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Friction/Torque question.

  1. Apr 20, 2007 #1
    1. The problem statement, all variables and given/known data
    A painter wishes to know whether or not she can safely stand on a ladder. The ladder has a mass M1 = 14 kg which is uniformly distributed throughout its length L = 8.6 m. The ladder is propped up at an angle theta = 52o. The coefficient of static friction between the ground and the ladder is mus = 0.45, and the wall against which the ladder is resting is frictionless. Calculate the maximum mass of the painter for which the ladder will remain stable when she climbs a distance d = 5.2 m up the ladder. (The painter's mass might be so low that only Lilliputian painters can safely ascend the ladder.)



    2. Relevant equations
    Fric = Us*N
    F=m*a
    Torque= r *(dot)F

    3. The attempt at a solution

    Right now I'm just looking for a poke in the right direction. I can't even figure out where to start. I know that the frictional force is going to be at a maximum when the weight is at the maximum. I think that the normal force will be the 137.2 N from the ladder + 9.8*the mass of the painter. But how do I figure out what the maximum Fric will be? I also know that the problem has to do with torque. Any help is appreciated, I'm new so I'm sorry if I didn't give it enough effort but I've been staring at it and my book for about an hour to an hour and a half and couldn't get anywhere.


    Thanks,
    Matt
     
  2. jcsd
  3. Apr 20, 2007 #2
    First step draw a free body diagram and list every single force that applies. The floor puts a normal force on the ladder, the wall puts a normal force on the ladder, weight of the ladder, weight of the painter. This is a statics problem meaning that the sum of the forces need to equal 0, if they didn't then she'd be falling. Try summing forces in the x and y directions. Once you find that you have too many unknowns try summing torques to your advantage, they have to sum to 0 as well. I hope that starts you in the right direction.
     
  4. Apr 20, 2007 #3
    So I drew it out after dinner and I came up with this.
    If m=mass of the painter, and Nx is the force by the ladder on the painter(in the x-direction), and Ny is the force by the ladder on the painter(in the y-direction) then my equations look like:

    (9.8m + 14*9.8)Cos(52) = .45(9.8m + 137.2)N - In the x-direction

    Ny = (9.8m + 137.2) - y-direction

    Ny^2 + Nx^2 = N^2

    I realize these are probably off and you all are chuckling at home at my attempt :rofl: but any help is appreciated. Still stuck.
    Thanks,
    Matt
     
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