Lesson Plan | Traditional Methodology | Surface Expansion

Objectives

Duration: (10 - 15 minutes)

This stage aims to present the main objectives of the lesson to the students, establishing a clear focus on what will be learned. This helps guide the students and prepare their minds for the concepts and problems that will be discussed throughout the lesson, ensuring they understand the importance and practical application of surface expansion.

Main Objectives

1. Understand the concept of surface expansion in different materials.

2. Learn to apply the formula for surface expansion to solve practical problems.

3. Understand how surface expansion affects holes in sheets.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to connect theoretical content to the students' real-life experiences, making the topic more interesting and relevant. By presenting practical examples and curiosities, the teacher can capture the students' attention and motivate them to better understand the phenomenon of surface expansion, preparing them for the more detailed concepts that will be discussed later.

Context

To start the lesson on surface expansion, begin by explaining how materials expand when heated. Use everyday examples, such as the functioning of train tracks, which need gaps between them to avoid deformation, or the expansion of metal bridges during summer. Highlight that expansion does not occur only in one dimension, as in linear expansion, but in two dimensions, affecting the surfaces of materials.

Curiosities

An interesting curiosity is that the Eiffel Tower in Paris can grow up to 15 centimeters during the summer due to thermal expansion. This phenomenon is a practical example of how surface expansion can affect large metal structures, showing the importance of considering these effects in engineering and construction.

Development

Duration: (50 - 60 minutes)

The purpose of this stage is to provide students with a detailed and practical understanding of surface expansion, including its definition, formula, and real-life applications. The topics and questions aim to consolidate theoretical knowledge and promote practical application, ensuring that students are able to solve problems related to surface expansion and understand the effects on sheets with holes.

Covered Topics

1. Definition of Surface Expansion: Explain that surface expansion is the increase in the area of a material when it is heated. Highlight that, unlike linear expansion, surface expansion occurs in two dimensions. 2. Surface Expansion Formula: Present the surface expansion formula: ΔA = A0 * β * ΔT, where ΔA is the change in area, A0 is the initial area, β is the coefficient of surface expansion of the material, and ΔT is the temperature change. Explain each term in detail. 3. Coefficient of Surface Expansion (β): Detail that the coefficient of surface expansion is specific to each material and is approximately double that of linear expansion (α). Discuss the importance of knowing β for different materials. 4. Practical Applications: Provide examples of how surface expansion is relevant in structures such as bridges, train tracks, and metal sheets with holes. Explain how engineers and architects consider surface expansion in their designs. 5. Problems Involving Holes in Sheets: Explain that when heating a sheet with a hole, both the sheet and the hole expand. Emphasize that the expansion of the hole can be calculated as if it were a solid area that also expands.

Classroom Questions

1. A square metal sheet of 2 m² is heated from 20°C to 100°C. If the coefficient of surface expansion of the metal is 2x10⁻⁵ °C⁻¹, what will be the new area of the sheet? 2. An aluminum plate with an initial area of 1.5 m² is subjected to a temperature increase of 80°C. The coefficient of surface expansion of aluminum is 48x10⁻⁶ °C⁻¹. Calculate the change in area. 3. A circular hole in a steel sheet has an initial area of 0.01 m². The sheet is heated, resulting in a temperature change of 50°C. If the coefficient of surface expansion of steel is 24x10⁻⁶ °C⁻¹, determine the new area of the hole.

Questions Discussion

Duration: (20 - 25 minutes)

The purpose of this stage is to review and consolidate the knowledge acquired throughout the lesson, ensuring that students have understood the concepts and can apply them in problem-solving. The detailed discussion of the questions allows for identifying possible difficulties and clarifying doubts, while the questions and reflections encourage active participation and critical thinking among the students.

Discussion

• Question 1: A square metal sheet of 2 m² is heated from 20°C to 100°C. If the coefficient of surface expansion of the metal is 2x10⁻⁵ °C⁻¹, what will be the new area of the sheet?

To solve this question, use the surface expansion formula: ΔA = A0 * β * ΔT.

A0 (Initial Area) = 2 m² β (Coefficient of surface expansion) = 2x10⁻⁵ °C⁻¹ ΔT (Temperature change) = 100°C - 20°C = 80°C

Calculation: ΔA = 2 * 2x10⁻⁵ * 80 = 0.0032 m²

New area: A = A0 + ΔA = 2 + 0.0032 = 2.0032 m²

• Question 2: An aluminum plate with an initial area of 1.5 m² is subjected to a temperature increase of 80°C. The coefficient of surface expansion of aluminum is 48x10⁻⁶ °C⁻¹. Calculate the change in area.

To solve this question, use the surface expansion formula: ΔA = A0 * β * ΔT.

A0 (Initial Area) = 1.5 m² β (Coefficient of surface expansion) = 48x10⁻⁶ °C⁻¹ ΔT (Temperature change) = 80°C

Calculation: ΔA = 1.5 * 48x10⁻⁶ * 80 = 0.00576 m²

Change in area: ΔA = 0.00576 m²

• Question 3: A circular hole in a steel sheet has an initial area of 0.01 m². The sheet is heated, resulting in a temperature change of 50°C. If the coefficient of surface expansion of steel is 24x10⁻⁶ °C⁻¹, determine the new area of the hole.

To solve this question, use the surface expansion formula: ΔA = A0 * β * ΔT.

A0 (Initial Area) = 0.01 m² β (Coefficient of surface expansion) = 24x10⁻⁶ °C⁻¹ ΔT (Temperature change) = 50°C

Calculation: ΔA = 0.01 * 24x10⁻⁶ * 50 = 0.000012 m²

New area of the hole: A = A0 + ΔA = 0.01 + 0.000012 = 0.010012 m²

Student Engagement

1. Question: What was the biggest challenge encountered when solving the surface expansion questions? How did you handle it? 2. Reflection: Think of other real-life examples where surface expansion might have a significant impact. How do these examples help understand the importance of this phenomenon? 3. Discussion: Considering the Eiffel Tower and its expansion in summer, what other structures or objects do you think are also affected by thermal expansion? Why? 4. Question: When calculating the expansion of a hole in a sheet, why do we consider the hole as an area that expands? How does this affect the final result? 5. Reflection: How can engineers and architects use the knowledge of surface expansion in their designs to ensure the safety and durability of structures?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to review and consolidate the main points discussed in the lesson, ensuring that students have a clear and cohesive understanding of the content. Furthermore, it reinforces the practical importance of the topic and its applications, motivating students to value the knowledge acquired and to recognize its relevance in their daily and professional context.

Summary

• Understanding the concept of surface expansion in different materials.
• Application of the surface expansion formula (ΔA = A0 * β * ΔT) to solve practical problems.
• Understanding the coefficient of surface expansion (β) and its relationship with the coefficient of linear expansion (α).
• Practical examples of surface expansion in structures such as bridges, train tracks, and metal sheets.
• Solving problems involving the expansion of holes in metal sheets.

The lesson connected theory with practice by presenting everyday examples and practical problems that illustrate how surface expansion affects materials and structures. Utilizing the formula for surface expansion and solving real problems, students were able to see the direct application of theoretical concepts in real-world situations, like the expansion of train tracks and metal bridges during the summer.

The topic of surface expansion is important for daily life as it directly affects engineering and the construction of structures. For example, the Eiffel Tower can grow up to 15 centimeters in summer due to thermal expansion. Understanding this phenomenon helps ensure the safety and durability of buildings and infrastructure, highlighting its practical relevance in daily life and in the careers of students who intend to pursue fields in engineering and architecture.