Question

Question #88f37

Answer 1

Well, it is equal only if the resultant of all the external forces is equal to zero AND the mass doesn't change.

Explanation:

Consider a system of say n particles. Now consider the total momentum `P` of all these particles:
`P=p_1+p_2+...+p_n`
Let us differentiate with respect to time:
`(dP)/(dt)=(dp_1)/(dt)+(dp_2)/(dt)+...(dp_n)/(dt)`
But `p=mv` so that`(dp)/(dt)=m(dv)/(dt)=ma` that is Force (from Newton's second law and assuming mass constant to stay out of the differentation);

Finally we see that:
`(dP)/(dt)=F_1+F_2+....F_n`

Here the forces on the right can be:

Internal forces that cancel each other because of Newton's third law;

External forces...but if their resultant is zero then:

`(dP)/(dt)=0`

But this is true only if `P="constant"` i.e., the total momentum is conserved or the initial momentum MUST be equal to the final one!

Hope I didn't confuse you...