I was reading a section about rocket propulsion in my general physics text and it came up with the following formula:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] m \frac{dv}{dt} = - v_{ex} \frac{dm}{dt} [/tex]

I don't have much trouble with this formula, but then it went ahead and substituted m dv/dt as the thrust experianced by the rocket. I feel a little hazy about this move because the mass isn't constant. If the net force on the rocket equals the rate of change of momentum, then it seems as if the following is equally valid:

[tex] \begin{align*}

F &= \frac{dp}{dt} = m \frac{dv}{dt} + v \frac{dm}{dt} \\

&= - v_{ex} \frac{dm}{dt} + v \frac{dm}{dt} \\

&= \frac{dm}{dt} ( v - v_{ex} )

\end{align*} [/tex]

Can someone clarify this for me?

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# Rocket Propulsion, Newton's second law

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