Prove the Law of Conservation of Momentum [5 MARKS]
Explanation: 2 Marks
Proof: 3 Marks
The law of momentum conservation can be stated as follows:
For a collision occurring between object 1 and object 2 in an isolated sytem. the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2.
Proving Law of Conservation of Momentum
Suppose two objects (two balls A and B, say) of masses mA and mB are travelling in the same direction along a straight line at different velocities uA and uB. And there are no other external unbalanced forces acting on them.
During collision which lasts for a time t, the ball A exerts a force FAB on ball B and the ball B exerts a force FBA on ball A.
Suppose VA and VB are the velocities of the two balls A and B after the collision respectively
then the rate of change in momentum in body A due to FBA is
FBA=mAvA−mAuAt
the rate of change of momentum in body B due to FAB is
FAB=mBvB−mBuBt
from the newton's third law of motion
FAB=−FBA
mBvB−mBuBt=−mAvA−mAuAt
⇒mAuA+mBuB=mAvA+mBvB
From this it is clear that the sum of initial momenta of objects before collision is equal to the sum of final momenta of object after collision, and thus it is the case of conservation of momentum in the absence of external force.