State The Law Of Conservation Of Momentum And Derive Related Expression​

Answers (1)

Principle of conservation of linear momentum states that if the net external force on a system of particles is zero, the linear momentum of the system remains constant. Or we can say that the sum of momenta of the two objects before collision is equal to the sum of momenta after the collision provided there is no external unbalanced force acting on them.

Derivation:-

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, respectively and there are no other external unbalanced forces acting on them. Let uA>uB and the two balls collide with each other. 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. Let vA and vB are the velocities of the two balls A and B after the collision, respectively.

The initial linear momentum of A is  and that of B is respectively.

Then the total initial linear momentum of the system is:

The rate of change of its momentum (or FAB , action) during the collision will be ;

 

Similarly, the final momentum of A is   and that of B is  respectively.

Then the total final linear momentum of the system is: 

The rate of change of momentum of ball B(=FBA or reaction) during the collision will be ;

According to the third law of motion, the force FAB exerted by ball A on ball B (action) and the force FBA exerted by the ball B on ball A (reaction) must be equal and opposite to each other. Therefore,

;

;

 

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