Intertial mass and determining the value of gamma

[daselocution]

Homework Statement

This is not a problem I was assigned, I am just trying to figure out how I could prove it to myself.

Basically, I am just wondering WHY the gamma value for relativistic momentum takes the form that it does, namely (1-u^2/c^2)^-.5

I've tried to prove this to myself a few times and I just cannot figure out how to do it. I am not sure if this is above my skill level and that is why I can't do it, as it was not addressed in my book nor was it addressed in my lecture. I tried to follow the same basic argument I used to show myself the value of gamma in the lorentz transformation, I just cannot figure out why the v^2 changes to u^2.

Even a qualitative answer would be helpful here.

Thanks a lot.

Homework Equations

The Attempt at a Solution

 

[mfb]

I just cannot figure out why the v^2 changes to u^2.

What are v and u in your derivation? That should be the same - the relative velocity between the two reference frames.