Fun for a girl and a boy

Check out this video of a falling slinky:

[Update: Video was wrong for a while. I think it should be right now.]

The person who made this, who seems to go by the name Veritasium, has some other sciency-looking videos on his YouTube channel, by the way. I haven’t checked out the others.

In principle, it should be obvious to a physicist that the bottom of a hanging slinky can’t start to move for quite a while after the top end is dropped. To be specific, the information that the top end has been dropped can’t propagate down the slinky any faster than the speed of sound in the slinky (i.e., the speed at which waves propagate down it), so there’s a delay before the bottom end “knows” it’s been dropped. But it’s surprising (at least to me) to see how long the delay is.

There are a couple of different ways to explain this. One is essentially what I just said: the bottom of the slinky doesn’t know to start falling because the information takes time to get there. The other is

[T]he best thing is to think of the slinky as a system. When it is let [go], the center of mass certainly accelerates downward (like any falling object). However, at the same time, the slinky (spring) is compressing to its relaxed length. This means that top and bottom are accelerating towards the center of mass of the slinky at the same time the center of mass is accelerating downward.

These are both right. Personally, I think the information-propagation explanation is a nicer way to understand the most striking qualitative feature of the motion (that the bottom stays put for so long). But if you wanted to model the motion in detail you’d want to write down equations for all the forces.

Anyway, it’s a nice illustration of a very common occurrence in physics: ¬†you can give two explanations of a phenomenon that sound extremely different but are secretly equivalent.

(I saw this on Andrew Sullivan’s blog, in case you were wondering.)

7 Responses to “Fun for a girl and a boy”

  1. Raymond says:

    This implies that a slinky dropped on the moon may exhibit a different type of behavior. This clearly requires additional experimental verification.

  2. Allen Downey says:

    I think it is more interesting than you are giving it credit for. You explain qualitatively why there is a delay, but the interesting part is that (to my eye at least) the top of the slinky accelerates quickly and then moves at constant speed. I think I have an explanation:

    If I am right, then the slinky basically pancakes from top to bottom. So imagine that initially the top is at h=1 and the bottom at h=0. At some point, the top x units have collapsed, but the bottom 1-x are still standing. So the center of mass is x(1-x) + (1-x)(1-x)/2. But since the slinky is in freefall, the center of mass, as a function of time, is 1/2 – 1/2 g t^2.

    Set them equal, solve and get x = sqrt(g) t, valid until t = 1 / sqrt(g) and x=1. So I think that’s why the top falls at constant speed.

    What do you think?

  3. Ted Bunn says:

    I don’t think your analysis is quite right, although it’s got some of the main features of the motion qualitatively right. The problem is that your center of mass calculation assumes that the linear mass density along the stretched slinky is uniform, but it’s not. The slinky is much more stretched at the top (so has a lower mass per unit length) than at the bottom. This is, I think, a pretty big effect.

  4. Ted Bunn says:

    In a followup post, I give an analysis based on Allen’s idea but incorporating what I think is the correct density profile: http://blog.richmond.edu/physicsbunn/2012/06/26/more-on-the-slinky/

  5. Tam software says:

    Great post, but from here the movie isn’t about the slinky anymore but particles …

  6. Ted Bunn says:

    Sorry about that! This should be a link to the right movie: http://youtu.be/uiyMuHuCFo4

  7. Im going to check out the movie now! Interesting topic Ted

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