Question

When a person stands on tiptoe on one foot (a strenuous position). The total gravitational force Fg on the body is
supported by the normal force n exerted by the floor on the toes of one foot. A mechanical model of the situation is made, where T is the force exerted on the foot by the Achilles tendon and R is the force exerted on the foot by the tibia. Find the values of (a) T, (b) R, and (c) 0 when Fg = 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:

$$\sum Fx=18R-25T=0$$

$$T^2=\frac{18^2}{25^2}R^2=(R\sin{15})^2+(R\cos{15}-700)^2\\R=427.4\ N\\T=\frac{18}{25}427.4=307.7\ N$$

$$307.7\sin{\theta}-427.4\sin{15}=0\\\theta=64.6\degree$$