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So, this is a question that just came to me. We all know that the derivative of momentum with respect to time is the definition of a force. $$ \frac{{\rm d}p}{{\rm d}t}=\frac{{\rm d}mv}{{\rm d}t}=m\frac{{\rm d}v}{{\rm d}t}=ma $$ However, that's assuming that the mass remains constant. What if the mass was changing? Such as if we had a rocket that lost like 90% of its mass as fuel? Well then, wouldn't the mass also be a variable there, so you wouldn't be able to just factor it out and treat it as a constant.

So how exactly would you find the force applied then?

UPDATE: I took calculus and understand why this question is pretty stupid

Physicyquestionasker
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You would simply just use the product rule. The definition of net force $\mathbf{F}$ is always given by

$$ \sum_i \mathbf{F}_i = \frac{d\mathbf{p}}{d t} = \frac{d}{dt} m(t)\mathbf{v}=\mathbf{v}\frac{dm}{dt} + m(t)\frac{d\mathbf{v}}{dt}.$$

InertialObserver
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    This may be correct mathematically but is not a correct application of Newton's second law. The reason for that is given here and the links therein. https://physics.stackexchange.com/questions/53980/second-law-of-newton-for-variable-mass-systems – Farcher Sep 05 '17 at 11:26