Question
Discuss one dimensional perfectly inelastic collision of two bodies. Obtain the expression for their velocities after collision. Discuss the special cases.
Solution
Consider two bodies A and B of masses m1 and m2 moving along the same straight line with velocities u1 and u2 respectively.
Let the two bodies undergo perfect inelastic collision.
In a perfect inelastic collision, the two bodies stick together, therefore the relative velocity of separation of two bodies after the collision is zero.
Let v be the velocity of combined masses after collision.
By conservation of momentum,
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Special cases:
Case (i):
Two bodies are of equal masses.
Putting
in equation (2), we get
Case(ii): When
is at rest.
Putting
in equation (2), we get
, is the velocity after collision.
Let the two bodies undergo perfect inelastic collision.
In a perfect inelastic collision, the two bodies stick together, therefore the relative velocity of separation of two bodies after the collision is zero.
Let v be the velocity of combined masses after collision.
By conservation of momentum,
...(1) ...(2) Special cases:
Case (i):
Two bodies are of equal masses.
Putting
in equation (2), we get Case(ii): When
is at rest. Putting
in equation (2), we get , is the velocity after collision.
