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Total energy is the sum of rest energy = and relativistic kinetic energy: = = + Invariant mass is mass measured in a center-of-momentum frame. For bodies or systems with zero momentum, it simplifies to the mass–energy equation E 0 = m 0 c 2 {\displaystyle E_{0}=m_{0}c^{2}} , where total energy in this case is equal to rest energy.
For example, for a speed of 10 km/s (22,000 mph) the correction to the non-relativistic kinetic energy is 0.0417 J/kg (on a non-relativistic kinetic energy of 50 MJ/kg) and for a speed of 100 km/s it is 417 J/kg (on a non-relativistic kinetic energy of 5 GJ/kg). The relativistic relation between kinetic energy and momentum is given by
Relativistic kinetic energy: The relativistic kinetic energy relation takes the slightly modified form: = = As is a function of , the non-relativistic limit gives / =, as expected from Newtonian considerations.
The general formula for the kinetic energy is =, where v is the velocity of the bullet and m is the mass of the bullet. Although both mass and velocity contribute to the muzzle energy, the muzzle energy is proportional to the mass while proportional to the square of the velocity. The velocity of the bullet is a more important determinant of ...
Kinetic energy in special relativity and Newtonian mechanics. Relativistic kinetic energy increases to infinity when approaching the speed of light, thus no massive body can reach this speed. Tests of relativistic energy and momentum are aimed at measuring the relativistic expressions for energy, momentum, and mass.
The fine structure energy corrections can be obtained by using perturbation theory.To perform this calculation one must add three corrective terms to the Hamiltonian: the leading order relativistic correction to the kinetic energy, the correction due to the spin–orbit coupling, and the Darwin term coming from the quantum fluctuating motion or zitterbewegung of the electron.
According to the latter mass value and the formula for relativistic energy, relative speed differences between light and neutrinos are smaller at high energies, and should arise as indicated in the figure on the right. Time-of-flight measurements conducted so far investigated neutrinos of energy above 10 MeV.
Since the mass of the bullet is much less than that of the shooter there is more kinetic energy transferred to the bullet than to the shooter. Once discharged from the weapon, the bullet's energy decays throughout its flight, until the remainder is dissipated by colliding with a target (e.g. deforming the bullet and target).