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In the rocket in deep space propulsion problem, you deal with a somewhat
similar situation. Your system of interest is losing mass rather than
gaining mass. We typically utilize conservation of momentum to obtain an
equation for the motion of rocket that typically appears as follows:
(total mass) a_cm = -U_exhaust* |dm/dt|
In this situation we don't hestitate to call the added terms
{-U_exhaust* |dm/dt|, in the rocket example} "the thrust " or maybe "the
force of the thrust".