Question

A flat curve on a highway has a radius of curvature $400m$. A car goes around a curve at a speed of $32m/s$. What is the minimum value of coefficient of friction that will prevent the car from sliding? ($g=9.8m/s^2$)

Answer 1

In order to prevent the vehicle from slipping away on a curve, the necessary centripetal force should be provided by the force of friction between the road and the wheels of the vehicle.

Force of friction$=\mu mg$ ----- here $\mu$ is the coeficient of friction(which depends on the two interacting surfaces), m is the mass of the car and g is the gravitational acceleration.

Centripetal force $=\frac{m{{}_V}^2}{r}$

both should be equal. So,

$\mu mg=\frac{m{{}_V}^2}{r}$

$\mu =\frac{{{}_V}^2}{rg}=\frac{{32}^2}{400\times 9.8}=\mathrm{0.261.}$

Note that $\mu$ is a dimensionless quantity and has no unit.