Does the KE Equation Apply in Relativistic Scenarios?

[sweetvirgogirl]

refer to the title.

I'm confused whether this eqn works in relativistic situations?

thanks in advance

 

[jtbell]

No, that equation does not work in relativistic situations. To get the corresponding relativistic equation, take the equations for relativistic kinetic energy and momentum and eliminate v between them:

$$K = \frac{m_0 c^2}{\sqrt{1 - v^2 / c^2}} - m_0 c^2$$

$$p = \frac{m_0 v}{\sqrt{1 - v^2 / c^2}}$$

Or, you can take the relativistic relationship between total energy, mass and momentum:

$$E^2 = (pc)^2 + (m_0 c^2)^2$$

substitute $E = m_0 c^2 + K$ (total energy equals rest energy plus kinetic energy), and solve for K.