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Ladder System

  1. Jan 6, 2008 #1
    1. The problem statement, all variables and given/known data
    A uniform ladder of weight WL and length L has its top against a vertical wall with friction coefficient
    μW and its foot on a smooth horizontal floor. A rope is attached to the foot of the ladder and secured
    to the base of the wall, with the ladder making an angle α with the horizontal. If a man of weight WM
    climbs the ladder, determine the tension in the rope when the man has climbed a distance d up the
    ladder. What is the maximum tension in the rope?

    2. Relevant equations
    F=ma, applied to the contact with the wall, the floor and rope.

    3. The attempt at a solution
    So i know i have to use the moments of a force about a point, and that point doesnt matter, but itd be really helpful to show me which one is the easiest from a solving purpose. I need help with the maximum tension in the rope part, cant think of anything to be honest.
  2. jcsd
  3. Jan 6, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Pick your favorite point! Just do it. (Hint: Pick one end of the ladder. Even better, pick both.)

    In addition to moments, use force equations.
  4. Jan 6, 2008 #3
    Ok, im getting that T = R (normal with vertical wall) as there are no other forces in that direction. But that seems a bit simple no? Is the maximum tension in the string, the tension just before it breaks yes? So the tension when the the ladder is about to slip?

    This is what happens when you leave 15 physics questions until the last night of your christmas break. Hahahahah.

    Edit- My equations;
    T = R
    N - Wm- Wl+ Fr= 0

    Torques at Foot of ladder;
    -RLSina= WmDCosa +1/2. Wl LCosa
    Last edited: Jan 6, 2008
  5. Jan 6, 2008 #4
    Found my mistake, easy enough in the end.
    Last edited: Jan 7, 2008
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