Amusement Park Physics Lab
Author: Tegan Durishin
Lab Partners: Anthony Farano, Thatcher David
Date Completed: 2 June 2014
Author: Tegan Durishin
Lab Partners: Anthony Farano, Thatcher David
Date Completed: 2 June 2014
Purpose
The purpose of this lab is to calculate centripetal acceleration on a swing using a homemade vertical accelerometer.
Theory
Equation for Centripetal Acceleration Equation for Velocity Law of Conservation of Energy
Experimental Technique
For this lab, our experimental technique involved using a homemade vertical accelerometer. We made our accelerometer out of a plastic tube, a spring, a weight, a paper clip, clear tape, red tape, and two end caps. Using a red marker, we marked a line where the bottom of the weight was at rest with the red tape in order to see where the weight is while experiencing 1g. Then by adding 3 more weights onto the string, we found the mark for 4g and then divided the rest of the tube into equal spaces to indicate 2g, and 3g. We took our vertical accelerometer to the Grove and taped it to one of the chain sides of a swing as close to the bottom as possible and measured the radius of the swing as well as the highest point and the lowest point of the swing. We then watched the accelerometer as Anthony swung back and forth. We noticed that the weight experienced 1g at the peaks of the swing and 2.6g at the lowest point. In order for the measurement to be correct, one must subtract a (g) since the weight sits at 1g on its own. Using that data, we found the velocity with the law of conservation of energy. Finally, we used the velocity to calculate the centripetal acceleration.
Data
The weight reached a maximum of 2.6g.
Highest point: 240cm = 2.40m
Lowest point: 49cm = .49m
Radius: 258cm = 2.58m
Velocity: 6.12m/s
Centripetal Acceleration: 14.51m/s/s
Highest point: 240cm = 2.40m
Lowest point: 49cm = .49m
Radius: 258cm = 2.58m
Velocity: 6.12m/s
Centripetal Acceleration: 14.51m/s/s
Analysis
Conclusion
In this lab we found the centripetal acceleration of a swing using the Law of Conservation of Energy, and the centripetal acceleration formula. We made measurements such as the highest and lowest points of the swing, the radius of the swing, and the gravitational g's the weight experienced. Using the height and the Law of Conservation of Energy, the velocity (V) was found. Next, we identified the centripetal acceleration through using the velocity and radius. When swinging, the vertical accelerometer reached 2.6 g at its lowest point. The calculated force came out to be 1.5g and our measured force was 1.6g. This is a 7.75% difference. One cause for this amount of error would be parallax error, since we did not watch the weight from the same eye level. Another source of error would be misconstruction since we used our own homemade vertical accelerometer which could have been made wrong. The last possible source of error would be that the results were skewed since we placed the accelerometer on the side chain of the swing and not nearer to the center of mass, or in the middle of his body.