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## Homework Statement

A roller coaster car on the frictionless track shown in the figure below starts from rest at height h. The track's valley and hill consist of circular-shaped segments of radius R. Find the formula for the maximum height h_max for the car to start so as to not fly off the track when going over the hill. Give you're answer as a multiple of R. Show that when R = 10m, h_max =15m.

http://img152.imageshack.us/img152/181/physquestion.jpg [Broken]

## Homework Equations

U=mgh

K=1/2 mv

^{2}

K=1/2 I [tex]\omega[/tex]

^{2}

I = mr

^{2}

[tex]\omega[/tex] = v/r

where [tex]\omega[/tex] is angular velocity

## The Attempt at a Solution

I attempted to use simple substitutions for I and [tex]\omega[/tex] and then combine the three equations so as to have a total energy of 0, but I can't seem to find a proper equation that works. Any suggestions/tips?

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