197 Relativistic Kinetic Energy Formula Derivation
A derivation of the relativistic kinetic energy formula that is used to obtain \(K_{\mathrm{rel}} = (\gamma - 1)mc^{2}\) from the work done by a force.
The relativistic kinetic energy is
\[ K_{\mathrm{rel}} = (\gamma - 1)mc^{2} \]
with
\[ \gamma = \dfrac{1}{\sqrt{1-\dfrac{u^{2}}{c^{2}}}} \]
where
- \(K_{\mathrm{rel}}\) is the relativistic kinetic energy.
- \(\gamma\) is the Lorentz factor.
- \(m\) is the rest mass.
- \(c\) is the speed of light in vacuum.
- \(u\) is the particle speed.
197.1 References
- OpenStax. University Physics Volume 3, §5.9 Relativistic Energy. — \(K=\int F\,dx\) with \(F=\dfrac{dp}{dt}\) yields \(K_{\mathrm{rel}}=(\gamma-1)mc^{2}\); electron example at \(u=0.990c\). https://openstax.org/books/university-physics-volume-3/pages/5-9-relativistic-energy
- Annihilation
- Constancy of the Speed of Light
- Contracted Length
- Coordinate Transformations
- Elastic Potential Energy Formula Derivation
- Electromagnetic Field Transformations
- Energy-Momentum Relation
- Events
- Field Tensor
- Four-Current
- Four-Momentum
- Four-Potential
- Frame
- Gravitational Potential Energy Formula Derivation
- Inertial Frame
- Inertial Reference Frames
- Kinetic Energy
- Kinetic Energy Formula Derivation
- Length Contraction
- Light Cone
- Lorentz Factor
- Lorentz Transformations
- Magnetism as a Relativistic Effect
- Mass-Energy Equivalence
- Massless Particles
- Minkowski Metric
- Minkowski Space
- Moving Clocks
- Newtonian Kinetic Energy Formula Derivation
- Non-Inertial Frames
- Nuclear Energy
- Particle Creation
- Photon Energy
- Potential Energy
- Potential Energy Formula Derivation
- Principle of Relativity
- Proper Length
- Proper Time
- Rapidity
- Reference Frames
- Relativistic Electrodynamics
- Relativistic Kinetic Energy Formula Derivation
- Relativistic Momentum
- Relativistic Momentum and Energy
- Relativity Principle
- Rest Energy
- Simultaneity
- Spacetime
- Spacetime Interval
- Time Dilation
- Total Energy
- Twin Paradox
- Velocity Addition
- Visualization of Spacetime
- Worldlines