A weightlifter performing a curl with a 320 N barbell stops the lifting motion with his forearms

in a horizontal position. (a) If the line of action of the weight of the barbell is 27 cm from the
axis of rotation (elbow joint), what is the magnitude of the moment that the elbow flexors must
exert to maintain that position? (b) If the weight of the weightlifter’s forearms and hands were
taken into account, would the moment that the elbow flexors had to exert be more or less than
that calculated in part (a)? If the biceps were the only elbow flexor muscle active (a rather
unlikely event) and its moment arm about the elbow joint was 4.3 cm, calculate the biceps
muscle force needed to maintain this equilibrium position.

To calculate the moment (torque) that the elbow flexors must exert to maintain the position, we first need to calculate the distance between the line of action of the weight and the elbow joint. Given that the line of action is 27 cm from the axis of rotation (elbow joint), this distance is also 27 cm.

(a) The magnitude of the moment is given by the formula:

Moment = Force × Distance

In this case, the force is the weight of the barbell, which is 320 N, and the distance is 27 cm (or 0.27 m). Plugging in the values:

Moment = 320 N × 0.27 m = 86.4 N·m

Therefore, the magnitude of the moment that the elbow flexors must exert to maintain that position is 86.4 N·m.

(b) If the weight of the weightlifter's forearms and hands were taken into account, the moment that the elbow flexors had to exert would be greater than that calculated in part (a). This is because the additional weight would increase the torque around the elbow joint. However, without the specific weight data for the forearms and hands, we cannot determine the exact increase in torque.

If the biceps were the only elbow flexor muscle active and its moment arm about the elbow joint was 4.3 cm (or 0.043 m), we can calculate the biceps muscle force needed to maintain this equilibrium position.

Using the formula from part (a):

Force × Distance = Moment

Force × 0.043 m = 86.4 N·m

Solving for Force:

Force = 86.4 N·m / 0.043 m ≈ 2,009 N

Therefore, the biceps muscle force needed to maintain this equilibrium position would be approximately 2,009 N.