## relativity energy

ryan6
Posts: 48
Joined: Sat Feb 06, 2010 3:12 pm

### relativity energy

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

iplayterran
Posts: 7
Joined: Thu May 13, 2010 8:29 pm

### Re: relativity energy

Yes they are the same thing. From the second one if you substitute $$p=\gamma m v$$ you recover the first equation.

Skullgrid
Posts: 59
Joined: Sat Aug 21, 2010 6:50 pm

### Re: relativity energy

redacted.
Last edited by Skullgrid on Fri Jan 18, 2013 8:41 pm, edited 1 time in total.

ryan6
Posts: 48
Joined: Sat Feb 06, 2010 3:12 pm

### Re: relativity energy

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

CarlBrannen
Posts: 381
Joined: Mon May 24, 2010 11:34 pm

### Re: relativity energy

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).

ryan6
Posts: 48
Joined: Sat Feb 06, 2010 3:12 pm

### Re: relativity energy

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

HappyQuark
Posts: 762
Joined: Thu Apr 16, 2009 2:08 am

### Re: relativity energy

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