Mass Energy Relation

Table Of Content

Principle

From Work-Energy theorem, the kinetic energy of a moving body is equal to the work done by the external force that imparts the velocity to the body at rest. If ‘F’ is the force acting on the body, the work done by the force on the body in raising its velocity from v = 0 to v = ‘v’ is given by :

Work

Derivation

Kinetic energy of the body,

Kinetic energy

But from the relation of variation of mass with velocity, the mass of body in motion is

Mass of body in motion

where m0, being rest mass of body.

Therefore, Ek becomes

Value of Ek

Substituting

Equation

we get

Ek

Thus the kinetic energy for a moving body is equal to ‘gain in mass’ times the square of speed of light. Then total energy (E) of the body is the sum of rest energy and kinetic energy of the body. That is,

E = Rest energy + Relativistic kinetic energy

E

E

Which is better known as Einstein’s mass-energy relation who states a universal equivalence between mass and energy?