Project: Collisions in Action - Understanding the Coefficient of Restitution

Contextualization

The concept of collisions and the coefficient of restitution are fundamental in the study of physics, specifically in mechanics, an area that focuses on the study of movement, its causes, and consequences. The coefficient of restitution (e) is a measure that allows us to quantify the "elasticity" of a collision. It is defined as the ratio between the final relative velocity and the initial relative velocity of the bodies involved in a collision. This coefficient can have values between 0 and 1, inclusive.

In a perfectly elastic collision (e=1), there is no loss of total kinetic energy. This means that the sum of the kinetic energies of the bodies before the collision is equal to the sum after the collision. In a perfectly inelastic collision (e=0), the bodies involved stick together after the collision and move together, implying a loss of kinetic energy.

There are also partially elastic collisions, which are those in which there is some loss of kinetic energy. In these cases, the value of e will be between 0 and 1.

In daily activities, we often find examples of collisions that can be classified according to the coefficient of restitution. A soccer ball, for example, when kicked against a wall, tends to return with a lower speed due to the dissipation of energy in the form of heat, sound, among others. This would be a partially elastic collision. On the other hand, a car accident in which the vehicles remain "glued" together after the crash exemplifies a perfectly inelastic collision.

The study of these concepts is not only essential for understanding physical phenomena but also very relevant in different areas, such as the design of cars and safety equipment, where it is important to understand the effect of collisions and how to mitigate their damage.

To delve deeper into the subject and ensure a solid foundation for project development, we recommend the following sources for consultation:

• Book "Physics for Scientists and Engineers" - Serway, Raymond.
• Website "Brasil Escola" - Physics Section, topic "Collisions"
• Video from "Khan Academy" - "What are elastic and inelastic collisions?"

Practical Activity

Activity Title: "Collisions in Action - Understanding the Coefficient of Restitution"

Project Goal

The objective of this project is to apply the concepts studied about collisions and the coefficient of restitution in a practical context. Students should conduct experiments, collect data, perform analysis and reporting, and finally, based on their findings, develop a device or mechanism that minimizes the damaging effects of a collision.

Detailed Project Description

Students will be divided into groups of 3 to 5 people and will be encouraged to use their critical thinking skills when carrying out experiments related to collisions and coefficients of restitution. The groups must then use the results of these experiments to design and build a device or mechanism that can minimize the effects of a collision.

Materials Needed

1. Assortment of objects made of different materials (tennis balls, ping-pong balls, rubber balls, wooden blocks, etc.)
2. A hard, flat surface (e.g., a table or the floor)
3. Measuring tape or ruler
4. Camera or smartphone to record the experiments
5. Variety of materials to build the device/mechanism (cardboard, glue, tape, rubber bands, etc.)
6. Calculator
7. Computer with spreadsheet software (Excel, Google Sheets, etc.) for data analysis

Detailed Step-by-Step Instructions for Carrying Out the Activity

1. Step 1 (Theoretical Study): All members of the group should review the recommended material and study about collisions, the coefficient of restitution, and their practical applications. This study should be carried out individually, but with group discussions to clear doubts and strengthen the understanding of the topic.

2. Step 2 (Experimentation): The group should carry out experiments with the various objects provided, recording the results. For example, dropping the balls from different heights and measuring the height reached after the bounce. Conduct the experiment multiple times to obtain an average.

3. Step 3 (Analysis and Discussion): Use the collected data to calculate the coefficient of restitution for the different objects. Compare these values and discuss the differences, linking them to the properties of the materials.

4. Step 4 (Design and Construction): Based on the analysis, the group should design and construct a device or mechanism that can minimize the effects of a collision. The group is free to use the available materials in the way they consider most appropriate.

5. Step 5 (Testing and Adjustment): Test the constructed device/mechanism and, if necessary, make adjustments based on the results obtained and new ideas that arise.

6. Step 6 (Documentation): Each group should prepare a project report, including all its parts: Introduction, Development, Conclusions, and Bibliography. They should also include photos and videos of the experiments and the device/mechanism, as well as tables of the data collected.

Project Deliverables

Each group must deliver:

1. Complete project report: The report should be well-structured and detailed, including all required parts (Introduction, Development, Conclusions, Bibliography). In the Introduction, students should contextualize the theme, its relevance, and the aim of the project. In the Development, they should explain the theory, clarify the experiments, indicate the methodology applied, and present the results obtained. The Conclusions should summarize the main points, lessons learned, and conclusions about the project. The Bibliography should list the sources used in the project.

2. Demonstration of the device/mechanism built: Each group should present a demonstration of the mechanism or device built, explaining its operation and the physics principles used in its development.

3. Data analysis: Each group should present a detailed analysis of the data collected during the experiments, explaining how it was used to calculate the coefficient of restitution and how it influenced the design of the device/mechanism.

The conclusion of the project requires a classroom presentation to share the learning and experiences. All group members should participate.