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, Fg, 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 b, 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 when Fg = n = 820 N. (For , enter the smaller of the two possible values between 0° and 90°.) T = N R = N = °

Explanation / Answer

their is no figure so i found it online
Sum vertical force components: Fy = T*cos - R*cos15º + 820 = 0
Sum horizontal force components Fx = T*sin - R*sin15º = 0
Sum moments about toe: Fx = R*18 - T*25 = 0

You have 3 equations in the 3 unknowns, T, R and . You should be able to solve that. (Hint: solve the second equation for sin: sin = R*sin15º/T; then solve for T from the third: T = (18/25)*R and substitute: sin = sin15º*(25/18). You now have and can replace sin and cos in the first two equations and solve for T and R.)

T*cos - R*cos15º + 820 = 0
T*sin - R*sin15º = 0
R*18 - T*25 = 0

From 2nd eq, T*sin = R*sin15º; sin = R*sin15º/T
Form 3rd eq, T = R*(18/25); put that in for T above to get
sin = R*sin15º/[R*(18/25)] = (25/18)*sin15º
sin = 0.359
= 21.1º

Put this in the 1st & 2nd eqs

0.933*T - 0.966R = -820
0.359*T - 0.259*R = 0

Multiply top by 0.359 and bottom by 0.933

0.933*0.359*T - 0.966*0.359*R = -0.359*820
0.359*0.933*T - 0.259*0.933*R = 0

subtract bottom from top

-0.933*R + 0.242*R = -294.38
0.691*R = 294.38
R = 426 N

then from the last T = R*(18/25) = 307 N

if the values of the figure are different then please put the values accordingly and get our answer

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