Question

18. BIO When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure P8.18a. The total gravitational force on the body, F. is supported by the force n exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure P8.18b, where T is the force exerted by the Achilles tendon on the foot and R is the force exerted by the tibia on the foot. Find the values of T, R, and 0 when F = n=700 N.

Answer 1

Sum vertical force components:

$$\sum F_y=T\cos{\theta}-R\cos{15}+700=0$$

Sum horizontal force components

$$\sum F_x=T\sin{\theta}-R\sin{15}=0$$

Sum moments about toe:

$$∑Fx=18R−25T=0$$

$$T^2=\frac{18^2}{25^2}R^2=(R\sin{15})^2+(R\cos{15}-700)^2$$

$$R=427.4\ N$$

$$T=\frac{18}{25}427.4=307.7\ N$$

$$307.7\sinθ−427.4\sin15=0\\θ=64.6°$$