In Example 8.1, the tension in the biceps tendon for a person doing a strict curl of a \(900 \mathrm{~N}\) barbell was found to be \(3900 \mathrm{~N}\). What fraction does this represent of the maximum possible tension the biceps tendon can support? You can assume a typical cross-section area of \(130 \mathrm{~mm}^{2}\).

Example 8.1

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EXAMPLE 8.1 Finding the force from the biceps tendon BIO In the joints of the human body, muscles usually attach quite near the joint. This means that muscle and tendon forces are much larger than applied forces. In weightlifting, where the applied forces are large, holding the body in static equilibrium requires muscle forces that are quite large indeed. In the strict curl event, a standing athlete lifts a barbell by moving only his forearms, which pivot at the elbow. The record weight lifted in the strict curl is over 200 pounds (about 900 N). FIGURE 8.2 shows the arm bones and the main lifting muscle when the forearm is horizontal. The distance from the tendon to the elbow joint is 4.0 cm, and from the barbell to the elbow 35 cm. FIGURE 8.2 An arm holding a barbell. a. What is the tension in the tendon connecting the biceps muscle to the bone while a 900 N barbell is held stationary in this position? b. What is the force exerted by the elbow on the forearm bones? PREPARE FIGURE 8.3 shows a simplified model of the arm and the forces acting on the forearm. F, is the tension force due to the tendon, is the downward force of the barbell, and F, is the force of the elbow joint on the forearm. As a simplification, we've ignored the weight of the arm itself because it is so much less than the weight of the barbell. Because F, and F, have no x-component, neither can F. If it did, the net force in the x-direction would not be zero, and the forearm could not be in equilibrium. Because each arm supports half the weight of the barbell, the magnitude of the barbell force is F = 450 N. FIGURE 8.3 Visual overview of holding a barbell. Lifting muscle (biceps) Tendon Elbow joint- 4.0 cm. 35 cm Known d = 4.0 cm d = 35 cm F-450 N d THE db Find F. Fe These forces cause torques about the elbow. F