I was looking through this forum, and I noticed one of those problems where a rocket ejects mass to get into orbit.(adsbygoogle = window.adsbygoogle || []).push({});

F=dp/dt

Now the arguments I saw went something like this:

p=mv

F=d(mv)/dt=v(dm/dt)+m(dv/dt)

But that equation is for a point particle I believe. All you can say for a rocket is:

F=m*a

where a is the acceleration of the center of mass.

For one thing, in the equation

F=d(mv)/dt=v(dm/dt)+m(dv/dt)

what is v? It's the relative velocity between the ejected mass and the rocket right? How does F=dp/dt "know" information about how the mass is going to be ejected? You could chuck the fuel with a small velocity or high velocity.

I think when you write

F=d(mv)/dt

you do that because relativity says m is a function of v (which is a function of t). But we are still assuming a point particle, and I don't think this expression can honestly be used for a rocket problem. However, I see everyone doing that, so I'm not too sure of myself on this one.

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# Rocket F=dp/dt

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