When a person stands on tiptoe (a strenuous position), the position of the foot

Question

When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in figure (a). The total gravitational force on the body, vector F g, is supported by the force n with arrow exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in figure (b), where vector T is the force exerted by the Achilles tendon on the foot and vector R is the force exerted by the tibia on the foot. Find the values of T, R, and when Fg = n = 635 N. (Do not assume that vector R is parallel to vector T .) T = N R = N = °

***please explain as in-depth as possible

Explanation / Answer

For rotational equilibrium, the sum of the moments about any point must be zero. Let's use the point where the normal force "n" acts.
M = 0 = T*25.0cm - R*cos15º*18.0cm
T = 0.6955*R

For vertical equilibrium, the sum of the vertical forces must be zero:
Fv = 0 = 635N + T*cos - R*cos15º = 635N + T*cos - 0.966*R

and finally, for horizontal equilibrium,
R*sin15º = T*sin substitute for T
0.2588*R = 0.6955*R*sin R cancels
sin = 0.372
= 21.8º

Substitute for T and in the vertical force equation:
0 = 635N + 0.6955*R*cos21.8º - 0.966*R = 635N - 0.320*R
R = 635N / 0.320 = 1984.3 N
T = 0.6955*R = 1380.0 N

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