Why Must the Normal Force Equal Zero at the Top of a Loop?

[Brett R.]

Homework Statement

In the normal loop the loop problem involving rotational energy where the marble goes down the hill and goes through a loop the loop, it asks for the minimum height of the hill to keep the marble on the track.

Homework Equations

But why does the normal force have to equal 0?

The Attempt at a Solution

I just don't know. How do we factor the idea that the marble doesn't fall off into the problem?

 

[haruspex]

But why does the normal force have to equal 0?

The normal force cannot be negative, agreed?
You are looking for the minimum initial height for it to stay on track. If the normal force at the top were greater than zero then a lower initial height could have been used.
Zero is the only remaining possibility.