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The problem in the image involves calculating the elongation of a copper bar under axial load using Hooke's Law for elastic deformation.

### Given dataThe problem in the image involves calculating the elongation of a copper bar under axial load using Hooke's Law for elastic deformation.

### Given 
- The bar has a square cross-section with side length \( 25 \, \text{mm} \) (\( 0.025 \, \text{m} \)).
- The initial length of the bar \( L_0 = 2.5 \, \text{m} \).
- The axial load \( F = 35 \, \text{kN} = 35 \times 10^3 \, \text{N} \).
- The Young's modulus \( E = 115 \, \text{GPa} = 115 \times 10^9 \, \text{Pa} \).

### To calculate:
- The elongation \( \Delta L \).

The formula for elongation under axial load is:

\[
\Delta L = \frac{F L_0}{A E}
\]

Where:
- \( F \) is the force,
- \( L_0 \) is the original length,
- \( A \) is the cross-sectional area,
- \( E \) is Young's modulus.

#### Step 1: Cross-sectional area \( A \)
Since the bar has a square cross-section, the area \( A \) is given by:

\[
A = \text{side}^2 = (0.025 \, \text{m})^2 = 6.25 \times 10^{-4} \, \text{m}^2
\]

#### Step 2: Calculate the elongation \( \Delta L \)

\[
\Delta L = \frac{35 \times 10^3 \times 2.5}{6.25 \times 10^{-4} \times 115 \times 10^9}
\]

Now let's compute this.The elongation \( \Delta L \) of the copper bar is approximately \( 1.22 \, \text{mm} \), which matches the provided option of **1.2 mm**.

Would you like more details or have any further questions?

Here are 5 related questions you might consider:
1. How does Young's modulus affect the elongation of a material?
2. What would happen to the elongation if the cross-sectional area was larger?
3. How is the stress on the material calculated in this context?
4. How would the elongation change if the axial force were doubled?
5. What are some real-world applications where such deformation calculations are critical?

**Tip**: Always make sure the units are consistent (e.g., converting mm to meters) to avoid calculation errors.

Uma barra de cobre experimenta uma deformação elástica possuindo uma secção transversal quadrada com 25 mm de lado, o seu comprimento inicial é de 2,5 m. A carga axial aplicada na barra é de 35 kN. Determine o seu alongamento. Ecu = 115 GPa.

This problem involves determining the elongation of a copper bar with a square cross-section under an axial load of 35 kN. The bar has an initial length of 2.5 m, a cross-sectional area of 25 mm by 25 mm, and a Young's modulus of 115 GPa. Learn how to apply Hooke's Law and the formula for elongation to solve this problem.

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