A roller coaster works by gravitational energy. The coaster car is pulled up to a high point and then released, rolling downwards on the track through all manners of curves and loops. I have a short roller coaster car that I pull up to the top of a hill of height \(H\). The coaster car is released from this height and must go around a perfectly circular vertical loop with a radius of 20 meters (and the bottom of the loop is on the ground). If I don't want the coaster car to fall off the loop at any point, what should be the minimum value of \(H\) in meters?
Details and assumptions
- Neglect friction and air resistance.
- Treat the roller coaster car as a point.