PhysicsProfessionalEnglish物理學專業(yè)英語PhysicsProfessionalEnglishB8CircularmotionNEWWORDSPage.34NEWWORDSPage.35第1頁GravitationalforceB9GravitationAllmassesattracteachotherwithagravitationalforce.Ifpointmassesm1andm2,areadistancerapart,andFistheforceoneach,thenaccordingtoNewton'slawofgravitation:第2頁Withasuitableconstant,theaboveproportioncanbeturnedintoanequation:B9GravitationGiscalledthegravitationalconstant.Itisfoundbyexperimentusinglargelaboratorymassesandanextremelysensitiveforce-measuringsystem.In51units,thevalueofGis6.67X10-11Nm2kg-2.第3頁Theequationontheleftisalsovalidforsphericalmassesofuniformdensity,withcentresrapart,asabove.Note:Newton'slawofgravitationisanexampleofaninversesquarelaw.Ifthedistancerdoubles,theforceFdropstoonequarter,andsoon.Gravitationalforcesarealwaysforcesofattraction.Gravitationalforcesareextremelyweak,unlessatleastoneoftheobjectsisofplanetarymassormore.B9Gravitation第4頁GravitationalfieldIfamassfeelsagravitationalforce,thenitisinagravitationalfield.Thegravitationalfieldstrength.

gisdefinedlikethis:B9GravitationForexample,ifamassof2kgfeelsagravitationalforceof10N,thengis5Nkg-1.第5頁Note:Gravitationalfieldstrengthisavector.gisavariableandcanhavedifferentvalues.Thesymbolgabovedoesnotimplytheparticularvalueof9.81Nkg-1neartheEarth'ssurface.Theforceactingonamassinagravitationalfieldcanbefoundbyrearrangingtheequationabove:F=mg.B9Gravitation第6頁Note:Thegravitationalfieldaroundasphericalmassisshownabove.Itiscalledaradialfieldbecauseofitsshape.Insidethemasstheequationontheleftdoesnotapply.gfallstozeroatthecentre.Equipotentiallinesareexplainedonthenextpage.B9Gravitation第7頁TheEarth’sgravitationalfieldstrengthB9GravitationAtthesurfaceIfMistheEarth'smass,Risitsradius,andgoisthegravitationalfieldstrengthatitssurface,then:(1)第8頁B9GravitationNote:gois9.81Nkg-1?Itismorecommonlyknownasg(withoutthe0)'Herehowever,the0hasbeenaddedtodistinguishitfromotherpossiblevaluesofg.Usingmeasuredvaluesofgo'R,andGintheaboveequation,theEarth'smassMcanbecalculated.WithRknown,theEarth'saveragedensitycanalsobefound.AbovethesurfaceInthiscase,g=GMlr2.Fromthisandequation(1),thefollowingresultisobtained:SoasthedistancefromtheEarthincreases,gdecreases.第9頁B9GravitationGravitationalpotentialWorkmustbedonetomoveamassagainstagravitationalfield.Above,massMcausesagravitationalfield.Massmhasbeenmovedthroughthisfield,fromaninfinitedistance(wherethegravitationalforceiszero),topointP.第10頁B9GravitationThegravitationalpotentialV(atpointP)isdefinedasV=W/mwhereWistheworkdoneinmovingamassmfrominfinity(∞)topointP.Note:Likeenergy,gravitationalpotentialisascalar.Atinfinity,thegravitationalpotentialiszero.Elsewhere,thegravitationalpotentialisnegative.Thisisbecausegravityisaforceofattraction.Workisdonebythemassasitispulledfrom00toP,sonegativeworkisdoneonit.Forexample,if1000Jofworkaredonebya2kgmasswhenitmovesfrom00toP,then-1000Jofworkaredoneonit.SoV=-1000/2=-500Jkg-1.第11頁B9GravitationLinkingpotentialandfieldstrengthAbove,work?WisdoneonasmallmassminmovingitfromPtoP'inauniformgravitationalfieldg.So,from(2):?W=m?vThisequationgivestheworkdoneonthemass.第12頁B9GravitationSoworkdonebymass=-m?vButworkdonebymass=forcexdistancemoved=mg?rSomg?r

=-m?VThereforeg=-?V/?rIncalculusnotation,thereisamoregeneralversionofthisequationwhichalsoappliestonon-uniformfields:Note:Intheaboveequations,theminussignindicatesthatgisinthedirectionofdecreasingpotential.第13頁B9GravitationGravitationalpotentialinaradialfieldAradialfieldisshownonpage34.Providedrisnotlessthantheradiusofthesphere:g=GM/r2Combiningthese,andusingcalculus,givesV=-GM/r第14頁B9GravitationNote:V∝1/r.Soifthedistancerdoubles,thegravitationalpotentialVhalves,andsoon.(Insidethemass,th