<DIV><IMG alt=\"\" src=\"https://s3.amazonaws.com/answer-board-image/52db7fe6-bd

Question

<DIV><IMG alt="" src="https://s3.amazonaws.com/answer-board-image/52db7fe6-bd13-4574-862a-7e09266647f2.gif" src_cetemp="https://s3.amazonaws.com/answer-board-image/52db7fe6-bd13-4574-862a-7e09266647f2.gif"><BR>The arm in the figure below weighs 36.0 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 = 1 N <BR>s = 2 N <BR></DIV>

Explanation / Answer

Summing moments about O we have

Ft*0.080*sin(12) - 45N*0.290m = 0

So Ft = 45*0.290/(0.080*sin(12)) = 784.5N

Now summing vertical forces

-45 + 784.5*sin(12) - Fs*sin(?) = 0

So Fs*sin(?) = -45 + 784.5*sin(12) = 118.125N (eqn 1)

Now sum horizontal forces

Fs*cos(?) - Ft*cos(12) = 0

Fs*cos(?) = 784.5*cos(12) = 767.356N (eqn 2)

Now square both eqns and add them

Fs^2*cos^2(?) + Fs^2*sin^2(?) = 767.356^2 + 118.125^2 =>

Fs^2 = 602789.963

So Fs = sqrt(602789.963) = 776.4N

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