Answer:
Momentum is conserved when the net external force on the system is zero
Explanation:
Here we call 'system' the two objects together.
It is possible to demonstrate that the total momentum of a system is conserved when the net external force acting on it is zero. In fact, Newton's second law states that:
[tex]F=ma[/tex]
where F is the net external force, m the mass of the system, a its acceleration.
Re-writing the acceleration as rate of change of velocity:
[tex]a=\frac{\Delta v}{\Delta t}[/tex]
we get:
[tex]F=\frac{m \Delta v}{\Delta t}[/tex]
However, assuming that the mass of the system does not change, the quantity at the numerator is just the change in momentum of the system:
[tex]\Delta p = m\Delta v[/tex]
So the equation becomes:
[tex]F=\frac{\Delta p}{\Delta t}[/tex]
And therefore, if the net external force on the system is zero, F = 0, we get
[tex]\Delta p = 0[/tex]
which means that the total momentum is conserved.
