The structure shown is a retractable tool holder that is used in a factory to support a...

The structure shown is a retractable tool holder that is used in a factory to support a tool at point D. When the tool is to be used, the worker will grasp the tool and apply a downward force to lower it to the position that is needed. When the tool is not in use, the spring causes the tool to retract so that it is out of the way. The spring has 2 lb/in. stiffness and assume W is vertical.

If the unstretched length of the spring is 30 in., and θ = α = 60° when W = 0, determine the value of that occurs when W = 15 lb. Note: Unlike Probs. 3.77–3.79, the system of equations for this problem is difficult to solve by hand, and software such as Mathematica or Maple is very helpful.