartstothisstatement–onewhichpredictsthebehaviorofstationaryobjectsandtheotherwhichpredictsthebehaviorofmovingobjects.Thesetwopartsaresummarizedinthefollowingdiagram.
2.Anotherdescription:
Thebehaviorofallobjectscanbedescribedbysayingthatobjectstendto"keepondoingwhatthey'redoing"(unlessacteduponbyanunbalancedforce).
没有外力,物体的运动状态是不会改变的。
物体的这种性质称为惯性。
所以牛顿第一定律也称为惯性定律。
第一定律也阐明了力的概念。
Ifatrest,theywillremaininthissamestateofrest.Ifthebodyismovingwithconstantvelocity,itwillcontinuetodoso.Thestateofmotionofanobjectismaintainedaslongastheobjectisnotacteduponbyanunbalancedforce.Allobjectsresistchangesintheirstateofmotion–theytendto"keepondoingwhatthey'redoing."
牛顿第一定律并不是在所有的参照系里都成立,实际上它只在惯性参照系里才成立。
因此常常把牛顿第一定律是否成立,作为一个参照系是否惯性参照系的判据。
3.Mathematicaldescription
if
themotionisuniform.
(1)Bynetforcewemeanthevectorsumofallexternalforcesexertedontheobject.
Ifthenetforce
exertedonanobjectiszero,theobjectcontinuesinitsoriginalstateofmotion.Thatis,if
anobjectatrestremainsatrestandanobjectmovingwithsomevelocitycontinueswiththatsamevelocity.
(2)Hereuniformmeans:
4.Examples
•afootballdoesn’tstopinmidair.
•apencilwon’trollunlessyourollit
5.Note
1)AnimportantwordhereisNET.Itmeans“total”or“sumofall”.Thenetforceisthevectorsumofallexternalforcesexertedontheobject.
2)Itisnotthatnoforceatallcanactonthebody.Itisjustthatalltheforcesmustaddtozero(canceleachotherout).
Whatifthebodyismovingwithavelocitywhichisnotconstant?
Whyisn’tthisdiscussed?
Part3Newton'sSecondLaw
Objectsatequilibrium(theconditioninwhichallforcesbalance)willnotaccelerate.AccordingtoNewton,anobjectwillonlyaccelerateifthereisanetorunbalancedforceactinguponit.Thepresenceofanunbalancedforcewillaccelerateanobject–changingitsspeed,itsdirection,orbothitsspeedanddirection.
Thesecondlawstatesthattheaccelerationofanobjectisdependentupontwovariables–thenetforceactingupontheobjectandthemassoftheobject.
1.Newton’ssecondlawofmotioncanbeformallystatedasfollows:
Theaccelerationofanobjectasproducedbyanetforceisdirectlyproportionaltothemagnitudeofthenetforce,inthesamedirectionasthenetforce,andinverselyproportionaltothemassoftheobject.
物体在受到合外力的作用会产生加速度,加速度的方向和合外力的方向相同,加速度的大小正比于合外力的大小与物体的惯性质量成反比。
2.Invectorequationform,andwiththeunitsofallquantitiesappropriatelychosen,wecanstateNewton’ssecondlawas
:
thenetforceisthevectorsumofalltheforcesactingontheobject.Forexample,Gravity,electricalandmagneticforces,etc.
:
theaccelerationoftheobject.
:
themassoftheobject,moreproperlytermedtheinertialmass.
它是矢量式,并且是瞬时关系。
3.Note
Fromtheequation,wecansee
♦The"netforce"equalsmasstimesacceleration;
♦Theaccelerationisdirectlyproportionaltothe"netforce;"inverselyproportionaltothemassoftheobject.
♦Theaccelerationisinthesamedirectionasthe"netforce;"
♦Anaccelerationisproducedbya"netforce."
物体受到的合外力,会产生加速度,可能使物体的运动状态或速度发生改变,但是这种改变是和物体本身的运动状态有关的。
4.AnotherformofNewton’ssecondlaw:
isthemomentumoftheobject.
.
equalsthefirsttimederivativesofthemomentum
.
Thisformallowsustoaccountforanobjectwithachangingmass.
Part4Newton’sthirdlaw
Whenyousitinyourchair,yourbodyexertsadownwardforceonthechairandthechairexertsanupwardforceonyourbody.Therearetwoforcesresultingfromthisinteraction—aforceonthechairandaforceonyourbody.
AccordingtoNewton,wheneverobjectsAandBinteractwitheachother,theyexertforcesuponeachother.
ThesetwoforcesarecalledactionandreactionforcesandarethesubjectofNewton'sthirdlawofmotion.
1.Formallystated,Newton'sthirdlawis:
"Foreveryaction,thereisanequalandoppositereaction."
