Question

sate law of conservation of linear momentum derive this law using netaon third law of motion.explain rewill of a gun .why recol velocit smaller than the velocity of bullet
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Answer 1

Explanation:

Law of conservation of momentum states that when two objects collide with each other , the sum of their linear momentum always remains same or we can say conserved and is not effected by any action, reaction only in case is no external unbalanced force is applied on the bodies.

Let,

mA = Mass of ball A

mB= Mass of ball B

uA= initial velocity of ball A

uB= initial velocity of ball B

vA= Velocity after the collision of ball A

vB= Velocity after the collision of ball B

Fab= Force exerted by A on B

Fba= Force exerted by B on A

Now,

Change in the momentum of A= momentum of A after the collision - the momentum of A before the collision

= mAvA−mAuA

Rate of change of momentum A= Change in momentum of A/ time taken

= tmAvA−mAuA

Force exerted by B on A (Fba);

Fba=tmAvA−mAuA........ [i]

In the same way,

Rate of change of momentum of B=

tmbvB−mBuB

Force exerted by A on B (Fab)=

Fab=tmBvB−mBuB.......... [ii]

Newton's third law of motion states that every action has an equal and opposite reaction, then,

Fab=−Fba [ ' -- ' sign is used to indicate that 1 object is moving in opposite direction after collision]

 

Using [i] and [ii] , we have

tmBvB−mBuB=−tmAvA−mAuA

mBvB−mBuB=−mAvA+mAuA

Finally we get,

mBvB+mAvA=mBuB+mAuA

This is the derivation of conservation of linear momentum.

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