- #1

hrithikguy

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## Homework Statement

Part of a roller-coaster ride involves coasting down an incline and entering a loop 8.00 m in diameter. For safety considerations, the roller coaster speed at the top of the loop must be such that the force of the seat on a rider is equal in magnitude to the rider's weigt. From what height above the bottom of the loop must the roller coaster descend to satisfy this requirement?

## Homework Equations

a_c = v^2/r

Conservation of Energy

## The Attempt at a Solution

m* a_c = mg

m* v^2/r = mg

v^2/r = g

v^2 = rg

mgh = 1/2 mv^2 + mg * 8

9.8 * h = 1/2 * rg + 8 * 9.8

9.8 * h = 1/2 * 4 * 9.8 + 8 * 9.8

h = 2 + 8

h = 10

However, the answer is 12.

Please guide me to the solution.

Thanks!