Question

derive the law of conservation of momentum​

Answer 1

Answer:

Answer is

Derivation of Conservation of Momentum

According to Newton's third law of motion, the impulsive force applied by the first object on the second one is equal and opposite to the impulsive force applied by the second object on the first object. ... This relation suggests that momentum is conserved during the collision.

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Answer 2

Answer:

Derivation of Conservation of Momentum

If no external force is exerted on the system of two colliding objects, the objects apply impulse on each other for a short interval of time at the point of contact. According to Newton’s third law of motion, the impulsive force applied by the first object on the second one is equal and opposite to the impulsive force applied by the second object on the first object.

During the one-dimensional collision of two objects of masses m1 and m2, which have velocities u1 and u2 before collision and velocities v2 and v2 after the collision, the impulsive force on the first object is F21

(applied by the second object) and the impulsive force on the second object is F12

(applied by the first object). Applying Newton’s third law, these two impulsive forces are equal and opposite i.e.

F21=−F12

If the time of contact is t, the impulse of the force F21

is equal to the change in momentum of the first object.

F21t=m1v1−m1u1

The impulse of force F12

is equal to the change in momentum of the second object.

F11t=m2v2−m2u2

From F21=−F12

,

F21t=−F12t

m1v1−m1u1

= −(m2v2−m2u2)

m1u1+m2u2=m1v1+m2v2

This relation suggests that momentum is conserved during the collision.