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Q 31E

Expert-verified
Found in: Page 318

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

We analyzed the biceps muscle example with the angle between forearm and upper arm set at 90o. Using the same numbers as in Example 9.4, find the force exerted by the biceps muscle when the angle is 120o and the forearm is in a downward position.

The force exerted by the biceps muscle is 407N.

See the step by step solution

Step 1: Given Data

The diagram for the biceps muscle is shown below:

Step 2: Calculation of the force

The free body diagram is shown below:

As the force applied by the biceps muscle is perpendicular to the forearm, applying the condition of equilibrium under torque, we can write,

$\begin{array}{rcl}{F}_{B}{r}_{1}& =& \left({W}_{a}{r}_{2}+{W}_{b}{r}_{3}\right)\mathrm{cos}30°\\ {F}_{B}& =& \left({W}_{a}\frac{{r}_{2}}{{r}_{1}}+{W}_{b}\frac{{r}_{3}}{{r}_{1}}\right)\mathrm{cos}30°\\ & =& \left(2.5×9.8×\frac{16}{4.0}+4×9.8×\frac{38}{4.0}\right)\mathrm{cos}30°\\ & =& 407\text{N}\end{array}$

Thus, the force exerted by the biceps muscle is 407 N.