# Energy-momentum Formula

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 m0, total energy E, and a momentum of magnitude p, where the constant c is the speed of light.

Energy = √( momentum2 (speed of light)2 + ((rest mass) (speed of light)2)2)

The equation is:

E = √ (p2 c2 + (m0 c2)2)

Where:

E: Energy

p: momentum

c: speed of light

m0: rest mass

Energy momentum Formula Questions:

1) A particle is moving with an energy of 400 kJ (kilojoules), it has a mass of 2*10(-9) g, what is its momentum?

Answer:

From the formula of the energy we find the momentum:

P = √ (E2 – (m0 c2)2)/c

P = √ ((400*103 J)2 – (2*10(-12) Kg (3*108 m/s)2)2)/(3*108 m/s)

P = √ (127600000000 J2)/(3*108 m/s)

P = 357211.4 J / (3*108 m/s) = 119070.4 *108 Kg*m/s

2) The momentum of a mass is 1012 Kg*m/s, if it rest mas is 10 ng, what is its energy?

Answer:

using the formula of the energy,

E = √ ((1012 Kg*m/s 3*108 m/s)2 + (10*10(-12) Kg (3*108 m/s)2))

E = √ (9 *1040 J2) = 3 *1020 J

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