Momentum conservation

It’s mid-semester break here at Waikato so I have time to breathe and get back to things other than teaching, such as seeing what the PhD students are up to. Yay.

But, here’s a comment about what I was talking about last week with the first year students: conservation of momentum.

If you look in first-year textbooks with regard to conservation of momentum in two dimensions, they tend to be full of examples about colliding billiard balls and car crashes. The former is a rather tedious example of an elastic collision (one in which kinetic energy is conserved) – the latter a nasty example of an inelastic-ish collision (in which the projectiles stick together after collision).  But there are a lot of more interesting examples to be found, and it’s always nice when I see a textbook that uses them.

For example, why not talk about the Large Hadron Collider, rather than billiard balls. The LHC collides protons together, and momentum is conserved. True, the products of the collision can be many and varied (maybe even a Higgs Boson – who knows?), and we’ll have to use special relativity to analyze them properly, but momentum will be conserved. It’s a nice topical example – far more inspiring than billiard balls and car crashes.

Here’s another example from the realm of the small – Compton scattering. This happens when a gamma ray or X-ray scatters elastically from an electron. The electron recoils, takes away energy from the gamma ray, which then changes its wavelength. Arthur Compton worked out that there was  a relationship between the observed change in wavelength of the wave and the angle through which the wave is scattered, and this could be explained by a single interaction between the gamma wave and the electron.  To do this he used momentum and energy conservation (it’s an elastic collision) – with the complication that it has to be done relativistically. In fact, Compton Scattering can be considered an experimental proof of special relativity and quantum mechanics – the experimental results tie in with the relativistic predictions. We get our third-year students to do this experiment, and it generally works very well. One can even extract the mass of the electron from the results.

Arthur Compton received a Nobel Prize in 1927 for what can be viewed as applying momentum conservation to a simple collision. I think it’s well worth talking about in first-year physics – students might struggle with the relativity bit, but the concepts are absolutely easy, and the result is really significant.

Better than car crashes for sure.


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