A femur is a bone in the leg whose minimum cross sectional area is about 4.0 x 10^-4 m^2. A compressional force in excess of 6.8 x 10^4 N will fracture this bone. A.) Find the maximum stress that this bone can withstand and B.) What is the strain that exists under a maximum stress condition?
A femur is a bone in the leg whose minimum cross sectional area is about 4.0 x 10^-4 m^2. A compressional force in excess of 6.8 x 10^4 N will fracture this bone. A.) Find the maximum stress that this bone can withstand and B.) What is the strain that exists under a maximum stress condition?
To find the maximum stress that the bone can withstand, we can use the formula:
Stress = Force/Area
A) Maximum stress = Force/Area
Maximum stress = (6.8 x 10^4 N) / (4.0 x 10^(-4) m^2)
To simplify the calculation, let's convert the area to scientific notation as well:
Maximum stress = (6.8 x 10^4 N) / (4.0 x 10^(-4) m^2)
= (6.8 x 10^4 N) / (4.0 x 10^(-4) m^2)
To divide two numbers in scientific notation, we divide the coefficients and subtract the exponents of the base:
Maximum stress = (6.8 / 4.0) x (10^4) / (10^(-4))
= 1.7 x 10^0 x 10^(4-(-4))
= 1.7 x 10^8 N/m^2
So the maximum stress that this bone can withstand is 1.7 x 10^8 N/m^2.
B) To find the strain, we can use Hooke's law, which states:
Strain = Change in length / Original length
It is given that the compressional force will fracture the bone, meaning it has reached its breaking point. At this point, the change in length is maximum. Therefore, the strain under maximum stress condition can be assumed to be the point where the bone fractures.
However, the problem statement does not provide any information about the original length or the change in length. As a result, without further data, we cannot determine the strain under the maximum stress condition.