# Falling slinky displays slow-motion causality

Researchers from the University of Sydney have explained why a spring dropped from a height - in this case the toy “slinky” – appear to ignore the force of gravity for a time. The very odd thing is that “if a slinky is hanging vertically under gravity from its top (at rest) and then released, the bottom of the slinky does not …

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#### Page:

Just cut it with pliers half way down. That will stop the signal.

#### Ah, Friday fun :)

If you model the static solution with lumped masses you get tension at a distance X links from the bottom of the spring is proportional to X. e.g. for 3 masses of 1kg connected by two massless springs and held up by a hand, tension in the bottom spring is 10N, the top spring is 20N, and the hand applies 30N (to balance the 30N weight of the device as a whole). So the bottom link is say 1m separate while the top link is only 1/2m separate. Effectively, each point is pulled down by the weight of the spring below, and that's more weight at the top and less at the bottom. It works just like undersea water pressure.

This is why you see in the video the spring starts out more stretched at the top and less at the bottom.

When that hand force disappears the spring will *not* compress uniformly towards the center of mass. In fact, the forces continue to balance for the bottom two masses while the top mass has a 30N downward force on it. Literally, acceleration of top mass is 3m/s and acceleration of all the other masses is zero. As the top link shrinks by X=1.5t^2 the second mass starts to experience acceleration of k.1.5.t^2 due to the created imbalance in the spring forces there. So that moves, and the bottom link shrinks, as Y=k/8.t^4 (integrate X twice). In other words, the acceleration of the second mass is zero, the rate of change of acceleration is zero, but the rate of change of the rate of change of acceleration is non-zero. The acceleration of the third mass has the 6th derivative of X be non-zero. For larger numbers of masses the final expression for the bottom link is something like k/N! * t^2N, which is "motionless" in anyone's book.

Once the top mass reaches the 2nd mass the spring force from above is now zero, so it's like the 2nd mass has been "released" in the same way the 1st one was, plus it gets an impulse from the collision. So now the situation is about the same, but one mass lower. Thus, we expect to see what the video shows - that the top mass is the only one which moves, until the spring force is eliminated, then the next mass starts to move, and so on. It's a highly non-linear situation.

So it can be deduced from Newtonian physics, but it's not a uniformly extended spring so the simple center-of-mass calculations don't work (and they predict something else anyway - that the bottom rises up). The center-of-mass will as usual obey Newton's law of gravitation but the behaviour around the CoM is not what you might expect. Anyone who claims this is not counter-intuitive isn't thinking about it hard enough ;) OTOH, papers describing what a game physics engine could figure out don't seem to be genuine "new physics" :)

#### Re: Ah, Friday fun :)

Some typos:

"So the bottom link is say 1m separate while the top link is only 1/2m separate"

Swap those two. The bottom is *less* separate; the top is *more* separate.

"(and they predict something else anyway - that the bottom rises up)"

Or it may fall :) It definitely doesn't seem to stay where it is for a long period of time.

#### Not slinky on stairs, but rather...

(As the commercial for an insurance company says) A slinky on an escalator.

The best part of the experiment should be to drop a ball at the same time as the slinky which would better show off the relations. Yes, this was suggested before.

#### Re: This isn't rocket science.

And this explains why the top of a slinky dress falls before the hem hits the carpet. Useful, that.

#### Wave propagation

This is an excelent physical demonstration of the difference between Wave Speed and Electron Speed in a power transmission line. Not because it is a good analog -- it is not a good analog -- but because it demonstrates two things: the wave speed is finite, and the result is unexpected.

Those two ideas are both difficult for many non-engineers dealing with any kind of transmission line. They expect wave speed to be non observable, and they expect that their ideas based on infinite wave speed will be correct.

#### Hmm..

So what you're telling me is if we could prevent the bottom of the slinky from ever finding out the top of the has been dropped, it would just sit there until otherwise informed? Sounds like the way we run our helpdesk..

Imagine the cost savings in travel if we could work out a way of implementing this slinky theory into the aircraft manufacturing process..

#### Re: The slinky is both falling and contracting at the same time.

Boy, don't you hate it when that happens.

I keep some tasteful porn around to counteract that.