Question

You want to design a circular racetrack of radius r 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 9 of the track, measured from the horizontal. Suppose the racecars actually round the track at a speed W> u. What additional radial force is required to keep the cars on the track at this speed? Express your answer in terms of m, r, u, W, and g.

Answer 1

Solution:- The forces acting on the car are illustrated below as, Fxcoso There are two forces acting on the car 1) One is the car's weight, F mg 2) Second one is the normal force, Fr which has two components in the x and y direction. Fay = F.cos θ Now, using the force equations, mo Here, o is the speed of the car and F is the radial force

Now, divide equation (1) by (2) as, F-, sin θ cos θ mg rg rg (c) If the car's speed is v, then the additional radial force needed is given by,