https://www.wired.com/2013/07/the-physics-of-that-gravity-defying-chain-...
https://www.youtube.com/watch?v=_dQJBBklpQQ
https://www.youtube.com/watch?v=-eEi7fO0_O0
https://www.youtube.com/watch?v=6ukMId5fIi0
This is a provisional explanation - I plan to write this up properly later - Jared
Method:
Place the chain inside the beaker, hold the beaker in your hand then throw one end over the side so that the end outside the beaker is longer than the section going between the top of the beaker and the coiled up chain (so that gravity is able to pull the rest of the chain out of the beaker). For the small plastic beaker currently in the box, 15m works best.
Let go and watch as the rest of the chain flies out of the beaker, producing a surprisingly wide arc into the air as it goes. If you're lucky you may see coils and loops, appearing to be frozen in space even as the chain continues to move.
Explanation:
The weight of the chain outside the beaker is greater than that of the free section inside the beaker, so the chain is pulled out, at some speed. However, due to Newton's 1st and 2nd laws, the individual beads of the chain can't change direction instantaneously. Instead, it takes a continuous force pulling them round in a circle until they are travelling downwards towards the floor - hence the arc.
If the chain hits the side of the beaker as it's doing this, the disturbance will attempt to travel away from the point of contact - i.e. back towards the bottom of the beaker. However, the chain is moving fast enough to counteract this, and so the net effect is that this disturbance barely moves. This is the reason for the standing coils and loops you might observe (it may be that the wave velocity equals the speed of the chain at this point, but I'd have to check this).
Further Points:
You could try drawing an analogy with siphoning a liquid using a long hose/straw.