Deriving Thrust from Newton II for Rocket Motors

[bon]

Homework Statement

Derive from Newton II the thrust (the force produced by the rocket exhaust) achieved by a rocket motor which ejects material with constant velocity u and mass ejection rate a.

Homework Equations

The Attempt at a Solution

Not sure...I know how to derive vf = vi + u ln(mi/mf) but that's not what its asking for..

So my attempt

F = mdv/dt

then using what we have for m i come to

F = a(vf-vi)/ln(M/m-at)

is this right?

 

[Andrew Mason]

Homework Statement

Derive from Newton II the thrust (the force produced by the rocket exhaust) achieved by a rocket motor which ejects material with constant velocity u and mass ejection rate a.

Homework Equations

The Attempt at a Solution

Not sure...I know how to derive vf = vi + u ln(mi/mf) but that's not what its asking for..

So my attempt

F = mdv/dt

then using what we have for m i come to

F = a(vf-vi)/ln(M/m-at)

is this right?

Newton's second and third laws of motion apply. Rather than F = ma, write the second law as:

$$\vec{F} = \frac{d\vec{p}}{dt}$$

The third law for an object on which no external forces act can be written:

$$\sum \vec{F_i} = \sum {\frac{d\vec{p_i}}{dt} = 0$$

which in this case reduces to:

$$\frac{d\vec{p_{rocket}}}{dt} = - \frac{d\vec{p_{gas}}}{dt}$$

For the gases fired out the end of the rocket, the velocity relative to the rocket is constant. What gives it a non-zero time rate of change of momentum?

AM