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Objects in equilibrium hinged platform with cable problem

  1. Apr 13, 2014 #1
    1. The problem statement, all variables and given/known data
    A hinged platform flagpole weighing 500 newtons is supported in the horizontal position by a cable as shown in figure 4.35 db4208af-4577-4e0c-9851-aba4c6f18afb.jpe . Find the tension in the cable and the horizontal and vertical forces at the hinge. Angle ø = 30°


    2. Relevant equations
    ∑F=0
    ∑T=0
    T= F* the lever arm


    3. The attempt at a solution
    What I did was created the three equations R cos θ -T cos 30=0 for the X forces
    where R is the resultant force of the wall acting on the hinge of the beam and T is the tension in the wire. The equation for the Y forces was R sin θ + T sin θ -500=0. Then I made the equation T sin 30 (x) -500 (1/2)(x)=0 for the sum of the torques is zero. My problem is I have four unknowns and only three equations meaning I can't substitute. What do I do now? The correct answer is T = 500 N and Rx= 433 N Ry= 250 N
     
    Last edited: Apr 13, 2014
  2. jcsd
  3. Apr 14, 2014 #2
    Maybe just go ahead and solve for R and T in terms of x and theta and see what happens.
     
  4. Apr 14, 2014 #3
    I don't think that will work because you have more unknowns than you have equations to work with. I tried it and it doesn't seem to work.
     
  5. Apr 14, 2014 #4
    if you did it correctly then I think you would see that one of those variables actually drops out
     
  6. Apr 14, 2014 #5
    Ok I see it now thanks!
     
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