A student is asked to find the force exerted by the biceps and the force at the elbow…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body

Life at Thermal Energy, Ch Bones, muscles, blood and body size

Problem

A student is asked to find the force

F_{\rm m}

exerted by the biceps and the force

F_{\rm J}

at the elbow joint when a person holds a

5\,\mathrm{kg}

mass in the hand with the forearm horizontal. The forearm is treated as a light rigid bar pivoted at the elbow; the biceps attaches

4\,\mathrm{cm}

from the elbow and pulls vertically upwards, and the mass is held

32\,\mathrm{cm}

from the elbow. Take

g = 9.8\,\mathrm{m\,s^{-2}}

. The working submitted is: "I will take torques about the hand, where the weight hangs, since that is where the interesting force acts. The weight then has zero moment arm, so its torque about this point is zero. The muscle acts at

32 - 4 = 28\,\mathrm{cm}

from the hand, and the elbow joint acts at

32\,\mathrm{cm}

from the hand. Since the elbow just carries the weight of the load, I will set

F_{\rm J} = W = 49\,\mathrm{N}

. Then torque balance about the hand gives

F_{\rm m} \times 28 = F_{\rm J} \times 32

, so

F_{\rm m} = 49 \times 32 / 28 = 56\,\mathrm{N}

." ((a)) Identify every error in this reasoning. ((b)) Redo the calculation correctly and state

F_{\rm m}

and

F_{\rm J}

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