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Theory:

In the previous sections, we learned about linear momentum.
 
In this section, we will discuss the conservation of linear momentum law and prove them with an example.
 
Principle of conservation of linear momentum:
There is no change in the linear momentum of a system of bodies as long as no net external force acts on them.
Let us prove the conservation of linear momentum law with the following example.
 
6(1).png
 
Proof:
Consider two bodies, A and B, having masses m1 and m2, move with an initial velocity u1 and u2 in a straight line.
 
Let the initial velocity of the body, A be higher than that of the body, B. i.e., u1u2.
 
During a period of time \(t second\), they tend to have a collision. After the impact, both bodies move along the same straight line with a velocity v1 and v2, respectively.
 
Force on body B due to A,

FB=m2v2u2t
 
Force on body A due to B,
 
FA=m1v1u1t
 
By Newton’s III law of motion,
 
\(Action\ force\ =\ Reaction\ force\)
 
FA=FBm1v1u1t=m2v2u2t(m1v1)m1u1t=(m2v2)m2u2tRemove"t"frombothsides,(m1v1)m1u1=(m2v2)m2u2(m1v1)m1u1=(m2v2)+m2u2(m1v1)+(m2v2)=m1u1+m2u2(eq.1)
 
The above equation (eq. 1) confirms in the absence of an external force, the algebraic sum of the momentum after collision is numerically equal to the algebraic sum of the momentum before collision.
 
Hence, the conservation of linear momentum law is proved.