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 (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 = √ (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