# Relativistic Energy Formula

The relativistic energy is the way that Einstein showed that the law of conservation of energy is valid relativistically, it means, the law of conservation of energy is valid in all inertial frames in high velocities approaching to the speed of light.

Relativistic energy = rest mass * speed of light squared / squared root [one minus (velocity / speed of light) squared]

The equation is:

E = mc^{2} / sqrt (1 – v^{2} / c^{2})

Where:

E: relativistic energy

m: rest mass (invariant mass)

v: velocity of the body

c: speed of light

Relativistic Energy Formula Questions:

1) What is the energy of a particle whit mass 4.2 x 10 ^{-27} kg and velocity 270.0 x 10^{6} m/s?

Answer:

We replace the data in the relativistic energy equation:

E = (4.2 x 10^{-27} kg)(3.0 x 10^{8} m/s)^{2} / sqrt [1 – (270.0 x 10^{6} m/s / 3.0 x 10^{8} m/s)^{2}]

E = 7.03 x 10^{-10} J

2) Find the velocity of a particle whose relativistic energy is 5.9 x 10^{-8} J and has a mass of 3.8 x 10 ^{-27} kg

Answer:

We cleared the velocity of the relativistic energy equation:

v = c sqrt (1 – (mc^{2} / E)^{2}

Then we replace the data:

v = 3.0 x 10^{8} m/s sqrt [1 – (3.8 x 10^{-27} kg(3.0 x 10^{8} m/s)^{2} / 5.9 x 10^{-8} J)^{2}]

v = 299.9 x 10^{6} m/s

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