Halliday, Resnick & Walker — Force and Motion–I: Problem 74

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 \( \rho = 7900 \text{ kg/m}^3 \). 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 \( T_{\text{main}} \) in the main cable when the beam is lifted at constant speed? What is the tension \( T_{\text{short}} \) in each short cable if \( d \) is (b) \( 1.60 \text{ m} \), (c) \( 4.24 \text{ m} \), and (d) \( 5.91 \text{ m} \)? (e) As \( d \) increases, what happens to the danger of the short cables snapping?