Suppose there is a rollercoaster on a frictionless track it, Ask an Expert

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Suppose there is a rollercoaster on a frictionless track. It is at the top of the track (the part where the rollercoaster suddenly drops off and you lose your stomach) and at the bottom of the track there is a loop of radius R. How high must the hill be, in terms of R, for the loop to be completed?

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