The femur is a bone in the leg whose minium cross-sectional area is about 3.60 E-4 m2. A compressional force in excess of 6.90 E4 N will fracture this bone.
(a) Find the maximum stress that this bone can withstand.
1 N/m2
(b) What is the strain that exists under a maximum-stress condition?
Stress, σ = force/area
=6.9E4/3.6E-4 N/m²
=1.92E8 N/m²
Strain depends on the Young's modulus, E, of bone, which varies from 5 to 30 GPa for a calcium content of 250 mg/g. We will take tha average of 20 GPa.
strain, ε
= σ / E
= 1.92E8 Pa / 20 GPa
= 0.0096 (approx. 1%)
Reference for E:
http://jeb.biologists.org/cgi/reprint/202/18/2495.pdf
(a) Well, if the femur can withstand a force in excess of 6.90 E4 N and the minimum cross-sectional area is 3.60 E-4 m2, then we can find the maximum stress by dividing the force by the cross-sectional area. So, the maximum stress is:
6.90 E4 N / 3.60 E-4 m2 = 1.92 E8 N/m2
(b) Now, if we know the maximum stress, we can find the strain by using Hooke's Law. But wait, what's Hooke's Law? It's like the law of elasticity but without the Stretch Armstrong references. It basically says that the strain (change in length) is proportional to the stress (force applied). So, the strain can be calculated by:
Strain = Stress / Young's Modulus
But since you didn't provide the Young's Modulus of the bone, I'm going to have to leave you hanging on this one. I guess you could say it's a bit of a strain not having all the information.
To find the maximum stress, we can use the formula:
Stress = Force / Area
Given that the compressional force in excess of 6.90E4 N will fracture the bone, we can substitute this information into the formula:
Stress = 6.90E4 N / 3.60E-4 m^2
Calculating this gives us:
Stress = 1.92E8 N/m^2
Therefore, the maximum stress that the bone can withstand is 1.92E8 N/m^2.
To find the strain, we can use Hooke's Law, which states that strain is equal to the stress divided by the Young's modulus (E):
Strain = Stress / E
Since the Young's modulus for the femur bone is not given in the question, we cannot calculate the exact strain.
To find the maximum stress that the femur bone can withstand, we will use the formula for stress:
Stress = Force / Area
In this case, the force is given as 6.90 E4 N and the minimum cross-sectional area is given as 3.60 E-4 m^2.
(a) Maximum Stress:
Stress = 6.90 E4 N / 3.60 E-4 m^2
= 1.92 E8 N/m^2
So, the maximum stress that this bone can withstand is 1.92 E8 N/m^2.
(b) Strain:
Strain is a measure of the deformation or elongation of an object relative to its original length. It is calculated using the formula:
Strain = Change in Length / Original Length
However, the given information does not provide the change in length or the original length of the femur bone. Therefore, we cannot determine the strain under a maximum-stress condition without this additional information.