# Objects in equilibrium hinged platform with cable problem

1. Apr 13, 2014

### BrainMan

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 . 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. Apr 14, 2014

### paisiello2

Maybe just go ahead and solve for R and T in terms of x and theta and see what happens.

3. Apr 14, 2014

### BrainMan

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.

4. Apr 14, 2014

### paisiello2

if you did it correctly then I think you would see that one of those variables actually drops out

5. Apr 14, 2014

### BrainMan

Ok I see it now thanks!

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