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Roller Coaster Question - Please Help

ntukza
in Applied Mathematics

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A roller coaster freewheels down a frictionless track from rest a height h above the ground. At the bottom the track becomes a vertical loop with diameter 2a = 16m. How high above the ground (value of h) must the roller coaster start if it is to reach the top of the vertical loop without lifting off the track?

 

The given answer is 20m. I would have thought that the roller coaster needs to start at a height equal to, or slightly more than, the diameter of the vertical circle at the bottom. Energy at start = energy at end, therefore mgh = mg2a, and h = 2a = 16m. Please help me understand why it is not so.

 

Thank you in advance

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