Question

A car travels at a steady 40.0 m/s around a horizontal curve of radius 200 m. What is the minimum coefficient of static friction between the road and the car's tires that will allow the car to travel at this speed without sliding?

Answer 1

Answer:

Coefficient of static friction between the road and the car's tire is 0.81

Explanation:

It is given that,

Velocity of the car, v = 40 m/s

Radius of the curve, r = 200 m

We need to find the minimum coefficient of static friction between the road and the car's tires that will allow the car to travel at this speed without sliding. Let it is equal to μ.

The centripetal force of the car is balanced by the force of friction as :

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

$\mu=\dfrac{v^2}{rg}$

$\mu=\dfrac{(40\ m/s)^2}{200\ m\times 9.8\ m/s^2}$

$\mu=0.81$

So, the coefficient of static friction between the road and the car's tire is 0.81 Hence, this is the required solution.