Larger animals have sturdier bones than smaller animals. A mouse\'s skeleton is

Question

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, 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. (Assume that a 70 kg person has a femur with a cross-section area (of the cortical bone) of 4.8 times 10^{-4} m^2, a typical value.)

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?

Explanation / Answer

C) Stress = Force/Area Force in the "scaled up man" is his weight which is proportional to his mass Area in the case of the "scaled up man" is the cross-sectional area of his femur. so in the 10X "scaled up" man his: Weight is 1000 times that of the original man Area is 100 times that of the original man Stress in femur = 1000/100 = 10 x that of the original man = 14%

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