The limiting stress for a typical human bone is `0.9xx10^(8) Nm^(-2)` while Young's modulus is `1.4xx10^(10) Nm^(-2)`. How much energy can be absorbed by two legs ( without breaking ) if each has typical length of 50 cm and an average cross-sectional area of `5 cm^(2)` ?

Answer

To solve the problem, we need to determine the maximum energy that can be absorbed by two human legs (bones) without breaking. We will use the given values of limiting stress, Young's modulus, length, and cross-sectional area of the bones.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Limiting stress for human bone, \( \sigma_{\text{max}} = 0.9 \times 10^8 \, \text{N/m}^2 \)
- Young's modulus for bone, \( Y = 1.4 \times 10^{10} \, \text{N/m}^2 \)
- Length of each leg, \( L = 50 \, \text{cm} = 0.5 \, \text{m} \)
- Cross-sectional area of each leg, \( A = 5 \, \text{cm}^2 = 5 \times 10^{-4} \, \text{m}^2 \)

2. **Calculate Maximum Strain (\( \epsilon_{\text{max}} \)):**
Using the relationship between stress, strain, and Young's modulus:
\[ \epsilon_{\text{max}} = \frac{\sigma_{\text{max}}}{Y} \]
Substituting the values:
\[ \epsilon_{\text{max}} = \frac{0.9 \times 10^8}{1.4 \times 10^{10}} = \frac{0.9}{1.4} \times 10^{-2} \approx 0.0643 \]

3. **Calculate Volume of One Leg:**
The volume \( V \) of a single leg can be calculated using:
\[ V = L \times A \]
Substituting the values:
\[ V = 0.5 \, \text{m} \times 5 \times 10^{-4} \, \text{m}^2 = 2.5 \times 10^{-4} \, \text{m}^3 \]

4. **Calculate Maximum Strain Energy per Unit Volume:**
The maximum strain energy per unit volume \( E \) is given by:
\[ E = \frac{1}{2} \sigma_{\text{max}} \epsilon_{\text{max}} \]
Substituting the values:
\[ E = \frac{1}{2} \times 0.9 \times 10^8 \times 0.0643 = 0.0289 \times 10^8 \, \text{J/m}^3 \]

5. **Calculate Total Strain Energy for One Leg:**
The total strain energy \( U \) for one leg is:
\[ U = E \times V \]
Substituting the values:
\[ U = 0.0289 \times 10^8 \times 2.5 \times 10^{-4} = 0.07225 \, \text{J} \]

6. **Calculate Total Strain Energy for Two Legs:**
Since there are two legs, the total energy absorbed by both legs is:
\[ U_{\text{total}} = 2 \times U = 2 \times 0.07225 = 0.1445 \, \text{J} \]

### Final Answer:
The total energy that can be absorbed by two legs without breaking is approximately **0.1445 J**.