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Static Equilibrium of hinge Question

  1. Mar 28, 2010 #1
    1. The problem statement, all variables and given/known data

    A stationary 3.0-m board of mass 6.0 kg is hinged at one end. A force is applied vertically at the other end, and the board makes a 30° angle with the horizontal. A 50-kg block rests on the board 80 cm from the hinge as shown in the figure below.

    http://img199.imageshack.us/img199/474/1235.gif" [Broken]

    (a) Find the magnitude of the force . Answer is F=160.23 N

    (b) Find the force exerted by the hinge. Fh=389.13 N

    (c) Find the magnitude of the force as well as the force exerted by the hinge, if the magnitude of the force is exerted, instead, at right angles to the board.
    The answer to the first part is 138.763 N. The second part is the one I cannot figure out.

    2. Relevant equations

    Fx: Force of hinge*cos(theta) = F*sin(theta)
    Fy: Force of hinge*sin(theta) = (M+m)g - F*cos(theta)

    3. The attempt at a solution

    Fh*sin(theta)/Fh*cos(theta) = [(6+50)(9.81)-(160.23)*cos(3)] / 160.23*sin(30) = 5.12509

    theta = arctan(5.12509) = 78.959 degrees

    Fh = [(160.23)*sin(30)]/cos(78.959) = 418.33 N (However, this answer is wrong)
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 28, 2010 #2


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    You seem to be assuming that the force on the hinge acts in the direction of the sloped board axis. This is not correct. Use Newton 1 in the x and y directions to solve for the hinge force components.
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