05.1 You are designing a banked turn for an exit ramp leaving the interstate. Th

Question

05.1 You are designing a banked turn for an exit ramp leaving the interstate. The radius of

curvature of the turn is 194 m.

(a) What must the banking angle be so that a car going 45 mph will not slide off the highway

when the road is icy? (Assume that there is no friction when the road is covered with ice.)

(b) If the coefficient of static friction between the tires and dry pavement is 0.20, what is the

maximum speed a car can traverse the exit ramp without sliding off when the exit ramp is dry?

Explanation / Answer

apply the formula of Banking roads as

banking angle tan theta = coefficient of friction u = v^2/rg

so

here

r = radius = 194 m

part A:

1 mph = 0.4470 m/s

so

tan theta = (45* 0.4470)^2/(194 *9.81)

tan theta = 0.212

theta = 12 deg

----------------------------------------------

apply V^2 = urg

V^2 = 0.2 * 194 * 9.81

v^2 = 380.628

v = 19.51 m/s

or V = 19.51/0.4470   = 43.74 mph

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