In order for you not to fall out of a roller coaster when it goes around a loop,

Question

In order for you not to fall out of a roller coaster when it goes around a loop, the speed must be sufficient such that the normal acceleration is great enough to counteract the Earth's gravity. In fact most roller coasters are designed such that when you are upside down in a loop, it feels the same as if you are right side up. Think of it this way: If earth has 1g pointing down, then for you to feel right side up while upside down, you need to be going fast enough to have 2g's of acceleration in the normal direction. (-1g + 2g = 1g). For the roller coaster shown, find the velocity at which the passengers will experience 1 g towards their feet at the top of the loop. Assume that the velocity is constant and the radius of the loop is 25 ft.

Explanation / Answer

V^2/r-g=-g

v^2/r=2g

v=12.216 m/s

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