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Ladder leaning against a wall

  1. Feb 19, 2012 #1
    Ladder of mass M and length L leans against a vertical wall. The friction factor between the ladder and ground is K. Calculate the minimum angle at which the ladder can stay in position without slipping off ignoring the friction between the wall and the ladder.

    Calculating momentum equilibrium
    [itex]N_2*L*sin(\theta) = 0.5*G*L*cos(\theta)[/itex]
    (N_2 = force between wall and ladder = KMg)
    (G = Mg)
    Which leads to
    [itex]tan(\theta) = \frac{1}{2K}[/itex]

    Anyhow, is this correct or am i missing something? I found a website giving an answer of
    [itex]tan(\theta) = 2K[/itex]

    What if i put a friction factor between the wall and the ladder? To this i get an answer of
    [itex]tan(\theta) = \frac{2K_2-1}{2K_1}[/itex]
    which feels wrong as it might result in a negative angle.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 19, 2012 #2

    ehild

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    Homework Helper
    Gold Member

    It is correct. Probably the other website denoted the other angle by theta.

    It really is not right. How did you get it?


    ehild
     
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