Development of 8+2 Experiments using apparatus with Cycloidal curves

Cycloidal curves, known for their properties as brachistochrones and tautochrones, offer valuable insights into fundamental mechanics concepts. This study presents the development of apparatuses facilitating ten distinct mechanics experiments utilizing cycloidal curves, aiming to enhance students' intuitive understanding of mechanics. The apparatuses are designed to be compact for easy use on a desk, allowing exploration of concepts such as momentum conservation, impulse, collisions, and safety mechanisms. They can be disassembled into two parts for convenient storage and have been adapted for simultaneous drop experiments. Additional experiments include comparing inclined planes, circular arcs, and cycloidal curves to verify the brachistochrone property, as well as exploring the isochronous nature of cycloidal pendulums, Galileo's inclined plane experiments, and inertia thought experiments. To improve observation and measurement accuracy, auxiliary devices have been developed to reduce errors when manually releasing marbles, and smartphone cameras can be utilized to clearly capture the rapid motion of the balls. This study aims to provide educational materials that apply cycloidal curves in practical lessons, facilitating effective mechanics experiments in high school integrated science, Physics I and II, and middle school science education. It seeks to connect scientific principles with real-life applications, encouraging thoughtful consideration and extending the meaning and value of these concepts. Through this research, it is anticipated that students will engage in hands-on experiments, creatively explore mechanics concepts, deepen their understanding, and connect scientific content with everyday life.