Question

The coefficient of friction between the tyres and the road is 0.1. Find the maximum speed allowed by traffic police for car to cross a circular turn of radius 10 m to prevent accident.

When a body moves on a circular path with constant speed and changing its direction of motion at every instant of time, then it is called uniform circular motion. The change in the direction of motion of the body gives the change in its velocity, and hence the body undergoes an acceleration, called radial acceleration or centripetal acceleration. Thus, according to Newton's second law of motion, a body cannot be accelerated itself. The external force required to maintain the motion of a body on a circular path is called centripetal force, Fc = mv²/r, where m, v and r are the mass of a body, velocity of the body and the radius of circular path.

Find the maximum speed at which a car can turn around a curve of 30 m radius on a level road, given the coefficient of friction between the tyres and the road is 0.4. [g = 10 m/s²]