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Static Equilibrium Door Problem

  1. Jun 16, 2012 #1
    1. The problem statement, all variables and given/known data
    A door made of a uniform piece of wood measures 1 m by 2 m and has a mass of 18kg. The door is entirely supported by two hinges, one at the bottom corner and one at the top corner. Find the force (magnitude and direction) that the door exerts on each hinge. Assume that the vertical force on each hinge is the same.


    2. Relevant equations



    3. The attempt at a solution
    .5m*18kg*g-2m*F2=0
    9mkg*g-2m*F2=0
    F2=9mkg*g/2m
    F2=44.145N

    This is the incorrect answer. The correct answer is 99N at 27 degrees right of vertical at the top and at 27 degrees left of vertical at the bottom. I think I am having so much trouble getting to this correct answer because I keep finding the force that the hinges exert on the door rather than the force that the DOOR exerts on the HINGES. I'm very stuck.

    FYI, I'm taking this through an online course and have thus have no instructor--just me and a textbook! Any help is sincerely appreciated!
     
  2. jcsd
  3. Jun 16, 2012 #2
    You have to take into account torque as well, this is why they gave you the dimensions of the door.
     
  4. Jun 16, 2012 #3
    He did take into account the torque, as is apparent from his equations. However, he only included the horizontal component of force, and not the vertical component. He needs to include the vertical component in order to calculate the overall magnitude of the force.
     
  5. Jun 16, 2012 #4
    You got F2 which is pulling the door the right/left depending on the layout.
    There's another force exerted on the hinge by the weight of the door.

    There are 3 ways of distributing the weight of the door on the hinges.
    1. Hanging from the top, no force exerted on lower hinge
    2. Pivotal at the botton hinge, no force exerted on the upper hinge.
    3. Equallly shared.
     
    Last edited: Jun 16, 2012
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