A 70.0 kg weight lifter is doing arm raises using a 7.50 kg weight in her hand.

Question

A 70.0 kg weight lifter is doing arm raises using a 7.50 kg weight in her hand. Her arm pivots around the elbow joint, starting 40.0 below the horizontal. Biometric measurements have shown that both forearms and the hands together account for 6.35 % of a person's weight. Since the upper arm is held vertically, the biceps muscle always acts vertically and is attached to the bones of the forearm 5.50 cm from the elbow joint. The center of mass of this person's forearm-hand combination is 19.0 cm from the elbow joint, along the bones of the forearm, and the weight is held 38.0 cmfrom the elbow joint.

A)What force does the biceps muscle exert on the forearm?

B) Find the magnitude of the force that the elbow joint exerts on the forearm.

C) Find the direction of the force that the elbow joint exerts on the forearm. (Upward or downward)

D) As the weight lifter raises her arm toward a horizontal position, will the force in the biceps muscle increase, decrease, or stay the same?

Explanation / Answer

A) Weight of (forearm + hand) combination, W = (0.0635 / 2) * 70 * 9.81 = 21.8 N

Let F be the force that the bicep exert on the forearm.

Net torque of all the forces about the elbow joint is zero.

Then,

(F * 5.5 * cos40o) - (21.8 * 19* cos40o) - (7.5 * 9.81 * 38 * cos40o) = 0

=> 5.5F = (21.8 * 19) + (7.5 * 9.81 * 38)

=> F = 583.65 N

B) Let Fej be the required force. Then,

Fej - 583.65 + 21.8 + (7.5 * 9.81) = 0

=> Fej = 488.3 N

C) The force acts downward.

D) All the forces are purely vertical irrespective of the angular position of the forearm. Their magnitudes don't change with angular position of the forearm. Hence, the force in the biceps will stay the same in horizontal position.

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