Chapter 27 : Collision of Elastic Bodies 559
27.8. LOSS OF KINETIC ENERGY DURING COLLISION
The kinetic energy may be broadly defined as the energy possessed by a body by virtue of its
mass and velocity. Mathematically kinetic energy,
(^12)
2
Emv=
where m = Mass of the body, and
v = Velocity of the body,
The loss of kinetic energy, during impact, may be obtained by finding out the kinetic energy
of the two bodies before and after the impact. The difference between the kinetic energies of the
system, gives the required loss of kinetic energy during impact. Consider two bodies A and
B having a direct impact.
Let m 1 = Mass of the first body,
u 1 = Initial velocity of the first body,
v 1 = Final velocity of the first body,
m 2 , u 2 , v 2 = Corresponding values for the second body,
e = Coefficient of restitution.
We know that kinetic energy of the first body, before impact
2
11
1
2
= mu
and kinetic energy of the second body, before impact,
2
22
1
2
= mu
∴ Total kinetic energy of the two bodies, before impact,
( )
22 22
111 22 1122
11 1
22 2
Emu mu mumu=+ = + ...(i)
Similarly, total kinetic energy of two bodies, after impact
( )
22 22
21122 1122
11 1
22 2
Emvmv mvmv=+= + ...(ii)