Answer:
[tex]\mu_s^{min}=0.885[/tex]
Explanation:
The centripetal force is provided by the static friction between the car and the road, and always have to comply with [tex]f\leq\mu_sN[/tex], so we have:
[tex]ma_{cp}=f\leq\mu_sN=\mu_smg[/tex]
Which means:
[tex]a_{cp}=\frac{v^2}{r}\leq\mu_sg[/tex]
So we have:
[tex]\frac{v^2}{gr}\leq\mu_s[/tex]
Which means that [tex]\frac{v^2}{gr}[/tex] is the minimum value the coefficient of static friction can have, which for our values is:
[tex]\mu_s^{min}=\frac{v^2}{gr}=\frac{(25m/s)^2}{(9.81m/s^2)(72m)}=0.885[/tex]
