A roller-coaster car may be represented by a block of mass 50.0 kg. The car is released from rest at a height h = 57.0 m above the ground and slides along a frictionless track. The car encounters a loop of radius R = 19.0 m at ground level, as shown. As you will learn in the course of this problem, the initial height 57.0 m is great enough so that the car never loses contact with the track.




1. Find an expression for the kinetic energy K of the car at the top of the loop.



2. Find the minimum initial height h_min at which the car can be released that still allows the car to stay in contact with the track at the top of the loop.