Maximum Height for a Car to Roll Over a Hill on a Frictionless Track

[port31]

Homework Statement

A car on the frictionless track starts from rest at height h. The tracks valley and hill
consists of a circular-shaped segments of radius R.
What is the maximum height h 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.

The Attempt at a Solution

ok I know that its potential energy is mgh when we let it go. And we need to put it at least
the height of R to make it the top of the hill on the other side.
But I am not sure how fast it can be going and not lift off the ground.
I know that it would have to exceed its weight. I am not sure how to relate the energy into force.

 

[CWatters]

Think about the path of the car over the top of the hill. It's a curve of radius R so what force do objects moving on a curved path experience?

 

[port31]

ok thanks.
so now I have
\frac{mv^2}{r}=mg
v=\sqrt{rg}
then
mg(h-r)=m\frac{rg}{2}
and this gets me the correct answer.
thanks for the help .