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. The biceps muscle connects to the bones of the forearm about 2 cm beyond the joint. Assume the forearm has a mass of 2 kg and a length of 0.4 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 object? (include unit check and reflection - a mathematical equation changing one variable on why the answer makes sense)

Explanation / Answer

Here we need to find the relationship between the force exerted by the muscle and the mass of the object.

We shall assume that the CM of the forearm is located at its middle of the length.

Length of biceps muscle connecting to bones of forearm = 2cm = 0.02m

Length of forearm = 0.4m
The summing of moments about the elbow is as shown below.
M = 0 = (F) (0.02m) - (2kg) ( ½(0.4m) ( 9.8m/s²) - (M) (0.4m) (9.8m/s²)

F = (3.92N·m + M * 3.92m²/s²) / 0.02m

F = 196N + M*196m/s²

This is the equation required between the force exerted by the biceps muscle and mass of object.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.