A roller coaster designer wants to make a coaster travel over the top of a circu

Question

A roller coaster designer wants to make a coaster travel over the
top of a circular hill so that the riders feel weightless. The circular
hill has a radius of r = 10 m. Before coming to the circular hill the
roller coaster goes down a large hill that is sloped at ? = 45?. You
may ignore all sources of friction or air resistance.
(a) Draw free body diagrams of the coaster on the large hill and on top of the circular hill. Your
arrows must be the correct length.
(b) How far above the top of the hill must the coaster start so that the riders will feel weightless at
the top of the hill.

Explanation / Answer

N = mg - mv^2/r = 0

v = sqrt(rg) = sqrt(9.8 x10) =9.90 m/s

so using energy conservation ,   mgh = mv^2 /2

h = v^2 /2g = 5 m

h = lsin45

l = 5/sin45 = 7.07 m

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