FM A B W₁ Wo F₁ FM Y a A B W₁ Br 1 C Wo

The figure shows a person wearing weight boots and doing lower leg flexion/extension exercise in a sitting position to strengthen the quadriceps muscles and a simple mechanical model of his leg. W1 is the weight of the lower leg, W0 is the weight of the boot, the magnitude of the pulling force applied to the tibia by the quadriceps muscles through the FM patellar tendon, the magnitude of the reaction force acting on the FJ tibiofemoral joint. Point O is the center of the tibiofemoral joint, point A is the point where the patellar tendon attaches to the tibia, point B is the center of gravity of the lower leg, point C is the center of gravity of the weight boot. The distances between point O and points A, B and C were measured as a=12 cm, b=24 cm and c=36 cm, respectively. The angle that the long axis of the tibia makes with the horizontal is β=39°, the angle between the line of action of the quadriceps muscle strength and the long axis of the tibia is α=16°. Points O, A, B and C lie along a straight line. The W0 weight of the boot is 0.6 times the W1 weight of the lower leg of the person (W0=0.6 W1). Since muscle strength is given as FM = 429 N;

Find the component (FJx) of the joint reaction force in the x direction. (Write your result in size N.)

a.
246,064

b.
184.55

c.
162.40

D.
282.97

e.
128.20