Halliday, Resnick & Walker — Equilibrium and Elasticity: Problem 6

6 In Fig. 12-19, a 25 kg block is held in place via a pulley system. The person’s upper arm is vertical; the forearm is at angle \(\theta = 30^{\circ}\) with the horizontal. Forearm and hand together have a mass of 2.0 kg, with a center of mass at distance \(d_1 = 15 \text{ cm}\) from the contact point of the forearm bone and the upper-arm bone (humerus). The triceps muscle pulls vertically upward on the forearm at distance \(d_2 = 2.5 \text{ cm}\) behind that contact point. Distance \(d_3\) is 35 cm. What are the (a) magnitude and (b) direction (up or down) of the force on the forearm from the triceps muscle and the (c) magnitude and (d) direction (up or down) of the force on the forearm from the humerus?