a 40 kg boy whose leg bones are 4 square cm in area and 50 cm long falls through a height of 2m without braeking his leg bones.If the bones can stand a stress of 0.9*10 power 8 N/sq meter,then the strain is

To determine the strain experienced by the boy's leg bones when he falls, we first need to understand the relationship between stress, strain, and the physical properties of the bones. Stress is defined as the force applied per unit area, while strain is the deformation experienced by the material in response to that stress. The formula connecting these concepts is given by:

Understanding Stress and Strain

Stress (\( \sigma \)) can be calculated using the formula:

Stress (σ) = Force (F) / Area (A)

In this scenario, we know the following:

• Mass of the boy (m) = 40 kg
• Area of the leg bones (A) = 4 cm² = 4 x 10^-4 m² (conversion to square meters)
• Stress limit of the bones = 0.9 x 10^8 N/m²

Calculating the Force

First, we need to calculate the force exerted on the bones when the boy falls. The force due to gravity can be calculated using:

Force (F) = Mass (m) x Gravitational Acceleration (g)

Assuming \( g \) is approximately 9.81 m/s², we find:

F = 40 kg x 9.81 m/s² = 392.4 N

Calculating the Stress on the Bones

Now, we can calculate the stress on the bones:

Stress (σ) = Force (F) / Area (A) = 392.4 N / (4 x 10^-4 m²) = 981,000 N/m² or 9.81 x 10^5 N/m²

Comparing Stress to Bone Strength

Next, we compare the calculated stress to the maximum stress the bones can withstand:

Maximum stress the bones can handle = 0.9 x 10^8 N/m² = 90,000,000 N/m²

Since 9.81 x 10^5 N/m² is much less than 90,000,000 N/m², the bones are safe from breaking under this stress.

Calculating Strain

Strain (ε) is defined as the ratio of the change in length to the original length of the material:

Strain (ε) = Stress (σ) / Young's Modulus (E)

However, we need the Young's Modulus for bone to calculate strain. For human bone, Young's Modulus is typically around 17 x 10^9 N/m². Now we can calculate the strain:

Strain (ε) = Stress (σ) / Young's Modulus (E) = (9.81 x 10^5 N/m²) / (17 x 10^9 N/m²)

Calculating this gives:

ε = 5.76 x 10^-5

Final Thoughts

The strain experienced by the boy's leg bones during the fall is approximately 5.76 x 10^-5. This value indicates that the bones are under stress but well within their capacity to withstand such forces without breaking. Understanding these concepts helps us appreciate the resilience of human bones and the physics behind falls and impacts.