Project: Marble in a Loop: An Exploration of Centripetal Acceleration

Context

Uniform circular motion, or UCM, is one of the most counterintuitive concepts in physics because it challenges our everyday experience of how objects move. In UCM, an object travels in a circle at a constant speed, but because the direction of the motion is constantly changing, the velocity is also constantly changing. Despite being a staple of theoretical physics, UCM is encountered in many everyday situations, such as a spinning jump rope, a rotating record, or a car going around a curve in the road.

A key feature of UCM, and one of its most complex concepts, is centripetal acceleration, the component of an object's total acceleration that is directed toward the center of the circular path. Without centripetal acceleration, an object moving in a circle would instead travel in a straight line.

Recognizing UCM and centripetal acceleration in our everyday lives and understanding the concepts behind them is a crucial step to understanding so many other physical phenomena. Similarly, developing the ability to calculate centripetal acceleration and apply the concept is a valuable skill that can be used across disciplines from engineering to astrophysics.

Hands-on Activity

Title: Marble in a Loop: An Exploration of Centripetal Acceleration

Project Goal:

The goal of this activity is to develop an understanding of the concept of centripetal acceleration and the principles of uniform circular motion (UCM) through the construction of a miniature roller coaster with a loop.

Detailed Project Description:

Teams will be responsible for constructing a marble roller coaster and measuring the velocity of the marble at various points along the track. The goal is to visualize how velocity changes throughout the track and to see centripetal acceleration in action as the marble goes through the loop.

Materials:

• Marbles
• Flexible plastic or PVC piping (for the track)
• Measuring tape
• Stopwatches
• Paper and pencils for recording data

Detailed Step-by-Step Instructions for Completing the Activity:

1. Teams will first design and build a marble roller coaster track that includes a loop.
2. Once the track is complete, teams will release a marble from the top of the track and use a stopwatch to measure the time it takes to travel through set distances along the track.
3. Measurements should be taken at multiple locations along the track: before, during, and after the loop.
4. Measurements should be repeated multiple times to ensure accuracy.
5. Using the data collected, teams will calculate the velocity of the marble at each measured location.
6. Centripetal acceleration will be calculated using the assumption that the marble is undergoing uniform circular motion when traveling through the loop.
7. Teams will discuss their results and connect them back to the theory they have studied.

Teams should work together throughout the building, planning, measuring, and data analysis processes. Groups should manage their time carefully to ensure that they complete all aspects of the project by the deadline.

Project Deliverables and Report:

Upon completion of the hands-on activity, teams will submit a formal lab report that includes the following sections:

1. Introduction: Students should define centripetal acceleration and uniform circular motion and explain how they are related. They should also discuss the real-world relevance of these concepts and state the goals of the project.
2. Methods and Materials: In this section, students should provide a detailed account of how they conducted the experiment, including how they built the track, measured the time, and calculated the velocity and centripetal acceleration. They should also include their data in a table.
3. Results: Students should analyze the results of their experiment and discuss how they relate to the theory. They should also discuss any challenges they encountered and how they overcame them.
4. Conclusion: In their conclusion, students should summarize the main findings of their experiment and evaluate their understanding of centripetal acceleration and uniform circular motion.
5. References: Students should list all sources that they consulted in completing the project.

The final report should be submitted within two weeks of the project due date and will be used to assess student learning.