Define the terms momentum and impulse . State and explain the law of conservation of linear momentum . Give examples .

Explanation

Momentum `bar((P))` : It is the product of mass and velocity of a body .
Momentum `bar((P))` = mass (m) `xx` velocity (v)
`thereforebar((P))=mbar(v)`
Impulse (J) : When a large force (F) acts on a body for small time (t) then product of force and time is called Impulse .
Impulse (J) = Force (F) `xx` time (t)
`therefore"Impulse"(J) = Fxxt`
Law of conservation of linear momentum:
There is no external force act on the system . The total linear momentum of the isolated system remains constant .
Proof : Let two bodies of masses say A and B are moving with initial moments `P_(A) and P_(B)` collided with each other . During collision they are in contact for a small time say `Deltat` . During this time of contact they will exchange their momenta. Let final momenta of the bodies are `P_(A)^(l)andP_(B)^(l)` . Let force applied by A on B is `F_(AB)` and force applied by B on A is `F_(BA)` .
From Newton's 3rd Law `F_(AB)=F_(BA)" or " F_(AB) Deltat=F_(BA)Deltat`
From 2nd Law `F_(AB)Deltat=P_(A)^(l)-P_(A)` change in momentum of A .
`F_(BA)Deltat=P_(B)^(l)-P_(B)` change in momentum of B .
`P_(B)^(l)-P_(A)-P_(B)^(l)-P_(B)" or " P_(A)+P_(B)=P_(B)^(l)+P_(B)^(l)`
i.e, sum of momentum before collision is equals to sum of momentum after collision .