Question

prove law of conservation of momentum

Answer 1

First off momentum = mass x velocity. You can prove the conservation of momentum (i.e. that it stays the same unless a force acts upon a body) from Newton's laws.

Force = mass x acceleration

Acceleration is the change of velocity over time so:

Force = mass x ((velocity1 - velocity2) / time)

Or:

Force = ((mass x velocity1) - (mass x velocity2)) / time

Because mass x velocity is momentum, we can say:

Force = (momentum1 - momentum2) / time

Or:

Force x time = momentum1 - momentum2

Meaning a change in momentum is caused by force multiplied by time. If there is no force (or no time for it to be applied), the left hand side of the equation is zero, meaning momentum1 = momentum2 (and therefore there is no change in momentum).

Therefore, without a force being applied for a period of time, momentum is conserved.

Answer 2

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Conservation 0f Momentum➫ A system in which the momentum of a system is constant if there are no external forces acting on the system.

Prove: Conservation 0f Momentum:-▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃⤵

➧Let the Body A = m1 & B = m2

➧Let their velocity be u1 & u2
(u1 > u2)

➧Momentum of Body
A = m1u1 & B = m2u2

❱ Initial & Final momentum of System
➾ m1u1 + m2u2

◉ Body A exert force of Action
➾ Fᴀʙ on Body B.

◉ Body B exert force of Reaction
➾ Fʙᴀ on Body A.

▸ Fᴀʙ = Body A
➾ m1 (v1 - u1) / t

▸ Fʙᴀ = Body B
➾ m2 (v2 - u2) / t

▸ Since, Action = - reaction
▸ So, Fᴀʙ = - Fʙᴀ

m1 (v1 - u1) / t = - m2 (v2 - u2) / t

▸ m1v1 - m1u1 = m2v2 + m2u2
▸ m1v1 - m2v2 = m1u1 + m2u2...✔

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Thanks...✊