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1、LessonSevenShipEquilibrium,StabilityandTrimThebasisforshipequilibriumConsiderashipfloatinguprightonthesurfaceofmotionlesswater.Inordertobeatrestorinequilibrium,theremustbenounbalancedforcesormomentsactingonit.Therearetwoforcesthatmaintainthisequilibrium(1)theforceofgravity,and(
2、2)theforceofbuoyancy.Whentheshipisatrest,thesetwoforcesareactinginthesameperpendicularline,and,inorderfortheshiptofloatinequilibrium,theymustbeexactlyequalnumericallyaswellasoppositeindirection.Theforceofgravityactsatapointorcenterwherealloftheweightsoftheshipmaybesaidtobeconce
3、ntrated:i.e.thecenterofgravity.Gravityalwaysactsverticallydownward.Theforceofbuoyancyactsthroughthecenterofbuoyancy,wheretheresultant,ofallofthebuoyantforcesisconsideredtobeacting.Thisforcealwaysactsverticallyupward.Whentheshipisheeled,theshapeoftheunderwaterbodyischanged,thusm
4、ovingthepositionofthecenterofbuoyancy.Now,whentheshipisheeledbyanexternalincliningforceandthecenterofbuoyancyhasbeenmovedfromthecenterlineplaneoftheship,therewillusuallybeaseparationbetweenthelinesofactionoftheforceofgravityandtheforceofbuoyancy.Thisseparationofthelinesofaction
5、ofthetwoequalforces,whichactinoppositedirections,formsacouplewhosemagnitudeisequaltotheproductofoneoftheseforces(i.e.displacement)andthedistanceseparatingthem.Infigure1(a),wherethismomenttendstorestoretheshiptotheuprightposition,themomentiscalledtherightingmoment,andtheperpendi
6、culardistancebetweenthetwolinesofactionistherightingarm(GZ).Supposenowthatthecenterofgravityismovedupwardtosuchapositionthatwhentheshipisheeledslightly,thebuoyantforceactsinalinethroughthecenterofgravity.Inthenewposition,therearenounbalancedforces,or,inotherwords,azeromomentarm
7、andazeromoment.Infigure1(b),theshipisinneutralequilibrium,andfurtherinclinationwouldeventuallybringaboutachangeofthestateofequilibrium.Ifwemovethecenterofgravitystillhigher,asinfigure1(c),theseparationbetweenthelinesofactionofthetwoforcesastheshipisinclinedslightlyisintheopposi
8、tedirectionfromthatoffigure1(a).Inthiscase,themomentdo
