Atwood's Device Lab
Title: Atwood's Device Lab
Partner: Abbey Applegate
Date: 11/11/14
Partner: Abbey Applegate
Date: 11/11/14
Purpose
The purpose of this lab is to use an Atwood's device to demonstrate Newton's Second Law and verify the concept of constant acceleration amongst two unequal masses connected by a pulley.
Theory
George Atwood was an English physicist who lived from 1746-1807. He is most renowned for his work with Atwood's machine, which consisted of two different masses attached using a stretch-less string to a frictionless pulley. The device was used to show a state of constant acceleration of the masses despite being different from each other. The device is still used to show Newton's Second and Third laws of motion today, and any machine built with a similar purpose and structure to the original (shown at left) is dubbed an "Atwood's device."
In order to calculate the predicted acceleration of the masses, we needed to derive an equation. First, I constructed the diagram at right to represent the pulley. We know that the mass of object b is heavier than the mass of object a. We also have to define the positive direction using the bold arrows on the diagram because the objects will be moving in opposite directions. To begin, we sum the forces on object a and solve for T as shown.
Similarly, we sum the forces on object b, paying special attention to the change in positive direction, and solve for tension.
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By setting the two tension equations equal to each other, we can solve for the acceleration in terms of both masses.
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Experimental Technique
The smart pulley apparatus and photo gates were set up as shown in the bottom left. Two hangers were attached to either end of a string and laid across the pulleys as shown in the middle image. Weight was stacked on both hangers and the photo gates were used to measure acceleration.
The constant mass method was used to differ the masses between the hangers. A total mass was maintained throughout, but mass was transferred from one side to the other so that the difference between the masses varied for each trial. One side was kept heavier than the other at all times. The masses started out very far apart and slowly got closer together.
The masses were then held at the same height dropped to measure the acceleration of the heavier mass downwards and the lighter mass upwards.
The constant mass method was used to differ the masses between the hangers. A total mass was maintained throughout, but mass was transferred from one side to the other so that the difference between the masses varied for each trial. One side was kept heavier than the other at all times. The masses started out very far apart and slowly got closer together.
The masses were then held at the same height dropped to measure the acceleration of the heavier mass downwards and the lighter mass upwards.
Data
The data collected is shown in the table at right. The masses of A and B represent the two separate hangers. The measured acceleration was taken from the slope of the velocity graphs for each trial as shown below at left.
Analysis
With the measured masses, we calculated the acceleration using the equation we derived earlier. All of these values are found in the table above.
We also found the percent difference between the measured acceleration and the calculated acceleration. All of these values are found in the data table above.
Conclusion
We set out to demonstrate that two unequal masses connected by a pulley would undergo constant acceleration. Because of the linear portion of the velocity versus time graph, we can conclude that constant acceleration is present.
The actual and predicted accelerations varied; some of the predicted accelerations were higher while others were lower than the experimental values, though most were relatively accurate. As the experiment progressed, we attempted to reduce error by stacking heavier weights on top of the lighter weights so that nothing would fly off of the hanger. We also held the hangers at more consistent heights and dropped them in the same manner each time.
It was observed that as the masses grew closer and closer together, the acceleration decreased. Therefore, it can be concluded that a heavier mass on one end, meaning a larger difference in the masses between the two hangers, contributed to a larger acceleration. Additionally, a smaller difference between the two hangers' masses contributed to a smaller acceleration.
The actual and predicted accelerations varied; some of the predicted accelerations were higher while others were lower than the experimental values, though most were relatively accurate. As the experiment progressed, we attempted to reduce error by stacking heavier weights on top of the lighter weights so that nothing would fly off of the hanger. We also held the hangers at more consistent heights and dropped them in the same manner each time.
It was observed that as the masses grew closer and closer together, the acceleration decreased. Therefore, it can be concluded that a heavier mass on one end, meaning a larger difference in the masses between the two hangers, contributed to a larger acceleration. Additionally, a smaller difference between the two hangers' masses contributed to a smaller acceleration.
References
Atwood's Machine. (n.d.). Retrieved November 15, 2014, from http://physics.kenyon.edu/EarlyApparatus/Mechanics/Atwoods_Machine/Atwoods_Machine.html
Giancoli, D. (1998). Physics: Principles with Applications (5th ed.). Upper Saddle River, N.J.: Prentice Hall.
Lahs Physics (n.d.). Retrieved October 6, 2014, from www.lahsphysics.weebly.com
Petersen, C., & Barwick, S. (2014, October 19). What is the Atwood Machine? Retrieved November 15, 2014, from http://www.wisegeek.com/what-is-the-atwood-machine.htm
Giancoli, D. (1998). Physics: Principles with Applications (5th ed.). Upper Saddle River, N.J.: Prentice Hall.
Lahs Physics (n.d.). Retrieved October 6, 2014, from www.lahsphysics.weebly.com
Petersen, C., & Barwick, S. (2014, October 19). What is the Atwood Machine? Retrieved November 15, 2014, from http://www.wisegeek.com/what-is-the-atwood-machine.htm