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Speed of car with changing mass problem

  1. Jun 20, 2009 #1
    Hello:

    An empty freight car of mass M starts from rest under an applied force F. At the same time, sand begins to run into the car at steady rate b from a hopper at rest along the track. Find speed when mass of sand m has been transferred.

    I have attached a drawing.

    So would this be: Let M(t) = mass as a function of time. So we have
    M(t) = M + bt
    And we have F = M(t)(dv/dt)
    So F(dt) = M(t)dv
    or dv = F(dt)/(M + bt)
    So wouldn't we have
    v = F/b*ln(M + bt)?
    But somehow this is wrong?
    Thanks.
     

    Attached Files:

  2. jcsd
  3. Jun 20, 2009 #2
    You've got it right up to dv = F(dt)/(M + bt)

    By doing a substitution of "M + bt" and then integrating accordingly, you should get

    v = (F/b)*ln((M + bt)/M)

    I think all that you did wrong was that you forgot to solve for the "t = 0" end of the integral.
     
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