Contextualization

Theoretical Introduction

Centripetal acceleration is a fundamental concept in physics and is the force that keeps an object moving in a circle. It is always directed towards the center of the circular path and its magnitude is constantly changing due to the object's movement. This happens because the direction of the object's velocity is always changing.

However, the speed's magnitude, or the rate at which the object moves, can remain constant. An example of this is an object in uniform circular motion, like a car racing on a circular track. Even though the car is moving at a constant speed, the direction is always changing, indicating that there is a centripetal acceleration acting on the car.

Centripetal acceleration can be calculated by the formula a = v^2 / r, where a is the centripetal acceleration, v is the object's velocity, and r is the radius of the circular path. This is something you will learn to calculate during this project.

Contextualization

Centripetal acceleration can be seen in many situations in everyday life. For example, when you are riding a bike and make a sharp turn, you lean towards the center of the curve to prevent the bike from tipping over. This is a manifestation of centripetal acceleration.

Furthermore, concepts related to centripetal acceleration are widely used in many fields of science and engineering, such as in astronautics for calculating the motion of planets and satellites, in engineering for calculating the forces acting on vehicles and structures, and in medicine to understand blood circulation in the human body.

I suggest you watch the video Centripetal Acceleration on YouTube, which clearly explains the concept and provides examples of where we see centripetal acceleration in our daily lives.

Additionally, I recommend reading the chapter on Circular Motion and Centripetal Acceleration from the book Physics for Scientists and Engineers, which offers an in-depth approach to the topic.

Practical Activity

Activity Title: Spheres in Rotation

Activity Objective:

The main objective of the activity is to analyze and calculate the centripetal acceleration in a simple system of rotating spheres.

Project Description:

In this activity, groups will build a device with rotating spheres and calculate the centripetal acceleration acting on one of the spheres when the device is rotated at a known angular velocity. The angular velocity will be changed, and the corresponding centripetal acceleration will be calculated and the results will be analyzed.

The device will be made with two spheres of equal sizes tied to a string, which will be, in turn, attached to a support. The support will be rotated at different speeds, and the radial distance of the spheres to the support will be measured to calculate the centripetal acceleration.

Required Materials:

• Two spheres of equal sizes (can be marbles or ping pong balls)
• String
• Ruler or tape measure
• Calculator
• Support to attach the string (can be a pencil sharpener or a clothespin)
• Stopwatch

Detailed Step-by-Step:

1. Tie the two spheres on opposite sides of a string with approximately 1m in length.

2. Attach the string to the support so that the spheres can rotate freely around the support.

3. Rotate the support at a constant speed and use the stopwatch to measure the time it takes for the spheres to complete one full rotation (this will be the rotation period T).

4. Use the measurement of the period T to calculate the angular velocity (w) using the formula w = 2π/T.

5. Measure the radial distance (r) from the spheres to the support.

6. Use the formula for centripetal acceleration (a = v^2 / r) to calculate the centripetal acceleration of the spheres (note that the velocity v can be found by the relation v = w*r).

7. Repeat steps 3 to 6 for different rotation speeds and analyze how the centripetal acceleration varies with angular velocity.

Project Delivery and Connection with Suggested Activities:

After completing the practical activity, students should prepare a written report with the following topics:

1. Introduction: The group should contextualize the theme of centripetal acceleration, its relevance, real-world applications, and the objective of this practical activity.

2. Development: The group should explain the theory behind centripetal acceleration and describe in detail the activity procedure, indicating the methodology used. They should present and discuss the results obtained, how the values of centripetal acceleration were obtained, and how these values varied with angular velocity.

3. Conclusions: The group should summarize the main points of the work, state the learnings obtained, and draw conclusions about the practical activity. Additional discussions, such as the effects of possible sources of error, should be included in this section.

4. Bibliography: The group should indicate the sources they relied on to carry out the activity, including books, web pages, videos, etc.

The written report should be presented in PDF format and complements the practical activity, as it requires students to assimilate the theoretical content, apply it in practice, and communicate the results obtained clearly and efficiently.