If a car goes through a curve too fast, the car tends to slide out of the curve, as discussed in Touchstone Example $6-8 .$ For a banked curve with friction, a frictional force acts on a fast car to oppose the tendency to slide out of the curve; the force is directed down the bank (in the direction in which water would drain). Consider a circular curve of radius $R=200 \mathrm{~m}$ and bank angle $\theta$, where the coefficient of static friction between tires and pavement is $\mu^{\text {stat }}$. A car is driven around the curve as shown in Fig. $6-72 .$ (a) Find an expression for the car speed $v^{\max }$ that puts the car on the verge of sliding out. (b) On the same graph, plot $v^{\max }$ versus angle $\theta$ for the range $0^{\circ}$ to $50^{\circ}$, first for $\mu^{\text {stat }}=0.60$ (dry pavement) and then for $\mu^{\text {stat }}=0.050$ (wet or icy pavement). In kilometers per hour, evaluate $v^{\max }$ for a bank angle of $\theta=10^{\circ}$ and for (c) $\mu^{\text {stat }}=0.60$ and (d) $\mu^{\text {stat }}=0.050 .$ (Now you can see why accidents occur in highway curves when wet or icy conditions are not obvious to drivers, who tend to drive at normal speeds.)