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 vector n 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 vector T , vector R , and ? when vector F g = 565 N. (Do not assume that vector R is parallel to vector T .)http://www.webassign.net/sercp/p8-16.gif

Explanation / Answer

solution: Sum vertical force components: ?Fy = T*cos? - R*cos15º + 565 = 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 + 656 = 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 = -730 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*730 0.359*0.933*T - 0.259*0.933*R = 0 subtract bottom from top -0.933*R + 0.242*R = -262 0.691*R = 262 R = 379 N then from the last T = R*(18/25) = 273 N

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