A roller coaster consists of a large hill, followed by a loop with a radius of 2

Question

A roller coaster consists of a large hill, followed by a loop with a radius of 20 meters. The roller coaster car starts at the top of the hill, gains speed as it rolls down, and then travels around the loop, starting at the bottom and turning the riders upside down at the top. You may neglect friction and air resistance. (For clarication: the bottom of the hill is at ground level, as is the bottom of the loop.

a) How high must the hill be to ensure that the people don't fall out?

b) Why doesn't the exact shape of the hill matter?

Explanation / Answer

By conservation of energy, the hill must be as high as the loop. The diameter of the loop is 2*20 m = 40 m.

Thus, the hill must at least be 40 METERS HIGH. [ANSWER, PART A]

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It is because gravitational force is a conservative force, and the work it does does not depend on the path. [ANSWER, PART B]

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