The center of mass velocity before and after collision and the change in center of mass velocity.

Answer to Problem 40TP
Center of mass velocity before collision is
Center of mass velocity before collision is
The change in the center of mass velocity of the system after collision will be zero.
Momentum is always conserved when no external force acts on the system.
Explanation of Solution
Given:
Mass of A is
Mass of B is
Initial velocity of mass A is
Initial velocity of mass B is
Formula used:
The conservation of momentum to find center of mass velocity of the bodies before collision is given by
Final velocity after collision will be calculated as
The conservation of momentum to find center of mass velocity of the bodies after collision is given by
Change in the center of mass velocity of the system after collision is given as
Calculation:
The conservation of momentum to find center of mass velocity of the bodies before collision is given by
Final velocity after collision will be calculated as
The conservation of momentum to find center of mass velocity of the bodies after collision is given by
Change in the center of mass velocity of the system after collision is given as
Conclusion:
Center of mass velocity before collision is
Center of mass velocity before collision is
The change in the center of mass velocity of the system after collision is zero.
In an isolated system, where no external force acts on the system, the net momentum is always conserved irrespective of the nature of the collision.
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