Chapter 12, Problem 66CP

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 θ of the hinge force is described by

$\tan \theta =\left(\frac{32}{3d+4}-1\right)\tan 53.0°$

(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, θ, and R as d increases differ from one another.