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## Homework Statement

A marble rolls down a track and around a loop-the-loop of radius R. The marble has mass m and radius r. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off?

## Homework Equations

What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off?

## The Attempt at a Solution

Find initial energy: mgh

Final energy tabulation: mg(2R) + 0.5mrg + 0.5(2/5)mr^(2)(v/r)^2

Set equal to initial energy, I obtain 2R+7/10 =h, which isn't the right answer, what did I do wrong?

I found the velocity at top by using newton's 2nd law, i get v = squareroot(rg). I find w using constraint of wr=v. I get 2/5(mr^2) using moment of inertia for a solid sphere.

Any help would be appreciated. I'm so confused why this doesn't work out.