Question

A person drives a car along a circular track on a level ground. a) Derive an expression for the maximum safe speed of the car.

Answer 1

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kvnmurty

KvnmurtyThe Sage

on a level road the only force that helps the car move in a circular path is the friction force.

let mu be coefficient of friction. Normal force on the car exerted by the ground is N = m g.

Friction = f = mu N = mu m g.

A centripetal force is needed to keep the car moving in a circular path. it is equal to m v^2/r.

so mv^2/r < mu m g

v^2 < mu r g.

Banking of curved roads is done to increase centripetal force. The slope provides a component of normal reaction force also to supply centripetal force. So vehicles can go with higher speeds at the curves.