Does a Falling Slinky Defy Gravity?

[Music]

So, this is the modeling that I've been doing. This was done with the purpose of trying to explain the data that was extracted from one of the movies of real falling slinky. What you see in this one is that the turns at the top are snapping together behind a front that propagates down.

So, the blue section at the top is the part that has collapsed. Initially, nothing's collapsed, and then more and more of the slinky is collapsed as that front runs down the slinky. How close is that to what actually happens? Well, I think that if you watch the movies, you can see that the turns don't collapse instantly.

So, how did you improve on that model? Well, I assume that there's essentially a fixed number of turns over which that collapse occurs behind the front. Those turns, they're not collapsing; they're not hammering together at the top. They gradually relax.

In fact, I've colored blue the section that is under collapse or has collapsed. That's far more obvious if you look at the other video. To me, this looks much more realistic, much more true. That's why I did it.

So, if someone asked you why, when you let go of the slinky, does the bottom not fall, what do you say? I'd say that when you're doing something, you're changing something at the top, and then there's a finite time for that information about the change to get to the bottom of the slinky. I mean, that happens even with a rigid bar, with a steel bar.

It's just that the time is very, very short. But a lot of people on the internet get uncomfortable with the term 'information'. I mean, what are we saying by information? In physics, it's a signal. It's something you know; whenever you do something physically to affect a change, causality is, you know, you do something, and there's a cause and an effect.

And between the two, information has to propagate; a signal has to propagate if they're not at the same location, physically at the same location. So, how long does it take for the compression wave to get from the top to the bottom? About a third of a second is the collapse time.

Is there any way to extend that time? Because, you know, if you decrease the spring constant, make it a softer spring, yes, then that takes longer to collapse, which sort of makes sense. The wave propagates more slowly.

If you make it more—if you increase the mass of the slinky, it gets longer as well; there's more inertia in that collapse process in the wave. Yeah, you need a kind of a heavy slinky that is very loose. It's odd, isn't it? You reckon like a lead slinky?

Well, if you have extended systems, then to consider the motion of the center of mass of an extended system, you only need to consider the external force that acts on the center of mass. And that's gravity, and that starts acting, you know, instantly, the instant this is released. It's there to begin with, but it's suspended; it's held up.

Once you take away that suspension, that center of mass has to start accelerating downward; it's instant. If you watch the movie, you see that the red dot, indeed, it's a good test for the modeling. The red dot does start to accelerate.

And you didn't build that into the model; you basically allowed that to, after the fact, calculate. You know, once you've got the model at each time step, I calculate where that center of mass is, and it does indeed start to fall immediately.

I think we were talking about this earlier, and you actually see the bottom of this thing start to rotate about now. So, there's some kind of torsional mode, some twisting mode signal that gets down to the bottom of the slinky first. It rushes ahead, but it doesn't actually release any tension, clearly, because the bottom just stays sitting there.

It's only when all those other turns come down that the tension is relaxed. I think this one's kind of neat. In this one, you don't let go of the top of the slinky, but you hold the slinky collapsed at the top and you release the bottom.

You keep the top fixed, and so what it does is it oscillates back and forth. That's a basic mode in which that whole thing can oscillate, and of course, that mode just depends in a simple way on the parameters of the slinky.

So, the period of oscillation of that mode is a good test for the parameters that we got out of the other modeling, out of the falling. This is a very basic mode; I think of this as a kind of breathing mode. It's this in and out, you know, every turn moves in a very simple way, in and out.

So, this breathing mode, or fundamental mode of oscillation.