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Having lots of difficulty with this statics+equilibrium problem.

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data

    A 43.4 kg, 3.2 m uniform ladder leans against a frictionless wall.* A 88.6 kg person is standing on the ladder down 1.18 m from the top of the ladder.* The ladder makes an angle of 53 degrees with the horizontal.* What is the minimum coefficient of static friction between the ladder and the ground so that the ladder does not slip?



    2. Relevant equations

    [tex]\sum[/tex]Fx=0
    [tex]\sum[/tex]Fy=0
    [tex]\sum[/tex][tex]\tau[/tex]=0
    Fgx = mgsin[tex]\vartheta[/tex]
    Fgy = mgcos[tex]\vartheta[/tex]
    Ff = [tex]\mu[/tex]*(normal force)

    3. The attempt at a solution

    So the way I saw this was, if you have the person on the ladder and it begins sliding down the vertical (toward the left on the horizontal) then the force of friction would inadvertently have to be to the right. (opposing the direction of motion). To find the coffecient of static friction, I'll need the value for the force of friction and the normal force. I am unclear on how to find the force of friction but I am assuming it can be isolated out when doing the [tex]\tau[/tex] = 0 step.

    1. The problem statement, all variables and given/known data

    A 200.00 kg uniform, horizontal beam is hinged at one end and at the other is supported by a cable that is at 13.3 degrees to the vertical.* * The beam is 2.00 m long.* Calculate the direction of the force at the hinge (measured with respect to the horizontal.


    2. Relevant equations
    Sum of all angles in a triangle = 180.



    3. The attempt at a solution
    So the vertical is perpendicular to the horizontal beam, making an angle of 90 degrees. We also know that the angle between the vertical and the supporting cable is 13.3 degrees. As such, 180-90-13.3 = 76.7.

    Is this correct reasoning?
     
    Last edited: Dec 6, 2009
  2. jcsd
  3. Dec 6, 2009 #2

    Lok

    User Avatar



    First : What are the forces that act upon the beam? Make a list. And a drawing(no need to post it).
     
    Last edited: Dec 6, 2009
  4. Dec 6, 2009 #3
    It was for the second question, but for the first. The forces acting upon the ladder are:

    Since the mass resting on the ladder is at an incline:
    -Downward force from the second mass (vertical component for force of gravity acting on second mass)
    -Horizontal component for the force of gravity acting on the second mass
    -Force of gravity acting on the ladder itself
    -Normal force acting on second mass (?)
    -Normal force acting on ladder
    -Frictional force from ground onto the ladder
     
  5. Dec 6, 2009 #4

    Lok

    User Avatar

    yeah must have been blind, tried to edit but you were faster :P

    There are of course to Normal forces acting on the ladder. Wall and ground. But good job.

    So for the beam there is as above :
    -gravity
    -Normal force ( hinge )
    -Tension ( beam )
    -Tension (cable) or call it a Force.

    Your reasoning is correct as both ends suffer the same forces, but the final angle is it up or down?
     
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