Question

state and derive law of conservation of momentum.​

Answer 1

Answer:

Conservation of momentum is a fundamental law of physics, which states that the total momentum of an isolated system is conserved. ... In other words, the total momentum of a system of objects remains constant during any interaction, if no external force acts on the system.

Answer 2

Answer:

Momentum Conservation Principle

Law of conservation of momentum states that For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.

The principle of conservation of momentum is a direct consequence of Newton’s third law of motion.

Explanation:

Derivation of Conservation of Momentum

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.

Consider two colliding particles A and B whose masses are m1 and m2 with initial and final velocities as u1 and v1 of A and u2 and v2 of B. The time of contact between two particles is given as t.

A=m1(v1−u1) (change in momentum of particle A)

B=m2(v2−u2) (change in momentum of particle B)

FBA=−FAB (from third law of motion)

FBA=m2∗a2=m2(v2−u2)t

FAB=m1∗a1=m1(v1−u1)t

m2(v2−u2)t=−m1(v1−u1)t

m1u1+m2u2=m1v1+m2v2

Therefore, above is the equation of law of conservation of momentum where m1u1+m2u2 is the representation of total momentum of particles A and B before the collision and m1v1+m2v2 is the representation of total momentum of particles A and B after the collision.