Calculate the force FM required of the deltoid muscle to hol

Calculate the force, FM required of the \"deltoid\" muscle to hold up the outstretched arm shown in the figure(Figure 1) . The total mass of the arm is 2.9 kg .

Calculate the magnitude of the force FJ exerted by the shoulder joint on the upper arm.

Solution

balancing moment about Fj acting point,

Net torque = 0

(0 x FJ ) - ( 0.12 x Fm x sin15) + ((0.24) x mg x sin90) = 0

Fm = 219.84 N .........Ans

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balancing forces in horizontal direction,

FJ_X = FMcos15 = 212.35 N

in vertical,

FJ_y = mg - Fmsin15 = (2.9 x 9.81) - (219.84 sin15)

FJ_y = 28.45 N

Fj = sqrt(212.35^2 + 28.45^2) = 214.25 N