Your leg bones (cross-sectional area about 9.50 cm2 ) experience a force of approximately 855 N when you walk. Find the fractional amount your leg bones are compressed by walking. Taking young modulus of bone to be Y = 1010 N/m2

To determine the fractional amount your leg bones are compressed while walking, we can use the relationship defined by Young's modulus. Young's modulus (Y) is a measure of the stiffness of a material and is defined as the ratio of stress to strain. In this case, we will calculate the stress applied to the leg bones and then find the resulting strain, which will allow us to determine the fractional compression.

Step-by-Step Calculation

1. Calculate Stress

Stress is defined as the force applied per unit area. The formula for stress (σ) is:

σ = F / A

Where:

• F = force applied (855 N)
• A = cross-sectional area (9.50 cm² = 9.50 x 10^-4 m²)

Now, substituting the values into the formula:

σ = 855 N / (9.50 x 10^-4 m²) = 900,000 N/m² (or Pa)

2. Calculate Strain

Strain (ε) is defined as the change in length (ΔL) divided by the original length (L). However, we can also express strain in terms of stress and Young's modulus:

ε = σ / Y

Substituting the values we have:

ε = 900,000 N/m² / (10^10 N/m²) = 0.00009

3. Determine Fractional Compression

The fractional amount that the leg bones are compressed is equivalent to the strain we just calculated. Therefore, the fractional compression of your leg bones while walking is:

Fractional Compression = 0.00009

Understanding the Implications

This means that for every unit length of your leg bones, they compress by 0.00009 units when you walk. In practical terms, this is a very small amount, indicating that bones are quite strong and resilient under normal walking conditions. The ability of bones to withstand such forces without significant deformation is crucial for maintaining mobility and overall skeletal health.

Real-World Analogy

Think of your leg bones like a sturdy metal spring. When you apply a force to the spring, it compresses slightly, but it returns to its original shape once the force is removed. Similarly, your bones can handle the stresses of walking without permanent deformation, thanks to their structural integrity and the properties defined by Young's modulus.

In summary, the fractional amount your leg bones are compressed while walking is 0.00009, illustrating the impressive strength and resilience of bone tissue under typical physical activity.