# Conservation of Energy - Roller Coaster

## Homework Statement

A roller coaster car has a mass of 800kg. It is released from the top of the hill A and moves without friction down the track. Determine the minimum exit velocity vD at ground level so that the car travels around both the circular loops (Loop B - Radius= 10m, Loop C - Radius= 7m) without leaving the track.

Diagram here,

## The Attempt at a Solution

To do this I thought that I would just use basic conservation of energy and trace the velocity of the roller coaster through both of the loops until it exits. In this problem the height isn't given, and must be calculated in another part of the problem.

Without knowning the height that the coaster begins at, how would I begin?

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You don't know the height at A but you do know the heights at B and C.

Your main concern here is that it makes the 10m loop. (It's like New York - if it makes it there, it will make it everywhere.)
Figure the minimum height of A to do that.
Then use that height to plug back into figuring the KE at the bottom of the hill because that will determine the Exit V.