# Objects in equilibrium hinged platform with cable problem

**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

http://ift.tt/1lZ63zh

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