物理类专业英语大作业Word格式.docx

物理类专业英语大作业Word格式.docx

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201201020118

院（系）：

理学院

专业班级：

物理1201

任课教师：

温俊清

完成时间：

2014年12月28日

Newton'

slawsofmotion

slawsofmotionarethreephysicallawsthattogetherlaidthefoundationforclassicalmechanics.Theydescribetherelationshipbetweenabodyandtheforcesactinguponit,anditsmotioninresponsetosaidforces.Theyhavebeenexpressedinseveraldifferentwaysovernearlythreecenturies,andcanbesummarisedasfollows.

Firstlaw:

Whenviewedinaninertialreferenceframe,anobjecteitherremainsatrestorcontinuestomoveataconstantvelocity,unlessacteduponbyanexternalforce.

Secondlaw:

ThevectorsumoftheforcesFonanobjectisequaltothemassmofthatobjectmultipliedbytheaccelerationvectoraoftheobject:

F=ma.

Thirdlaw:

Whenonebodyexertsaforceonasecondbody,thesecondbodysimultaneouslyexertsaforceequalinmagnitudeandoppositeindirectiononthefirstbody.

ThethreelawsofmotionwerefirstcompiledbyIsaacNewtoninhisPhilosophiNaturalisPrincipiaMathematica（MathematicalPrinciplesofNaturalPhilosophy）,firstpublishedin1687.Newtonusedthemtoexplainandinvestigatethemotionofmanyphysicalobjectsandsystems.Forexample,inthethirdvolumeofthetext,Newtonshowedthattheselawsofmotion,combinedwithhislawofuniversalgravitation,explainedKepler'

slawsofplanetarymotion.

Overview

slawsareappliedtoobjectswhichareidealisedassinglepointmasses,inthesensethatthesizeandshapeoftheobject'

sbodyareneglectedtofocusonitsmotionmoreeasily.Thiscanbedonewhentheobjectissmallcomparedtothedistancesinvolvedinitsanalysis,orthedeformationandrotationofthebodyareofnoimportance.Inthisway,evenaplanetcanbeidealisedasaparticleforanalysisofitsorbitalmotionaroundastar.

Intheiroriginalform,Newton'

slawsofmotionarenotadequatetocharacterisethemotionofrigidbodiesanddeformablebodies.LeonhardEulerin1750introducedageneralisationofNewton'

slawsofmotionforrigidbodiescalledtheEuler'

slawsofmotion,laterappliedaswellfordeformablebodiesassumedasacontinuum.Ifabodyisrepresentedasanassemblageofdiscreteparticles,eachgovernedbyNewton'

slawsofmotion,thenEuler'

slawscanbederivedfromNewton'

slaws.Euler'

slawscan,however,betakenasaxiomsdescribingthelawsofmotionforextendedbodies,independentlyofanyparticlestructure.

slawsholdonlywithrespecttoacertainsetofframesofreferencecalledNewtonianorinertialreferenceframes.Someauthorsinterpretthefirstlawasdefiningwhataninertialreferenceframeis;

fromthispointofview,thesecondlawonlyholdswhentheobservationismadefromaninertialreferenceframe,andthereforethefirstlawcannotbeprovedasaspecialcaseofthesecond.Otherauthorsdotreatthefirstlawasacorollaryofthesecond.TheexplicitconceptofaninertialframeofreferencewasnotdevelopeduntillongafterNewton'

sdeath.

Inthegiveninterpretationmass,acceleration,momentum,and（mostimportantly）forceareassumedtobeexternallydefinedquantities.Thisisthemostcommon,butnottheonlyinterpretationofthewayonecanconsiderthelawstobeadefinitionofthesequantities.

Newtonianmechanicshasbeensupersededbyspecialrelativity,butitisstillusefulasanapproximationwhenthespeedsinvolvedaremuchslowerthanthespeedoflight.

sfirstlaw

Thefirstlawstatesthatifthenetforceiszero,thenthevelocityoftheobjectisconstant.Velocityisavectorquantitywhichexpressesboththeobject'

sspeedandthedirectionofitsmotion;

therefore,thestatementthattheobject'

svelocityisconstantisastatementthatbothitsspeedandthedirectionofitsmotionareconstant.

Thefirstlawcanbestatedmathematicallyas

Consequently,

∙Anobjectthatisatrestwillstayatrestunlessanexternalforceactsuponit.

∙Anobjectthatisinmotionwillnotchangeitsvelocityunlessanexternalforceactsuponit.

Thisisknownasuniformmotion.Anobjectcontinuestodowhateverithappenstobedoingunlessaforceisexerteduponit.Ifitisatrest,itcontinuesinastateofrest（demonstratedwhenatableclothisskilfullywhippedfromunderdishesonatabletopandthedishesremainintheirinitialstateofrest）.Ifanobjectismoving,itcontinuestomovewithoutturningorchangingitsspeed.Thisisevidentinspaceprobesthatcontinuallymoveinouterspace.Changesinmotionmustbeimposedagainstthetendencyofanobjecttoretainitsstateofmotion.Intheabsenceofnetforces,amovingobjecttendstomovealongastraightlinepathindefinitely.

