So I came across a Mythbusters video with Adam Savage working with some kids testing something about suspended objects held up with something stretchy (bungee cord, slinky etc) and how the bottom of the stretchy bit, and whatever it is holding up, hovers a bit while the released tension propagates down. In the video, they suspend a car using a bungee cord and drop it twice, first just the car, and then with a tank of water equal in weight to the car at the other end of the bungee. In the first drop, the car hovers for 95 milliseconds before falling and in the second drop it hovered 146 milliseconds before falling (and being crushed by the water tank).
While they did show that this happens, they didn’t really explain why. I understand that it takes time for the release to travel down the stretchy bit, but why does it take somewhat close to twice as long when you have equal weight at both ends?
Here is a link to the video if you want to watch it.
The elastic rope is exerting an upward force (opposed to gravity) on the car and a downward force (in conjunction with gravity) on the water tank. When the link is cut/released above the water tank (no longer suspending it from the crank), that force between the car and water tank from the elasticity of the rope remains and causes a net force less than that of gravity to be exerted on the car initially, and in excess of gravity on the water tank initially. So they then accelerate from rest at different rates initially while there is some jerk (a change not in position or velocity, but in acceleration) as the rope eventually contracts. If you ran this experiment in zero gravity (or in free fall from start to impact/collision) then the elasticity of the rope itself would cause the two objects to be drawn towards one another even without gravity. That would be “up” for the car and “down” for the water, relative to some reference point somewhere along the rope (perhaps the center of gravity for the two-mass system?).
Inertia (resistance to a change in motion) is to blame for the water tank’s ability to continue to “draw up” (exert an upward force on the car that, while not greater than gravity, initially helps to counteract the pull of gravity in part) on the car via the rope even as it is released from the crane above it.
Apart from that, I’m not sure what they meant by “hover.” Obviously things need time to accelerate from zero. That’s true even when things are set immediately into free fall from a position of relative rest. Motion may not (actually, never will) be “immediately” apparent if you play the video in slow (enough) motion. It’s not clear to me at all that they really defined what they meant by “hovering” particularly for the experiment with only the car and no other weight above it. Because while there is some mass to the rope, I doubt it counts for much against the mass of the car, and I wouldn’t be shocked to learn that it fell essentially at free fall as if there was no elasticity in the rope.
The center of mass of the overall system – upper weight, stretchy cord, and lower weight – falls normally, with no hesitation. The energy stored in the cord pulls a little on the lower weight. With the upper weight, the energy in the cord is drawing the upper weight downward faster than it would fall all on its own, and the lower weight “hesistates” in accordance.
So, to translate what you both said @Trinopus and @ASL_v2.0, into vaderese; the system of car and bungee is contracting towards the center of the of the system by way of the stored energy in the stretched bungee. For a measurable amount of time, 95/1000 of a second, for bungee and car only, that energy is enough to move the car up at the same rate that gravity moves the car down. The system with equal mass at both ends takes a little longer, 146/1000 of a second because there is more mass to get moving?
Regardless of the weight of the rope*, the upwards force on the car does not stop until the traveling wave reaches the car.
On slow motion video, you can see this happen. You can see that the top end of the rope is accelerating, and that the car is not.
Wave speed of an elastic rope depends on weight (it is not the only parameter). With a light rope, the wave reaches the car faster, but it is still the case that the car doesn’t start accelerating until the wave reaches the car, having the result that rope moves before the upward force on the car is removed.
*A weightless rope would move infinitely fast, so the delay would be zero in the limit. But on the other hand, ropes aren’t weightless, and the wave speed of a rope is not infinitely fast.
In putting all of their attention on the car, they missed an opportunity for an explanation of the physics. If they had also had slo-mo on the water tank they would have seen that the tank dropped much faster than if they had dropped just the tank with no bungee and no car.
IME watching this show they are more interested in true/false than explaining physics.
And that right there is the problem. They could easily have taken a few seconds, perhaps even a minute out of a segment with plenty of fluff to quickly explain the physics. Not to a super high level of detail. No need to throw up equations. But to at least explain that this isn’t some magical property at work here.
They might also have dropped something like a bowling ball from the same height and shot similar footage in slow motion to get an idea for just how prominent this “hovering” effect is for an object released into free fall at t=0 with no elastic rope. My sense is that the presence of an elastic rope, without some significant mass for inertia at the other end, would have a negligible effect once released. But it seems @Melbourne is less convinced. Fair enough. If only the “Mythbusters” had seen fit to help settle that argument.
I think there are two different things happening here; in the conventional slinky demonstration, there is just the fact that forces are being transmitted through a flexible spring at a finite speed that is slow enough to be discernible by eye.
With the car+water tank thing, there’s a lot of mass at the top of the system which has to freefall - without the water tank there, the elastic cord can contract faster than freefall as it recoils from being in tension - so with the water tank attached, the top of the cord falls slower than it would on its own, so the car is not released as abruptly to fall itself. (I think this is what Trinopus said)
Third-party rumor has it that the people making the show understood the physics of all their episodes, but the producers only wanted simplistic entertainment.
That doesn’t change the fact that they didn’t explain the physics. Only proffers a possible explanation as to why. The show still failed, whether it was the “talent” or the writers or the producers. Whether they knew better or not.
Just for fun… Hang the large weight (a car) from a high overhead crane. Tie a stretchy cord down to a lesser weight (a golf cart) and the stretch the cord farther by pulling the golf cart another ten feet lower than where it would ordinarily hang. You have to anchor it.
When you release the whole system (by cutting both upper and lower anchors) the golf cart actually moves upward for a little bit.
(I think… I’m not totally sure… Replace the golf cart with a bowling ball… I haven’t got the Mythbusters’ budget!)
Is the wave traveling down the cord relevant? I would think it is a matter of the center of mass of the system in free fall determining the position of the overall system, and the force exerted by the contraction of the cord determining the relative positions of its components. If you assume infinite wave speed and contraction consistent with a given spring constant, I would think you still get a car that is stationary for a moment.
We are used to force being transmitted either slowly, or instantaneously, and we have trouble getting our minds around problems where there are a mixture of things happening at different speeds, too fast to see, but too slow to ignore.
I’m not even sure what you described there makes sense; infinite wave speed requires a completely incompressible, completely inelastic medium (which is impossible, but it’s also the opposite of anything like a spring)
This article here is a very interesting musing on the questions about the speed of propagation in stuff and the deeper realities that flow from that.
This guy is a fun combo of serious science tinkerer and not-quite crank. He’s not advocating anything nuts, just a lot of things that involve looking at our mainstream scientific view of the world from a different angle than we’re used to. Which leads to lots of cool insights. At one time he was a 'Doper too.
His site is a real throwback to the early days of the amateur-written WWW. For anyone who’d physics-curious and especially as to electricity, the whole site warrants a thorough tour. I’d been all over it 20 years ago and still remembered the impact of the article i cited…
It took me a few minutes to recall enough of his name and enough keywords to find him again. I’m frankly surprised his site still exists at all. But it was worth it.