Question
Deduce law of conservation of momentum from Newton’s third law of motion.
Solution
Consider two bodies A and B of masses mA and mB moving in the same direction along a straight line.
The bodies are moving with velocities uA and uB respectively, such that uA > uB.
They collide for time t.
After collision, let their velocities become v1 and v2.
Now, according to Newton's third law of motion,
The forces are equal and opposite.
That is,
Total momentum before collision = Total momentum after collision.
Thus, total momentum of the two bodies is conserved provided no external force acts on them.
This proves the law of conservation of momentum.
