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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!