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when to use relativistic versus classical energy

Posted: Thu Jul 24, 2014 8:22 pm
by csj
I think I have generally figured out when it is appropriate to use the relativistic expression for energy ($$E^{2} = (pc)^{2} + (mc^{2})^{2}$$) versus the classical ($$E=\frac{p^{2}}{2m}$$), but I want to make sure and/or learn of any other ways ETS might want us to use one or the other. I've found in general that if a question is put in terms of, for instance, MeV/c^2 it is logical to use the relativistic case, and also I've found that often the use of the word "free" (i.e. a free electron) can also suggest to use relativistic. Are there any other general times to use one or the other?

Re: when to use relativistic versus classical energy

Posted: Tue Sep 01, 2015 11:30 am
by Chiron
In general you will want to use the relativistic energy any time a particle is moving at any rate nearing the speed of light, which generally means any speed which is, or can be, provided in terms of 'c'. For most problems you should be able to identify this from the context. Also, remember that when in doubt you can always use relativistic equations. They reduce to classical ones at low energy. However, the relativistic ones are generally much more work.

If you, or anyone else, has any questions please feel free to ask.