Lesson Plan | Active Learning | Momentum and Impulse: Coefficient of Restitution

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 7 minutes)

The Objectives stage is essential to establish the focus of the lesson and ensure that all participants, both students and teacher, are aligned regarding what will be learned and practiced. By clearly detailing the objectives, students can better direct their efforts for prior study and in-class participation, maximizing the effectiveness of learning. This section is designed to start the class with a solid foundation, allowing a smooth transition to practical activities and subsequent discussions.

Main Objectives:

1. Understand the concept of restitution coefficient and its importance in describing collisions.

2. Identify and differentiate types of collisions (elastic and inelastic) based on the behavior of the restitution coefficient.

3. Apply the restitution coefficient in calculations to determine the speeds of objects before and after collisions.

Side Objectives:

1. Develop logical and mathematical reasoning skills by applying physical concepts to practical problems.

Introduction

Duration: (15 - 20 minutes)

The Introduction serves to engage students with the content they studied previously, connecting it with real-life and everyday situations. The problem situations stimulate students to apply theoretical knowledge in practical contexts, preparing the ground for solving more complex problems in class. The contextualization, in turn, helps to show the relevance of the restitution coefficient in real situations, increasing students' interest and motivation to explore the topic further.

Problem-Based Situations

1. Imagine you are in a physics lab and your teacher asks you to calculate the speed of a cart before and after colliding with a second cart. Both carts have different masses. How would the restitution coefficient help solve this problem?

2. A billiard ball collides with another of equal mass. If the first ball was initially in motion and after the collision moves at 1 m/s, and the second ball moves at 2 m/s after the collision, what is the restitution coefficient of this collision?

Contextualization

The restitution coefficient is not just an abstract concept; it plays a crucial role in many everyday events and in various fields such as automotive collision engineering, sports physics, and even in natural disaster simulations. For example, understanding how the restitution coefficient affects the propagation of waves after earthquakes can help in preventing future damage. Furthermore, curiosities such as why some sports balls bounce more than others, even when initially thrown at the same speed, can be explained by this concept.

Development

Duration: (65 - 75 minutes)

The Development stage is crucial to consolidate students' prior knowledge with practical activities that involve applying the concepts of impulse, momentum, and especially the restitution coefficient. These activities are designed to be engaging and contextualized, allowing students to explore the theme creatively and interactively. Through solving problems in teams and applying concepts in everyday situations playfully, students can deepen their understanding and practical skills in physics.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Cultural Clash: A Musical Inelastic Collision

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of the restitution coefficient in a practical and playful situation, reinforcing the understanding of the physical phenomenon through a creative and musical approach.

- Description: In this playful activity, students are divided into groups and each group represents a different continent. Each continent has its own round of musical presentations, where 'instruments' are balls of different sizes and textures. The challenge is to perform inelastic collisions between the balls to produce different sounds. Each continent must use their knowledge of the restitution coefficient to choose which 'instruments' (balls) to use and how to collide them to create the desired sounds.

- Instructions:

• Divide the class into groups of up to 5 students, each representing a different continent.

• Provide each group with a set of balls of different sizes and materials.

• Explain that they must plan and execute inelastic collisions between the balls to create pleasant sounds.

• The groups must use their knowledge of the restitution coefficient to decide how to collide the balls to produce the desired sounds.

• Each group will have time to prepare and rehearse their 'songs'.

• After rehearsals, each group will present to the class, explaining how the restitution coefficient influenced their choices and the final result.

Activity 2 - The Mystery of the Lost Collision

> Duration: (60 - 70 minutes)

- Objective: Develop investigative skills and apply physical concepts to solve a practical and intriguing problem.

- Description: Students, divided into groups, take on the role of detectives at a crime scene where two cars collided. Each toy car has a different restitution coefficient. Students need to use the available physical data and their knowledge of the restitution coefficient to reconstruct how the cars collided and what their speeds were before and after the collision.

- Instructions:

• Divide the class into groups of up to 5 students, each being a 'detective team'.

• Present the 'crime scene' with two toy cars, marked with their restitution coefficients.

• Provide students with rulers, stopwatches, and any other necessary materials.

• The groups must measure the distances traveled by the cars after the collision and the time it took for each car to come to a complete stop.

• Based on these measurements, they must calculate the initial and final speeds of each car.

• Each group will present their conclusions and the thought process to the class.

Activity 3 - Physics on the Dance Floor: Elastic Collisions to the Rhythm of Science

> Duration: (60 - 70 minutes)

- Objective: Explore the concept of elastic collisions in a creative and dynamic way, applying physical principles in an entertainment context.

- Description: In this activity, students, organized into groups, design a dance floor where the movements of the dancers are determined by elastic collisions. Each group must choose different songs and map the movements of the dancers based on the principles of conservation of energy and momentum, using the restitution coefficient to adjust the intensity of the collisions.

- Instructions:

• Divide the students into groups of up to 5 participants, each group responsible for designing a part of the dance floor.

• Each group chooses a song and must determine the movements of the dancers based on elastic collisions.

• Students must use their physics knowledge to calculate the restitution coefficient necessary for the dancers to move according to the conserved kinetic energy.

• The groups set up their sections of the dance floor in the lab or classroom, implementing their choices of elastic collisions.

• After setting up, the groups present their dance floor to the class, explaining how they used the concept of restitution coefficient in creating the movements.

Feedback

Duration: (15 - 20 minutes)

The Feedback stage is essential to consolidate students' learning, allowing them to articulate what they learned and reflect on the application of concepts in real and practical contexts. This discussion also helps the teacher to assess students' understanding and identify any areas that may need additional review. Furthermore, by sharing their experiences and listening to their peers, students develop communication skills and learn from one another.

Group Discussion

After the completion of practical activities, gather all students for a group discussion. Start the discussion with a brief introduction, highlighting the importance of sharing discoveries and challenges faced during the activities. Encourage each group to present a summary of what was done and discuss the main conclusions. Use targeted questions to stimulate deeper reflection on how the restitution coefficient influenced their different experiences and what they learned from each practical situation.

Key Questions

1. How did the restitution coefficient affect the decisions you made during the activities?

2. Was there any surprise or challenge in applying the concept of restitution coefficient in practical collisions?

3. How was the knowledge of impulse and momentum applied during the activities?

Conclusion

Duration: (5 - 10 minutes)

The Conclusion stage is essential to consolidate learning, ensuring that students have a clear and integrated understanding of the subject matter. By summarizing and connecting the discussed content, this section helps reinforce students' memory and establish a clear link between theory and practice. Additionally, by emphasizing the relevance of the learned concepts, students are motivated to value the discipline and apply the knowledge in their daily lives and future careers.

Summary

To conclude, we recapped the main points addressed in today's class: the restitution coefficient, its application in different types of collisions, and how to calculate speeds involving these collisions. We recalled practical activities such as 'Cultural Clash', 'The Mystery of the Lost Collision', and 'Physics on the Dance Floor', which provided a playful and in-depth approach to the concept.

Theory Connection

Through the practical activities, we were able to connect the theory studied with practice, demonstrating how the restitution coefficient is applied in real and everyday situations. This approach not only consolidated theoretical knowledge but also showed students the importance and versatility of the concept in various practical applications, from engineering to entertainment.

Closing

Finally, it is crucial to highlight the relevance of studying impulse and momentum with the restitution coefficient. These concepts are fundamental not only for understanding physical phenomena but also for application in technology, engineering, and even in everyday activities such as sports and vehicle safety. Understanding these concepts helps students perceive physics in action and its importance in solving practical problems and developing new technologies.