h a l f b a k e r yFewer ducks than estimates indicate.
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Newton's cradle is that executive toy which
consists of a row of metal balls suspended
in a row. You lift the left hand one up and
let it swing back. Its momentum is
transferred through the row to the right-
hand ball, which swings up by the same
amount, then back again, click click click
click. All very symmetrical.
I would like an inhomogeneous Newton's
cradle, in which the balls are all of the
same diameter, but of different masses.
They could be made of different metals
(steel, aluminium, depleted uranium), or
they could just have internal hollows of
different sizes.
Suppose the heaviest ball were on the left
and the lightest on the right. You swing
the left ball out by, say, an inch, and let it
fall back. The lighter, right-hand ball
should swing out by a greater amount
(conservation of momentum). The result
would be a sort of assymetric oscillator.
I had hoped that this would give an
intriguingly uneven timing to the clicks
(CLICK......click. CLICK.....click. CLICK...),
but on reflection I think that the light and
heavy balls would all swing with the same
period (an ideal pendulum's period
depends only on its length). However, at
least the clicks would sound different
(CLICK.. click.. CLICK..click).
Newton's cradle
http://en.wikipedia...iki/Newton's_cradle
[MaxwellBuchanan, Sep 29 2007]
Vaguely related non-contact momentum transfer.
Executive_20Pendula
Shameless Elf-promotion [egbert, Oct 02 2007]
[link]
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So make the cradle's frame slant upwards at one end. You'd get different pendulum lengths, and different click times. But you'd only be able to use one ball at each end . . . or would you get some really strange effects? |
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The slanty cradle is a good idea, but I
prefer the incongruity of an apparently
symmetrical device acting asymmetrically. |
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I'm not sure. But I have a strong suspicion
that the ball-within-ball would behave
exactly the same as a solid ball with the
same total mass. (I guess you'd have to
make a small allowance for the fact that
the centre of mass of the ball-within-ball
could change, but aside from this, I don't
think it would matter). |
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What about if you configured the balls in a v or w shape, (row of balls then one at point of direction change then row of balls etc.) with the balls on the points swinging directly away from the point, not too sure on exactly how they would interact, but I think it might allow you to use balls of differing masses on those points, just might have to tune it to the correct frequency by pendulum length, so that nothing overlaps and cancells. You would get a lot of overlap, ( I think) but that might give you something of the effect that you are after. |
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Or just go balls to the wall, so to speak- Slanted top rail for different pendulum lengths, different metals, and hollow balls with a tiny little ball hanging inside the bigger balls from it's own string- unseen but still causing some form of permutation in movement. Chaos, I say, chaos! |
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Yes, that is very nice. But I have never heard of a better one than the one Death has on his desk in his study. It is one heavy ball and a lead slab. Let go of ball and there is one slow thud. Repeat. |
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Gosh - many ingenious suggestions!
With the ball-in-ball, yes I agree it
would add some irregularity, but I
suspect it would also dissipate a lot of
energy (small ball bouncing around in
big one, losing a little bit of energy
each time it rattles around) and hence
damp the motion more quickly. With
the W-shaped arrangement - not sure
what would happen here. Maybe a Y-
shape (one ball swings into the base of
the stem of the "Y", and causes balls at
the tips of both arms of the "Y" to fly
out?) would work better - I think asking
the momentum to turn an assymetric
corner might cause problems. Re the
muscle-wire cradle, yes, but I think the
impacts have to be almost face-to-face
(ie, at right angles to the plane of the
wires supporting any one ball) - but
nice nevertheless. |
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I'd certainly like to see a Y-shaped cradle. The strings might be a trick, but each V could be replaced with one rigid rod from the ball up to a bearing. |
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If you still want asymmetric action on a normal-appearing cradle, substituting rigid rods might help. They'd make it possible to shift the weight up and down a little, which is the only way to change the period of a pendulum. Ball-in-ball wouldn't do much good, if the ball was loose. But if you could put a VERY heavy weight in the top of a hollow ball on a shaft at one end of the cradle, and the bottom of the ball at the other, you'd get some difference. |
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Clever idea - I'm thinking it should be able to build this relatively easily by drilling holes in ping-pong balls and filling them with different substances - e.g. solder (don't melt it, just push solder wire through the hole into the ball until you can't cram any more in), sand, polyfilla, silicone rubber sealant, water (remember the seal the holes), jam, etc. |
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I think the loose solder, sand etc would damp the
oscillations. (How well would a ping-pong ball filled with
sand bounce?) |
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A solid filling of sealant or other materials would work,
though. |
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Actually, thinking about it, silicone rubber sealant is the way to go. It's reasonably dense, and will stick to the inside of the ping-pong balls. Then the effect you want will be acheived by filling your balls with different amounts of silicone rubber sealant. For some reason filling the balls
half-full, quarter-full, one-eighth-full,
one-sixteenth-full, etc. feels to me to be the right approach. |
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You could also change the density by mixing different substances with the sealant before filling the balls - lead shot and bits of polystyrene packing chip might be sensible choices. |
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//an ideal pendulum's period depends only on its length// Strictly, that is only true of an object describing a cycloid path. The period of a simple pendulum changes with amplitude, although it is relatively constant for small amplitudes. |
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If you wish to change the period of the balls without changing their appearance, how about large hollow balls with their mass concentrated at different points by attachemnet of weights inside. |
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A hollow ball could hav a hole drilled through and a mass attached to a rod passing through that hole. Adjusting the position of the mass on the rod changes the centre of mass of the ball while it's external appearance remains. |
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I'm not sure of the effects of misalignment between the point of contact to the next ball vs. the centre of mass. |
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Finally...a use for old record players! |
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Place a standard Newton's cradle on it, with one end on track 1, and the other end sort of nearer the center. |
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Oooh! [Ling] that could be the most excellent idea I have
heard all day. |
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Why, thanks MB. I believe that is truly a compliment from you. |
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