Car on a banked curve

Question

You want to design a circular racetrack of radius L such that cars of mass m can go around the track at speed u without the aid of friction or other forces other than the perpendicular contact force from the track surface. Find an expression for the required banking angle θ of the track, measured from the horizontal. Your answer should be expressed in terms of m, L, u, and g.Suppose the racecars actually round the track at a speed V > u. What additional radial force is required to keep the cars on the track at this speed? Express your answer in terms of m, L, u, V, and g. (I already got the first expression can't figure the second one)

Answer 1

If the angle is θ, the velocity is u, the racetrack radius is L, the acceleration due to gravity is g then we have on a smooth track:

tan θ = (u²)/(L.g)

 

The additional force the car will need is the frictional force between the tires and the surface.