Search results
Results from the WOW.Com Content Network
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 discrete approximations of continuum mechanics as in the finite element method, there may be more than one way to construct the mass matrix, depending on desired computational accuracy and performance. For example, a lumped-mass method, in which the deformation of each element is ignored, creates a diagonal mass matrix and negates the need ...
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
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.
Definition of the Lorentz factor γ. The Lorentz factor or Lorentz term (also known as the gamma factor [1]) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves.
The kinetic theory of gases applies to the classical ideal gas, which is an idealization of real gases. In real gases, there are various effects (e.g., van der Waals interactions, vortical flow, relativistic speed limits, and quantum exchange interactions) that can make
The same relations in different notation were used by Lorentz in 1913 and 1914, though he placed the energy on the left-hand side: ε = Mc 2 and ε 0 = mc 2, with ε being the total energy (rest energy plus kinetic energy) of a moving material point, ε 0 its rest energy, M the relativistic mass, and m the invariant mass.
The kinetic energy term for a free particle in the absence of an electromagnetic field is just where is the kinetic momentum, while in the presence of an electromagnetic field it involves the minimal coupling =, where now is the kinetic momentum and is the canonical momentum.