An engineer wants to design a circular racetrack of radius R such that cars of mass M can go around the track at speed U without the aid of friction or other forces other than the perpendicular contact force from the track surface.
Find an expression for the required banking angle θ of the track, measured from the horizontal. Express the answer in terms of M, R, U, and g.
Suppose the race cars actually round the track at a speed ω >U. What additional radial force Fr is required to keep the cars on the track at this speed? Express the answer in terms of M, R, U, ω , and g.
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