Contextualization

Theoretical Introduction

Energy is a fundamental concept in physics that refers to the ability to do work. The term 'potential energy' is often used to describe the energy stored in an object due to its position relative to other objects, tensions, or internal stresses. Gravitational Potential Energy (GPE) is a form of potential energy that refers to the work that would be needed to move a mass against the force of gravity.

GPE is calculated by multiplying the object's mass, the acceleration due to gravity (in the case of Earth, approximately 9.8 m/s²), and the height relative to the reference point. The relationship between gravitational potential energy, kinetic energy (energy due to motion), and total energy (the sum of potential and kinetic energy) forms the basis for the first law of thermodynamics, or the law of conservation of energy. This law establishes that energy cannot be created or destroyed, only transformed.

GPE is a fundamental concept in classical physics and provides the basis for understanding other concepts such as work and kinetic energy, which will also be explored in this project.

Theme Contextualization

Gravitational potential energy is a concept that is quite present in our daily lives, even if we are not always aware of it. When we lift an object off the ground, for example, we are increasing its gravitational potential energy. Similarly, when a bird flies, it is converting gravitational potential energy into kinetic energy.

This energy is essential for the operation of many modern technologies, from wind parks (where wind potential energy is converted into electrical energy) to hydroelectric power plants (where the water in a reservoir has gravitational potential energy that is converted into electrical energy).

Practical Activity: 'Energy Roller Coaster'

Activity Title

'Energy Roller Coaster: Designing and Analyzing the Track'

Project Objectives

• Understand the concept and application of gravitational potential energy and kinetic energy.
• Apply physics and mathematics concepts to solve practical problems.
• Develop teamwork skills, time management, critical thinking, and problem-solving skills.

Project Description

Groups will need to develop a roller coaster out of cardboard or other recyclable materials so that, when releasing a marble at the beginning of the track, it can reach the end. The challenge is to apply the concepts of gravitational potential energy and kinetic energy to develop a path that allows this to happen.

Required Materials

• Cardboard or other recyclable material for building the track
• Adhesive tape
• Marble
• Ruler
• Scale
• Calculator
• 2D or 3D drawing software (optional)

Step by Step

1. Form groups of 3 to 5 students. Each group will be responsible for the entire project, including conception, planning, construction, testing, and analysis of the track.

2. Research gravitational potential energy and how height and mass affect this energy.

3. Make the necessary calculations to determine how much gravitational potential energy the marble will have at different points on the track.

4. Based on these calculations, draw the roller coaster track that the marble should follow. Also, consider the concepts of kinetic energy and the need to convert gravitational potential energy into kinetic energy for the marble to complete the track.

5. Use cardboard and adhesive tape to build the roller coaster according to the drawing.

6. Perform tests, observe the behavior of the marble, and adjust the track as needed.

7. Analyze the results, discuss what worked and what did not work, and what adjustments had to be made.

8. Write the report, following the instructions below.

Project Deliverables and Report Writing

At the end of the project, in addition to the built roller coaster, groups must submit a detailed report, approximately 10 to 15 pages long, containing four main sections:

1. Introduction: Explain the theory of gravitational potential energy and its practical application in the roller coaster. Contextualize the importance of the theme, in general and for the project carried out.

2. Development: Describe in detail how the project was developed, from group formation, through research and theoretical study, the design and construction of the roller coaster, the tests and adjustments made, to the final version of the track. Include in this section the methodology used, the problems encountered and how they were solved, and the calculations made to determine the gravitational potential energy and kinetic energy at different points on the track.

3. Conclusion: Summarize the main points of the work, report the lessons learned, the challenges encountered and how they were overcome, and the conclusions drawn from the project experience.

4. Bibliography: List the sources consulted in the project development. Remember to correctly attribute all materials consulted, including books, articles, videos, and internet sites.

The project evaluation will be based on the built roller coaster, the group's performance during the project, and the report submitted.