Atwood’s Machine Abstract: Ideally, Atwood’s Machine consists of two masses, connected by a massless inelastic string threaded over a frictionless pulley. In this experiment, the dependence of the acceleration on the two masses was investigated. Introduction Atwood’s Machine is represented schematically to the left. Upon inspection, Newton’s Second Law for the system can be derived: For m1: (1) For m2: (2) Solving the (1) for N, followed by substitution into (2), yields the following equation:
Rearranging terms and solving for a: (3) By using the photogate and the LoggerPro software, the acceleration of the system may be determined, as well as the dependence on the masses.
Procedure A series of masses were placed on either side of the pulley, released from rest and allowed to accelerate a distance of at least 40 cm. The velocity of the system was plotted vs. time, the acceleration determined from the slope of the least-squares line.
Initially, the total mass in the system was kept constant, beginning with 200 grams on each side.
After each trial, 20 grams from one side was transferred to the other. For the second part of the experiment, the difference between the two masses was kept at a constant 20 grams, adding an equal amount of mass to each side. Apparatus Necessary Equipment: Windows PC, LabPro Interface, Logger Pro software, Vernier Photogate, Super Pulley, mass set, string. All materials provided by the Bemidji State University Department of Physics.
Analysis As can be seen from the chart to the left, the acceleration is proportional to the difference between the two masses, as predicted from equation (3).
Also shown on the chart is the predicted acceleration, calculated from (3); note that they are both proportional, and differ only a constant. Part I| | | Part II| | | a, calc, m/s2| a, exp, m/s2| % Diff| a, calc, m/s2| a, exp, m/s2| % Diff| 0| 0| n/a| 0. 892| 0. 821| 8. 0| 0. 245| 0. 196| 20. 1| 0. 755| 0. 695| 7. 9| 0. 491| 0. 434| 11. 6| 0. 54| 0. 601| 8. 1| 0. 736| 0. 672| 8. 6| 0. 577| 0. 523| 9. 4| 0. 981| 0. 912| 7. 0| 0. 516| 0. 464| 10. 2| For the second part of the experiment, the difference between the two masses was kept constant. As can be seen from the chart to the left, the acceleration is inversely proportional to the total mass of the system, resulting in a hyperbolic curve. This trend was also predicted by equation (3); note, once again, that the calculated acceleration and the experimental value differ by only a constant.
Discussion In both sections of the experiment, the curve generated by plotting the aexp against the mass (either the difference or total) differed from the calculated acceleration by a constant value. This value represents the value of gravity at the elevation and latitude of University and any inaccuracies introduced by the ‘massless’ string and ‘frictionless’ pulley. Schematic representation of the Atwood’s Machine: “Atwood machine. ” Wikipedia, The Free Encyclopedia. 24 Sep 2009, 13:18 UTC. 24 Sep 2009 .