Question

1.state and prove law of conservation of momentum in case of two bodies of masses M1 and M2 collide each other.

plz answer this fastly guys...​

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.

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

Momentum of mass m2 after collision=m2u2

Momentum of mass m1 after collision=m1v1

By using the definition of impulse, change in momentum of mass m1 is,

Answer 2

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.

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 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

Momentum of mass M2 after collision=M2u2

Momentum of mass M1 after collision=M1v1

A= M1(v1-u1)

( change in momentum of particle A)

B= M2 (v2-u2)

( change in momentum of particle B)

F(BA)= F(AB)

(from third law of motion)

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.

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