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Falling Chain

  1. Apr 17, 2009 #1
    1. The problem statement, all variables and given/known data
    A chain of mass M and length L is suspended vertically with the lower end touching a scale.
    the chain is released and falls onto the scale.
    what is the reading of the chain when a length x is fallen?
    neglect the size of individual links

    2. Relevant equations
    dp = IMPULSE=F*dt

    3. The attempt at a solution
    Well this is what I've done so far.
    the velocity of the specific part of the chain when it hits the scale is V= sqrt(2gx)
    F1= Mgx/L -weight of a X part of the chain.
    now the second force is quite a problem.
    F2=dp/dt=d(mv)/dt =V(dm/dt)......
    what do I do from here??
    i need to express dm/dt with the information i got, but cant find a way... =trying to translate it to words: the rate the mass hits the chain or...? I'm kinda stuck.
    Any help appreciated!
    Thank You.
    Last edited: Apr 17, 2009
  2. jcsd
  3. Apr 17, 2009 #2

    Doc Al

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    Staff: Mentor

    Express dm in terms of dx. (You're doing fine. :wink:)
  4. Apr 18, 2009 #3
    well i thought about v*M/L (for dm/dt)the only thing i found that works with the units mass/seconds)
    but which v do i place here if it's right?

    for dm alone it's xM/L?
    Thanks Al.
  5. Apr 18, 2009 #4

    Doc Al

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    Staff: Mentor

    dm = M/L dx, so dm/dt = M/L dx/dt = M/L v, where v is the speed of the piece of chain (dm) hitting the scale, which you already found in post #1.
  6. Apr 18, 2009 #5
    thanks Al, i got 3Mgx/L
    and it seems like the right answer.


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