As a result of a temperature rise of 32°𝐶, a bar with a crack at its center buckles upward. The fixed distance 𝐿_0 is 3.77 m and the coefficient of linear expansion of the bar is 25×10^(−6)/°𝐶. Find the rise 𝑥 of the center

Answer 1

To find the rise 𝑥 of the center, we need to use the formula for thermal expansion:

𝑥 = 𝐿₀ * α * Δ𝑇

Where:
- 𝑥 is the rise of the center
- 𝐿₀ is the fixed distance (3.77 m)
- α is the coefficient of linear expansion (25×10^(−6)/°𝐶)
- Δ𝑇 is the change in temperature (32°𝐶)

Substituting the given values into the formula:

𝑥 = 3.77 m * (25×10^(−6)/°𝐶) * 32°𝐶

Simplifying the expression:

𝑥 = 3.77 m * (0.000025/°𝐶) * 32°𝐶

𝑥 = 3.77 m * 0.0008

𝑥 ≈ 0.003016 m

Therefore, the rise 𝑥 of the center is approximately 0.003016 meters.