Chapter 6, Problem 68P

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 Fig. 6-11. (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° to 50°, 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° 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.)