Answer
$\mu=0.062$
Work Step by Step
All units must be in SI units. Therefore, the speed must be converted to meters per second using dimensional analysis. $$\frac{40km}{1hr} \times \frac{1hr}{60min} \times \frac{1min}{60s} \times \frac{1000m}{1km}$$ $$=11m/s$$ Centripetal force is equal to $$F_c=\frac{mv^2}{r}$$ This force needs to be equal to the force of friction $F_f=\mu_smg$. This yields $$\mu_smg=\frac{mv^2}{r}$$ Eliminating $m$ yields $$\mu_sg=\frac{v^2}{r}$$ Solving for $\mu_s$ yields $$\mu_s=\frac{v^2}{rg}$$ Substituting known values of $g=9.8m/s^2$, $v=11m/s$, and $r=200m$ yields a coefficient of friction of $$\mu_s=\frac{(11m/s)^2}{(200m)(9.8m/s^2)}$$ $$\mu_s=0.062$$
