The bones of the forearm (radius and ulna) are hinged to the humerus at the elbo

Question

The bones of the forearm (radius and ulna) are hinged to the humerus at the elbow (figure below). The biceps muscle connects to the bones of the forearm about 2 cm beyond the joint. Assume the forearm has a mass of 2.1 kg and a length of 0.44 m. When the humerus and the biceps are nearly vertical and the forearm is horizontal, if a person wishes to hold an object of mass M so that her forearm remains motionless, what is the relationship between the force exerted by the biceps muscle and the mass of the object? (In other words, find a mathematical expression between force and mass.)

PS I have posted this question before and received the incorrect answer of (2.156M + 2.2638)

Explanation / Answer

Let F be the force exerted by the biceps on the forearm.

The net torque on the forearm about the elbow joint is zero since the forearm is motionless.

(F * 0.02) - (2.1 * 9.81 * 0.44 / 2) - (M * 9.81 * 0.44) = 0

=> 2F = (M * 9.81 * 44) + (2.1 * 9.81 * 22)

=> F = 215.82M + 226.611

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