Figure 12.21 shows the foot and lower leg of a person standing on the ball of on

Question

Figure 12.21 shows the foot and lower leg of a person standing on the ball of one foot. Three forces act on the foot to maintain this equilibrium: the tension force T in the Achilles tendon, contact force FC at the ankle joint, and the normal force N of the ground that supports the person's weight. The person's mass is 40 kg and the force application points are as indicated in Fig. 12.21.

(a) Find the magnitude of the tension in the Achilles tendon. (kN)

(b) Find the magnitude of the contact force at the ankle joint.(kN)

Explanation / Answer

If we approximate the bones in the foot as a massless, planar, rigid body, the equilibrium conditions for the ? situation depicted in ? 14-42 are: Fig. Fx = T sin 25? - FC,x = 0, Fy = T cos 25? + N - FC,y = 0, ? and ( t )ankle joint = N (12 cm) - T (7 cm) sin 115? = 0. Then with N = 70 × 9.8 N, one ?nds (a) T = N (12 cm)/(7 cm) sin 115? = 1.30 kN, and (b) FC,x = T sin 25? =v 0.548 kN, FC,y = T cos 25? + N = 1.86 kN, and FC = 2 2 FC,x + FC,y = 1.94 kN.

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