A person holds a 50.0-N sphere in his hand. The forearm is horizontal, as shown in Figure 12.9a. The biceps muscle is attached 3.00 cm from the joint, and the sphere is 35.0 cm from the joint. Find the upward force exerted by the biceps on the forearm and the downward force exerted by the
upper arm on the forearm and acting at the joint. Neglect the weight of the forearm.

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Accepted Answer

We simplify the situation by modeling the forearm as a bar as shown in Figure 12.9b, where F is the upward force exerted by the biceps and R is the downward force exerted by the upper arm at the joint. From the first condition for equilibrium, we have, with upward as the positive y direction,

(1) [latex] \sum F_{y}=F-R-50.0 N =0 [/latex].

From the second condition for equilibrium, we know that the sum of the torques about any point must be zero.
With the joint O as the axis, we have

[latex] \sum au=F d-m g \ell=0 [/latex].

[latex] F(3.00 cm )-(50.0 N )(35.0 cm )=0 [/latex].

[latex] F=583 N [/latex].

This value for F can be substituted into Equation (1) to give R ! 533 N. As this example shows, the forces at joints and in muscles can be extremely large.

Question 12.2: A person holds a 50.0-N sphere in his hand. The forearm is h...

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