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A problem involves a car of mass m going down a track from a height H,...

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Physics

A problem involves a car of mass m going down a trackfrom a height H, and round a loop of radius r. The loop isfrictionless.

It asks for the minimum cut-off speed required, at thehighest point in the loop (call it point D), such that the carmakes it round the loop without falling. I know the solution; Ishould set the centripetal accleration equal to 9.81. In otherwords, contact force with the track at point D is equal tozero.

But I tried solving it by conservation of energy. Atpoint D, the car is at a height 2r from ground level. Therefore, inorder for the car to reach that height at point D, it mustinitially have a potential energy of mg(2r). Meaning, it should bereleased from a height H = 2r.

I got the wrong answer and I'm confused why thathappened. Isn't that how conservation of energy work? Pleaseclarify, where's the error in my solution?

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