Halliday, Resnick & Walker — Rotation: Problem Problem_92

The Michael Jackson lean. In his music video "Smooth Criminal," Michael Jackson planted his feet on the stage and then leaned forward rigidly by \(45^{\circ}\), seemingly defying the gravitational force because his center of mass was then well forward of his supporting feet (Fig. 10.39a). The secret was in the shoes patented by Jackson: Each heel had a vee-shaped notch that he caught on a nail head slightly protruding from the stage. Once the heels were snagged on the nail heads, he could lean forward without toppling. The rotation axis was through each nail head, which was just below an ankle. The feat required tremendous leg strength, particularly of the Achilles tendon that connects the calf muscle (at distance \(d = 40 \text{ cm}\) from the ankle) to the heel (Fig. 10.39b). That tendon is at \(\phi = 5.0^{\circ}\) from the leg bone and from the rigid orientation of Jackson's body. Jackson's mass \(m\) was \(60 \text{ kg}\), his height \(h\) was \(1.75 \text{ m}\), and his center of mass was \(0.56h\) from his ankle. What was the tension \(T\) in the tendon when Jackson's body was at \(\theta = 45^{\circ}\) from the stage?