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Friction and weight

  1. Apr 10, 2007 #1
    1. The problem statement, all variables and given/known data

    A lightweight rope is wrapped around a 100lb drum, passes over a frictionless pulley, and is attached to weight, W. The coefficient of friction is 0.50. Determine the maximum amount of weight that can be supported by this arrangement.

    I've drawn a picture, showing what I think are the forces on everything.

    I need help solving this, as I'm not sure how to actually do it. The answer, I have(given to me) is W=75lbs.

    2. Relevant equations



    3. The attempt at a solution

    Forces in x direction = 0 = Fa - Nb + Tw
    Forces in y direction = 0 = Na + Fb - 100

    Not sure if there is a moment(and if so, where do I take it about).....also, if not.....I'm not sure how to solve this next.

    Thank you,
    Brad
    View attachment friction.bmp
     
  2. jcsd
  3. Apr 10, 2007 #2

    Doc Al

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    Staff: Mentor

    Why not take moments about the center of the drum? Hint: If the drum is just about to turn, what can you say about the friction forces?
     
  4. Apr 10, 2007 #3

    AlephZero

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    Homework Helper

    You have 5 unknowns Fa Na Fb Nb and Tw so you need 5 equations.

    You have 2 equations already.

    When the drum starts to rotate, Coulombs law of friction says
    Fa = mu.Na and Fb = mu.Nb That makes 4 equations.

    You can get a 5th equation by taking moments. If doesn't matter where you take moments about. Choose a point which several forces pass through, so they have zero moment and you get a simpler equation.
     
  5. Apr 10, 2007 #4
    Ok......so now, I took the moment about the center.

    Counterclockwise

    M = 0 = Fb(d/2) + Fa(d/2) - Tw(d)

    And the 2 equations above. I'm totally lost as to how I mathematically solve these though, or where I start. Also, I don't know the diameter(d)....so not sure how the moment equation will help.....
     
  6. Apr 10, 2007 #5

    Doc Al

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    Staff: Mentor

    Good.

    Why is one force times d while others are times d/2?

    The d drops out, so you don't need the actual value.

    If you answer my question/hint about friction, you'll be able to rewrite Fb and Fa in terms of Nb and Na. (Similar to what AlephZero told you to do.) Then you'll have 3 equations and 3 unknowns--solve!
     
  7. Apr 10, 2007 #6
    Ok......I was saying it was the diameter/2.....or the radius. I don't know what I was thinking....I found that mistake, and will try to solve it now....see if I can do it....not sure.
     
  8. Apr 10, 2007 #7
    yes, I did solve it(it feels good....haha). Thank you for all of your help, I sure appreciate it!!!
     
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