Question

State the law of conservation of momentum and derive it from newton's third law of motion.

Answer 1

The sum of momentum of two objects before collision is equal to the sum of momentum after collision and o external unbalanced force acting on them. This is conservation of momentum.

Suppose two balls with mass mA and mB with velocity uA and uB. uA> uB and two balls collide. The collision lasts for t time and ballA exerts fAB on B ball and it exerts fBA on ballA the velocities become vA and vB. The momenta of A before after collision are mAvA and mAuA resp. The rate of change of momentum are

m(vA-uA)/tA [during collision]

m (vB-uB)/tB [******]

According to third law

fAB=-fBA

m (vA-vA)/tA=-m (vB-vB)/tB

mAuA+mBuB=mAvA+mBvB