Mechanics of a chain climbing out of a jar

I’m not sure if this has a name for it, but if it does please edit it in.

I first saw this in high school. The physics teacher, Mr. Wilde (who lived up to his name) gave us a demonstration of Newton’s first law. He had a straight mouthed jar with a long bead chain in it. “Objects in motion want to stay in motion. Here the chain must go up in order to get out of the jar. It’ll want to continue to go up until gravity wins out.” Is more or less what he said.

Years later I bought a brass bead chain and had done this very same demonstration several times.

What I have noticed is that the higher it has to fall, the higher the chain climbs. This of course makes sense, there’s more potential energy.

Even later, I got a chance to record the chain with a high speed camera and view the lab demonstration’s larger and heavier bead chain*. Here it was noticed that mass affects the height as to which the chain climbs. It was suspected at first that a heavier chain would climb just the same or higher, but it was the exact opposite – it barely climbed at all. This video shows the heavier chain held at a higher elevation than the previous video. Only when we did it in a four story stairwell did it climb into the air (in retrospect, we shouldn’t’ve done that when classes were changing).

What I want to know is if there has been any work in describing this demonstration and if it can explain how high the chain will climb based on how high it can fall (and if it takes mass into account).