Rocket propulsion equation: what's the error here?

[yucheng]

Homework Statement

N/A

Relevant Equations

N/A

Equation for rocket motion:
$$\frac{d \mathbf{P}}{d t} = M\frac{d \mathbf{v}}{d t} - \mathbf{u}\frac{d M}{d t}$$

But $$\mathbf{F}=\frac{d \mathbf{P}}{d t}=M\frac{d \mathbf{v}}{d t}$$

So $$M\frac{d \mathbf{v}}{d t} = M\frac{d \mathbf{v}}{d t} - \mathbf{u}\frac{d M}{d t}$$

And $$- \mathbf{u}\frac{d M}{d t}=0$$

Now, what's wrong? Thanks in advance!

 

[yucheng]

Ok, I messed up. Momentum is conserved. So $\mathbf{F}=0$!

 

[kuruman]

Ok, I messed up. Momentum is conserved. So $\mathbf{F}=0$!

I am glad you sorted that out because it saved me some writing. More generally $\vec F$ represents the sum of external forces acting on the rocket. Also, you should be using total, not partial derivatives here.