You are designing a banked turn for an exit ramp leaving the interstate. The rad

Question

You are designing a banked turn for an exit ramp leaving the interstate. The radius of curvature of the turn is 200 m.

(a) If the banking angle is 15o , at what speed must the car be going so that it does 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 0.15, what is the minimum speed a car can traverse the exit ramp without sliding down the incline when the exit ramp is dry?

Explanation / Answer

r = 200 m
Banking angle, = 15 o
(a)
tan() = (v^2/g*r)
tan(15) = v^2/(9.8*200)
v = 22.9 m/s

Speed must the car be going, v = 22.9 m/s

(b)
u = 0.15

For min speed,
v_min = [g * r * (sin – * cos ) ÷ ( cos + s * sin )]
V_min = [200 * 9.8 (sin15 – 0.15 * cos 15) ÷ ( cos 15 + 0.15 * sin 15)
V_min = 14.9 m/s

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