Given that E(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}= c^{2}p^{2}+ m_{o}^{2}c^{4}-----------(1);

where p represents the relativistic momemtum p=[tex]\gamma[/tex]m_{o}u,

show that m=(p^{2}c^{2}-T^{2})/(2Tc^{2}) where m is the relativistic mass of the particle,and T it's kinetic energy.

2. Relevant equations

E= T+m_{o}c^{2}-------(2)

3. The attempt at a solution

I start by saying p^{2}c^{2}= E^{2}-m_{o}^{2}c^{4}(from (1)), subtracting T^{2}from both sides gives

p^{2}c^{2}-T^{2}= E^{2}-m_{o}^{2}c^{4}-T^{2}. Now using (2) i expand E;

p^{2}c^{2}-T^{2}= (T+m_{o}c^{2})^{2}-m_{o}^{2}c^{4}-T^{2}which gives

p^{2}c^{2}-T^{2}= T^{2}+2Tm_{o}c^{2}+m_{o}^{2}c^{4}-m_{o}^{2}c^{4}-T^{2}; simplifying

p^{2}c^{2}-T^{2}= 2Tm_{o}c^{2}Now dividing by 2Tc^{2}gives

(p^{2}c^{2}-T^{2})/(2Tc^{2}) = (2Tm_{o}c^{2})/(2Tc^{2}) I now have the required LHS of (1),

This yields (p^{2}c^{2}-T^{2})/(2Tc^{2}) = m_{o}, NOT m !!!!!!!

Where have i gone wrong !!!??

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# Homework Help: Special Relativity, equation help needed

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