A car of mass m is going around a circular turn of radius R, which is banked at an angle β with respect to the ground. Assume there is friction between the wheels and the road. Let μs be the coefficient of static friction and g the magnitude of the gravitational acceleration. You may neglect kinetic friction (that is, the car's tires do not slip). Derive an expression for the range of possible speeds vmin≤v≤vmax necessary to keep the car moving in a circle without slipping up or down the embanked turn. Express your answer in terms of some or all of the following: μs, β, m, R and g.
Provide your expressions for both vmin and vmax.
vmin=?
vmax=?
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