Example 12  Bone Compression

In a circus act, a performer supports the combined weight (1640 N) of a number of colleagues (see Figure 10.30). Each thighbone (femur) of this performer has a length of 0.55 m and an effective cross-sectional area of 7.7×10–4 m2. Determine the amount by which each thighbone compresses under the extra weight.

The entire weight of the balanced group is supported by the legs of the performer who is lying on his back. (Image courtesy of Ringling Brothers and Barnum & Bailey, THE GREATEST SHOW ON EARTH.)
Figure 10.30  The entire weight of the balanced group is supported by the legs of the performer who is lying on his back. (Image courtesy of Ringling Brothers and Barnum & Bailey®, THE GREATEST SHOW ON EARTH®.)

Reasoning  The additional weight supported by each thighbone is , and Table 10.1 indicates that Young’s modulus for bone compression is 9.4×109 N/m2. Since the length and cross-sectional area of the thighbone are also known, we may use Equation 10.17 to find the amount by which the additional weight compresses the thighbone.

Solution The amount of compression DL of each thighbone is

This is a very small change, the fractional decrease being DL/L0=0.000 11.



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