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A chain falling from a table

Experiments and webpage by Gaspar Palacio (Highschool internship 06/2012)

   This problem of chains falling from a table is more tricky than it seems. The thing is to roll up the chain on the edge of a table, and let the end fall on the ground. On a normal speed, it's difficult to see something, but we filmed it at 420fps (fig.1), and we noticed that the chain was going up as the time went by. We tried loads of different dispositions, but no one worked, as you can see on the videos (fig. 2 and 3). 

Fig.1 : This is the best configuration we found, we can see that the chain is always rising up,  and stops when it reaches its (probably) maximum height.

Fig.3 :We had the idea to remove space between each turnings, but as you can see, it rises only at the end, and not as we'd have expected.

    Then, we decided to see if some friction could change something, so we took a plank of wood, that has friction in one direction, and not in an other. As you can see on the videos (fig.4 and 5), friction doesn't change anything. After that, we decided to change something in the disposition : something to keep the chain from moving (we can see the chain turns back), and a arc of circle on a different direction. As you can see (fig.6 and 7), it changes something.

Fig.4 and 5 : same chain, same disposition, just a plank of wood turned on a different direction. This shows that the friction is not very important for this problem.

Fig. 6 and 7 : still the same chain, but not same disposition than chains above. We can see that on the lefter video, the chain rise up more quickly, and the righter chain doesn't move at all.

    We're starting to understand a bit what's happening with this chain. We think that the chain rises because of a geometrical problem. Actually, there may be a balance between space between turnings, and the number of turnings : when the chain gets to a turning, there's too much length it has to deliver, and this space has to be somewhere, so the chain goes up. When there's too much space between turnings, the length can be deliver without having to rise, and when the nuber of turnings are too big, the chain just don't move at all, and falls normally. So this motion between two turnings is very important : from left to right, with a constant and appropriate velocity, that give to the chain the possibility to rise up.

    We still can't say anything we're sure enough, but if you're interested about chains, you can take a look to James Hanna's work. Our work stops here, but may be continued after.