Newtonplacedthefirstlawofmotiontoestablishframesofreferenceforwhichtheotherlawsareapplicable.ThefirstlawofmotionpostulatestheexistenceofatleastoneframeofreferencecalledaNewtonianorinertialreferenceframe,relativetowhichthemotionofaparticlenotsubjecttoforcesisastraightlineataconstantspeed.Newton'

sfirstlawisoftenreferredtoasthelawofinertia.Thus,aconditionnecessaryfortheuniformmotionofaparticlerelativetoaninertialreferenceframeisthatthetotalnetforceactingonitiszero.Inthissense,thefirstlawcanberestatedas:

Ineverymaterialuniverse,themotionofaparticleinapreferentialreferenceframeфisdeterminedbytheactionofforceswhosetotalvanishedforalltimeswhenandonlywhenthevelocityoftheparticleisconstantinф.Thatis,aparticleinitiallyatrestorinuniformmotioninthepreferentialframeфcontinuesinthatstateunlesscompelledbyforcestochangeit.

slawsarevalidonlyinaninertialreferenceframe.Anyreferenceframethatisinuniformmotionwithrespecttoaninertialframeisalsoaninertialframe,i.e.GalileaninvarianceortheprincipleofNewtonianrelativity.

ssecondlaw

Thesecondlawstatesthatthenetforceonanobjectisequaltotherateofchangeofitslinearmomentumpinaninertialreferenceframe:

Thesecondlawcanalsobestatedintermsofanobject'

sacceleration.SinceNewton'

ssecondlawisonlyvalidforconstant-masssystems,masscanbetakenoutsidethedifferentiationoperatorbytheconstantfactorruleindifferentiation.Thus,

whereFisthenetforceapplied,misthemassofthebody,andaisthebody'

sacceleration.Thus,thenetforceappliedtoabodyproducesaproportionalacceleration.Inotherwords,ifabodyisaccelerating,thenthereisaforceonit.

Consistentwiththefirstlaw,thetimederivativeofthemomentumisnon-zerowhenthemomentumchangesdirection,evenifthereisnochangeinitsmagnitude;

suchisthecasewithuniformcircularmotion.Therelationshipalsoimpliestheconservationofmomentum:

whenthenetforceonthebodyiszero,themomentumofthebodyisconstant.Anynetforceisequaltotherateofchangeofthemomentum.

Anymassthatisgainedorlostbythesystemwillcauseachangeinmomentumthatisnottheresultofanexternalforce.Adifferentequationisnecessaryforvariable-masssystems.

ssecondlawrequiresmodificationiftheeffectsofspecialrelativityaretobetakenintoaccount,becauseathighspeedstheapproximationthatmomentumistheproductofrestmassandvelocityisnotaccurate.

sthirdlaw

Thethirdlawstatesthatallforcesexistinpairs:

ifoneobjectAexertsaforceFAonasecondobjectB,thenBsimultaneouslyexertsaforceFBonA,andthetwoforcesareequalandopposite:

FA=−FB.Thethirdlawmeansthatallforcesareinteractionsbetweendifferentbodies,andthusthatthereisnosuchthingasaunidirectionalforceoraforcethatactsononlyonebody.Thislawissometimesreferredtoastheaction-reactionlaw,withFAcalledthe"

action"

andFBthe"

reaction"

.Theactionandthereactionaresimultaneous,anditdoesnotmatterwhichiscalledtheactionandwhichiscalledreaction;

bothforcesarepartofasingleinteraction,andneitherforceexistswithouttheother.

ThetwoforcesinNewton'

sthirdlawareofthesametype（e.g.,iftheroadexertsaforwardfrictionalforceonanacceleratingcar'

stires,thenitisalsoafrictionalforcethatNewton'

sthirdlawpredictsforthetirespushingbackwardontheroad）.

Fromaconceptualstandpoint,Newton'

sthirdlawisseenwhenapersonwalks:

theypushagainstthefloor,andthefloorpushesagainsttheperson.Similarly,thetiresofacarpushagainsttheroadwhiletheroadpushesbackonthetires—thetiresandroadsimultaneouslypushagainsteachother.Inswimming,apersoninteractswiththewater,pushingthewaterbackward,whilethewatersimultaneouslypushesthepersonforward—boththepersonandthewaterpushagainsteachother.Thereactionforcesaccountforthemotionintheseexamples.Theseforcesdependonfriction;

apersonorcaronice,forexample,maybeunabletoexerttheactionforcetoproducetheneededreactionforce.

Importanceandrangeofvalidity

slawswereverifiedbyexperimentandobservationforover200years,andtheyareexcellentapproximationsatthescalesandspeedsofeverydaylife.Newton'

slawsofmotion,togetherwithhislawofuniversalgravitationandthemathematicaltechniquesofcalculus,providedforthefirsttimeaunifiedquantitativeexplanationforawiderangeofphysicalphenomena.

Thesethreelawsholdtoagoodapproximationformacroscopicobjectsundereverydayconditions.However,Newton'

slawsareinappropriateforuseincertaincircumstances,mostnotablyatverysmallscales,veryhighspeedsorverystronggravitationalfields.Therefore,thelawscannotbeusedtoexplainph