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Mass Ratio Question

  1. Feb 23, 2007 #1
    1. The problem statement, all variables and given/known data
    A single-stage rocket is fired from rest from a deep-space platform, where gravity is negligible.

    If the rocket burns its fuel in a time of 50.0 s and the relative speed of the exhaust gas is v_ex=2100 m/s, what must the mass ratio m_{0}/m be for a final speed v of 8.00 km/s (about equal to the orbital speed of an earth satellite)?

    2. Relevant equations

    v-v0= -v_exln(m/m0) = v_exln(m0/m)

    3. The attempt at a solution

    having a rough time understanding the equation, any tips or hints?

    Any help would be greatly appreciated.
     
    Last edited: Feb 23, 2007
  2. jcsd
  3. Feb 23, 2007 #2
    I wonder if you are supposed to make a formula for the mass ratio as a function of time (it does vary). Is the mass lost at a constant rate?
     
  4. Feb 23, 2007 #3
    It doesn't say that it has to be which i would assume it shouldn't be. All I know about the question is what you see. So to answer your question, i don't know. I was hoping someone would be able to answer that lol.
     
  5. Feb 23, 2007 #4
    Does the rocket start from rest? If so, and you only care about the mass ratio and t=50 sec., then you just have to work out the log equation.
     
  6. Feb 23, 2007 #5
    Yes, it appears that it is starting from rest. How would I go about finding the mass ratio? Also, the log equation?

    How do I go about finding the mass of the rocket? (is that even the right question to ask)
     
    Last edited: Feb 23, 2007
  7. Feb 23, 2007 #6
    updated the original question.
     
  8. Feb 23, 2007 #7

    D H

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    I'll help with the equation. It is known as the Tsiolkovsky rocket equation.

    [tex]\Delta v = v_{\text{exhaust}}
    \ln\left(\frac{m_{\text{init}}}{m_{\text{final}}}\right)[/tex]

    where

    [itex]v_{\text{exhaust}}[/itex] is the exhaust speed relative to the rocket
    [itex]m_{\text{init}}[/itex] is the initial (pre-burn) mass of the rocket
    [itex]m_{\text{final}}[/itex] is the final (post-burn) mass of the rocket
    [itex]\ln(x)[/itex] is the natural logarithm function.

    The problem gives [itex]v_{\text{exhaust}}[/itex] and [itex]\Delta v[/itex] and simply asks for the mass ratio [itex]{m_{\text{init}}}/{m_{\text{final}}}[/itex]. Can you proceed with this?
     
  9. Feb 23, 2007 #8
    Let me do the math really quickly and i'll show you what I got.
     
  10. Feb 23, 2007 #9
    so is it MR=v_delta/v_exln?
     
    Last edited: Feb 23, 2007
  11. Feb 23, 2007 #10
    ok, i got it. thank you =)
     
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