F8. Car on Banked Curved Road with and Without Friction

We consider the physics problem of a banked road for a curve. We first derive a formula that relates the angle of a banked curved road to the speed necessary to take the curve when the road is completely icy (no friction) at the curve. Then we consider weather conditions where there is friction between the tire and the road. We derive a formula that relates the static friction needed to support a car taking a turn with coefficient of friction µs, radius R, velocity v, and banked angle Θ. We then find the maximum speed the car can take the turn without skidding up the bank.