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Tension and Hinge Force Problem

  1. Jul 13, 2014 #1
    1. The problem statement, all variables and given/known data

    The 135-N uniform beam from which 14-N wooden blocks are suspended is pinned to the ground. The beam is then supported by a cable (attached at the center of the beam) to allow the blocks to hang freely.

    If the blocks are attached two-fifths and three-fifths of the way up the beam, θc=12° and θb=20°, what tension must the cable supply?
    What is the hinge force at the bottom of the beam?

    The image can be seen here: http://i.imgur.com/tVm7RMS.jpg


    2. Relevant equations

    τ = rmgsinθ
    Fx = 0
    Fy = 0


    3. The attempt at a solution

    I'm not even sure where to begin tackling this problem. The two angles given are throwing me off, so I can't decide when or how to use either and if I should find the hinge forces first or the wire tension. Any help to point me in the right direction would be greatly appreciated!
     
  2. jcsd
  3. Jul 13, 2014 #2

    ehild

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    Draw all force vectors. Find their horizontal and vertical components and write up the equations of equilibrium for the beam. Two for the x and y components of the forces and one for the torque.


    ehild
     
  4. Jul 13, 2014 #3


    Does this seem correct? It's the closest thing I could think of. Also, would I substitute 1 for L, since the blocks are given as fractions along the beam?



    Fx: Tension*cos12 - HingeForce*cos20 = 0



    Fy: Tension*sin12 + HingeForce*sin20 - 135 N - 14 N = 0



    τorque = (-gravity*.5Length*cos20) + (-gravity*(2/5+3/5)Length*cos20) + (Tension*.5Length*cos12) + (HingeForce*cos20)
     
    Last edited: Jul 13, 2014
  5. Jul 13, 2014 #4

    ehild

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    But nobody knows what are the meanings of the letters.

    ehild
     
  6. Jul 13, 2014 #5

    Oops... :p

    Just corrected it.
     
  7. Jul 13, 2014 #6

    ehild

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    A hinge can exert force to any direction, not only in the direction parallel to the beam.
    What do you mean on "gravity" in the equation for the torque?
    If you wrote the torque with respect to the hinge, what is the torque of the hinge force?????

    ehild
     
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