Determine the angleof banking so as to minimizethe wearand tear of the tyres ofcar negotiating a banked curve

Determine the angleof banking so as to minimizethe wearand tear of the

1.	Determine the angleof banking so as to minimizethe wearand tear of the tyres ofcar negotiating a banked curve
Answer» Solution :Letthe surfaceof the roadmakeangle `theta`withhorizontal surface. THENTHE normalforcemakesthe sameangle`theta` with the verticalwhenthe cartakesa turnthereare twoforcesactingon thecar. IGravitationalforce mg(downwards ) (ii)Normalforce N(perpendicular tosurface) Thenormalforcecan be resolvedintotwocomponents . N cos `theta`and Nsin`theta ` . The gravitionalforce mgandcompoenetNsin`theta ` willprovidethenecessarycentripetalacceleration. ByusingNewton'ssecondlaw . N cos `theta= mg` N sin `theta = (MV^(2))/(r )` By dividingthe equationwe get tan `theta= (V^(2))/(r g) ` `v= sqrt( rg tan theta)` Thebankingangle `theta ` and RADIUSOF curvatureof theroador trackdeterminesthe safe speedof the carat theturnin