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Ladder against wall. (If you help me, you are a legend).

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data

    A uniform ladder AB, of weight W and length 2.5m rests against a smooth vertical wall OA with its foot on smooth horizontal ground OB. The ladder is in a vertical plane perpendicular to the wall. It is kept in position with OA=2m and OB=1.5m by a light rope OC joining O to a point C on the ladder such that angle COB=theta. Show that the tension T in the rope is given by

    T=(3W)/(8cos(theta)-6sin(theta))

    2. Relevant equations

    This is just a moments question.

    3. The attempt at a solution

    I've tried taking moments about B, but don't seem to get why there are two terms in theta in that equation.
     
  2. jcsd
  3. Oct 10, 2011 #2

    SammyS

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    Show what you have tried, and where you are stuck, so we can help you.
     
  4. Oct 10, 2011 #3
    I'm really not sure how to proceed. If I take moments about B, there seem to be two forces I need to include: the tension in the rope, and the weight force. Am I correct?
     
  5. Oct 10, 2011 #4

    SammyS

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    Use the moment about A.
     
  6. Oct 10, 2011 #5
    When I try moment about A,
    Clockwise moment is due to the tension, with value moment=2Tcostheta. as well as weight.
    Anticlockwise moment is due to the normal force at B (which is twice the weight force), hence moment here is 0.75W.
    Then solving I get T=3W/(8costheta). So where does the -6sintheta come from?
     
  7. Oct 10, 2011 #6

    SammyS

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    Does the problem state anything about the location of point C? (I doubt that it does.)
     
  8. Oct 10, 2011 #7
    Nope, C can vary.
     
  9. Oct 10, 2011 #8

    SammyS

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    Why do you say that the normal force is twice the weight force?
     
  10. Oct 10, 2011 #9
    I'm not sure. Should it be the same?

    And can you explain where that -6sin theta comes from?
     
  11. Oct 10, 2011 #10

    SammyS

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    A component of T is vertical. The normal force at B must cancel both the force of gravity and the vertical component of T.
     
  12. Oct 10, 2011 #11
    Isn't this accounted for in calculating the clockwise moment of the overall tension?

    Oh, I see. The normal force at B also takes into account this vertical component. FML.
     
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