Serway & Jewett — Static Equilibrium and Elasticity: Problem 32

When a person stands on tiptoe on one foot (a strenuous position), the position of the foot is as shown in Figure P12.32a. The total gravitational force \(\vec{F}_g\) on the body is supported by the normal force \(\vec{n}\) exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure P12.32b, where \(\vec{T}\) is the force exerted on the foot by the Achilles tendon and \(\vec{R}\) is the force exerted on the foot by the tibia. Find the values of \(T\), \(R\), and \(\theta\) when \(F_g = 700 \text{ N}\).