Answer
(a) The minimum coefficient of static friction to prevent sliding is $\mu_s = 0.375$.
(b) The maximum speed to round the curve safely is 14.4 m/s.
Work Step by Step
(a) In this situation, the force of static friction provides the centripetal force to go around the curve.
$F_f = \frac{mv^2}{r}$
$mg~\mu_s = \frac{mv^2}{r}$
$\mu_s = \frac{v^2}{gr} = \frac{(25.0~m/s)^2}{(9.80~m/s^2)(170.0~m)}$
$\mu_s = 0.375$
The minimum coefficient of static friction to prevent sliding is $\mu_s = 0.375$.
(b) Let $\mu_s = \frac{0.375}{3} = 0.125$
$mg~\mu_s = \frac{mv^2}{r}$
$v = \sqrt{gr~\mu_s}$
$v = \sqrt{(9.80~m/s^2)(170.0~m)(0.125)}$
$v = 14.4~m/s$
The maximum speed to round the curve safely is 14.4 m/s.
