Question

Large 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 is so, consider that the stress on a femur for a 70 kg man standing on one leg is 1.4% of the bone's tensile strength (100 x 10^6 N/m^2). A typical value for the cross-sectional area of an adult's femur bone is 4.8 x 10^-4 m^2. A. The diameter of the femur increases by a factor of five. What will be its new cross-sectional area? B. The man's body will increase by a factor of 5 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 his femur? D. How does your previous result explain why large animals require a larger percentage of bone mass than small animals?

          Large 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 is so, consider that the
stress on a femur for a 70 kg man standing on one leg is 1.4% of
the bone's tensile strength (100 x 10^6 N/m^2). A typical value for
the cross-sectional area of an adult's femur bone is 4.8 x 10^-4
m^2.
A. The diameter of the femur increases by a factor of five. What
will be its new cross-sectional area?
B. The man's body will increase by a factor of 5 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 his femur?
D. How does your previous result explain why large animals
require a larger percentage of bone mass than small animals?

Added by Christian L.

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