# The arm weighs 44.0 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force t in the deltoid muscle and the force s of the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown. t=N s=N

The arm weighs 44.0 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force t in the deltoid muscle and the force s of the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown.
t=N
s=N
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Jeffrey Jordon

Weight of the arm

Applying equlibrium conditions $\sum \tau =0$

Magnitude of tension force

Now apply the first conditions of equlibtium

Along xaxis

$\sum {F}_{x}=0$

${F}_{x}^{\prime }-{F}_{t}\mathrm{cos}{12}^{\circ }=0$

${F}_{x}^{\prime }={F}_{t}\mathrm{cos}{12}^{\circ }$

Along y axis

$\sum {F}_{y}=0$

So the force F, extered by the shoulder. On the humerces to hold the arms in the position

${F}_{s}=s=\sqrt{{F}_{x}^{\prime 2}+{F}_{y}^{\prime 2}}$