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### relativity energy

Posted: Tue Aug 24, 2010 1:42 pm
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
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
redacted.

### Re: relativity energy

Posted: Thu Aug 26, 2010 11:59 pm
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
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
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
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