The mystery behind the self-siphoning beads Recently, I saw this video, showing the phenomenon of the self-siphoning beads.  Dangling one end of a coiled string of beads outside of the container, a single pull is needed to cause all the beads to fall out.  Why is this so?  My main question: It is also observed that the longer and more coiled the string of beads is, the higher the exiting beads will "jump".  Why?  This not only defies the principle of gravity that I learnt, but also the fact that energy cannot be created!
 A: first edit: Since originally posting my answer I have been lying in bed thinking about it and realized it isn't right. rather than going out to watch the explainer video I am instead going to go back to bed and work out the right answer. 
Second edit: it is now 5 hours later and I am awake again, here is what I have figured out (without watching the explainer video): 
the guy in the video lifts the free end of the chain of beads through a certain distance above the level of bead chain in the jar, and releases it. 
this portion of bead chain then falls freely under the influence of gravity and thereby possesses a certain velocity and momentum at that instant when the falling portion of the chain has no more slack in it.
at that moment, the chain goes tight and is ready to begin applying tension upon the stationary portion of the chain inside the jar. the momentum of the falling chain imparts an impulse on the next bead of the chain sitting in the jar which has been stationary until then. the impulse is sufficient to boost the bead ballistically upwards off the surface of the bead pile. 
meanwhile, the falling portion of the chain continues to pull on the rest of the chain in the jar and we note that the bead chain's path through the air in the vicinity of the lip of the jar assumes a curved path: up over the lip of the jar, and then down.
the beads occupying the curve are hence being whipped around in a semicircle (or something close to it) which means they are being acted upon by centrifugal force during their tenure in the curve.
that centrifugal force is asserted as a tension in the bead chain which is experienced by the next chain in the string which is at rest in the top of the jar, and it launches upwards in response. 
the centrifugal force generated by the reversal of direction of the chain then keeps the chain tight and, along with the tension being provided by the portion of the chain which is falling outside the jar, furnishes the tension needed to keep lifting more chain out of the jar. 
meanwhile, the free end of the string has hit the floor below which means the velocity at which the bead string is falling is now fixed, as is the tension developed in the balance of the string length. 
the radius of curvature of the loop of bead chain flying out of the jar adjusts itself dynamically so the centrifugal force experienced by the beads occupying it is just sufficient to balance the tension in that portion of the chain between the jar and the floor.
the position of the apex of the upward-moving chain matches the height at which the guy in the video originally lifted the free end of the chain to begin the process. 
as long as the chain as a whole is in motion, it is in tension along its entire moving length, and it is this tension which lifts beads in the chain up and out of the jar. 
The "loop" of moving beads jumps around its equilibrium position in the air because of how the bead string happens to be coiled about inside the jar. 
the apparent loop height appears to diminish with time as the jar empties, but this is because that height represents the distance between the topmost level of chain in the jar and the top of the loop, not the top of the jar.  
A: That is a cool video! They also link to an "explainer video".
Once a few beads are free to fall, they do (because of gravity). Falling converts potential energy to kinetic energy, but they share their kinetic energy with the other beads, giving them the energy to move. 
Now since the chain hangs over the edge of the container, it can only pull the inner beads up. When the falling chain is long enough, it pulls with so much force that the resting beads jump.
You could describe the system mathematically like this:
$E = Mgh + \frac{1}{2}ms^2 - \text{frictional losses}$
where $M$ is the mass of all the beads, $h$ is the average height of the beads, $m$ is the mass of the moving beads, and $s$ is the speed the beads are moving at. (Since the beads are fairly rigid, they are all going about the same speed, so you can add all of their masses.) Notice that the average height decreases as the beads move to the ground. This gives a lot of kinetic energy which goes up the chain (increasing $s$). Since the beads in the container can only move up, they move up with speed $s$.
A: The faster you pull the first beads out, the higher the chain will rise. Sounds logical, not? They won't fall out over the edge by themselves (if you put a piece of the chain outside the jar) because in that case, an infinite acceleration is required to pull the other beads around the edge. And the longer the chain falls to the ground, the lower the top of the parabola gets because the chain that's falling accumulates mass, so the reaction of the beads inside gets bigger and both effects make the top go lower, until the chain hits the floor.
As said, when you give the first beads an upwards motion, a reaction force from the other beads won't let chain get as high as in the case of a free-falling chain. The beads fall faster and faster when not in contact with the floor. When the first beads hit the floor a steady state stream of beads comes into existence, and this stream has a parabolic form, with a fixed height (in the ideal case) and this height depends only on the force upwards you gave to the first part of the chain, and the height from which they fall (like I said in the first part). When the beads are still all in the air (before touching the floor) the top of the parabola gets less high, to take on a fixed value when the first bead reaches the ground.
Maybe I said two times the same, but better said too much as too little (of course telling it one time will be the best, but I just wanted to clarify).
