The arm in the figure below weighs 36.5 N. The force of gravity acting on the ar

Question

The arm in the figure below weighs 36.5 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force vector F t in the deltoid muscle and the force vector F s exerted by the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown.

t = N s = N The arm in the figure below weighs 36.5 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force vector F t in the deltoid muscle and the force vector F s exerted by the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown.

Explanation / Answer

umming moments about O we have Ft*0.080*sin(12) - 41.5N*0.290m = 0 So Ft = 41.5*0.290/(0.080*sin(12)) = 724N Now summing vertical forces -41.5 + 724*sin(12) - Fs*sin(?) = 0 So Fs*sin(?) = -41.5 + 724*sin(12) = 109N (eqn 1) Now sum horizontal forces Fs*cos(?) - Ft*cos(12) = 0 Fs*cos(?) = 724*cos(12) = 708N (eqn 2) Now square both eqns and add them Fs^2*cos^2(?) + Fs^2*sin^2(?) = 708^2 + 109^2 => Fs^2 = 513398 So Fs = sqrt(513398) = 717N

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