A circular curve of highway is designed for traffic moving at 60 km/hr. Assume t

Question

A circular curve of highway is designed for traffic moving at 60 km/hr. Assume the traffic consists of "ordinary" cars (no negative lift).
a) If the radius of the curve is 150 m, what is the correct angle of banking of the road?
b) If the curve were not banked, what minimum coefficient of friction between tires and road would be required to keep traffic from skidding out of the turn when traveling at 60 km/hr?

for a, i have found W (omega) the angular velocity and T (period) but now i cant seem to find theta (angle).

Explanation / Answer

60km/hr = 16.667m/s Find the horizontal acceleration out using a=v^2/R = 16.667^2/150 = 1.85m/s^2 then the force using f=ma Use the trig functions to find the amount of that force acting parallel to the road. Friction force must equal that. You need the gravitational force acting down. use f=mg Use the trig functions to find the component perpendicular to the road. Add to that the force acting perpendicular to the road due to the centrifugal force. Friction force equals the sum of those two forces times coefficient of friction The mass will cancel out.

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