A race car driving on a banked track that makes an angle θ with the horizontal rounds a curve for which the radius of curvature is R.

Part A

There is one speed vcritical at which friction is not needed to keep the car on the track. What is that speed in terms of θ and R? Express your answer in terms of the variables R, θ, and the acceleration due to gravity g. vcritical =

Part B

If the coefficient of friction between tires and road is μ, what maximum speed can the car have without going into a skid when taking the curve? Express your answer in terms of the variables R, θ, μ and the acceleration due to gravity g. vmax =