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Conservation of Momentum Set-Up

  1. Jun 22, 2009 #1
    1. The problem statement, all variables and given/known data

    An empty freight car of mass M starts moving from rest with a constant applied force F0. At the same time, coal runs into the car at steady rate b from a hopper above the car at rest along the track. Calculate the velocity of the car as a function of time.

    GIVEN: M = 1400 kg; F0 = 42000 N; b = 150 kg/s; t = 6.5 s.

    2. Relevant equations

    I have a problem setting up conservation of momentum problems; I was wondering if there are some basic steps or factors to always look at, and help me understand the anatomy of them.

    3. The attempt at a solution

    I tried treating this like a rocket ship problem-

    Fexternal = F0 = d(mv)/dt

    F0*dt = d(mv) -->

    F0 = v*dM/dt + M*dv/dt = v*b + M*dv/dt

    to differentiate--> F0 - v*b = M*dv/dt
    --> (1/m)dt = (1/b)(1/F0/b - v)*dv

    V(t) = [F0/b]*[1-e-b*t/m]

    And plugging in I get 140.45 m/s which is not correct.

    will someone help me understand the anatomy of the conservation of momentum, any helpful links are also appreciated. Thanks!
    Last edited: Jun 22, 2009
  2. jcsd
  3. Jun 22, 2009 #2
    Your problem is that you forgot that m(t) = M + bt, so when you separated variables, your LHS should have been (1/(M+bt))dt

    Think that should fix it.

    I got: << solution edited out by berkeman >>
    Last edited by a moderator: Jun 22, 2009
  4. Jun 22, 2009 #3
    YEAH! Thank you for your help!
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