# Car rolling down a track.

1. Jul 21, 2012

### port31

1. The problem statement, all variables and given/known data
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?
3. 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 im not sure how fast it can be going and not lift off the ground.
I know that it would have to exceed its weight. Im not sure how to relate the energy into force.

#### Attached Files:

• ###### car ramp.JPG
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2. Jul 22, 2012

### 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?

3. Jul 22, 2012

### 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 .