Problem 2) How much does a 4ft long piece of concrete sidewalk expand when the temperature increases by 50 degrees Fahrenheit?
Problem 2) How much does a 4ft long piece of concrete sidewalk expand when the temperature increases by 50 degrees Fahrenheit?
Chapter2: Loads On Structures
Section: Chapter Questions
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![**Problem 2**: How much does a 4 ft long piece of concrete sidewalk expand when the temperature increases by 50 degrees Fahrenheit?
*Explanation*
This problem is an application of the thermal expansion concept. When the temperature of an object changes, its dimensions typically change as well. The amount by which the concrete sidewalk expands can be calculated using the formula for linear expansion:
\[ \Delta L = \alpha \times L_0 \times \Delta T \]
- \(\Delta L\) is the change in length.
- \(\alpha\) is the coefficient of linear expansion for concrete.
- \(L_0\) is the original length of the sidewalk (4 feet in this case).
- \(\Delta T\) is the change in temperature (50 degrees Fahrenheit).
To solve the problem, the specific coefficient of linear expansion (\(\alpha\)) for concrete would need to be used. This is often provided in tables of material properties. Once \(\alpha\) is known, it can be plugged into the formula along with the given values to find the change in length, \(\Delta L\).
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This type of question is commonly used in educational settings to illustrate thermal physics, material science, and applied mathematics. Students may explore the practical implications of thermal expansion in civil engineering and construction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1815343-0e1e-45bc-b31a-0935809f9211%2F81de3d3e-a7f3-4f96-ab06-2fc00714c6f3%2Fypblvmk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 2**: How much does a 4 ft long piece of concrete sidewalk expand when the temperature increases by 50 degrees Fahrenheit?
*Explanation*
This problem is an application of the thermal expansion concept. When the temperature of an object changes, its dimensions typically change as well. The amount by which the concrete sidewalk expands can be calculated using the formula for linear expansion:
\[ \Delta L = \alpha \times L_0 \times \Delta T \]
- \(\Delta L\) is the change in length.
- \(\alpha\) is the coefficient of linear expansion for concrete.
- \(L_0\) is the original length of the sidewalk (4 feet in this case).
- \(\Delta T\) is the change in temperature (50 degrees Fahrenheit).
To solve the problem, the specific coefficient of linear expansion (\(\alpha\)) for concrete would need to be used. This is often provided in tables of material properties. Once \(\alpha\) is known, it can be plugged into the formula along with the given values to find the change in length, \(\Delta L\).
---
This type of question is commonly used in educational settings to illustrate thermal physics, material science, and applied mathematics. Students may explore the practical implications of thermal expansion in civil engineering and construction.
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