The arm in the figure below weighs 42.1 N . The force of gravity acting on the a

Question

The arm in the figure below weighs 42.1 N.

The force of gravity acting on the arm acts through point A. Assume that  L1 = 0.0890m, L2 = 0.332m  and ? = 12.3

The arm in the figure below weighs 42.1 N. The force of gravity acting on the arm acts through point A. Assume that L1 = 0.0890m, L2 = 0.332m and ? = 12.3 degree . Determine the magnitude of the tension force Ft in the deltoid muscle. Determine the magnitude of the tension force Fs of the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown. Determine the angle of tension force Fs relative to the x-axis.

Explanation / Answer

By Sum of torques starting at pivot point O...

Ftsin(12.3)(.089) = (42.1)(.332)

Ft = 737 N

Then by sum of forces Ftsin(alpha) = Fs(sin theta) + Fg

737 sin(12.3) = Fs(sin theta) + 42.1

Fs(sin theta) = 114.9

Also Ftcos(alpha) = Fs(cos theta)

737cos(12.3) = Fscos(theta)

Fs cos(theta) = 720

Fs = 720/cos theta)

720tan(theta) = 114.9

tan(theta) = .16

theta = 9.07 degrees

Fs = (720)/cos(9.07)

Fs = 729 N

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