i. Let two bodies A and B of masses m1 and m2 move with initial velocity \(\overrightarrow{u}_1\) and \(\overrightarrow{u}_2\), respectively such that particle A collides head on with particle B i.e., u1 > u2.
ii. If the collision is perfectly inelastic, the particles stick together and move with a common velocity \(\overrightarrow{\text{v}}\) after the collision along the same straight line.
loss in kinetic energy = total initial kinetic energy – total final kinetic energy.
iii. By the law of conservation of momentum,
m1u1 + m2u2 = (m1 + m2)v
∴ v = \(\frac{m_1u_1+m_2u_2}{m_1+m_2}\)
iv. Loss of Kinetic energy,
v. Both the masses and the term (u1 – u2)2 are positive. Hence, there is always a loss in a perfectly inelastic collision. For a perfectly inelastic collision, as e = 0, the loss is maximum.