The steel railroad increases its length
when exposed to heat from 70 0F to
95 0F. The coefficient of thermal
expansion is11.7 x 10 - 6 m/m - 0C.
Find the strain.
A. 4.53 x 10 - 4 B. 1.
625 x 10 - 4 C. 2.625 x
10 - 4 D. 3.53 x 10 - 4

To calculate the strain in the steel railroad due to the increase in temperature, we can use the formula:

\[
\text{Strain} = \alpha \times \Delta T
\]

Where:
- \(\alpha\) is the coefficient of thermal expansion (given as \(11.7 \times 10^{-6}\) m/m°C),
- \(\Delta T\) is the change in temperature in °C.

### Step 1: Convert the temperature difference from Fahrenheit to Celsius

The temperature difference in Fahrenheit is:

\[
\Delta T_{F} = 95^\circ F - 70^\circ F = 25^\circ F
\]

To convert Fahrenheit to Celsius:

\[
\Delta T_{C} = \frac{5}{9} \times \Delta T_{F} = \frac{5}{9} \times 25 = 13.89^\circ C
\]

### Step 2: Calculate the strain

Now, we can calculate the strain:

\[
\text{Strain} = 11.7 \times 10^{-6} \, \text{m/m}^\circ C \times 13.89^\circ C
\]

Let me calculate that.The calculated strain is \( 1.625 \times 10^{-4} \).

Therefore, the correct answer is:
**B. \(1.625 \times 10^{-4}\)**.

Would you like further details or have any other questions?

Here are 5 related questions to expand your understanding:
1. How does thermal expansion affect different materials like steel and aluminum?
2. What factors can influence the coefficient of thermal expansion?
3. How would the strain change if the temperature difference were larger?
4. Why do engineers need to account for thermal expansion in railroad tracks?
5. Can you derive the relationship between strain and stress due to thermal expansion?

**Tip:** Always ensure that the temperature units are consistent when calculating strain or thermal effects.

The steel railroad increases its length when exposed to heat from 70°F to 95°F. The coefficient of thermal expansion is 11.7 x 10^-6 m/m°C. Find the strain. A. 4.53 x 10^-4 B. 1.625 x 10^-4 C. 2.625 x 10^-4 D. 3.53 x 10^-4

Learn how to calculate the strain in a steel railroad due to thermal expansion when the temperature changes from 70°F to 95°F. This problem covers key concepts such as strain, thermal expansion, and temperature conversion. Suitable for students in Grades 10-12.

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