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The second law of Sir Isaac Newton or also known as the fundamental relation of dynamics : $$\vec{F}=m\vec{a}$$ Which can be derived using the definition of the force : $$\vec{F}=\frac{d\vec{p}}{dt}$$ But only if $m$ is treated as a constant. What if $m$ is not a constant? absolutely we're not having the same result. Then what we must apply $F=ma$ or $F=dp/dt$ ?

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In classical mechanics mass is always a constant. Matter is conserved (it gets a little more complicated in relativity and quantum mechanics but that need not concern us here). When dealing with a question involving "variable mass", for example rocket propulsion, one must divide the mass into the parts which are moving differently. See e.g. Rocket equation. The force accelerating the rocket is $ma$, where $m$ is variable. It is NOT $ma + v\dot m$

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  • $\begingroup$ This answer should be awarded 'correct answer'. +1 from me. $\endgroup$
    – Gert
    May 11, 2020 at 21:17
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if m=const both are the same, if m ist not constant like in rockets you have to use change of impulse .

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