91Ó°ÊÓ

The center of mass of an extended object is that point at which the net force can be assumed to act for determining the object's translational motion as a whole.

From table 7-1,

The mass of the upper arm is \({m_{{\rm{UA}}}} = 6.6\;{\rm{units}}\).

The mass of the lower arm is \({m_{{\rm{LA}}}} = 4.2\;{\rm{units}}\).

The mass of the hand is \({m_{\rm{H}}} = 1.7\;{\rm{units}}\).

The diagram of an outstretched arm is shown below.

The center of mass of an outstretched arm can be calculated asshown below:

\({x_{{\rm{CM}}}} = \frac{{{m_{{\rm{UA}}}}{x_{{\rm{UA}}}} + {m_{{\rm{LA}}}}{x_{{\rm{LA}}}} + {m_{\rm{H}}}{x_{\rm{H}}}}}{{{m_{{\rm{UA}}}} + {m_{{\rm{LA}}}} + {m_{\rm{H}}}}}\)

Substitute the values in the above equation.

\(\begin{array}{l}{x_{{\rm{CM}}}} = \frac{{\left( {6.6} \right)\left( {81.2 - 71.7} \right) + \left( {4.2} \right)\left( {81.2 - 55.3} \right) + \left( {1.7} \right)\left( {81.2 - 43.1} \right)}}{{\left( {6.6} \right) + \left( {4.2} \right) + \left( {1.7} \right)}}\\{x_{{\rm{CM}}}} = \frac{{\left( {6.6} \right)\left( {9.5} \right) + \left( {4.2} \right)\left( {25.9} \right) + \left( {1.7} \right)\left( {38.1} \right)}}{{\left( {6.6} \right) + \left( {4.2} \right) + \left( {1.7} \right)}}\\{x_{{\rm{CM}}}} = 18.9\; \approx 19\;{\rm{units}}\end{array}\)

Thus, the CM of an outstretched arm is 19% of the person’s height, along the line from shoulder to hand.