A while ago a vid made the rounds: a Slinky is held unrolled in the air, and when the person holding it lets it go the base stays put (“floating”) until the upper rings collapse onto it. In the original YouTube post the physics prof gives a two-sentence explanation. I am left unsatisfied and ask the Dope for a more thorough explanation, given SD constraints. Here is a better-produced vid of the same thing.
I’m reframing the phenomenon this way: say a metal plate is “supported,” more or less, by a stream of bullets from a gun below. Even after the shooting stops, there are still bullets en route, and until they run out the plate is supported, seemingly magically, even when the gun is off.
What’s the question, exactly? Your model of a plate suspended (so to speak) by bullets impacting from below would work. It could happen.
The entirety of the slinky, taken as an object, is falling, 32 feet per second per second. The center of gravity of the slinky is probably not wandering around very much: the slinky is pretty much vertically symmetrical. So the c.o.g. is falling at 32 feet per second per second.
If the base happens to be pulled upward by the contracting force of the spring at 32 feet per second per second – perfectly possible – then the base would appear to be stationary. The base would be stationary with respect to the ground. It isn’t falling…yet. Once the spring’s energy has all been expended, and the slinky is in “neutral” extension – neither stretched nor compressed – the upward motion of the bottommost ring would cease, and the whole toy would continue to fall. That bottommost ring would be subject to an extra acceleration, to match velocities (and acceleration) with the c.o.g. of the whole toy.
(And I use “last ring” in the loose sense one might use of the “last groove” of an old phonograph record.)
Not only is this perfectly possible, it’s exactly what would be expected. Before the release, the slinky was in equilibrium: The upward spring force from the portions above any given ring, the downward spring force from the portions below that ring, and the downward weight force of the ring itself are all in balance. When the top of the slinky is released, the configuration of the lower sections of the slinky remains the same, so all of these forces remain the same, and thus remain in balance. It’s only once the compression wave has had a chance to propagate to a particular section that the configuration changes, and that section begins to fall.
As I recall from doing the math on this situation some years ago, the base starts moving downward immediately (obviously, I’m dealing with a spring that’s short enough that speed of light issues don’t apply), but it’s moving downward very slowly at first - the motion of the base is a combination of a sinuosidal oscillation of the length of the whole spring (which moves the base upward relative to the center of mass), and downward acceleration of the center of mass, resulting in an initial downward velocity proportional to t^3 instead of t, so for very small t, it looks like the base isn’t moving.
There are other youtube videos about this done with better explanations. The slow mo guys in the OP’s video are mostly about making cool slow motion videos. They don’t tend to say much about the physics of things.
Yeah. It occurred to me after i posted that the period of the sine wave I mentioned above is the speed of the compression wave, so we’re likely describing the same effect from different perspectives.
Here’s a (very simplified) analysis. Two objects of mass m are connected by a massless spring (with negligible unstretched extent) with a spring constant of m. When the top mass is held at height h (on a planet with gravity, g), the lower mass hangs down to h-gm/k. When the upper mass is released, the lower mass velocity is
-gt+gm/2k*sqrt(2k/m)*sin(sqrt(2k/m)t)
when t is small, sin(sqrt(2k/m)t) approximately equals sqrt(2k/m)t minus a factor proportional to t[sup]3[/sup]. The term proportional to t cancels, so the lower mass doesn’t move at all initially, but later accelerates very fast. This fits the compression wave description, but I prefer to think of the motion as a superposition of the spring contracting (bringing the ends together) and the spring as a whole falling - initially, the contraction exactly cancels at the lower mass, while the upper mass moves faster than a free-falling object would.
How’s the physics/engineering rap, as far as it goes, in this article, The Single Helix?
ETA: the speed of the compression wave is critical to the behavior of the thing as a toy: massive and slow plastic rings for the kids compared with the original metal slats, given equivalent stairs.
Similarly, if you’re holding a metal bar vertically from the top of it, and you drop it, the top begins to fall first by an insignificant amount, and then the rest of it. Of course, a metal rod is approximately a perfect rigid body so you don’t see this and I doubt it’s even experimentally detectable, but this is in reality how all things fall. It takes a while for the forces to propagate through.
Does this depend on the mass distribution of the slinky? At first I thought if you made a slinky lighter towards the bottom, the bottom would move up, but if it’s like you say, it won’t matter.
There is some famous example of a rod with with Lorentz contraction, in relativistic physics of course, where energy at the in side just won’t make it, so to speak, at the other side, come hell or high water, without it.
It was just touched upon in a now-going physics thread; I found it after chasing down a something map…I’ll find it.
Hm. What about the same experiment, but with a rope? If I push on the top of a rope, I wouldn’t expect the bottom to go any faster, at least not in the same way that a rigid body like a steel rod would…
I guess what I’m asking is, how does the rigidity of the body correlate with the effect?
The second is superb. A physics guy filmed and modeled the event, plotting c.o.g. motion during collapse. He also mentioned how, although not in spring form, a tap on a rod obeys the same physics of a traveling c.o.g. As the compression wave moves.
He pointed out something interesting, that, because the collapse was not linear–he suspended it from a building, and the upper coils toppled over, jiggling the lower ones–the bottom rungs began rotating, but the “float” continued.
The arrival of the “information signal” of the compression wave to the final rung and for system motion to begin need not be the first one, as torsion/shear had no bearing on the tension/compression component.
Why does it travel faster? If this could be fleshed out I would appreciate it.
