Contextualization

The study of motion is one of the fundamental pillars of physics. Among the various types of motion that we can observe, Simple Harmonic Motion (SHM) and Uniform Circular Motion (UCM) are two of the most important.

Simple Harmonic Motion is characterized by an oscillatory movement, that is, one that repeats periodically. Meanwhile, Uniform Circular Motion is characterized by a movement that occurs in a circular path at a constant speed. These two concepts may seem distinct at first glance, but they are closely related!

Several phenomena in our daily lives can be explained by these two forms of motion. The movement of tides, the swinging of a pendulum, the movement of planets around the sun, the movement of gears in a clock, and even the beating of our hearts are classic examples of applications of these concepts.

Now, imagine if we could understand SHM and UCM and their relationships in such a way that we could predict and calculate such phenomena? It is a challenging task, but very possible! With an understanding of these fundamental concepts, it is possible to develop a deeper insight into physics and its applications in various fields, from engineering and technology to medicine and biology.

Atividade Prática

Activity Title: Connecting Oscillations and Rotations: An Analysis of SHM and MCU

Project Objective

This project aims to understand and demonstrate the relationship between Simple Harmonic Motion (SHM) and Uniform Circular Motion (UCM) through a practical experience, developing technical and socio-emotional skills.

Detailed Project Description

The groups, with 3 to 5 students each, will build a simple pendulum and a rotating disk as a representation of SHM and UCM respectively. Through observations and measurements made on these equipment, the students will explore and discover the relationship between these two types of motion.

Required Materials

• A strong string or cord (approximately 1 meter)
• A marble or other small and heavy object
• A sturdy piece of cardboard or plywood
• Colorful pens or markers
• A clock or timer
• A tape measure or large ruler
• A compass or a round object to trace a circle
• A support to hang the pendulum (can be a tripod, a lamp stand, etc.)

Detailed Step-by-Step for Activity Execution

Step 1: Construction of the simple pendulum (SHM Representation)

1. Tie the marble or other heavy object to one end of the string.
2. Hang the other end of the string on the chosen support, making sure it can swing freely.
3. Adjust the length of the pendulum (the distance from the ball to the fixing point) to about one meter.
4. Mark the equilibrium point, that is, the point where the pendulum stays when not in motion.

Step 2: Construction of the rotating disk (UCM Representation)

1. Use the compass to draw a circle on the cardboard or plywood. The circle should have the same radius as the length of the pendulum built before.
2. Carefully cut out the circle.
3. Mark the center of the circle.

Step 3: Observation and Measurement

1. Define a starting point for the pendulum's movement (it should be the same for each measurement).
2. One group member should be responsible for moving the pendulum, while another member will be responsible for using the timer.
3. Record the time it takes for the pendulum to complete one full oscillation (back and forth).
4. Repeat the process several times to obtain an average of the times.
5. Repeat steps 1 to 4 for the movement of the rotating disk.

Project Delivery

Upon completing the practical part of the project, the groups must write a written document (report) with the following parts:

1. Introduction: Provide context for SHM and UCM, their applications, and relevance. Explain the project's objective and the relevance of the experiments conducted.
2. Development: Describe in detail the processes of constructing the experiments and the theory of SHM and UCM. Explain the methodology used (how the measurements were taken, how the times were calculated, etc.). Present the results of the observations and experiments and discuss how they demonstrate the relationship between SHM and UCM.
3. Conclusion: Reaffirm the main points of the project, share what the group learned through this experience. Discuss any difficulties the group faced and how they overcame them.
4. Bibliography: List all sources of information consulted to carry out the project.

Remember, the main goal is to discover the relationship between SHM and UCM in a playful and practical way. Each group member will be evaluated not only for understanding the concept but also for the ability to work collaboratively, time management for project delivery, proactivity, and creativity during the project execution.