A car traveling at constant speed $v$ rounds a level curve, which we take to be a circle of radius $R$. If the car is to avoid sliding outward, the horizontal frictional force $F$ exerted by the road on the tires must at least balance the centrifugal force pulling outward. The force $F$ satisfies $F=\mu m g,$ where $\mu$ is the coefficient of friction, $m$ is the mass of the car, and $g$ is the acceleration of gravity. Thus, $\mu m g \geq m v^{2} / R .$ Show that $v_{R},$ the speed beyond which skidding will occur, satisfies $$v_{R}=\sqrt{\mu g R}$$ and use this to determine $v_{R}$ for a curve with $R=400$ feet and $\mu=0.4 .$ Use $g=32$ feet per second per second.