Elements of the lower arm are shown in the figure. The weight of the forearm is 4.7 lb with mass center at G. Determine the combined moment about the elbow pivot O of the weights of the forearm and the sphere. What must the biceps tension force be so that the overall moment about O is zero? The moment is positive if counterclockwise, negative if clockwise.
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Question

Elements of the lower arm are shown in the figure. The weight of the forearm is 4.7 lb with mass center at G. Determine the combined moment about the elbow pivot O of the weights of the forearm and the sphere. What must the biceps tension force be so that the overall moment about O is zero? The moment is positive if counterclockwise, negative if clockwise.
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rockets31 · Answer

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mathmate · Answer

In problems of this type, it is best to draw a diagram showing forces and distance only, in order to visualize the relevant data.
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The pivot is at O, so all moments must be taken about O.
Moments are calculated by multiplying a force by the perpendicular distance from the pivot, about which moments are taken.
In this problem, all perpendicular distances are given, except that of the weight of the forearm G.  However, the angle is known, so the perpendicular distance is 
x=5.5sin(46$^\circ$).
Now take moments about O, assuming counter-clockwise is positive moment, and clockwise moment is negative.
$\sum$ moments = T(2")-4.7(5.5sin(46))-8.8(12.8)
For the system to be in equilibrium, $\sum$ moments =0.
Hence 
$\sum$ moments = T(2")-4.7(5.5sin(46))-8.8(12.8) = 0
Solve for T in the preceding equation to find the force of the bicep.