Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem Problem_15

Forces \(\vec{F}_1\), \(\vec{F}_2\), and \(\vec{F}_3\) act on the structure of Fig. 12.19, shown in an overhead view. We wish to put the structure in equilibrium by applying a fourth force, at a point such as \(P\). The fourth force has vector components \(F_h\) and \(F_v\). We are given that \(a = 2.0 \text{ m}, b = 3.0 \text{ m}, c = 1.0 \text{ m}, F_1 = 20 \text{ N}, F_2 = 10 \text{ N}\), and \(F_3 = 5.0 \text{ N}\). Find (a) \(F_h\), (b) \(F_v\), and (c) \(d\).