A freeway off-ramp is a quarter- circle of roadway of radius R = 50 m, as shown

Question

A freeway off-ramp is a quarter- circle of roadway of radius R = 50 m, as shown in the two figures below. (a) What is the ideal banking angle ? of a section of this road, if the speed of the cars on it is v = 15 m/s? At this ideal angle no friction is re- quired for the cars to keep from slipping off the road. (b) What minimum coefficient of friction ?s is neces- sary so that a car at rest on this section will not slip sideways? (c) For the ?s found in part (b), what is the maximum speed a car can drive on this section with- out slipping sideways?

Explanation / Answer

Ideal angle of banking = v^2/Rg

tan theta = 225/50 * 9.8

theta = arctan(0.459)

b)ug = v^2/r

u * 9.8 = 225 /50

u = 0.459

c) the maximum speed is 15 m/s

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