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Inhomogeneous Newton's Cradle

CLICK...click... CLICK...click
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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).

MaxwellBuchanan, Sep 29 2007

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]

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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?
baconbrain, Sep 29 2007
  

       The slanty cradle is a good idea, but I prefer the incongruity of an apparently symmetrical device acting asymmetrically.
MaxwellBuchanan, Sep 29 2007
  

       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).
MaxwellBuchanan, Sep 29 2007
  

       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.
the dog's breakfast, Sep 29 2007
  

       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!
NotTheSharpestSpoon, Sep 29 2007
  

       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.
zeno, Sep 29 2007
  

       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.
MaxwellBuchanan, Sep 30 2007
  

       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.   

       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.
baconbrain, Sep 30 2007
  

       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.
hippo, Nov 17 2010
  

       Thank you!   

       I think the loose solder, sand etc would damp the oscillations. (How well would a ping-pong ball filled with sand bounce?)   

       A solid filling of sealant or other materials would work, though.
MaxwellBuchanan, Nov 17 2010
  

       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.
hippo, Nov 17 2010
  

       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.
Wrongfellow, Nov 17 2010
  

       //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.
spidermother, Nov 17 2010
  

       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.   

       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.   

       I'm not sure of the effects of misalignment between the point of contact to the next ball vs. the centre of mass.
Twizz, Nov 17 2010
  

       Finally...a use for old record players!   

       Place a standard Newton's cradle on it, with one end on track 1, and the other end sort of nearer the center.
Ling, Nov 17 2010
  

       Oooh! [Ling] that could be the most excellent idea I have heard all day.
MaxwellBuchanan, Nov 17 2010
  

       ...   

       Isaac Who-ton?
DrWorm, Nov 17 2010
  

       Why, thanks MB. I believe that is truly a compliment from you.   

       At least for today.
Ling, Nov 18 2010
  
      
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