A roller coaster car on the frictionless track shown in the figure below starts

Question

A roller coaster car on the frictionless track shown in the figure below starts from rest at height h. The track consists of circular-shaped segments of radius R.

http://www.webassign.net/knight/p10-53.gif

(a) What is the maximum height hmax from which the car can start so as not to fly off the track when going over the hill? Give your answer as a multiple of R. (Hint: First find the maximum speed for going over the hill.)
hmax =_______

(b) Evaluate hmax for a roller coaster that has R = 14 m.
_______m

Explanation / Answer

for the rollar coaster to not fly

mv^2/r = mg

V = rg

mg(h-r) = 1/2 m v^2

h-r = 1/2x r

h= 1.5r

b)

h = 21m

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