Question

derive the law of conservation of momentem​

Answer 1

Consider 2 colliding particles A and B whose masses are m1 and m2 with initial and final velocity as u1 and v1 of A and u2 and v2 of B.

The time of contact between 2 particles is t.

A = m1( v1-u1)

Change in momentum of A.

B = m2(v2-u2)

Change in momentum of B

Fba = -Fab

( 3rd law of motion)

F BA = m2× a2

$\frac{m2(v2 - u2}{t}$

Fab = m1 × a1

$\frac{m1(v1 - u1)}{t}$

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 collision and m1v1+m2v2 is the representation of total momentum of particles A and B after collision.