Physics Circular Motion Level: Misc Level

If a car goes around a curve too fast, it tends to slide out of the curve since the frictional force is not large enough to provide the necessary centripetal force . one way to get around this is to create a banked curve in which a centripetal force is present even in the absence of friction, as shown below . the vertical component of the normal force N equals mg, and the horizontal component of the normal force provides the centripetal force .

(a) Calculate an expression for the maximum speed a car can maintain around a curve of radius R banked at angle ? E valuate it for R=200 m and ? =10%