Answer
(a) Please refer to the free-body diagram.
(b) The minimum coefficient of static friction is $\mu_s = 0.28$.
(c) The answer to part (b) does not depend on the person's mass.
Work Step by Step
(a) Please refer to the free-body diagram.
(b) We can find a person's speed $v$.
$v = (0.60~rev/s)(\frac{2\pi ~r}{1~rev})$
$v = (1.2\pi ~r)~m/s$
We can find the normal force $F_N$.
$F_N = \frac{m~v^2}{r}$
$F_N = \frac{m~(1.2\pi ~r)^2}{r}$
$F_N = m~(1.2\pi)^2~r$
We can find the minimum coefficient of static friction.
$F_N~\mu_s = mg$
$m~(1.2\pi)^2~r~\mu_s = mg$
$\mu_s = \frac{g}{(1.2\pi)^2~r}$
$\mu_s = \frac{9.80}{(1.2\pi)^2(2.5)}$
$\mu_s = 0.28$
The minimum coefficient of static friction is $\mu_s = 0.28$.
(c) The answer to part (b) does not depend on the person's mass.
