Question

please give me the mathematical expression of law of conservation of momentum​

Answer 1

Answer:

aw of conservation of momentum states that when two bodies collides the total momentum is conserved i.e the total momentum after collision and total momentum before collision is same.

suppose,

two bodies of mass m1 and m2 moves with initial velocity u1 and u1 after some time t the collide and then they again began to move woth final velocity v1 an v2.

according to newton's third law of motion we know that

Force applied by 1st body = opposite force applied by 2nd body

i.e

F = - F (because the reaction force is applied in opposite direction )

as force = mass × acceleration

so,

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

( Acceleration = final velocity- inital velocity/ time)

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

m1v1 -m1u1 = -m2v2 + m2u2

m1v1 + m2v2 = m2u2 + m1u1

as, we can see that total momentum after and before the collision is same

thus, the momentum is conserved.

Answer 2

Newton's third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction. This idea was used by Newton to derive the law of conservation of momentum. ... B=m_{2}(v_{2}-u_{2}) (change in momentum of particle B)