- #1

martinhiggs

- 24

- 0

## Homework Statement

I have to find a relation for kinetic energy as a function of the lorentz factor, KE(gamma). It can only depend on the lorentz factor or on a constant.

## Homework Equations

[tex]E_{tot} = \gamma m_{0} c^{2} [/tex]

[tex]E_{tot} = KE + m_{0}c^{2} = \sqrt{p^{2}c^{2} + m_{0}c^{4}}[/tex]

[tex]\gamma = \sqrt{1 + \frac{v^{2}}{c^2}}[/tex]

## The Attempt at a Solution

I thought that the best place to start would be:

[tex]E_{tot} = KE +m_{0}c^{2}[/tex]

[tex]KE = E_{tot} - m_{0}c^{2}[/tex]

Also I know that

[tex]E_{tot} = \gamma m_{0}c^{2}[/tex]

Substituting this in I get:

[tex] KE = \gamma m_{0}c^{2} - m_{0}c^{2} [/tex]

I'm now not sure how to carry on, to get rid of the masses from the equation. Everything I try to do to remove them causes me to have another variable, like energy to then get rid of.

Any suggestions, pointers or help would be greatly appreciated, I've been stuck on this problem for 12 hours now!