Question

A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12.0 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from slipping

Answer 1

Explanation:

The centripetal force $F_c$ on the car must equal the frictional force f in order to avoid slipping off the road. Let's apply Newton's 2nd law to the y- and x-axes.

$y:\:\:\:\:N - mg = 0$

$x:\:\:F_c = f \Rightarrow \:\:\:m \dfrac{v^2}{r} = \mu N$

or

$m \dfrac{v^2}{r} = \mu mg$

Solving for $\mu$,

$\mu = \dfrac{v^2}{gr} = \dfrac{(12.0\:\frac{m}{s})^2}{(9.8\:\frac{m}{s^2})(52\:m)} = 0.28$