Relativistic Energy


Energy-momentum Relation (Invariant Energy)

$$ \large E^2 = (pc)^2 + (mc^2)^2 $$

where

$E$: total energy (relativistic energy)

$p$: momentum of magnitude

$m$: rest mass (invariant mass)

$c$: speed of light

  • GRE Physics GR1777 Problems 036 and 093

Kinetic Energy

$$ \large \begin{split} \text{(Kinetic Energy)} & = \gamma mc^2 - mc^2 \\ & = (\gamma - 1)mc^2 \end{split} $$

where

$$ \large \gamma = \frac{1}{\sqrt{1-(v/c)^2}} $$
  • GRE Physics GR1777 Problem 085

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