Another elegant approach for deriving an expression for Kinetic energy is the
Classical Relativistic approach using famous Einstein's mass- Energy
relationship i.e.,
E = mc2,
Where,
E = Total energy of the particle = rest mass energy + Kinetic energy....(1)
and 'm' = Relativistic mass of the particle i.e., mass of the particle when its
velocity is v
'c' = Speed of light in vacuum
Rest mass of the particle is taken = m0
m = m0/
(1 -v
2/c
2)=m
0(1 -v
2/c
2)
-1/2
or m = m0(1 + v2/2c2 + neglecting higher terms) =m0(1 + v2/2c2)
( as here v<<c)
Therefore, E = m0c2(1 + v2/2c2) =m0c2+ m0v2/2 ........(2)
Where, m0c2 = Rest mass energy
Therefore Kinetic energy of the particle = m0v2/2
NOTE: REMEMBER THIS FORMULA FOR KINETIC ENERGY HOLDS GOOD
ONLY FOR THE CASES WHERE v<<c, WHAT WE CALL THE NON
RELATIVISTIC CASE. WHEREAS, IF WE CONSIDER RELATIVISTIC CASE
WHERE, VELOCITY OF PARTICLE IS COMPAREBLE TO THE VELOCITY OF
LIGHT, THE KINETIC ENERGY TERM INVOLVES HIGHER POWERS OF
v2/c2 THAT WERE OTHERWISE NEGLECTED IN DERIVING ABOVE
EXPRESSION.
Moderation Team
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