Question

state the prove the law of conservation of momentum? ​

Answer 1

Answer:

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Answer 2

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Law of conservation of momentum

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 law of conservation of momentum is an important consequence of Newton’s third law of motion.

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Derivation 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.

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)

$=>F { \small{BA}} = m{ \small{2 }}× a{ \small{ \small{2}}} = \frac{m2(v2 - u2}{t} \\ \\ </p><p>=>F{ \small{AB}} = m{ \small{1}} \times a{ \small{1}} =\frac{m1(v1 - u1)}{t}$

$=>\frac{m2(v2 - u2)}{t} = \frac{m1(v1 - u1)}{t} \\ \color{green}{=>m1u1 + m2u2 = m1v1 + m2v2}$

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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Law of Conservation of Momentum Examples

Following are the examples of law of conversation of momentum:

• Air-filled balloons
• System of gun and bullet
• Motion of rockets