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 x 10−4 m2, a typical value.)
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?

Answer 1

Answer:

$a_s=4.8\times 10^{-2}~m^2$

Explanation:

Given:

cross sectional area of the bone, $a=4.8 \times 10^{-4} ~m^2$

factor of up-scaling the dimensions, $s=10$

Since we need to find the upscaled area having two degrees of the dimension therefore the scaling factor gets squared for the area being it in 2-dimensions.

The scaled up area is:

$a_s=a\times s^2$

$a_s=[4.8 \times 10^{-4}]\times 10^2$

$a_s=4.8\times 10^{-2}~m^2$