Question

What is the maximum speed at which a car can safely travel around a circular track of radius 142 meters if the coefficient of friction between the tires and the road is 1.07? Include units in your answer. Answer must be in 3 significant digits.

Answer 1

Given that the radius of the circular path is r = 142 m and the coefficient of the friction is

$\mu=1.07$

The condition for the car to travel safely is

Frictional force = centrifugal force

$\mu mg=\frac{mv^2}{r}$

Here, m is the mass of the car and the acceleration due to gravity is g = 9.8 m/s^2.

v is the maximum speed of the car.

$\begin{gathered} v=\sqrt[]{ugr} \\ =\sqrt[]{1.07\times9.8\times142} \\ =38.58\text{ m/s} \end{gathered}$