Contextualization

Throughout history, humans have always had the need to understand the world around them. To do so, they divided the universe into various areas of knowledge, such as Physics. Within Physics, the study of motion and its causes, also known as Dynamics, holds a prominent status. And it is within Dynamics that we find Uniformly Varied Circular Motion (MCUV), which is the object of our analysis.

MCUV is a motion that occurs in a plane, where a body describes a circular trajectory and its speed varies uniformly. In this type of motion, we observe two types of acceleration: tangential (or linear) acceleration and centripetal (or radial) acceleration. Tangential acceleration is related to the change in speed magnitude, while centripetal acceleration is related to the change in speed direction.

Understanding MCUV is essential to explain a variety of phenomena we observe in everyday life and in nature. For example, the change in speed of a car when making a turn, or the movement of planets around the Sun are examples that involve understanding MCUV. Furthermore, understanding this theme is crucial for the development of various technologies, such as autonomous vehicle control, spacecraft projects, amusement park construction, among others.

As sources for further study, we suggest the book "Conceptual Physics" by Paul G. Hewitt and the website Brasil Escola in the topic of "Uniformly Varied Circular Motion". Additionally, the YouTube channel The Physicist Tourist has a series of explanatory videos on the subject.

Practical Activity

Title: Acceleration in Curves: An Analysis of MCUV in Real Life

Project Objective:

The objective of this project is to provide students with a practical understanding of MCUV and its real-world applications. Students will have the opportunity to experiment, collect data, and analyze the performance of different vehicles, from bicycles to cars, while making turns. This will be aligned with the study of socio-environmental, economic policies, and sustainability in relation to types of engines and energy alternatives.

Detailed Project Description:

Students, divided into groups of 3 to 5, will first conduct a literature review on MCUV and the factors that affect acceleration in curves. They will then work together to collect field data, which includes recording and analyzing different vehicles making turns to calculate tangential and centripetal accelerations.

The group will also investigate the efficiency of different types of engines and their socio-environmental and economic implications, comparing a vehicle powered by fossil fuel with an electric one, for example. This project will integrate Physics with Geography and Social Sciences through the analysis of energy policies and socio-environmental issues.

The following key theoretical concepts will be addressed in this project:

• MCUV and its equations.
• Tangential and centripetal acceleration.
• Analysis of energy efficiency of engines.
• Socio-environmental and economic impact of different types of engines.

Required Materials:

• Stopwatch
• Measuring Tape
• Camera or smartphone for recording
• Technical specifications data of selected vehicles
• Computer with spreadsheet software for data analysis

Detailed Step-by-Step for Activity Execution:

1. Literature Review: Students should conduct an investigation, based on books, reliable websites, and videos, on the concepts of MCUV, acceleration in curves, and energy efficiency of engines.

2. Experimentation Plan: Students will develop a plan on how they will record the different vehicles making turns, what type of vehicles they will use, and how they will collect the necessary data.

3. Data Collection: Implement the experimentation plan and collect the data. Ensure that time and distance measurements are done accurately and perform several attempts for each of the vehicles.

4. Data Analysis: Students will calculate the centripetal and tangential accelerations of the vehicles in the curves and, based on the technical specifications data, will analyze the energy efficiency of the different engines.

5. Final Report: Students will develop a project report that will include an introduction with the work context, details of the development and methodology used, discussion of the results, conclusion with the learnings obtained, and Bibliography used.

Project Deliverables:

The final delivery of this project includes the presentation of the written report and an oral presentation of the project and the results obtained. The report should be written considering the four main topics:

1. Introduction: The student should contextualize MCUV, its relevance and application in the real world as well as the objective of this project.

2. Development: It should explain the theory behind MCUV, the methodology used, explain the activities of data collection and analysis, and present and discuss the results obtained.

3. Conclusion: The student should summarize the main points, explaining the learnings obtained and the conclusions drawn from the project.

4. Bibliography: Indicate the sources they relied on to work on the project such as books, web pages, videos, etc.

The project should promote the development of technical skills in analyzing socio-environmental, political, and economic issues, calculating accelerations, and socio-emotional skills such as time management, communication, problem-solving, creative thinking, and proactivity.