Mass Ratio Question

  • Thread starter cycam
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  • #1
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Homework Statement


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)?

Homework Equations



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

The Attempt at a Solution



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

Any help would be greatly appreciated.
 
Last edited:

Answers and Replies

  • #2
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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?
 
  • #3
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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.
 
  • #4
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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.
 
  • #5
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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:
  • #6
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updated the original question.
 
  • #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?
 
  • #8
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Let me do the math really quickly and i'll show you what I got.
 
  • #9
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so is it MR=v_delta/v_exln?
 
Last edited:
  • #10
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ok, i got it. thank you =)
 

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