Rollercoasters and Loops and Normal Forces

AI Thread Summary
To find the normal force at the top of a loop in a rollercoaster, the equation derived is FN = Fc - Fg, where Fc is the centripetal force and Fg is the gravitational force. The user initially calculated that the normal force is zero, indicating a minimum height scenario. However, further discussion clarified that a general equation is needed to express the normal force at any height using only the variables m, g, and r. The user seeks assistance in formulating this general equation. The goal is to accurately determine the normal force at the top of the loop for varying heights.
komarxian
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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 = Fc = FN+Fg ∴ Fc=FN+Fg ∴FN = Fc - Fg ∴ N=mV2/r - mg

The Attempt at a Solution


Fc=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.
 
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