Chapter 8, Problem 65GP

Larger animals have sturdier bones than smaller animals. A mouse’s skeleton is only a few percent of its body weight, compared to 16% for an elephant. To see why this must be so, recall, from Example 8.10, that the stress on the femur for a man standing on one leg is 1.4% of the bone’s tensile strength. Suppose we scale this man up by a factor of 10 in all dimensions, keeping the same body proportions. Use the data for Example 8.10 to compute the following.

a. Both the inside and outside diameter of the femur, the region of cortical bone, will increase by a factor of 10. What will be the new cross-section area?

b. The man’s body will increase by a factor of 10 in each dimension. What will be his new mass?

c. If the scaled-up man now stands on one leg, what fraction of the tensile strength is the stress on the femur?