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Chapter 9: Q 40PE (page 319)

Consider a method for measuring the mass of a person鈥檚 arm in anatomical studies. The subject lies on her back, extends her relaxed arm to the side and two scales are placed below the arm. One is placed under the elbow and the other under the back of her hand. Construct a problem in which you calculate the mass of the arm and find its center of mass based on the scale readings and the distances of the scales from the shoulder joint. You must include a free body diagram of the arm to direct the analysis. Consider changing the position of the scale under the hand to provide more information, if needed. You may wish to consult references to obtain reasonable mass values.

Short Answer

Expert verified

The center of mass should be near the elbow.

Step by step solution

01

Given Data

The force acting on the upward is Fm.

The weight of the arm is W and the load is L.

02

Calculation of the distance of pivot

The diagram of the forearm is shown below:

According to the condition of equilibrium under the force we get,

FM=FE+W+L

The maximum weight appears on the scale when the scale is placed below the elbow as the center of mass is located near the elbow. The scale reading increases as the distance from the shoulder increases.

The total torque will also be zero under the equilibrium.

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