"a problem involves a car of mass m going down a track from a height h, and round a loop of radius r. the loop is frictionless.
it asks for the minimum cut-off speed required, at the highest point in the loop (call it point d), such that the car makes it round the loop without falling. i know the solution; i should set the centripetal accleration equal to 9.81. in other words, contact force with the track at point d is equal to zero.
but i tried solving it by conservation of energy. at point d, the car is at a height 2r from ground level. therefore, in order for the car to reach that height at point d, it must initially have a potential energy of mg(2r). meaning, it should be released from a height h = 2r.
i got the wrong answer and i'm confused why that happened. isn't that how conservation of energy work? clarify, where's the error in my solution? "