A crossing guard holds a STOP sign at arm’s length, as shown in FIGURE 11-63. Her arm is horizontal, and we assume that the deltoid muscle is the only muscle supporting her arm. The weight of her upper arm is W_u = 18 N, the weight of her lower arm is W_l = 11 N, the weight of her hand is W_h = 4.0 N, and the weight of the sign is W_s = 8.9 N. The location where each of these forces acts on the arm is indicated in the figure. A force of magnitude ƒ_d is exerted on the humerus by the deltoid, and the shoulder joint exerts a force on the humerus with horizontal and vertical components given by ƒ_x and ƒ_y, respectively.

(a) Is the magnitude of ƒ_d greater than, less than, or equal to the magnitude of ƒ_x? Explain. Find 

(b) ƒ_d,

(c) ƒ_x, 

(d) ƒ_y. (The weights in Figure 11-63 are drawn to scale; the unknown forces are to be determined. If a force is found to be negative, its direction is opposite to that shown.)

Deltoid muscle STOP Humerus Radius lna CROSSING CUARD Axis -18 Wh W. W. Free-Body Diagram of the Arm 65 cm 42 cm 18 cm 14 cm