A roller coaster rider has a mass of 80 kg and is riding in the coaster shown in the figure. If the vehicle has a speed of 10.0 m/s at the top of the first hill (assume same height as the top of the circle above Point A):
a) how "heavy" does the rider feel at point A?
b) how heavy does the rider feel at point B?
The Attempt at a Solution
Potential Energy at the top of the first hill: 80 * 9.8 * 20 = 15,680J
Kinetic energy at the top of the first hill: 0.5 * 80 * 10^2 = 4,000J
Total energy: 19,680J
At the bottom of the first hill, all that energy is kinetic, so:
0.5 * 80 * v^2 = 19,680J
v = 22.18m/s
Ac = 22.18^2/10 = 49.20m/s^2
F = ma = 80 * 49.20 = 3,936N - That's the answer to Part A
But then there's an issue. The potential energy at point B is mgh = (80)(9.8)(30) = 23,520J. That's more energy than the system has. I don't know how the rider is going to make it to point B without falling back down, so I certainly don't know how heavy he feels. Is my approach to solving this totally incorrect?
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