Question

state and prove the law of conservation of linear momentum from newton 2nd and 3rd law?​

Answer 1

Answer:

Law of conservation of momentum states that the after the collision of two objects,the sum of initial and final momentum of first object is equal to the sum of initial and final momentum of second object.

DERIVATION

let there be two objects A and B

let there masses be m1 for A and m2for B

initial momentum of first object=m1u1(u for initial velocity)

final momentum of first object=m1v1

initial momentum of second object =m2u2

final momentum of second object =m2v2 change in momentum of first object =m1v1-m1u1

change in momentum of second object =m2v2-m2u2

,according to second law of motion

rate of change of momentum is directly proportional to the force

so, for A rate of change of momentum =m1v1-m1u1/t = Fof B( as force was applied to A by B)

forB = m2v2-m2u2/t = F of A

but according. to third law of motion

force of action = force of reaction

so, F of A = -F of B because one force is acting in opposite direction.

m2v2-m2u2/t = -(m1v1-m1u1/t)

as time period is same so 5 will get canceled

m2v2-m2u2= - m1v1+m1u1

take initial and final momentum on equal sides

m2v2+m1v1= m1u1+ m2u2

Hence derived

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