Engineering a highway curve. If a car goes through a curve

Chapter , Problem 68

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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 u, where the coefficient of static friction between tires and pavement is ms. A car (without negative lift) is driven around the curve as shown in Fig. 6-11. (a) Find an expression for the car speed vmax that puts the car on the verge of sliding out. (b) On the same graph, plot vmax versus angle u for the range 03 to 503, first for ms " 0.60 (dry pavement) and then for ms " 0.050 (wet or icy pavement). In kilometers per hour, evaluate vmax for a bank angle of u " 103 and for (c) ms " 0.60 and (d) ms " 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.)