Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem Problem_33

Figure 12.35a 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 12.35b 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 \( T_s = 600 \text{ N} \). Figure 12.35c 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 \( \vec{F}_a \).