Introduction
This experiment aimed to investigate the relationship between tension, mass, radius of motion, and angular speed. The experiment involved varying one independent variable while keeping the others constant and tabulating the corresponding tension values (Abrutyn & McCaffree, 2021). The link between tension, mass, radius of motion, and angular speed was determined using the equations Tension = m(v²/r) and ω = 2π/T. The results were analyzed and graphed, and the conclusion was drawn that tension is directly proportional to mass and tangential speed squared and inversely proportional to the radius of motion.
Data
The independent variables were mass, radius of motion, and angular speed, while the dependent variable was the tension in the cord (Abrutyn & McCaffree, 2021). Data were collected by changing one variable while holding the other variables steady and recording the results in a table. Firstly, the angular speed was changed with different constants, then the same data was checked against the radius of motion, and then with the changed mass.
Results
The results showed that tension increased as mass and tangential speed squared increased, and tension decreased as the radius of motion increased. The data was tabulated as follows.
Table 1 – Experiment Data
The relationship between tension, angular speed, mass, and radius of motion was calculated using the equations: Tension = m(v²/r) and ω = 2π/T, where m is mass, v is tangential speed, r is the radius of motion, and ω is angular speed, using the equation v = rω. To test this data, the Tangential speed variable was added. The calculated values were tabulated as follows.
Table 2 – Calculation Results
The tension in the cord was found to be directly proportional to the square of the angular speed and inversely proportional to the radius of motion (Abrutyn & McCaffree, 2021). Mass did not significantly affect tension, as expected. Graphs of tension vs. mass, radius, and angular speed were expected to be straight lines through the origin, inverse, and direct relationships, respectively, with y-intercepts of zero.
Conclusion
The data collected and analyzed in this experiment demonstrated the relationships between tension, mass, radius of motion, and angular speed as predicted by the equations Tension = m(v²/r) and ω = 2π/T. Expectations from the statistics and the experimental table were confirmed. These relationships are important in understanding the behavior of objects in circular motion. They can be used in various applications, such as designing roller coasters or analyzing the motion of planets in our solar system.
Reference
Abrutyn, S., & McCaffree, K. (2021). Introduction: The centripetal force of theory, theorists, theorizing. In Theoretical Sociology (pp. 1-11). Routledge.