Calculating Initial Height for Marble to Roll Along Loop-the-Loop Track

[suspenc3]

A small solid marble of mass m and radius r will roll without slipping along A loop-the-loop track, if it was released from rest somewhere on the straight section of track from what initial height h above the bottom of the track must the marble be released so that it is on the verge of leaving the track? (the radius of the loop-the-loop is R)

Also assumes the marbles radius << loops radius

Ive seen problems like this in conservation of energy..whats the difference campared to this?

 

[kp]

It is a conservation of energy problem. You have two kinds of kenetic energy to resolve when dealing with a rolling sphere. "I" know, but do you know?

 

[emptymaximum]

This problem can be solved with conservation of energy, but it doesn't have to be. So the relation to conservation of energy problem is that it is one.

You could also do it fairly easily with Newton's 2nd as well.

Also, there is only one kinetic energy. Do you mean that there is another component of kinetic energy because the ball is rotating about its horizontal axis? Doesn't matter. The rotation is about the centre of mass of the marble, and for a sphere of uniforn density it is at the centre of the sphere. So the rotation of a point on the surface of the sphere has nothing to do with the motion of the centre of mass of the sphere in the co-ordinate system of the loop.

how i saw this problem was: a roller coaster on a smooth track is elevated to some height, realeased and goes through the loop. How high does it need to be when it starts in order to make it through the loop..