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]

It's not at all clear why you should consider 1/2*mv2 as the KE, instead of a higher power of v.

Well, the 1/2*mv² term is just the non-relativistic kinetic energy. The full kinetic energy is the entire series (aside from the mc² term). But when the velocity is very small compared to c, then only the lowest power of v matters and so that gives you the "non-relativistic" kinetic energy which is used in Newtonian physics. It's a "leading order approximation" to the (more) exact theory given by relativity.

Me too! I suspect this was discovered empirically, though... so it's not a totally artifical situation brought on by the teachers.

Well, most things in physics were discovered empirically at some point. What's neat is that theorists have been smart enough to come up with a limited number of axioms (quantum field theory plus general relativity) from which you can derive all the rest of the equations of physics. The only semi exception to this might be statistical mechanics which... as I mentioned in another thread, sort of has its own axioms... which follow mostly from pure logic & statistics. The only missing link is proving that quantum field theory and general relativity give rise to more complicated sturctures that obey the statistical laws we'd expect... I'm not sure if this has been fully proven yet, there may be a few holes in it yet.