Special Relativity derivations ...

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1. Sep 1, 2015

The problem statement, all variables and given/known data
Using the special relativity formulae
p = mv / [1 - (v/c)2]
E2 = p2c2 + m2c4
derive linear relations between:
(i) momentum and mass;
(ii) energy and mass;
(iii) energy and momentum,
which involve only c, c2, β = v/c, and γ (= 1/sqrt(1 - β2))

The attempt at a solution

I am pretty sure the answer to (i) is p = γmv = γmβc, although I am unsure if this counts as a linear relation.
I suppose for (ii) I should be aiming for E = mc2, and for (iii) maybe I should be trying to get to E = pc (although I think this only applies to massless particles), but I haven't had much luck thus far.
I know these aren't really that hard, but for some reason my brain is just drawing blanks with these.

Many thanks for help and patience.

2. Sep 1, 2015

robphy

I think that here "linear" means that the two variables being related are each of first-power (no squares or square roots).
So, (i) is fine.
It seems that you have three quantities: p,m,E (mutually related by the above).... and you wish to find the relations between pairs chosen from those three.
So, what would you get for (ii)?

3. Sep 2, 2015

Sorry, a bit confused. I am pretty sure for (ii) I am meant to get E = mc2. My main problem is getting there from the formulae the question provided. Does that make sense? ...

4. Sep 2, 2015

robphy

With these symbols, $E\neq mc^2$ in general.