Chapter 18.5, Problem 51P

Lifting is done using the two springs, each of which is attached to the anchor bracket at A and to the counterbalance shaft at B and C. As the door is raised, the springs begin to unwind from the shaft, thereby assisting the lift. If each spring provides a torsional moment of M = (0.7θ) N·m, where θ is in radians, determine the angle θ₀ at which both the left-wound and right-wound spring should be attached so that the door is completely balanced by the springs, i.e , when the door is in the vertical position and is given a slight force upward, the springs will lift the door along the side tracks to the horizontal plane with no final angular velocity. Note: The elastic potential energy of a torsional spring is $V_0=\frac{1}{2}k{\theta }^2$, where M = kθ and in this case k = 0.7 N·m/rad.