A curved section of roadway is in the shape of a circular arc of 410-m radius. The curved section is horizontal, not banked. The coefficient of friction for tires and the roadway is 0.40. What is the maximum safe driving speed for this unbanked, curved section of roadway?

IF the Road is not banked then, we have no bending of car towards the vertical.

The friction force between the tyres and ground supplies the centripetal force needed to negotiate the curve.

m v² / r = Mu N = Mu m g Mu = coefficient of friction

g = acceleration due to gravity m = mass of car, N normal reaction from ground

so v = √ (Mu r g) = √ 0.40 * 410 * 9.8 = 40.09 m/sec

This is the maximum speed which is safe. If it is exceeded, friction can not supply centripetal force. So tyres will skid and car will go away from the curve.

v = 144 km ph