Variable mass systems

Question

I'm studying this article:
https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec14.pdf
and I have the following doubt:
On page 3, when he derives the equation of motion (11), he says that the external forces $mathbf{F}$ acts only on $m$, and not also on $dm$ (see equation (9)). Why? If we think that $mathbf{F}$ is the gravity force (as he does in the following pages in the Rocket example), then why $dm$ does not feel gravity?

Vincent Fraticelli · Answer

I think it is because the force $vec{F}$ is proportional to the mass of the system: most often, it is the gravitational force $vec{F}=mvec{g}$ and therefore on the mass $dm$, $vec{dF}=dmvec{g}$ which leads to a second order term, in $dmdt$, for the impulse.

Answered by Vincent Fraticelli on July 22, 2021

R.W. Bird · Answer

The reaction force on the rocket engine depends on the change in momentum of dm which is caused by the engine, but not that caused by gravity.

Variable mass systems

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