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relativity energy

Posted: Tue Aug 24, 2010 1:42 pm
by ryan6
I am trying to self study this stuff.

I do not understand the difference between

E = \gamma m c^2

and

E^2 = (pc)^2 + (mc^2)^2

Are these the same thing, how do I know when to use which?

On problem 20 on test 8677, grephysics.net says to use the first one. But when I try to use the second one, I keep getting 0.6c, which is wrong and I do not understand why. Thanks

Re: relativity energy

Posted: Tue Aug 24, 2010 2:25 pm
by iplayterran
Yes they are the same thing. From the second one if you substitute p=\gamma m v you recover the first equation.

Re: relativity energy

Posted: Tue Aug 24, 2010 11:13 pm
by Skullgrid
redacted.

Re: relativity energy

Posted: Thu Aug 26, 2010 11:59 pm
by ryan6
It seems like a lot of the relativity problems that I have run into on GRE stuff are simply time dilation/length contraction. Is it worth practicing and memorizing the full Lorentz transformation equations? I always have trouble with determining the order of events and remembering the time transformation equation but dont want to cram anymore in than I have to at this point

Re: relativity energy

Posted: Fri Aug 27, 2010 12:28 am
by CarlBrannen
Time dilation and length contraction both use \sqrt{1-v^2/c^2} which is a little less than unity for small velocities. Just remember to multiply or divide by it in such a way that time gets increased (dilated) while length gets decreased (contracted).

Re: relativity energy

Posted: Fri Aug 27, 2010 11:43 am
by ryan6
yeah, youre right. Iv got that. But im talking about applying transformation to events using

t' = \gamma(t-\frac{v}{c^2}x)

I havent run into those types of problems (or velocity addition problems) on GRE stuff yet

Re: relativity energy

Posted: Fri Aug 27, 2010 12:12 pm
by HappyQuark
ryan6 wrote:yeah, youre right. Iv got that. But im talking about applying transformation to events using

t' = \gamma(t-\frac{v}{c^2}x)

I havent run into those types of problems (or velocity addition problems) on GRE stuff yet


Here is an example of velocity addition and time dilation on PGRE 9277

http://physicsgrad.com/pgre/9677-37/
http://physicsgrad.com/pgre/9277-38/