Kinetic Energy

• Towards understanding nuclear reactions, first we will define kinetic energy.
• From the theory of relativity, we conclude that mass and energy are interconvertible.
• The total energy of a particle, whose mass is M can be written as

(1)

• In the above equation C is the velocity of light.
• When a particle is at rest, we can write the energy possessed by it as the rest mass energy and can be written as

(2)

In the above equation M₀ is the rest mass.

• From the theory of relativity, we note that the mass, M, changes with velocity, V, and this can be represented by

(3)

• Now if we would like to extract the energy from a moving particle by slowing it down to zero velocity, then the extractable energy shall be

(4)

• This we shall define as kinetic energy and denote it as T.
• Thus T is the difference between the total energy and the rest mass energy.
• Now we will try to connect this to the kinetic energy in Newtonian Mechanics.
• From Eq. (4) and Definition of T, we can write

(5)

• Substituting for M from Eq. (3), we get,
  
  

  (6)

if

• Thus for V << C, the kinetic energy reduces it to the classical Newtonian mechanics definition.
• To decide on a criterion for up to what velocity we can use Newtonian mechanics, consider the case of V = 0.1 C.
• From Eq. (6), we get,

• Thus for V<0.1C, the Newtonian Mechanics is adequate as the results are within 0.75%.