两个物体之间的作用力和反作用力,在同一条直线上,大小相等,方向相反。
Thestatementmeansthatineveryinteraction,thereisapairofforcesactingonthetwointeractingobjects.Themagnitudeoftheforceonthefirstobjectequalsthemagnitudeoftheforceonthesecondobject.Thedirectionoftheforceonthefirstobjectisoppositetothedirectionoftheforceonthesecondobject.
2.Thepropertyofactionandreactionforces
Theforce
exertedbyobject1onobject2isequalinmagnitudeandoppositeindirectiontotheforce
exertedbyobject2onobject1.
Theactionforceisequalinmagnitudetothereactionforceandoppositeindirection.
Inallcases,theactionandreactionforcesactondifferentobjects.
物体之间的相互作用是通过力体现的。
并且指出力的作用是相互的,有作用必有反作用力。
它们是作用在同一条直线上,大小相等,方向相反。
Forcesalwayscomeinpairs–equalandoppositeaction-reactionforcepairs.
(1)作用力和反作用力是没有主次、先后之分。
同时产生、同时消失。
(2)这一对力是作用在不同物体上,不可能抵消。
(3)作用力和反作用力必须是同一性质的力。
(4)与参照系无关?
3.Examples
♦Considertheflyingmotionofbirds.Abirdfliesbyuseofitswings.Thewingsofabirdpushairdownwards.Inturn,theairreactsbypushingthebirdupwards.Themagnitudeoftheforceontheairequalsthemagnitudeoftheforceonthebird;thedirectionoftheforceontheair(downwards)isoppositetothedirectionoftheforceonthebird(upwards).Foreveryaction,thereisanequal(insize)andopposite(indirection)reaction.Action-reactionforcepairsmakeitpossibleforbirdstofly.
♦Whenagunisfired,theforceofthegasproducedbyburninggunpowderhurlsoutthebullet.ByNewton'slaw,thegunitselfrecoilsbackwards.
♦Thosefamiliarwithsmallboatsknowthatbeforejumpingfromaboattothedock,itiswisetotietheboattothedockfirst,andtograbahandholdonthedockbeforejumping.Otherwise,evenasyoujump,theboat"magically"movesawayfromthedock,possiblymakingyoumissyourleaporpushingtheboatoutofreach.ItisallinNewton'sthirdlaw:
asyourlegspropelyourbodytowardsthedock,theyalsoapplytotheboatanequalforceintheoppositedirection,whichpushesitawayfromthedock.
Problem:
Whenyouplayaball,whydoesitbounceupandtheearthstandstill?
Part5Conservationofmomentum
Thethirdlawmayberestatedintermsofmomentum.
Twoobjectslabeled1and2,isolatedfromtheoutsideworldandinteractingwitheachother.
FromEq.(1-2)thesecondlaw
Theforceonobject1istherateofchangeofitsmomentum
Theforceonobject2istherateofchangeofitsmomentum
ThenEq.(1-8)
becomes
or
Thus,thevector
isconstantintime
aconstantvector(1-9)
where
isthetotalmomentum.
WerefertoEq.(1-9)asthelawofconservationofmomentum.
ThelawofconservationofmomentumisagreatsimplificationwhenNewton’slawsareappliedtoacomplicatedinteractionbetweentwoobjects.
Part6Hooke’sLaw
1.Hooke’sLaw
RobertHooke,whoin1676stated:
在弹性限度内,弹簧的弹力F和弹簧的伸长量(或压缩量)成正比
Whenaspringisstretchedorcompressedbyanamount
fromitsequilibriumposition,itexertsaforcegivenby
onamassattachedtoitsend.
Mathematically,
(1)
isknownasthespringforce.
(2)Theconstantofproportionality,
istheknownasthespringconstant,
(3)
isthedisplacementofthebodyfromitsequilibriumposition(at
=0).
(4)TheminussigninHooke’slawtellsusthattheforceisarestoringforce,tendingtomovethemassbacktotheequilibriumpositionofthespring.
ThisparticularforcelawisknownasHooke’slaw.
Figure1a.Whenthedisplacementistotheright(
>0)thespringforceisdirectedtotheleft(
<0).
Figure1b.Whenthedisplacementistotheleft(
<0)thespringforceisdirectedtotheright(
>0).
Figure1c.InbothcasesshowninFigures1aand1b,theeffectofthespringforceistoreturnthesystemtotheequilibriumposition.Atthisposition,
=0andthespringisunstretched,signifying
=0.
2.theequationofmotion
ByNewton’ssecondlaw,theequationofmotion:
Thesolutiontakestheform
:
theamplitudeofthemotion
:
thephase,determinedbyin
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