Rocket Thrust

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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 thats 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?
 

Answers and Replies

  • #2
Andrew Mason
Science Advisor
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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 thats 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:

[tex]\vec{F} = \frac{d\vec{p}}{dt}[/tex]

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

[tex]\sum \vec{F_i} = \sum {\frac{d\vec{p_i}}{dt} = 0[/tex]

which in this case reduces to:

[tex]\frac{d\vec{p_{rocket}}}{dt} = - \frac{d\vec{p_{gas}}}{dt}[/tex]

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
 

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