Engineering a highway curve if a car goes through a curve too fast, the car tends to slide out of the curve. For a banked curve with friction, a frictional force acts on a fast car to oppose the tendency to slide out of the curve; the force is directed down the bank (in the direction water would drain). Consider a circular curve of radius R = 200 m and bank angle θ, where the coefficient of static friction between tires and pavement is µ_s. A car (without negative lift) is driven around the curve as shown in Figure.

(a) Find an expression for the car speed v _max that puts the car on the verge of sliding out.

(b) On the same graph, plot v _max versus angle θ for the range 0^o to 50^o, first for µ_s = 0.60 (dry pavement) and then for µ_s = 0.050 (wet or icy pavement). In kilometers per hour, evaluate v _max for a bank angle of θ = 10^o and for 

(c) µ_s = 0.60 and 

(d) µ_s = 0.050. (Now you can see why accidents occur in highway curves when icy conditions are not obvious to drivers, who tend to drive at normal speeds.)