Chapter 5, Problem 74P

Lifting cable danger. Cranes are used to lift steel beams at construction sites (Fig. 5.45a). Let’s look at the danger in such a lift for a beam with length $L=12.0\text{m}$, a square cross-section with edge length $w=0.540\text{m}$, and density $\rho =7900\text{k}\text{g}/m^3$. The main cable from the crane is attached to two short cables of length $h=7.00\text{m}$ symmetrically attached to the beam at distance $d$ from the midpoint (Fig. 5.45b). (a) What is the tension Tmain in the main cable when the beam is lifted at constant speed? What is the tension Tshort in each short cable if $d$ is (b) 1.60 m, (c) 4.24 m, and (d) 5.91 m? (e) As $d$ increases, what happens to the danger of the short cables snapping?