Height of ramp given normal force in circular loop

[mastergaurang]

Homework Statement

The attachment shows the problem. The normal force at the top of the loop is 3 g's (as in g-force).

Homework Equations

PE = mgh
KE = .5mv²
Fc = $\frac{mv²}{r}$
PE + KE = PE' + KE'
v = $\sqrt{2gh}$

The Attempt at a Solution

The normal force would be: 30 * mass.

Since he's at the top of the loop, the formula would be:
Fnet = Fc = (mv²)/r = Fnormal + mg

I have tried to cancel the mass out and to formulate a system of equations but I think I'm missing something. One formula I got is by setting PE equal to KE (for h, but only at the bottom before the skater goes up the loop):
h = $\frac{.5v²}{g}$

I am starting to think that I need the radius/velocity. Any ideas?

 

[rock.freak667]

The Attempt at a Solution

The normal force would be: 30 * mass.

Since he's at the top of the loop, the formula would be:
Fnet = Fc = (mv²)/r = Fnormal + mg

Right so you can get v² from this.

I have tried to cancel the mass out and to formulate a system of equations but I think I'm missing something. One formula I got is by setting PE equal to KE (for h, but only at the bottom before the skater goes up the loop):
h = $\frac{.5v²}{g}$

I am starting to think that I need the radius/velocity. Any ideas?

Yes you will need the radius since v² will be in terms of the radius 'r'.

You are also correct in that h = ½v²/g, so you can use the v² you found above here.