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1、UniversityPhysicsAINo.4TheGravitationalForceandtheGravitationalFieldClassNumberNameI．ChoosetheCorrectAnswer1.ThemagnitudeoftheforceofgravitybetweentwoidenticalobjectsisgivenbyF0.Ifthemassofeachobjectisdoubledbutthedistancebetweenthemishalved,thenthenewforceofgravitybetweentheobjec
2、tswillbe（A）(A)16F0(B)4F0(C)F0(D)F0/2Solution:GMmThemagnitudeofthegravitationalforceisF=,accordingtotheproblem,wegetgrav2r224GmGmF′==16=16Fgrav220(r/2)r2.Asphericalsymmetricnonrotatingbodyhasadensitythatvariesappreciablywiththeradialdistancefromthecenter.Atthecenterofthebodytheacce
3、lerationoffreefallis(C)(A)Definitelylargerthanzero.(B)Possiblylargerthanzero.(C)Definitelyequaltozero.Solution:Accordingtotheshelltheorem1,atthecenterofthebody,theforceactedonthebodyiszero,sotheaccelerationofthebodyiszero.3.Theaccelerationduetogravityinaholedugintoanonuniformspher
4、icallysymmetricbody(C)(A)willincreaseasyougodeeper,reachingamaximumatthecenter.(B)willincreaseasyougodeeper,buteventuallyreachamaximum,andthendecreaseuntilyoureachthecenter.(C)canincreaseordecreaseasyougodeeper.(D)mustdecreaseasyougodeeper.Solution:Foranonuniformsphericallysymmetr
5、icbody,theforceofgravitydependsonthedistancefromthecenter,whichisrelatedtohowthedensityofthebodychangedwithrespecttothedistancefromthecenter,forinstance:accordingtotheGauss’slawofgravityrrg⋅ds=4πGM=4πGρdV∫s∑i∫2rwhenρ=Ar,theaccelerationgwillincreaseasyougodeeper,whenρ=Artheracceler
6、ationgwilldecreaseasyougodeeper.II.FillingtheBlanks1.Twomassesm1andm2exertgravitationalforcesofequalmagnitudeoneachother.ShowthatifthetotalmassM=m1+m2isfixed,themagnitudeofthemutualgravitationalforceoneachofthetwomassesisamaximumwhenm1=m2(Fill).Solution:GmmGm(M−m)1211Themag
7、nitudeofthegravitationalforceisF==,grav22rrdFG(M−2m)M1Weget=0⇒=0⇒m=21dmr21Thenm=m.122.AmassmisinsideauniformsphericalshellofmassM′andamassMisoutsidetheshellasshowninFigure1.mThemagnitudeofthetotalgravitationalforceonmisdMMmF=G.(s+R)2−d2sRM′Solution:rrrF=F+FFig.1totalM'onmMonmrQF=0
8、M'onmrr∴F=FtotalMonmGMmGMm∴F==tot
