Question

Prove that Linear momentum is conserved. m1u1 +m2u2 = m1v1=m2v2 *​

Answer 1

Let's assume that bodies of mass m1 and m2 are colliding and their initial and final velocities are same as provided in question.

Now,

Force experienced by m1 is :

$\rm \: F_{m1} = \dfrac{m_{1} v_{1} - m_{1}u_{1}}{t}$

Force Experienced by m2:

$\rm \: F_{m2} = \dfrac{m_{2} v_{2} - m_{2}u_{2}}{t}$

• Now, according to NEWTON'S 3RD LAW, action and reaction forces and equal and opposite.

$\rm \: F_{m1} = - F_{m2}$

$\rm \implies \: \dfrac{m_{1} v_{1} - m_{1}u_{1}}{t} = -\dfrac{m_{2} v_{2} - m_{2}u_{2}}{t}$

$\rm \implies \: m_{1} v_{1} - m_{1}u_{1} =-( m_{2} v_{2} - m_{2}u_{2})$

$\rm \implies \: m_{1} u_{1} + m_{2}u_{2} = m_{1} v_{1} + m_{2}v_{2}$

[Hence Proved]