Answer:
[tex]\mu_s=0.41[/tex]
Explanation:
The frictional force must be equal to the centripetal force in order to keep the car from sliding off the road. So, we have:
[tex]\sum F_x: F_c=F_f(1)[/tex]
The centripetal force is given by:
[tex]F_c=ma_c\\\\F_c=m\frac{v^2}{r}(2)[/tex]
And the frictional force is defined as:
[tex]F_f=\mu_sN\\\sum F_y: N=mg\\F_f=\mu_smg(3)[/tex]
Replacing (2) and (3) in (1):
[tex]m\frac{v^2}{r}=\mu_smg\\\mu_s=\frac{v^2}{gr}\\\mu_s=\frac{(20\frac{m}{s})^2}{(9.8\frac{m}{s^2})(100m)}\\\mu_s=0.41[/tex]
