Question

prove that law of conservation of momentum from newtons 3 law of motion​

Answer 1

Answer:

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Answer 2

The law of conservation states that the total momentum of an object is conserved(is not destroyed) before and after collision of the objects

Proof

Consider two balls of different mass. Let the mass of the first ball be 'MA' and the second ball be 'MB'. Let they incide in motion at initial velocity 'uA' and 'uB' respectively in time 't'.

Now we know that the momentum of an object is product of the mass and velocity produced by the object.

Hence, P(momentum) = m (mass) * v(velocity).

Thus initial momentum of ballA is

MA*uA

And ball B is

MB *uB.

Now we know that after collision the ball produces its final velocity VA and VB respectively. Hence the final momentum becomes

MA*VA and MB * VB

According to the law

MA *uA+MB*uB = MA*VA + MB*VB.

Proof is that we know that during the collision of the ball the ball applies equalent and opposite force on each other hence

FA-B = - FB-A

We know that force =ma

MA(VA-uA/t) =-MB(VB-uB/t)

MA*VA-MA*uA=-MB*VB+MB*uB

MA *uA+MB*uB = MA*VA + MB*VB.

Hence proved.