Introduction

Throughout its history, Physics has been characterized by its intense dialogue with phenomena observed in concrete reality. More than that, it has provided tools to explain such phenomena, allowing us to predict and even manipulate their occurrence. One such phenomenon that we will explore in this project is collisions, and in particular, a fundamental concept for understanding them, which is the coefficient of restitution.

According to Physics, a collision occurs when two or more particles interact for a time interval, resulting in a change in their velocities. These collisions can be classified as elastic, partially elastic, and inelastic. The difference between them lies in the way in which kinetic energy is conserved. In a perfectly elastic collision, the total kinetic energy is conserved, while in an inelastic collision there may be a loss of kinetic energy.

The key concept that allows us to differentiate between these types of collision is the coefficient of restitution. It measures the elasticity of a collision and is defined as the ratio between the final relative velocity and the initial relative velocity of the colliding bodies. Through the coefficient of restitution we can calculate the velocity of the bodies after the collision.

Contextualization

The study of collisions and the coefficient of restitution is of enormous value because they manifest themselves in an infinity of phenomena in our daily lives and in diverse areas of science and technology. For example, in civil engineering, the coefficient of restitution can be used to understand how building materials react to impact, providing important data for the safety of structures.

In sports, determining the coefficient of restitution of a golf ball, for example, can help to understand how it will behave when hit by the club. Furthermore, the concept of collision is fundamental in the analysis of traffic accidents, to determine the velocities involved and even the possible culprits. That is, the coefficient of restitution and collisions are concepts that have a wide spectrum of practical applications.

A reliable source in Portuguese for delving deeper into these concepts is the book "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca (6th Edition). In addition, the YouTube channel "Física Universitária" has a series of explanatory videos about collisions and the coefficient of restitution. And, of course, we cannot forget the website "Brasil Escola," which has sections dedicated to Physics, including explanations and examples about collisions and the coefficient of restitution.

Practical Activity

Activity Title: "Collisions in Action: The Influence of the Restitution Coefficient"

Project Objective:

To understand through practical experiments the concepts of collision and the coefficient of restitution. In addition, to stimulate teamwork, the division of tasks, and scientific writing.

Detailed Description of the Project:

This project will be carried out in groups of 3 to 5 students with a completion deadline of one month. The objective is to study different types of collisions, using balls of different materials and measuring their velocities after the collision. The students must also calculate the coefficient of restitution and analyze the elastic behavior of the balls. The project will require approximately five to ten hours of work per student.

Necessary Materials:

• Three balls of different materials (for example, rubber, steel, and plastic)
• A rigid and smooth flat surface (such as a table)
• A camera capable of recording in slow motion
• Measuring tape
• Computer with software for video analysis (this could be Tracker, which is available free of charge)

Step by Step:

1. Step: Form the groups and distribute the tasks. This could include gathering materials, carrying out the experiment, analyzing the data, and writing the report.

2. Step: Gather the necessary materials for the experiment. Remember that the balls should be more or less the same size, but made of different materials.

3. Step: Carry out the experiment. Place the ball at a fixed height (for example, 1 meter) and let it fall vertically onto the flat surface. Use the camera to record the fall of the ball in slow motion. Repeat this procedure for all the balls, always from the same drop point.

4. Step: Analyze the video to measure the velocity of the ball before and after the collision with the flat surface. To do this, use a video analysis software, such as Tracker.

5. Step: Now, calculate the coefficient of restitution for each ball, using the equation for the coefficient of restitution: e = (Vf – V0) / (Vi – V0), where V0 is the velocity of the surface (which in this case is zero), Vi is the velocity of the ball before the collision, and Vf is the velocity of the ball after the collision.

6. Step: Analyze the results and discuss them with the group. How does the material of the ball affect the coefficient of restitution? What type of collision (elastic, partially elastic, inelastic) occurred in each case?

7. Step: Finally, write a detailed report about the experiment, including an introduction to the theme, a description of the experiment, and a discussion of the results. Each member of the group should contribute to a part of the report.

Project Delivery:

The students will deliver two main products: a video of the experiment and a written report. The video should clearly show the carrying out of the experiment and the analysis of the collisions in slow motion. The report, on the other hand, needs to detail:

1. Introduction: Contextualize the theme, its relevance and application in the real world, and the objective of this project.
2. Development: Detail the theory of collisions and the coefficient of restitution, explain the experiment, the methodology used, and present the results obtained and the discussion about them.
3. Conclusion: Restate the main points, explicitly stating what was learned and the conclusions about the project.
4. Bibliography: Indicate the sources used to work on the project, such as books, web pages, videos, etc.

The written report must be delivered in a digital format, preferably in a Google Docs document to facilitate collaboration among the members of the group. It is important that all the members of the group participate in the writing of the report, whether collecting data, analyzing the results, or writing the parts of the document. This is an excellent opportunity to practice scientific writing skills and teamwork.