Kinetic Energy (Relativistic)

The Relativistic Kinetic Energy calculator compute the kinetic energy of an object accounting for velocities where relativity has a measurable effect.

INSTRUCTIONS: Choose units and enter the following:

• (M) Mass (default units are "u", atomic units)
• (V) Velocity (default units are "c", multiples of the speed of light)

Kinetic Energy (E_K):  The calculator returns the kinetic energy in Mega-electron volts (MeV).  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula for relativistic kinetic energy is:

         `E_K = (m•c²)/sqrt(1 - "v²/c²") - m•c²`

where:

• E_K is the relativistic kinetic energy
• m is the mass
• v is the velocity
• c is the speed of light

This equation computes the relativistic kinetic energy E_K for a mass traveling at a relativistic velocity.  If the speed of the mass, m, is a significant portion of the speed of light, c, it is necessary to use the this equation to compute the Kinetic Energy.

Relativistic kinetic energy is energy possessed by any object due to motion when the effect of relativity is accounted for.  For most objects traveling at small fractions of the speed of light, relativistic effects are generally insignificant for practical application.  However, when the speed of a mass is a significant fraction of the speed of light, then it is necessary to account for relativistic effects to produce usable calculations of kinetic energy.

The equation for Kinetic Energy, E_K bears resemblance to the famous Mass-Energy Equivalence equation, E = mc² introduced by Einstein, which includes both kinetic energy and rest mass energy.  The equation for kinetic energy alone is the deduction of the rest mass energy component from this total.

The kinetic energy is equivalent to the work required to accelerate an object from rest to the speed, v.   Therefore, as can be seen from the equation, as v approaches the the speed of light, the resulting energy approaches infinity.  Thus, an infinite amount of work (an apparent impossibility) is required to accelerate a mass to the speed of light.

Energy Calculators

• Kinetic Energy:                                    `KE= 1/2 *m * v^2`
• Kinetic Energy (change of velocity):    `KE = 1/2*m*(V_1-V_2)^2`
• Relativistic Kinetic Energy:                    `E_K = (m*c^2)/sqrt(1 - v^2"/"c^2") - m*c^2`
• Potential Energy:                                  `U(y) = m*g*y`
• Potential Energy of Gravity (two bodies):   `U(G) = - (G*m1*m2)/r`
• Nuclear Binding Energy:                       `E = m*c^2`
• Quantum Energy (Planck's Equation):   `E = h*f`
• Energy of a Particle in a Box:                `E_n=(n^2h^2)/(8mL^2)`
• Molecular Kinetic Energy:                      `KE = 3/2 * k_B *T`
• Electrostatic Potential Energy:               `E_(el) = k_e * (Q_1*Q_2)/d`
• Photon Energy from Wavelength:          `E = (h*c)/lambda`
• Heat Energy to Change Material Temperature:  `Q = C * m *DeltaT`

Mass-Energy-Light Calculators

• E = m•c² (mass/energy equivalent)
• m = E/c² (mass from energy)
• E = m•γ•c² (mass/energy equivalent not at rest)
• E = h•ν (Quantum Energy)
• p = m•γ•v (Relativistic Momentum)
• c (Speed of light) = 2.99792458E8 m/s
• c² (Speed of Light Squared) = 931.46 MeV/u
• Lorentz factor (`gamma`)
• KE ≈ m(1+v²/(2c²)-1)c² (Relativistic Kinetic Energy)