Background

The study of collisions and the coefficient of restitution is fundamental to understanding various natural phenomena and engineering multiple technologies used in our daily lives. From the collision of two soccer balls in a game to the design of car bumpers, all these situations involve understanding what happens when two bodies collide.

To understand collisions, we first need to understand what conservation of momentum is. In a collision, the total momentum before the collision is equal to the total momentum after the collision. This is the principle of conservation of momentum. Momentum is the product of an object's mass and its velocity. Its unit in the International System is the kilogram meter per second (kg.m/s).

From this knowledge, we will introduce the coefficient of restitution (e). This coefficient is a measure that tells us what fraction of the original velocity is preserved after a collision. That is, it gives us an idea of how "elastic" a collision is. When the coefficient of restitution is 1, we have a perfectly elastic collision, where all the kinetic energy is conserved. When this coefficient is 0, we have a perfectly inelastic collision, where kinetic energy is not conserved.

Relevance

The importance of understanding collisions is highly relevant in our daily lives. Its application is seen in various areas. In the automotive industry, this concept is used to design vehicle bumpers to reduce impact in the event of collisions. In civil engineering, it is applied to calculate the impact of earthquakes on structures and buildings. In sports, it is present in the analysis of the impact of balls and the collision between players.

In addition to its practical applications, understanding collisions and the coefficient of restitution is crucial for understanding more advanced concepts in physics, such as thermodynamics and quantum physics. Therefore, mastering this subject is an important step for those who wish to enter the universe of physics and science in a deeper way.

Hands-on Activity: "Colliding Balls: A Study on Coefficient of Restitution"

Project Objective

The objective of this project is for you, in groups of 3 to 5 students, to study in practice the concepts of collisions and coefficient of restitution, conducting a series of experiments and interpreting the results.

Detailed Description of the Project

You will perform experiments with different types of balls, of different materials and sizes, to determine their coefficients of restitution. You will then analyze the data obtained and write a detailed report explaining the theory learned, the experiments performed, and the conclusions reached.

Required Materials

• Balls of different materials and sizes (tennis balls, ping pong balls, soccer balls, etc.)
• Tape measure or measuring tape
• Video camera (can be a smartphone camera)
• Stopwatch
• Spreadsheet for data entry

Step by Step

1. Gather in groups of three to five students.
2. Gather the materials needed for the project.
3. Choose a ball and measure its height. Write down this information.
4. Drop the ball from a fixed height and record the motion with the video camera.
5. Observe the recording and measure the time it takes for the ball to reach the ground (fall time) and the height reached after the first bounce (bounce height).
6. Repeat the experiment three times for each ball and take the average of the measurements to obtain more accurate data.
7. Using the data collected, calculate the coefficient of restitution for each ball using the formula: e = sqrt(h2 / h1), where h1 is the drop height and h2 is the bounce height.
8. Discuss the results. Why did some balls have higher coefficients of restitution than others? How does this relate to the material and size of each ball?
9. Record your findings and prepare to write the written document.

Written Document

To complete the project, you will need to write a report containing the following topics:

• Introduction: Contextualize the topic by explaining what collisions, momentum, and coefficient of restitution are. Also, include the purpose of this project.
• Development: Describe the theory behind collisions and coefficient of restitution. Explain the experiment you performed, the methods you used, and present the results obtained. Remember to include tables or graphs to illustrate your data and make the report more understandable.
• Conclusion: Conclude the paper by restating your main points. What were the coefficients of restitution of each ball? What does this say about the material and size of each ball? What did you learn from this project?
• Bibliography: Cite the sources you used for the project. Don't forget to include the books, websites, and videos you consulted.

Remember that the report should reflect the work of all group members. Everyone should contribute to the writing and make sure their understanding of the project is well represented in the document.

The project will last one week. We wish you all a delicious learning journey!