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Classical Mechanics: linear resistance

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider a rocket subject to a linear resistive force, f= -bv but no other external forces. Using the equation mv'= -m'*vext+Fext show that if the rocket starts from rest and efects mass at a constant rate k= -m' then its speed is given by v=(k/b)vex[1-(m/m0)^b/k]

    3. The attempt at a solution
    so i thought maybe I was suppose to integrate both sides of the equation
    mv'= -m'*vext+Fext, but then i really didn't know where to go from there. Any help?
  2. jcsd
  3. Dec 7, 2008 #2
    I think your missing piece of information is to realize that the mass of the rocket depends on time:

    [tex]m(t) = m_0 - kt[/tex]
  4. Dec 7, 2008 #3
    Do I not need to integrate then? I just don't know where the power of b/k comes from.
  5. Dec 8, 2008 #4
    You still need to integrate, but the integral is different.
  6. Dec 8, 2008 #5
    I still can't get this one to work out. Am I still missing information? I tried starting with the equation mv'= -m'*vext+Fext. I solved for v'. and then substituted in the equation m0-kt. But then I didn't know where to go from there.
  7. Dec 8, 2008 #6
    help, I'm still stuck, can any one help me?
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