Answer:
[tex]\mu_s=0.61[/tex]
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:
[tex]\sum F_y:N=mg\\\sum F_x:F_f=F_c[/tex]
The frictional force is given by:
[tex]F_f=\mu_s N=\mu_s mg[/tex]
The centripetal force is defined as:
[tex]F_c=ma_c=m\frac{v^2}{r}[/tex]
Here v is the linear speed and r is the radius of the circular motion. Replacing this equations:
[tex]\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[/tex]
