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Falling chains (Photo credit: Ruina lab)In 2011, a team of physicists at Cornell University in Ithaca, New York showed that when a falling chain hits something (say, a table), it might, contrary to all intuition, speed up and fall faster than it would if it fell freely.  By carefully studying its mechanics, they showed how the impact could actually pull the remainder of the chain downwards.  As this picture from their experiment shows, they were right.  The two strange-looking chains were dropped from the same height at the same time, but the one on the left, which fell into a pile on a table, fell faster than an identical chain falling past the table.

Falling chainAnoop Grewal, Phillip Johnson, and Andy Ruina made their discovery by taking a second look at a classic physics textbook problem involving a chain falling into a pile. The standard solution assumes that the last link in the falling chain (shown in red in the picture) effectively disconnects from the link above when it hits the pile — in other words, that it stops without affecting the rest of the chain.  It’s a reasonable assumption, given how loosely links are connected and the way chains generally behave.  The team weren’t convinced that it would always hold, though, so they decided to work out the mechanics of what would happen if the assumption wasn’t true.  If the last link in the chain continued to interact with the link above it, it could exert a force on the falling portion of the chain.  Depending on the strength and direction of that force, the last link might push back against the remaining length of chain and slow it down or it might pull on the chain, speeding its fall.

How would such a mechanism actually work in practice?  The team came up with several different designs where the last link could pull on the remainder of the falling chain  The most straightforward one is based on the idea of a tilted rod hitting the floor.  Since the rod is at an angle, one end will strike the floor first; the other end of the rod will pivot around the contact point with the ground, making it fall faster .  The free end speeds up for the same reason that you turn quickly if you grab onto something while running or skating: conservation of angular momentum.

A falling rod

When a rod falling at an angle hits the floor, the free end speeds up.

Anything attached to the free end of the rod (say, a rope connecting it to the rest of the chain) will get tugged downwards by the free end.  In this way, the impact with a surface actually creates a force which “pulls” in the rest of the chain.  It’s counter-intuitive and may even sound crazy, but it’s true.  The trio built chains based on their design — they look something like a wonky rope-ladder — and used a high-speed camera to film a pair of them falling side-by-side.  Just as they’d predicted, the chain that hit the table fell faster than the free-falling one (click the picture to see a video):

Falling chains (credit: Ruina lab)

The chain on the left hits the table and so falls faster (click image for video) [credit: Ruina lab]

They also tested an “ordinary” link chain, which turns out to behave just the way you would expect.  In this case, the last link actually disconnects from the rest of the falling chain and doesn’t pass along any force, meaning the assumption used to solve the textbook problem is valid in this case.

Falling link chain (Photo credit: Ruina lab)

Impact with a table doesn’t speed up an ordinary link chain, since the last link decouples from the rest of the chain (click picture for video) [credit: Ruina lab]

Given that we can measure and understand fluctuations in the universe’s infancy, it’s pretty striking that we’re still learning new things about something as familiar as a falling chain.  I often end posts by marvelling at the vast richness of the world, but this time its our ability to persistently question and precisely conceive the world that amazes me.  It’s wonderful that science — the same kind of science that enables us to build durable bridges and lightweight airplanes, to loft satellites to the edge of the solar system and to explore the deepest ocean valleys — enabled these researchers to predict and confirm such an odd, counter-intuitive result in something so seemingly mundane and straightforward.  Tiny mysteries and everyday wonders abound, just waiting to be discovered and described by an inquiring mind — and that’s part of what makes science so great!

Ref
Grewal, A., Johnson, P., & Ruina, A. (2011). A chain that speeds up, rather than slows, due to collisions: How compression can cause tension American Journal of Physics, 79 (7) DOI: 10.1119/1.3583481
(There’s also a preprint version of the article freely available on the Ruina lab webpage.)

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