Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem 18

18 Figure 12-26a shows a vertical uniform beam of length $L$ that is hinged at its lower end. A horizontal force $\vec{F}_a$ is applied to the beam at distance $y$ from the lower end. The beam remains vertical because of a cable attached at the upper end, at angle $\theta$ with the horizontal. Figure 12-26b gives the tension $T$ in the cable as a function of the position of the applied force given as a fraction $y/L$ of the beam length. The scale of the $T$ axis is set by $T_s = 800 \text{ N}$. Figure 12-26c gives the magnitude $F_h$ of the horizontal force on the beam from the hinge, also as a function of $y/L$. Evaluate (a) angle $\theta$ and (b) the magnitude of $F_a$.