Derive lorentz transform for energy

[gboff21]

Homework Statement

Derive the relation:
E' = \gamma (E + \beta p c)

Homework Equations

p&#039; = \gamma p \\<br /> E^{2} = p^{2} c^{2} + M^{2}c^{4}

The Attempt at a Solution

start off with stationary frame S E=mc^{2}
then in moving frame S' E&#039;^{2} = p&#039;^{2} c^{2} + E^{2}:
lorent transform momentum:
E&#039;^{2} = \gamma^{2} m^{2} v^{2}c^{2} + E^{2}
and that's as far as I get!

 

[Simon Bridge]

$E=\gamma mc^2$

That "p", in the equation you are supposed to prove, is unprimed.
Is that significant?

 

[gboff21]

Yes the p is supposed to be unprimed.

I've solved it now. Thanks anyway.
Here it is for anyone who's having the same problem:
You start off (or derive it as I had to, to understand it) with the lorentz transform for velocities in two frames u = \frac{u&#039;+v}{1+frac{uv}{c^{2}}}
Know that E&#039;=\gamma m_{0}c^{2} because in the stationary frame S, only rest mass provides energy.
You expand out gamma with u' given above and recognise that p&#039;=\gamma p
simplify and you get an answer!