It is very dangerous to expand N2 into F = mdv/dt + v dm dt.
1) If part of an object merely "drops off" of a mother object, with no "push
off" force, there is no interactive force, and no exchange of momentum
between the two system parts.
2) Rockets, conveyor belts, etc (where there is an interaction force) are
best handled by the Momentum-Impulse theorem. F*dt = Pf - Pi.