## The physics of a rising chain

Posting will be light this morning as Professor Ceiling Cat has cat stuff to do. In the meantime, entertain yourself with two videos of a remarkable phenomenon of physics: the slinking chain. The first shows the phenomenon, and the second goes into greater detail.

A longer video:

If you want a more detailed explanation for this weird phenomenon, a long one (which also accurately predicts the chain’s speed) is given at Empirical Zeal. It may be more than you want to read, but at lest read the first and last parts. The answer involves changing momentum.

h/t: Michael

1. Posted July 3, 2013 at 4:01 am | Permalink

Or why physics is more amazing than religion…

2. docbill1351
Posted July 3, 2013 at 5:31 am | Permalink

Chain o’ Beads is nothing compared to a Roll o’ Toilet Paper that Kink unwound when he was a kitten.

3. Torbjörn Larsson, OM
Posted July 3, 2013 at 6:05 am | Permalink

That was new. But refreshing.

And now I want to go out play with beads!

4. John Taylor
Posted July 3, 2013 at 6:15 am | Permalink

I’m not sure that his solution for velocity is correct. A very popular physics problem is the old chain hanging off a table problem. This problem is somewhat similar. What causes the chain to pick up speed is gravity. The length of chain above the top of the beaker can not contribute to increasing the speed of the chain because on average it has not fallen through gravity (half going up, half going down). If anything the portion of the chain above the beaker should reduce the overall velocity of the chain because it adds mass that has to be accelerated. The amount of chain above the beaker should reduce to the velocity as it does in the formula for the old chain hanging off the table problem. In the case where H >>> l the formulas should reduce to the same thing.

When I solve it using an analysis of potential gravitational energy and kinetic energy that is what I find and the solution is much simpler. Of course that analysis does nothing to explain the interesting behaviour.

5. John K.
Posted July 3, 2013 at 6:19 am | Permalink

I would have explained as the beads having a particularly low ability to bend (as compared to a regular rope or string), so the downward momentum of the chain will have a tendency to pull the top part up as the motion runs into the limit the chain can bend. This makes the chain go clear of the edge of the container, eliminating the frictional force that would normally occur there, and making the phenomenon continue more easily.

A regular rope can do this as well if enough of it is falling out of the edge of the container, it just does not have as much of the counter-intuitive upward motion that the bead chain does. Also, the rope will be heavier per unit length, so the momentum at the top will require greater force to pull it up, also producing a less impressive effect that will be unlikely to clear the edge of the container.

Holding the container higher gives the rest of the chain more momentum as it falls since less of it comes to rest on the ground, to contribute less momentum. Higher momentum imparts more force to the top, making the chain spring up higher.

This may all be in the 3rd explanation link, I have not read it yet. Apologies if I am being redundant!

• John K.
Posted July 3, 2013 at 6:29 am | Permalink

Ah, perhaps I am wrong about the unit mass of the chain having an effect. t may well cancel out. Corrections welcome!

I also occurs to me that the beads will bounce away from the container when they do actually hit it to mitigate losses to friction as compared to a rope or string, but that seems like a minor contributing factor.

Now I need to find an inflexible rope and try this with a bucket, if only I could find the time . . .

• cherrybombsim
Posted July 3, 2013 at 9:57 am | Permalink

I got a hold of one of these chains when I was about 10 years old and had all kinds of fun with it. This is the right explanation.

6. nurnord
Posted July 3, 2013 at 10:20 am | Permalink

Jerry, the second ‘longer’ vid is…the same vid !

• nurnord
Posted July 3, 2013 at 10:21 am | Permalink

Hmm, the second on the comments page IS the longer one, but on the general article page, it is the first vid duplicated…weird !

• Posted July 3, 2013 at 10:26 am | Permalink

No it’s not. The first is contained within the second, but the second is a lot longer and has more stuff.

7. Posted July 3, 2013 at 2:22 pm | Permalink

I wish that instead of just holding it up, they had gone to some scenic tower and let the full and increasing lower length of the chain pull the beads out of the jar. How high would it rise?

8. Theo Bromine
Posted July 4, 2013 at 7:21 am | Permalink

I once had a cat (the dear departed Kizhe) whose favorite toy was a ~2m length of chain like this. He would come running from just about anywhere around the hose if he heard the sound of it being moved, then he would take it and proudly carry it around the house (occasionally playing fetch with it if the mood struck him). (I guess the chain was too short to do its own tricks.)

• Theo Bromine
Posted July 4, 2013 at 7:23 am | Permalink

from around the HOUSE, not the HOSE :/