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Apologies in advance if this is too basic a question for Phys.SE. I don't want to dumb down this venerable institution. :)

My wife and I just watched this TV ad for Kit-Kat where a crew of crane operators line their wrecking balls up to form an enormous Newton's Cradle. It left us wondering if the basic premise is feasible. If the wrecking balls were perfectly aligned would it work? I imagine the lack of lateral stability inherent in having only one anchor point per "ball" would be a problem, but what else (if anything) stops this from working for real?

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Theoretically it would be feasible, as the law of conservation of energy is a universal principle, regardless of how large the system is. I think is would be difficult to realize a very large model like shown in the ad. First of all, the balls aren't exactly rigid. The larger the balls get, the larger the area of contact becomes, thereby increasing dissipation of energy. Coming to the ad, it is clearly a product of modern day computer graphics. If we assume a length of 50 m for the hanging chain, the time period of the pendulum, $2\pi\sqrt{\frac{L}{g}}$ ~ 14 s. Clearly the time period of the pendulum in the video is much much smaller. Further in reality, the balls would initially break-up due the elastic response of the balls (the balls are a little 'springy' and obey Hooke's Law). Then each ball would oscillate about a mean position (yes all the balls move! We don't notice this as the time period of the individual oscillations is quite small compared to the time period of the main balls). And finally due to dissipation of energy, the balls would settle down. A very realistic simulation has been done on Newton's Cradle by Stefan Hutzler et al. A video of the simulation can be found here.

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Wonderful answer - exactly what I was after. Thanks! –  Simon Whitaker Feb 1 '11 at 22:09
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This was funny enough for me to break away from work. In principle this would work, but the crade has each ball suspended by two lines at an angle. That keeps the balls elastically colliding in a line. The wreaking balls are suspected by a single cable. Unfortunately I think the set up might only work for a couple of periods before the balls start to get out of allignment.

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One way of looking at the question is to rephrase it as follows: "A small steel ball, raised to a height of a few times its diameter, bounces well. Does this behavior scale to a large steel ball?"

This is a question for engineers. To bounce well means that the collision is "elastic". A sufficiently large ball will collide inelastically and this will ruin the equations of Newton's cradle. (That is, while momentum is still conserved in an inelastic collision, the momentum will not be transferred through the intermediate balls to the one on the end because this requires conservation of energy.)

So there's an engineering limit to how large you can make Newton's cradle. It's due to the requirement that the collisions be elastic. To find that limit you have to know the strength of the materials involved. I might add some calculations and try and figure this out, it's a cool question...

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protected by Qmechanic Dec 28 '13 at 20:14

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