Question

When a car of mass 1200 kg, going with speed 30 m/s, rounds an unbanked curve of radius 150 m, what is the minimum coefficient of static friction LaTeX: \left(\mu_s\right)( μ s ) needed to ensure that it does no skid?

Answer 1

Answer:

$\mu_s=0.61$

Explanation:

In order for the car does not slip, the frictional force must be equal to the centripetal force due to the circular motion. According to the free body diagram:

$\sum F_y:N=mg\\\sum F_x:F_f=F_c$

The frictional force is given by:

$F_f=\mu_s N=\mu_s mg$

The centripetal force is defined as:

$F_c=ma_c=m\frac{v^2}{r}$

Here v is the linear speed and r is the radius of the circular motion. Replacing this equations:

$\mu_smg=m\frac{v^2}{r}\\\mu_s=\frac{v^2}{gr}\\\mu_s=\frac{(30\frac{m}{s})^2}{(9.8\frac{m}{s^2})(150m)}\\\mu_s=0.61$