The femur is a bone in the leg whose minimum cross-sectional area is about 3.60 10-4 m2. A compressional force in excess of 6.90 104 N will fracture this bone.
(a) Find the maximum stress that this bone can withstand.
(b) What is the strain that exists under a maximum-stress condition
(a) Stress = Force/Area
= 6.90 10^4/3.60 10^-4 m2
= ___ N/m^2 (or Pascals)
(b) You need Young's modulus (E) for bone material. You will have to look it up. It probably varies with type of bone and the person's age.
Strain = Stress/E
See http://www.engin.umich.edu/class/bme456/bonefunction/bonefunction.htm
To find the maximum stress that the bone can withstand, we can use the formula:
Stress = Force / Area
(a) Maximum Stress:
Given:
Force (F) = 6.90 * 10^4 N
Area (A) = 3.60 * 10^-4 m^2
Substituting the values into the formula:
Stress = 6.90 * 10^4 N / 3.60 * 10^-4 m^2
Dividing the values:
Stress ≈ 1.92 * 10^8 N/m^2
Therefore, the maximum stress that this bone can withstand is approximately 1.92 * 10^8 N/m^2.
To find the strain that exists under a maximum-stress condition, we can use Hooke's Law:
Strain = Stress / Young's Modulus
However, since the Young's Modulus of bone is not provided in the question, we cannot determine the exact strain. The Young's Modulus refers to the stiffness or elasticity of a material, and it varies for different materials. Without this information, we cannot calculate the exact strain.
Please note that the relationship between stress and strain follows Hooke's Law, which states that the stress on a material is directly proportional to the strain produced in the material, as long as the material is within its elastic limit.