Aroller coaster car of mass m is on a track that forms a circular loop of radius r in the vertical plane. if the car is to just maintain contact with the track at the top of the loop, what is the minimum value for its speed at that point?

v = \sqrt{Rg}

Explanation:

As the car just maintain the contact at the top point of the circular track, it means the weight of the car is just balance by the centripetal force acting on the track.

Let v be the speed of the car.

M g = Mv^2 / R

g = v^2 / R

v^2 = R g

v=ir = 3x15 =45 v

e/c, where e is its total energy