Question

prove law of conservation of momentum mathematically (small ,class9)​

Answer 1

Answer:

Law of conservation of momentum states that total momentum of system remains conserved in the absence of external force.

Proof:

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.Let the two bodies remain in contact with each other for a small interval "delta t".

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.Let the two bodies remain in contact with each other for a small interval "delta t".Let F12 be the average force exerted by mass m1 on m2, and let F21 be the force on m2 due to m1.

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.Let the two bodies remain in contact with each other for a small interval "delta t".Let F12 be the average force exerted by mass m1 on m2, and let F21 be the force on m2 due to m1.Let v1 and v2 be the velcoities of two bodies after collision.

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.Let the two bodies remain in contact with each other for a small interval "delta t".Let F12 be the average force exerted by mass m1 on m2, and let F21 be the force on m2 due to m1.Let v1 and v2 be the velcoities of two bodies after collision.Momentum of mass m1 before collision=m1u1

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.Let the two bodies remain in contact with each other for a small interval "delta t".Let F12 be the average force exerted by mass m1 on m2, and let F21 be the force on m2 due to m1.Let v1 and v2 be the velcoities of two bodies after collision.Momentum of mass m1 before collision=m1u1Momentum of mass m2 after collision=m2u2

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.Let the two bodies remain in contact with each other for a small interval "delta t".Let F12 be the average force exerted by mass m1 on m2, and let F21 be the force on m2 due to m1.Let v1 and v2 be the velcoities of two bodies after collision.Momentum of mass m1 before collision=m1u1Momentum of mass m2 after collision=m2u2Momentum of mass m1 after collision=m1v1

Consider a body of mass m1 moving with velocity U1, striking against another body of mass m2 moving with velocity U2.Let the two bodies remain in contact with each other for a small interval "delta t".Let F12 be the average force exerted by mass m1 on m2, and let F21 be the force on m2 due to m1.Let v1 and v2 be the velcoities of two bodies after collision.Momentum of mass m1 before collision=m1u1Momentum of mass m2 after collision=m2u2Momentum of mass m1 after collision=m1v1By using the definition of impulse, change in momentum of mass m1 is,

(check the figure)

Explanation:

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