physics test cases

[gusl]

What's your favorite equational derivation in physics? I'm testing my equational theorem prover.

If you know any of physics arguments that use any non-standard reasoning (e.g. using diagrams), please please let me know.

Also, if you have any problems which involve semantic reasoning... maybe boring textbook examples will be good enough.

If you're wondering why I'm asking, it's because my thesis is titled "Automating Normal Science".

Ok.. back to Halliday & Resnick.

Comments

[spoonless.livejournal.com]

Actually, I just realized why you're probably confused... and it's my fault. I should have written "powers of v/c" rather than "powers of v". The way I wrote it you would expect the terms to get larger and larger, but in fact they get smaller and smaller.

I'm used to doing everything in units where c=1 in which case what I wrote would work fine... but in SI units you'd have to factor out a c before doing the expansion. So I should have written:

E ~= mc² [ 1 + 1/2*(v/c)² + higher powers of (v/c) ]

which when multiplied out gives you exactly the terms I wrote, except that the expansion is in terms of v/c not just v. So for v/c much less than 1, every term will be negligible compared to the last... which makes only the first term matter when you actually go to measure the energy. Only when v gets close to c do the other terms become significant, although they're always there to some extent.