3
$\begingroup$

Where does the relativistic formula

$$p~=~\frac{1}{c}\sqrt{T^2 +2mTc^2}$$

come from? What is the derivation from Einstein's formula? $T$ is the kinetic energy $m$ is the mass $p$ is the momentum.

$\endgroup$
3
  • 4
    $\begingroup$ Can you add a bit more context? what is $T$ here? $\endgroup$ Jul 26 '15 at 12:40
  • $\begingroup$ Some more context on where you saw this equation would be better as well. $\endgroup$
    – Kyle Kanos
    Jul 26 '15 at 14:45
  • $\begingroup$ In /gamma decay $\endgroup$ Jul 26 '15 at 14:46
2
$\begingroup$

We can write total energy $E$ two ways: \begin{equation} E^2=p^2c^2+m^2c^4 \\ E=T+mc^2, \end{equation} where $T$ is kinetic energy. Eliminating $E$ from those two equations will give you the desired result.

$\endgroup$
2
$\begingroup$

Hint: $T = E - E_0 = m\gamma c^2 - mc^2 = mc^2(\gamma -1)$ and $p = |\vec p| = m\gamma |\vec v| = m\gamma v$

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.