A circular curve of highway is designed for traffic moving at 75 km/h. (a) If the radius of the curve is 145 m, what is the correct angle of banking of the road? ° with respect to the horizontal (b) If the curve were not banked, what would be the minimum coefficient of friction between tires and road that would keep traffic from skidding out of the turn when traveling at 75 km/h?

a) 16.97o b) 0.305

Explanation:

Using bank angle formula

Tan (bank angle) = V^2 / (r*g)

Where V = speed of the traffic = 75Km/hr, converting it to m/s = 75 * 1000m / (3600s) = 20.833m/s, r = radius of the curved path in metres and g = acceleration due to gravity in m/s^2

Tan (bank angle) = 20.833 ^2 / (145 * 9.81) = 0.305

Bank angle = tan inverse of (0.305) = 16.97o

b) Using the formula when the road is unbanked

Vmax = √coefficient friction * r * 9.81

V^2 max / (r*g) = coefficient of friction

Coefficient of friction = 0.305