A popular demonstration for illustrating elastic collisions and the conservation of energy and momentum in the classroom is C7-11: Collisions of Balls of Equal Masses. Also popularly called Newton’s Cradle, as it helps us illustrate Newton’s laws of motion even if Newton himself may never have had one, you can find these in many places as entertaining desk toys; but they show us some important physics.

 You can see the demonstration in action in our new video featuring Dave Buehrle.

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 The simplest and most straightforward explanation for the behaviour of this device is just that – that it is an application of basic conservation laws. The collisions between these hard steel spheres are very nearly elastic, so nearly all of the momentum of the incoming spheres is transferred to the outgoing spheres, and nearly all the energy as well so they rise to the same height on the other side. A pendulum swinging back and forth is a classic illustration of the exchange between kinetic energy (from the velocity of the pendulum) and gravitational potential energy (the potential energy the stationary pendulum has as a result of its position when paused at the top of its swing). And this demonstration is, in a sense, just a set of pendula all swinging together, exchanging their energies and momenta, and we can simplify it be treating only the displaced balls as a single pendulum.

 You can likewise see this illustrated in this simulation by B. Surendranath of Hyderabad: https://www.surendranath.org/GPA/Dynamics/NewtonsCradle/NewtonsCradle.html 

Try it out at home and see what happens when you change the number of balls you move and how far you move them.

However, we can also explore more complex analyses. We could also analyze the system as a series of coupled oscillators, transferring energy between them much like a phonon in a crystal lattice – the “wave” of motion does have an observable speed, after all, so we could look at it as a propagation problem. Or we could treat each ball as a mostly elastic but slightly inelastic mass, and calculate its interactions with each of the other balls. This might give us an even more accurate picture of

This is a good example of just how the process of doing physics works. No mathematical model of a physical system is every perfect, and different models can be “right” for different situations. We choose the way of modeling a system that bests helps us understand the system at the level we need to understand it at, whether it’s an atom or a galaxy or a desk-top toy.

 To explore more about this device, consider reading the article “Newton’s Cradle and Scientific Explanation” by David Gavenda and Judith Edgington in The Physics Teacher.  https://aapt.scitation.org/doi/pdf/10.1119/1.2344742