Physics Riding a loop-the-loop?

[Eats Dirt]

Homework Statement

A car in an amusement park ride rolls without friction around the track it starts from rest at a point A from height H above the bottom of the loop. treat the car as a particle. what is the minimum value of height (in terms of R radius)such that the car doesn't fall off the very top of the ramp.

Homework Equations

E=mgh
gravity constant
Fc=.5mv^2
K=.5mv^2

The Attempt at a Solution

i don't really know where to start but ill give it a shot.
2R is the height of the

so mgh-mg2R= 1/2mv^2


i don't really know what else to do -_-

since mgh-mg2R=1/2mv^2 could you assume that v approaches 0 then mgh=mg2R which makes sense to me because if the surface is frictionless then energy is being conserved so does this mean if the height from which it came = the height of what it needed to go to?

 

[PeterO]

Homework Statement

A car in an amusement park ride rolls without friction around the track it starts from rest at a point A from height H above the bottom of the loop. treat the car as a particle. what is the minimum value of height (in terms of R radius)such that the car doesn't fall off the very top of the ramp.

Homework Equations

E=mgh
gravity constant
Fc=.5mv^2
K=.5mv^2

The Attempt at a Solution

i don't really know where to start but ill give it a shot.
2R is the height of the

so mgh-mg2R= 1/2mv^2


i don't really know what else to do -_-

since mgh-mg2R=1/2mv^2 could you assume that v approaches 0 then mgh=mg2R which makes sense to me because if the surface is frictionless then energy is being conserved so does this mean if the height from which it came = the height of what it needed to go to?

You don't want to merely get the cart back up to the top of the loop-the-loop, you want it to stay on the track, so it has to have a specific speed [at least] so the hill will need to be higher. How much higher is the question.