Calculate the magnitude of the force. FM. required of the \"deltoid\" muscle to

Question

Calculate the magnitude of 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 3.3 kg. Express your answer to two significant figures and include the appropriate units. Calculate the magnitude of the force F_j exerted by the shoulder joint on the upper arm. Express your answer to two significant figures and include the appropriate units. Calculate the angle (to the horizontal) at which the force F, acts. Express your answer in degrees using two significant figures.

Explanation / Answer

Sum the moments about the shoulder joint.the force Fj produces no torque there.
M = 0 = Fm * 12cm * sin15º - 3.3kg * 9.8m/s² * 24cm
Fm = 250 N

B) we break Fj into components along verrtical and horizontal

vertical: Fv = Fm*sin15º - mg = 250N*sin15º - 3.3kg*9.8m/s² = 32.4 N
horizontal: Fh = Fm*cos15º = 241.5 N
Fj = (Fh² + Fv²) = 244 N

(c) theta= arc tan (Fv/Fh) =arctan (32.4/241.5) =7.64o

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