A 92-kg man's thighbone has a relaxed length of 0.56 m, a cross-sectional area of 6.0 10-4 m2, and a Young's modulus of 1.2 1010 N/m2. By how much does the thighbone compress when the man is standing on both feet?
1 µm
7.5 x 10-1 m
To find out by how much the thighbone compresses when the man is standing on both feet, we can use Hooke's Law, which states that the deformation of an elastic object is directly proportional to the force applied to it.
Hooke's Law can be written as:
ΔL = (F * L) / (A * Y)
Where:
ΔL is the change in length (the compression)
F is the force applied (the weight of the man)
L is the original length of the bone
A is the cross-sectional area of the bone
Y is the Young's modulus of the bone
First, let's calculate the force applied:
The weight of the man can be calculated as the mass multiplied by the acceleration due to gravity:
Weight = mass * g
Given that the mass of the man is 92 kg and the acceleration due to gravity is approximately 9.8 m/s^2:
Weight = 92 kg * 9.8 m/s^2
Weight = 901.6 Newtons
Now, let's substitute the values into the equation:
ΔL = (F * L) / (A * Y)
ΔL = (901.6 N * 0.56 m) / (6.0 * 10^-4 m^2 * 1.2 * 10^10 N/m^2)
Calculating this expression gives us the compression of the thighbone.