In the human arm, the forearm and hand pivot about the elbow joint. Consider a s

Question

In the human arm, the forearm and hand pivot about the elbow joint. Consider a simplified model in which the biceps muscle is attached to the forearm 3.80 cm from the elbow joint. Assume that the person's hand and forearm together weigh 15.0N and that their center of gravity is 15.0 cm from the elbow (not quite halfway to the hand). The forearm is held horizontally at a right angle to the upper arm, with the biceps muscle exerting its force perpendicular to the forearm

Now the person holds a 80.0-N weight in his hand, with the forearm still horizontal. Assume that the center of gravity of this weight is 33.0 cm from the elbow.

find the magnitude of the force that the elbow joint exerts on the forearm.

Explanation / Answer

Let force exerted by the biscep muscle = F

moment due to this force = F x 3.8

moment due to the weight of the arm = 15 x 15 Ncm

moment due to the weight being held = 80x 33 Ncm

now the moment due to the force by biscep muscle balances the moment due to the weight of the arm and the weight being lifted

thus

F x 3.8 = 15 x 15 + 80 x 33

F = 753.9 N

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