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
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.
To find the rise 𝑥 of the center of the bar, we can use the formula for linear expansion:
𝑥 = 𝐿₀ * 𝛼 * Δ𝑇
Where:
𝑥 = rise at the center of the bar
𝐿₀ = initial length of the bar
𝛼 = coefficient of linear expansion
Δ𝑇 = change in temperature
Given:
𝐿₀ = 3.77 m
𝛼 = 25×10^(−6)/°𝐶
Δ𝑇 = 32°C
Let's substitute the given values into the formula:
𝑥 = 3.77 m * (25×10^(−6)/°𝐶) * 32°C
Now, let's calculate the result:
𝑥 = 3.77 m * (25×10^(−6)/°𝐶) * 32°C
𝑥 = 0.000025 * 3.77 m * 32°C
𝑥 = 0.03016 m
Therefore, the rise 𝑥 of the center of the bar is 0.03016 meters.