Question

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

Answer 1

The new cross sectional area and tensile stress is mathematically given as

A=4.8*10^{-4}m^2

X=14:100

Cross sectional area and stress on the femur

Question Parameters:

To see why this must be so, recall, that the stress on the femur for a man standing on one leg is 1.4%

we scale this man up by a factor of 10 in all dimensions

that a 70 kg person has a femur with a cross-section area

a)

Generally the New cross sectional area  is mathematically given as

100A=100*4.8*10^{-4}

A=4.8*10^{-4}m^2

b)

From the initial statement we see that  the fraction of the tensile strength is the stress on the femur  and will be

$X=\frac{14}{100}$

X=14$

X=14:100

For more information on fraction

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Complete 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 10-4m², a typical value.)

Part 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? Express your answer using two significant figures.

Part B

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