Atwood's Device Lab By: Julia Banning, Megan Nanovic, and Taya Wentz 11/12/15
Purpose: To derive an equation to find the acceleration of two masses according to a pulley system. After finding the accelerations from the equations and from the actual experiment, we can calculate the percent differences.
Experimental Technique:
During this experiment on Atwood's Device, I measured the acceleration of two masses differing by twenty grams each of the three times by placing a photo-gate on the pulley system.
Conclusion: The calculated and experimental accelerations of the three different trials all have about the same percent difference. The percent difference of the accelerations is not too bad, but it is not too great either, as you can see in my data table and sample calculation. The major contributions to the differences in the calculated and experimental accelerations could be a shaky release of the lighter mass. Also, some factors could have not been accounted for, such as the actual pulleys (even though they are essentially frictionless) and maybe the placement of the photo gate sensor. In order to reduce error, multiple trials between the masses were conducted. Then there was an attempt to hold the string in a straight line below the pulley so that there would be no swing. Overall, this experiment proved that the acceleration based off of Atwood's Device could be slightly different than the acceleration that was calculated from the derivation that we devised.
Theory: George Atwood was a tutor at Trinity college who later published his book titled "A Treatise on the Rectilinear Motion and Rotation of Bodies, with a Description of Original Experiments Relative to the Subject" in 1784. In the book, he described twelve different experiments that utilized his unique pulley systems. According to various scientists, Atwood "materially contributed to the progress of science, by multiplying the modes of illustration, which experimental exhibitions afford for the assistance of the instructor."
This is the derivation that was utilized in order to find the accelerations of three different masses:
This is the Free Body Diagram to demonstrate the forces that are displayed during the process of testing the Atwood's Device:
Data and Analysis: My data table and graphs for this experiment are shown below:
Based on these graphs, we could utilize the following equations to determine the acceleration of the object and the percent difference between the calculated and experimental accelerations: