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Homework Help: Rocket Thrust

  1. May 13, 2010 #1

    bon

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    1. The problem statement, all variables and given/known data

    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.


    2. Relevant equations



    3. 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?
     
  2. jcsd
  3. May 13, 2010 #2

    Andrew Mason

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    Homework Helper

    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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