Rollercoasters and Loops and Normal Forces

[komarxian]

Homework Statement

<I will attach a diagram below> In terms of m, g and r. FInd the normal force at the top of the loop.

Homework Equations

∑F = F_c = F_N+F_g ∴ F_c=F_N+F_g ∴F_N = F_c - F_g ∴ N=mV²/r - mg

The Attempt at a Solution

F_c=mV²/r - mg and V²=ra and a=g ∴C=mrg/r ∴C = mg ∴mg-mg=N ∴ N=0 N. BUT after discussing with a guy in AP Physics C at my school, he said that this is solving for the minimum height. SO I think I need to solve for the general equation to solve for the normal force at the top of the loop at any height using the variables m, g, and r only (I'm pretty sure that's what my instructions meant). Could anyone help please? I will send an image of my work as well.

 

[komarxian]