The arm in the figure below weighs 37.4 N . a) The force of gravity acting on th

Question

The arm in the figure below weighs 37.4 N.

a)The force of gravity acting on the arm acts through point A. Assume that L1 = 0.0780m, L2 = 0.288m and ? = 10.9

The force of gravity acting on the arm acts through point A. Assume that L1 = 0.0780m, L2 = 0.288m and ? = 10.9 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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