# An engineer wants to design a circular racetrack of radius Lsuch that cars of mass M can go around the track at speed Wwithout the aid of friction or other forces other than theperpendicular contact force from the track surface.Find an expression for the required banking angle 0 of thetrack, measured from the horizontal. Express the answer interms of M, L, W, and g.Suppose the race cars actually round the track at a speedu > W. What additional radial force F, is required to keepF, =the cars on the track at this speed? Express the answer interms of M, L, W, u, and g.||

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Step 1

The figure shows the racetrack of the car and the forces acting on the car.

Step 2

According to the centrifugal force due to rotation,

The net force acting on the curved path of the car moves in the race track to balance the motion of car,

Step 3

Rewrite the above relation to find the banking angle.

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