Question

Prove the law of conservation of Momentum. Use it to find the recoil velocity of a gun when a bullet is fired from it.

Answer 1

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Momentum of a body is the energy stored in a body due to it's motion.

Now, Law of conservation of momentum States that the Total momentum of a system of bodies remains same if no external force acts on it.

Let's prove Law of conservation of momentum by Newton's third law of motion. :

Let's say there are two bodies A and B of masses

M1 and M2 respectively. Both are moving with a initial velocity u1 and u2 respectively. (u1>u2) , thus at a point they will collide. Now let's say both bodies move with final velocities v1 and v2 after collision.

Now the rate of change of momentum Of the body B due to force exerted by A will be The difference between it's final momentum and initial momentum / time. Numerically it will be :

Its final momentum will be = mass × final velocity=

m2v2

Initial momentum will be = mass × initial velocity=

m2u2

$F_B = \frac{∆p}{t} = \frac{m_2 </p><p>v_2 - m_2 u_2 </p><p></p><p></p><p>}{t}$

Similarly the rate of change of momentum of A due to force exerted by B will be :

$F_A = \frac{∆p}{t} = \frac{m_1v_1 - m_1u_1}{t}$

Now according to Newton's third law of motion : Every action has an equal and opposite reaction, thus we can say :

$F_b = - F_A$

After inputting the values we get : Further see the attachment.

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BY SCIVIBHANSHU

THANK YOU

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