College Physics (4th Edition)

(a) The frictional force is $3500~N$ (b) The frictional force does not necessarily have a magnitude of $\mu_s~N$.
(a) The force of static friction provides the centripetal force to keep the car moving around the curve. We can find the frictional force: $F_f = \frac{mv^2}{r}$ $F_f = \frac{(1400~kg)(32~m/s)^2}{410~m}$ $F_f = 3500~N$ The frictional force is $3500~N$ (b) The frictional force does not necessarily have a magnitude of $\mu_s~N$. In fact, it would be very dangerous if $F_f = \mu_s~N$, because $\mu_s~N$ is the maximum possible force of static friction. If $F_f = \mu_s~N$, then just a slight increase in speed would mean that the force of static friction would not be able to keep the car moving around the curve, and the car would start slipping off the road.