How high to complete the loop?


A little roller coaster (see attached image) is at a certain height h and starts moving downwards, Neglecting the friction and drag. From what height does the coaster have to start in order to complete a full loop with radius a without coming of the track? h should be expressed in a.


I feel like somehow the potential energy formulas should be involved here. But how do I calculate how much energy/momentum is required to have such a centripetal force so that the coaster stays on its track. Obviously the slope doesen’t seem to affect anything so it’s just the height that should be related to the radius of the loop.

Attached Images
File Type: jpg Loop.jpg (15.7 KB)

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