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Homework Help: Speed of moving mass as it loses mass

  1. Feb 12, 2010 #1
    1. The problem statement, all variables and given/known data
    A Freight Car of Mass M contains a mass of sand m. At t=0, a constant horizontal force i applied in the direction of rolling, and at the same time a port in the bottom is opened to let the sand flow out at a constant rate dm/dt. Find the speed of the freight care when all the sand is gone. Assume the car is at rest at t=0


    2. Relevant equations
    F= ma
    mv = mv - conservation of momentum?


    3. The attempt at a solution
    If there were no sand leaking from the bottom of the train, then the train would be accelerating at a constant acceleration because F= (M+m)a and the masses would be constant. However, the mass is changing, so the acceleration will be increasing over time. I'm just not sure how I can put these into a mathematical answer
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 12, 2010 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi lei123! Welcome to PF! :wink:
    Just do it step by step …

    what is the mass at time t? …

    what is the acceleration at time t? :smile:
     
  4. Feb 12, 2010 #3

    ehild

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    Homework Helper

    The momentum is not conserved as there is an external force, and also the mass is changing. Moreover, F=ma is valid for a body of constant mass. Newton formulated his second law in a more general form, so it was valid even for changing mass:

    "The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed."

    F*dt = d (mv)

    that is F = d(mv)/dt = v*dm/dt +m*dv/dt.


    ehild
     
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