Serway & Jewett — Static Equilibrium and Elasticity: Problem 50

In the What If? section of Example 12.2, let d represent the distance in meters between the person and the hinge at the left end of the beam. (a) Show that the cable tension is given by \(T = 93.9d + 125\), with T in newtons. (b) Show that the direction angle \(\theta\) of the hinge force is described by \(\tan \theta = \left( \frac{32}{3d + 4} - 1 \right) \tan 53.0^\circ\). (c) Show that the magnitude of the hinge force is given by \(R = \sqrt{8.82 \times 10^3 d^2 - 9.65 \times 10^4 d + 4.96 \times 10^5}\). (d) Describe how the changes in T, \(\theta\), and R as d increases differ from one another.