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Using a "successive impact model" (as if each ball were seperated from the other ones), I produced the following animations:

enter image description here

You can see any combination of balls with masses of 1 or 2 (left) or 1 and 4 (right).

Unfortunately, I do not have any Newton cradle to make some experiments, and I'd like to compare my results with observations. I contacted the author of this website, which is the most instructive one I found about asymmetric Newton cradle. In particular, he writes that the "OoO" configuration behaves as the "ooo" one, which is not what I simulate. But the author is not sure whether who is wrong because he did the experiments a long time ago.

I am especially interested in asymmetric Newton cradle with simultaneous impacts: left and right balls collinding at the same time.

Please let me know if you have any idea on where to find such experimental data.

Edit Just of few general remarks to avoid extending the comments.

  • Energy and momentum are conserved. However, they are sufficient to ensure uniqueness of the post-impact velocities only when there are 2 balls. The successive impact model precisely consists in propagating the impact ball after ball, and therefore leads to a unique solution (which conserves momentum and energy globally).

  • From the waves point of view, changing the mass of a ball can be done by increasing the diameter, or the density (or a combination of both). This simple model cannot account for such subtleties of course, but maybe it does not matter when the balls are "small enough".

  • Even if I think it's quite basic, following WetSavannaAnimalakaRodVance's comment, I am ready to hand out my Mathematica code to anybody who wants it. I'll check for good ways to share it.

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  • $\begingroup$ You can find dozens, if not hundreds of companies on the internet which are selling steel balls of any size and shape (:-)). Why not build your own and then you know exactly what you are doing? $\endgroup$ – CuriousOne Jun 16 '16 at 19:44
  • $\begingroup$ 2 small & 1 large lhup.edu/~dsimanek/scenario/collide.AVI $\endgroup$ – Farcher Jun 16 '16 at 20:02
  • $\begingroup$ @Farcher Yes, that's the website I am referring to in the website (and it matches the animation, btw). $\endgroup$ – anderstood Jun 16 '16 at 20:07
  • $\begingroup$ @CuriousOne That's a possibility I am considering, but i) I don't want to buy measurement devices, while some labs might have published accurate data, ii) I know there is no simple experiment (you always end up facing difficulties you had not foreseen). $\endgroup$ – anderstood Jun 16 '16 at 20:09
  • $\begingroup$ @anderstood: presumably, you have a computer or a phone with a webcam if you're posting here. For an experiment like this, that, plus a meterstick/ruler and maybe a scale is all you need. $\endgroup$ – Jerry Schirmer Jun 16 '16 at 21:01
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Experimental results can deviate from ideal. Outcomes depend sensitively on small differences in mass and alignment, and the extent to which kinetic energy is conserved. Alignment of non-identical balls is much more difficult. Considerable effort and expense may be required to achieve reliable results.

Although Simanek displays his apparatus, his webpage mostly contains animations. The only video clip (ooO <--> Ooo) does agree reasonably well with your simulation (#2 and #5). Perhaps his other videos were less convincing and left out for that reason.

Simanek's observation that the OoO collision is symmetrical might have been correct for the size of balls he used. (Judging by his video clip, I suspect that his apparatus did not actually show perfect symmetry.) In your simulation, although the 2:1 mass collision is not symmetrical, the 4:1 mass collision is much closer. Probably the n:1 collision gets more symmetrical as as n --> infinity.

Your simulation implements conservation of kinetic energy as well as momentum perfectly, so it ought to be more reliable than experimental results, which cannot guarantee perfectly elastic collisions and perfect alignment. However, investigating the differences with experiment may unearth interesting physics, particularly when the "successive impact model" does not apply.

The following Wolfram simulation includes the transfer of compression waves along the chain of balls :

http://demonstrations.wolfram.com/PhenomenologicalApproximationToNewtonsCradle/#

There are a number of very detailed and informative answers on the operation of and ideal conditions for Newton's Cradle already on Physics SE, such as

Newton's cradle
Newton's Cradle: why does it stay symmetric?

The group at California Institute of Technology (cited in the Wolfram demo) seems to have done the most recent published research (2008). They report different results when the balls are initially touching vs a small gap between them. You could try contacting them about their results :

https://www.researchgate.net/publication/253981162_Newton's_cradle_undone_Experiments_and_collision_models_for_the_normal_collision_of_three_solid_spheres

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  • $\begingroup$ Thank you. That also what I suspect (that Simanek made the experiments with exactly that), but I cannot validate or reject this assumption without further observations. I had also seen these two weblinks, but I don't see what they bring to the discussion. $\endgroup$ – anderstood Jun 17 '16 at 0:31
  • $\begingroup$ @anderstood : The weblinks support my contention that experimental results are not very reliable for unequal masses, which are more difficult to align. $\endgroup$ – sammy gerbil Jun 17 '16 at 1:12
  • $\begingroup$ I see. Thank for the edit. I'll check this soon. And yes my solutions satisfy momentum and energy conservation, but those two conditions are not sufficient to ensure uniqueness. $\endgroup$ – anderstood Jun 17 '16 at 2:16

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