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Rocket Physics

  1. Oct 4, 2014 #1
    1. The problem statement, all variables and given/known data
    The first stage of a space vehicle consumed fuel and oxidizer at the rate of 1.60 multiply.gif 104 kg/s with an exhaust speed of 3.05 multiply.gif 103 m/s. Find the acceleration the vehicle had just as it lifted off the launch pad on the Earth, taking the vehicle's initial mass as 3.00 multiply.gif 106 kg.

    2. Relevant equations
    Momentum = mv

    3. The attempt at a solution
    So I tried to use math logic, but I'm not sure if its even logical...
    Mi = initial mass of rocket
    Vi = initial velocity of rocket (0)
    Ve = velocity of exhaust stuff
    dV = change in velocity
    dM = change in mass of rocket
    dm = change in mass of stuff expelled
    dM = - dm

    (Mi+dM)(Vi+dV) + Vedm = 0
    (Mi+dM)(Vi+dV) - VedM = 0
    MiVi + VidM +MidV+dMdV - VedM
    Vi = 0, so
    MidV+dMdV = VedM
    multiply everything by (1/dt):
    Mi*dv/dt + dM*dV/dt = Ve*dM/dt
    solving for since acceleration = dv/dt, solving for dv/dt gets:
    a = (Ve*dM/dt)/(Mi+dM) = -16.4.

    It cannot be a negative acceleration so obviously something is wrong...
     
  2. jcsd
  3. Oct 4, 2014 #2

    SteamKing

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    IDK why you are using 'math logic', whatever that is. Rocket science is mostly about physics, so you should have your physics cap on.

    If you start with first principles, F = ma always keeps popping up, but this form of Newton's second law isn't in its most general form. What you want is to write the second law in terms of a change in momentum for the rocket and the exhaust products, like so:

    cdf58c24f9a3384007a1cbaab39efd57.png

    where Fi is the net force acting on the rocket, m is the mass of the rocket at time t, v is the velocity of the rocket, ve is the velocity of the exhaust, and dm is the change in the mass of the rocket due to burning the rocket fuel.

    For more details, see:

    http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
     
  4. Oct 4, 2014 #3

    Orodruin

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    All of the quantities in your expression are positive in the way you have defined them so you should find a positive answer. You also should put some units on your answer or it will be unclear what you are actually answering (i.e., in this case m/s^2).

    Another issue is: Should you include gravity in the acceleration of the rocket? If it is just taking off from the launch pad, it is definitely not negligible.
     
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