You ride a roller coaster car of mass 1500 kg down a frictionless track a distan

Question

You ride a roller coaster car of mass 1500 kg down a frictionless track a distance H = 23m above the bottom of a loop as shown. If the loop is 15 m in diameter, the downward force of the rails on your car when it is upside down at the top of the loop is

You ride a roller coaster car of mass 1500 kg down a frictionless track a distance H = 23m above the bottom of a loop as shown. If the loop is 15 m in diameter, the downward force of the rails on your car when it is upside down at the top of the loop is

Explanation / Answer

distance between start and top of loop is (23m - 15m) => 8m

Kinetic energy=Potentail energy
(1/2) m v^2 = m g h
v^2 = 2 g h
v^2 = 2 9.81m/s^2 8m
v^2 = 156.96 m^2/s^2

v=12.52m/sec

F(c) = m v^2 / r
F(c) = 1500kg 156.96 m^2/s^2 / 7.5m
F(c) = 31392N

Some of that force is provided by the track, and some by gravity.
F(g) + F(track) = F(c)
F(track) = F(c) - F(g)
F(track) = F(c) - m g
F(track) = 31392N - 14715N
F(track) = 16677N

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