The large quadriceps muscle in the upper leg terminates at its lower end in a te

Question

The large quadriceps muscle in the upper leg terminates at its lower end in a tendon attached to the upper end of the tibia. The forces on the lower leg when the leg is extended are modeled as in Figure (b), where vector T is the force of tension in the tendon, vector w is the force of gravity acting on the lower leg, and vector F is the force of gravity acting on the foot. Find vector T when the tendon is at an angle of 25.0° with the tibia, assuming that w = 34.0 N, F = 14.5 N, and the leg is extended at an angle of 40.0° with the vertical. Assume that the center of gravity of the lower leg is at its center, and that the tendon attaches to the lower leg at a point one fifth of the way down the leg.

Explanation / Answer

First, we resolve all forces into components parallel to and perpendicular to the tibia. Note that

wy = (34.0 N) sin 40.0deg = 21.85 N

Fy = (14.5 N )sin 40.0deg = 9.32 N ,

and T y = sin 25.0 * T

Using T = 0 for an axis perpendicular to the page and through the upper end of the tibia gives

(Tsin25)*d/5 - (21.85)d/2 - (9.32)d = 0

=> T = 239.519 N

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