Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem Problem_40

Figure 12.40a shows a horizontal uniform beam of mass \(m_b\) and length \(L\) that is supported on the left by a hinge attached to a wall and on the right by a cable at angle \(\theta\) with the horizontal. A package of mass \(m_p\) is positioned on the beam at a distance \(x\) from the left end. The total mass is \(m_b + m_p = 61.22 \text{ kg}\). Figure 12.40b gives the tension \(T\) in the cable as a function of the package’s position given as a fraction \(x/L\) of the beam length. The scale of the \(T\) axis is set by \(T_a = 500 \text{ N}\) and \(T_b = 700 \text{ N}\). Evaluate (a) angle \(\theta\), (b) mass \(m_b\), and (c) mass \(m_p\).