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.

Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.

(a) To calculate the magnitude of the moment that the elbow flexors must exert, we can use the equation:

Moment = Force x Distance

The force in this case is the weight of the barbell, which is given as 320 N. The distance is the perpendicular distance from the line of action of the weight to the axis of rotation (elbow joint), which is given as 27 cm (or 0.27 m).

So, the moment can be calculated as:

Moment = 320 N x 0.27 m
= 86.4 Nm

Therefore, the magnitude of the moment that the elbow flexors must exert is 86.4 Nm.

(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 more than that calculated in part (a). This is because the weight of the forearms and hands would add to the total weight of the system and increase the moment.

To calculate the biceps muscle force needed to maintain this equilibrium position, we can use the equation:

Moment = Force x Distance

The moment in this case is the same as calculated in part (a), which is 86.4 Nm. The distance is the moment arm of the biceps muscle about the elbow joint, which is given as 4.3 cm (or 0.043 m).

So, the biceps muscle force can be calculated as:

86.4 Nm = Force x 0.043 m

Solving for Force:

Force = 86.4 Nm / 0.043 m
= 2009.3 N

Therefore, the biceps muscle force needed to maintain this equilibrium position is approximately 2009.3 N.

To answer the first part of the question (a), we need to calculate the moment that the elbow flexors must exert to maintain the horizontal position of the forearms while holding the barbell.

The formula to calculate the moment is:

Moment = Force x Distance

Given:
- Force (weight of the barbell) = 320 N
- Distance (line of action) = 27 cm = 0.27 m

Substituting the values into the formula, we can calculate the moment:

Moment = 320 N x 0.27 m
Moment = 86.4 N∙m

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

Moving on to the second part of the question (b), if we were to consider the weight of the weightlifter's forearms and hands in addition to the weight of the barbell, the moment that the elbow flexors need to exert would indeed be different than the calculation in part (a).

To calculate the new moment, we would need additional information such as the weight of the forearms and hands. If we assume the combined weight of the forearms and hands to be x newtons, the new moment can be calculated as:

New Moment = (Weight of the barbell + Weight of forearms and hands) x Distance

The moment arm for the biceps muscle is given as 4.3 cm = 0.043 m.

To determine the biceps muscle force needed to maintain the equilibrium position (if the biceps were the only active elbow flexor muscle), we can use the equation:

Force = Moment / Moment Arm

Given:
- Moment (calculated in part (a)) = 86.4 N∙m
- Moment Arm = 0.043 m

Substituting the values into the equation, we can calculate the biceps muscle force:

Force = 86.4 N∙m / 0.043 m
Force ≈ 2013 N

Therefore, the biceps muscle force needed to maintain the equilibrium position is approximately 2013 N.