Contextualization

Theoretical Introduction

Physics deals with exploring and understanding the phenomena of the world around us. Here, we will focus on the analysis of motion, more specifically, curvilinear motion. When an object moves in a curved path, it is subject to forces that act on it and cause variations in its velocity or direction. The force responsible for keeping an object in motion on a curved path is known as centripetal force.

Centripetal force is a force that always acts perpendicular to the direction of motion and points towards the center of the circle. This force is the result of interactions between moving objects and their environment, and it can be due to gravity, tension, friction, among others. The amount of centripetal force required to keep an object in curvilinear motion is proportional to the object's mass, its velocity, and inversely proportional to the radius of the curve.

The concept of curvilinear motion is accompanied by other relevant concepts such as centripetal acceleration (or radial acceleration), which is the acceleration of an object in motion along a curved path that is always directed towards the center of the curve, and angular velocity, which is a measure of how fast an object moves around a circular path.

Contextualization

Understanding and calculating forces in curvilinear motion is a vital skill in many fields of science and engineering. In biomechanics, for example, scientists use these concepts to better understand how humans and animals move. Similarly, engineers use these principles to design vehicles, aircraft, and other systems that move in curved paths.

Furthermore, the concept of forces in curvilinear motion is widely applied in fields such as astrophysics and geoscience. The planets in our solar system, for instance, travel in curved paths around the sun due to gravitational force. Therefore, understanding these forces is crucial for making accurate predictions about the motion of celestial bodies. Moreover, we know that the Earth rotates around its own axis, an example of curvilinear motion, and understanding this rotation is important for natural phenomena such as the day-night cycle and the seasons.

To start our study, here are some reliable resources to consult:

• Brazil School: What is circular motion
• Just Physics: Circular Motion
• Khan Academy (explanatory video in Portuguese): Introduction to Circular Motion

Practical Activity

Activity Title: Cardboard Roller Coaster

Project Objective:

The objective of this activity is to design and build a roller coaster for a marble using cardboard, in order to apply the concepts of centripetal force and curvilinear motion. Students will explore these concepts through the creation of a functional project, applying physics knowledge in the process.

Detailed Project Description:

Students, working in groups of 3 to 5 people, will have to create a roller coaster for a marble. This roller coaster should have at least two loops and two steeply inclined curves, allowing the marble to complete the entire course without additional assistance after an initial push.

Required Materials:

1. Cardboard
2. Marbles
3. Adhesive tape
4. Ruler
5. Material for cutting cardboard (such as a utility knife)
6. Pencil

Step by Step:

1. Planning: Students should first sketch the roller coaster project on paper, identifying where the curves and loops will be placed.

2. Base Construction: The next step is to build the base of the roller coaster. Cut the cardboard into wide strips to create the track. Use adhesive tape to join the pieces as needed.

3. Curve Construction: Create the curves and loops, remembering that the marble needs sufficient speed to overcome gravity and complete the loops. Use adhesive tape to secure the curves and loops to the base.

4. Testing: Test the marble on the roller coaster, making adjustments as necessary until the marble can complete the entire course without stopping.

5. Calculations: After the roller coaster is functional, students should measure the initial height of the marble, the radius of the loops and curves, and the time it takes for the marble to travel the track. With this data, students will be able to calculate the initial velocity of the marble, the centripetal force in the loops and curves, and the acceleration of the marble.

Project Deliverables:

• Report: Students must write a report detailing the entire process. The report should include a theoretical introduction contextualizing the applied physics concepts (forces in curvilinear motion, centripetal force, etc.), a detailed description of the project development (planning, construction, testing, and calculations) highlighting the difficulties and solutions found during the process. In the conclusion, students should reflect on what they learned during the project, both in terms of physics concepts and teamwork, time management, and problem-solving skills. Finally, all resources used for the project must be listed in the bibliography.

• Presentation: In addition to the report, students will have to give a 10 to 15-minute presentation on the project. This presentation should cover the theoretical concepts involved, the demonstration of the roller coaster in operation, discussions on the difficulties encountered and resolved, and the lessons learned.

Remember, the goal of the project is to apply the concepts of centripetal force and curvilinear motion in a practical project, developing teamwork, time management, and problem-solving skills. Have fun!