# Energy momentum Formula

The energy–momentum relation is a relativistic equation that relates an object's rest mass, its total energy and momentum. Holds for systems such as a particle or macroscopic body, having intrinsic rest mass m_{0}, total energy E, and a momentum of magnitude p, where the constant c is the speed of light.

Energy = √( momentum^{2} (speed of light)^{2} + ((rest mass) (speed of light)^{2})^{2})

The equation is:

E = √ (p^{2} c^{2} + (m_{0} c^{2})^{2})

Where:

E: Energy

p: momentum

c: speed of light

m_{0}: rest mass

Energy momentum Formula Questions:

1) A particle is moving with an energy of 400 kJ (kilo joules), it has a mass of 2*10^{(-9)} g, what is it momentum?

Answer:

From the formula of the energy we find the momentum:

P = √ (E^{2} – (m_{0} c^{2})^{2})/c

P = √ ((400*10^{3} J)^{2} – (2*10^{(-12)} Kg (3*10^{8} m/s)^{2})^{2})/(3*10^{8} m/s)

P = √ (127600000000 J^{2})/(3*10^{8} m/s)

P = 357211.4 J / (3*10^{8} m/s) = 119070.4 *10^{8} Kg*m/s

2) The momentum of a mass is 10^{12} Kg*m/s, if it rest mas is 10 ng, what is its energy?

Answer:

using the formula of the energy,

E = √ ((10^{12} Kg*m/s 3*10^{8} m/s)^{2} + (10*10^{(-12)} Kg (3*10^{8} m/s)^{2}))

E = √ (9 *10^{40} J^{2}) = 3 *10^{20} J

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