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 compact bone) of 4. 8×10−4m2, a typical value. ).

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

the 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