The large quadriceps muscle in the upper leg terminates at its lower end in a tendon attached to the upper end of the tibia (see figure (a)). 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 (the magnitude of) vector T when the tendon is at an angle θ of 25.0° with the tibia, assuming that w = 35.0 N, F = 12.4 N, and the leg is extended at an angle θ 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.

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 (see figure (a)). 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 (the magnitude of) vector T  when the tendon is at an angle θ of 25.0° with the tibia, assuming that w = 35.0 N, F = 12.4 N, and the leg is extended at an angle θ 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.