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Rocket's Initial Mass

  1. May 3, 2017 #1
    The problem states:
    Typical chemical fuels yield exhaust speeds of the order of 103 m/s. Let us imagine we had a fuel that gives v0 = 3 × 105 m/s. What initial mass of fuel would the rocket need in order to attain a final velocity of 0.1c for a final mass of 1 ton?

    I derived the equation in the first part of the problem:
    \begin{equation}
    v - v_0 = v_e \ln(\frac{m_0}{m})
    \end{equation}

    Solving for the initial mass, m, yields
    \begin{equation}
    m_0 = me^{\frac{\Delta v}{v_e)}}
    \end{equation}

    I plug in that.

    0.1c = 3.0*10^7
    v0 = 3.0*10^5
    vee = 1.0*10^3
    v - v0 = 3.0 *10^7 - 3.0*10^5 = 2.97*10^7
    m = 1000 kg
    I plug in these numbers and I am getting infinity. What am I doing wrong?

    Thanks!
     
  2. jcsd
  3. May 3, 2017 #2

    mfb

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    Staff: Mentor

    The initial velocity should be 0, not 3*105 m/s.

    3*105 m/s is the exhaust velocity of the hypothetical fuel, the number for chemical rockets is just given as comparison. The number will be very large, but you should't get infinity anywhere.

    Please work with units, that makes it easier (especially for you) to spot mistakes.
     
  4. May 3, 2017 #3
    I'm confused, how is the initial velocity zero? It says that the fuel gives us a v0 of 3.0*105?

    The problem is when I plug in the values of the conditions into my final equation, (equation 2).
     
  5. May 3, 2017 #4

    scottdave

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    Based on your formulas, m0 calculates to (1000 kg)*e^29700, which is approx 3.5 x 10^12901 (not infinity), but too large for your calculator.
     
  6. May 3, 2017 #5
    Thank you!
     
  7. May 3, 2017 #6

    haruspex

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    If that v0 is the initial speed of the rocket then the question makes no sense. How can the fuel give it that initial speed, before any fuel is burnt? I believe v0 is the exhaust speed, and the question is saying that although a typical exhaust speed is only 1000m/s, just suppose we had one with an exhaust speed 300 times as great.
     
  8. May 3, 2017 #7

    mfb

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    That is how I interpreted the question as well.
     
  9. May 4, 2017 #8

    scottdave

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    In perspective, the mass of the Earth is 5.97 x 10^24 kg.
     
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