Contextualization

Physics is a science that seeks to explain natural phenomena. Within this science, mechanical energy can be considered as the ability of a body to do work. Expressed in Joules, it is composed of two forms: kinetic energy, associated with the movement of an object, and potential energy, associated with the position of an object in a field of forces.

Simple Harmonic Motion (SHM) is one of the fundamental concepts of physics, characterized by a repetitive and regular motion, such as the swing of a pendulum or the motion of a spring. In this type of motion, the total mechanical energy (kinetic energy and potential energy) is always constant, indicating its conservation.

In the study of SHM, it is observed that energy is constantly transferred between kinetic and potential forms. The concept of energy conservation in SHM is fundamental for understanding various physical phenomena in the real world, such as the motion of planets around the sun (which is approximately harmonic) and the motion of electrons in atoms.

The theme of mechanical energy SHM is of great importance, as it is present in many practical applications of everyday life, such as in civil and mechanical engineering, astronomy, electronics, among others. For example, the study of harmonic motion is essential to understand how oscillation electrical circuits in vehicles, cell phones, and computers work. In addition, bridges, when subjected to constant oscillation (such as that caused by car traffic), can resonate and break if not well designed.

Reliable resources for deepening and study:

1. Book "Physics for Scientists and Engineers" by Paul A. Tipler and Gene Mosca.
2. Explanatory video from Manual do Mundo Channel - The incredible perpetual motion machine
3. Explanatory video from Ciência Todo Dia Channel - What is Energy Conservation?
4. University of São Paulo website - Simple Harmonic Motion (SHM) and Energy Conservation
5. Scientific dissemination article - Mechanical Energy
6. Scientific dissemination article - What is Simple Harmonic Motion (SHM)?

Practical Activity

Title: Creating and Analyzing a Simple Pendulum

Project Objective:

The objective of this project is to understand the concept of mechanical energy (kinetic and potential) in Simple Harmonic Motion (SHM) through the creation and analysis of a simple pendulum.

Detailed Project Description:

Students, in groups of 3 to 5, should create a simple pendulum using low-cost and easily accessible materials. After creating the pendulum, the group should carry out a series of experiments to analyze the pendulum's swing under different conditions and observe the conservation of mechanical energy.

Required Materials:

1. Resistant wire or string of about 1 meter;
2. A heavy object to function as a weight for the pendulum (e.g., a marble, a stone, a keychain);
3. Ruler or measuring tape;
4. Stopwatch (can be on the cell phone);
5. Camera to record the experiment (optional).

Detailed Step-by-Step for Activity Execution:

1. Create the pendulum by tying the heavy object (pendant) to the end of the wire or rope. Attach the other end to an elevated support, such as a table, chair, or wall hook.
2. Adjust the length of the wire so that the pendant is 1 meter from the ground.
3. With the pendant at rest, mark the initial position.
4. Move the pendant away from its equilibrium position (initial position) at a small angle and release it, allowing it to swing back and forth.
5. Use the stopwatch to time how long it takes for the pendulum to complete 10 full oscillations. Calculate the period of one oscillation by dividing the total time by 10.
6. Record all measurements and observations.

Project Deliverables:

After completing the practical activity, students should produce a report containing the following sections:

1. Introduction: In this section, they should contextualize the theme of the simple pendulum in Simple Harmonic Motion (SHM), describing the importance and application of this concept in the real world. They should also present the project's objective.

2. Development: Students must explain the theory behind the simple pendulum in SHM, explaining the activity in detail. In this section, they should detail the methodology of the experiment, including the materials used, the step-by-step construction of the pendulum, the procedures for measuring the oscillation time, and how this measurement relates to kinetic and potential energy. They should also present and discuss the results obtained, including tables or graphs, if appropriate.

3. Conclusion: In this part, students should recap the main points of the project, specify the learnings acquired, and draw conclusions about energy conservation in SHM.

4. Bibliography: It is essential that students indicate the sources from which they obtained information for the project, including books, web pages, videos, etc.