Project: Billiards Ball Collisions

Context

Physics in its study of matter and energy encompasses a wide range of phenomena, from subatomic particles to the expansion of the universe; and in the middle of this spectrum, we have collisions. Collisions are common events in our daily lives, from a simple bump of two people in a corridor to car crashes, which are important objects of study in vehicular safety.

In this project, we will delve into two-dimensional collisions. The concepts of linear momentum (or impulse), energy conservation, and coefficient of restitution are essential to properly understand and analyze this type of collision, and they are fundamental in Physics for the range of situations where they can be applied.

The linear momentum, in the context of collisions, allows us to analyze how the quantity of movement of a body is transferred to another during a collision. Energy conservation, on the other hand, is a fundamental principle which states that the total energy of an isolated system remains constant, no matter what happens. Finally, the coefficient of restitution gives us a measure of the “loss” of kinetic energy during the collision, that is, of the transformation of kinetic energy into other types of energy.

Collisions, especially in two dimensions, have several practical applications. Vehicular safety engineers study the physics of collisions to design safer cars. In medicine, the principles of collisions can help better understand the biomechanics of trauma. In sports, the study of collisions can improve technique in games like billiards, hockey, among others.

We recommend that students use the following resources to deepen their knowledge on the topic and as a basis for the project:

1. Classical Physics: Linear Momentum and Collisions - Prof. Marcelo Boaro
2. Modern Physics: Two-Dimensional Collisions - Prof. Paulo Célio
3. Book: Physics for Scientists and Engineers - Volume 1, by Paul A. Tipler and Gene Mosca.

Hands-on Activity

Activity Title: Billiards Ball Collisions

Project Goal

Develop a deeper understanding of the topics of linear momentum, energy conservation, and coefficient of restitution, through the study of two-dimensional collisions, using billiards balls as a reference.

Detailed Description of the Project

In this project, student groups will be challenged to simulate and analyze various collisions of billiard balls in two dimensions. By doing this, they will be able to see how linear momentum, energy conservation, and the coefficient of restitution influence the behavior of the balls after the collision.

Required Materials

• A billiards table with at least three balls.
• A camera to record the collisions.
• A computer with access to video analysis software (such as Tracker, which is free).

Step-by-Step Instructions for the Activity

1. Research: Begin by researching linear momentum, energy conservation, and the coefficient of restitution. Understand how these concepts apply to two-dimensional collisions.

2. Preparing the Experiment: Set up a billiards table with at least three balls. Position two balls at one point on the table and the third ball at a position such that when it is launched, it causes a collision.

3. Recording the Collision: Record the collision between the balls with a camera.

4. Analyzing the Collision: Use video analysis software to track the motion of the balls before and after the collision. This information can be used to calculate the linear momentum, change in energy, and coefficient of restitution during the collision.

5. Interpreting the Data: Analyze the data obtained and interpret the results based on what you have learned about linear momentum, energy conservation, and the coefficient of restitution. Do this for several collisions, changing the initial velocity and angle of impact, for example.

6. Final Report: Finally, each group should prepare a detailed report that discusses the experiments performed, the data collected, the analysis, and the conclusions. The report should address the following topics:

   • Introduction: Contextualization of the theme, its relevance, application in the real world, and the goal of the project.
   • Development: Explain the theory behind linear momentum, energy conservation, and coefficient of restitution. Describe the experiment, the methodology used, and discuss the data obtained.
   • Conclusion: Conclusions drawn about the project, summarizing its main points and the lessons learned.
   • Bibliography: The basis for the work done on the project such as books, web pages, videos, etc.

This project should be carried out by groups of 3 to 5 students, and each student should spend between 5 to 10 hours working on the project. The project is due in one month.