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Derive an expressionformaximumspeedthe carcan havesafeturnon a leveledcircular road . |
Answer» Solution :In aleveledcircularroad, skiddingmainlydependson thecoefficientof staticfriction`mu_s`thecoefficientofstaticfrictiondependson thenatureof thesurfacewhichhasamaximumlimiting value, toavoidthisis problem usuallythe outeredgeof theroadis slightlyraisedcomparedto inneredgethisis calledbankingof roadsor tracks. thisintroducesan inclination, andthe angleis calledbankingangle . Letthe SURFACEOF theroadmakeangle` theta`withhorizontalsurface, thenthe normalforcemakesthe sameangle `theta `with thevertical. whenthe cartakesa TURN, thereare twoforcesactingon the CAR : (a) GravitationalforceMg( downwards) (b )NormalforceN ( perpendicularto surface ) We canresolvethe normalforceintotwocomponentsN` cos thetaand Nsin theta `thecomponent balancesthe downwardgravitionalforce.mg.andcomponentwillprovidethe necessarycentripetalacceleration. by usingNewtonsecondlaw . Thebankingangle ` theta `and radiusof curvatureof theroador trackdeterminesthe safespeedof htecar attheturning. If thespeedofcarexceedsthissafespeedthenitstartstoskidoutward butfrictionalforcecomesintoeffect andprovidesand additionalcentripetalforceto preventthe outwardskidding.Atthe sametime, if thespeedof htecar islittlelesserthansafespeed, itstartsto skidinwardandfrictionalforcecomesintoeffect whcihreducescentripetalforce to preventinwardskidding .Howeverif htespeedof THEVEHICLE is sufficientlygreaterthanthe correctspeedthenfrictional forcecannotstopthecarfromskidding. 
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