Question

state and prove the law of conservation of momentum.

give proper answer and full answer plz
I will give you points​

Answer 1

Answer:

Formula used: p = mv, FAB=−FBA and F=dpdt. Complete answer: Law of conservation of momentum states that unless an external force is applied, the two or more objects acting upon each other in an isolated system, the total momentum of the system remains constant.

Answer 2

Explanation:

Law of conservation of momentum:

states that unless an external force is applied, the two or more objects acting upon each other in an isolated system, the total momentum of the system remains constant.

As we know that the momentum ‘p’ of the body of mass m and moving with velocity v is given by

p = mv →(1)

Using equation (1), we can write

Change in momentum of a body = (Mass of the body)(Final velocity – Initial velocity) →(2)

Using equation (2), the change in the momentum of body A is given by

Change in momentum of body A = (Mass of body A)(Final velocity of body A – Initial velocity of body A)

⇒ Change in momentum of body A = m1(v1−u1)

Using equation (2), the change in the momentum of body B is given by

Change in momentum of body B = (Mass of body B)(Final velocity of body B – Initial velocity of body B)

⇒ Change in momentum of body B = m2(v2−u2)

According to Newton’s third law of motion, we can say that for any action there occurs an equal and opposite reaction.

i.e., Force applied by body B on body A = Force applied by body A on body B

⇒FAB=−FBA →(3) where negative sign shows that both forces occur in opposite directions

According to Newton’s second law of motion, force applied F to a body is equal to the rate of change of momentum p of the body with respect to time

F=dpdtF=Δpdt →(4)

Using equation (4), we have

Force applied by body B on body A FAB=Change in momentum of body ATime taken=m1(v1−u1)t

Using equation (4), we have

Force applied by body A on body B FBA=Change in momentum of body BTime taken=m2(v2−u2)t

Using equation (3), we get

⇒m1(v1−u1)t=−m2(v2−u2)t⇒m1(v1−u1)=−[m2(v2−u2)]⇒m1v1−m1u1=−(m2v2−m2u2)⇒m1v1−m1u1=−m2v2+m2u2⇒m1v1+m2v2=m1u1+m2u2

The above equation represents that the total momentum of the system after collision is equal to the total momentum of the system before collision.

Therefore, the law of conservation of momentum is proved.