A 89.0 kg person stands on one leg and 90% of the weight is supported by the upper leg connecting the knee and hip joint-the femur. Assuming the femur is 0.640 m long and has a radius of 1.90 cm, by how much is the bone compressed?
You will need to look up Young's modulus (Y) for femur bone material.
Then use
deltaL = L*(stress)/Y
Stress = M g/area
To determine the compression of the bone, we need to calculate the force acting on it and use Hooke's law to find the compression.
First, let's calculate the force supported by the femur bone.
Since 90% of the person's weight is supported by the femur, we can calculate the force as follows:
Force = Weight * Percentage Supported
= (89.0 kg * 9.8 m/s^2) * 0.90
Next, let's calculate the cross-sectional area of the bone.
The cross-sectional area of a bone can be calculated using the formula for the area of a circle:
Area = π * (radius)^2
In this case, the radius is given as 1.90 cm. However, we need to convert it to meters before calculating the area.
Radius = 1.90 cm = 0.019 m
Now we can calculate the force supported by the cross-sectional area of the bone:
Force supported by the bone = Force / Cross-sectional area
Finally, we can use Hooke's law to calculate the compression of the bone. Hooke's law states that the compression of a spring-like material is directly proportional to the force applied to it.
Hooke's law equation: F = k * x
where F is the force, k is the spring constant, and x is the compression.
Since we need to find the compression, we can rearrange the equation as follows:
x = F / k
Now, the spring constant (k) depends on the material properties of the bone. Without this information, it is not possible to directly calculate the compression.
However, we have provided the necessary steps to determine the compression once the spring constant is known.