The Mass of a Pendulum vs. its Period
Zach Pabis, Charles Stewart, Dylan Torrey
August 31st, 2018
Zach Pabis, Charles Stewart, Dylan Torrey
August 31st, 2018
Research Question: How does the mass of a pendulum affect its period?
The independent variable in this lab was the mass of the pendulum, while the dependent variable was the period of the pendulum. Controls included how far the pendulum was pulled back, the length of the pendulum, and the person (Charles) who released the pendulum and timed each period. The testing was completed in less than a class period, limiting any effects from the environment of the room.
To ensure that our control variables would have as small of an effect on the experiment, we used the same pendulum for each of our tests, making sure not to alter the length or position on the table. Using the edge of the table for reference, the pendulum was pulled back to the same angle each time. The pendulum was composed of a hanging string on which a small rack was attached, on which could be placed additional weight. Due to the strings relatively low mass and that it remained unchanged throughout the experiment, it was considered a constant and was not measured. The small rack had a mass of 50 grams, and additional 100 grams worth of metal masses were added to the rack after each previous mass was timed. A total of six different masses were timed in 100 gram increments, resulting in a maximum mass of 550 grams, providing a wide range of data. Each of the six masses was let go from the same table corner and timed three times, to minimize the effect of human reaction time. An iPhone was used to time each swing, and was operated by the same person who dropped the pendulum, thus ensuring that the actions of timing and letting go of the pendulum would be as close to synchronized as possible. After the time for each trial was measured, it was promptly written down in the lab notebook. Afterward, the three times recorded for each mass were averaged to account for human reaction time.
The independent variable in this lab was the mass of the pendulum, while the dependent variable was the period of the pendulum. Controls included how far the pendulum was pulled back, the length of the pendulum, and the person (Charles) who released the pendulum and timed each period. The testing was completed in less than a class period, limiting any effects from the environment of the room.
To ensure that our control variables would have as small of an effect on the experiment, we used the same pendulum for each of our tests, making sure not to alter the length or position on the table. Using the edge of the table for reference, the pendulum was pulled back to the same angle each time. The pendulum was composed of a hanging string on which a small rack was attached, on which could be placed additional weight. Due to the strings relatively low mass and that it remained unchanged throughout the experiment, it was considered a constant and was not measured. The small rack had a mass of 50 grams, and additional 100 grams worth of metal masses were added to the rack after each previous mass was timed. A total of six different masses were timed in 100 gram increments, resulting in a maximum mass of 550 grams, providing a wide range of data. Each of the six masses was let go from the same table corner and timed three times, to minimize the effect of human reaction time. An iPhone was used to time each swing, and was operated by the same person who dropped the pendulum, thus ensuring that the actions of timing and letting go of the pendulum would be as close to synchronized as possible. After the time for each trial was measured, it was promptly written down in the lab notebook. Afterward, the three times recorded for each mass were averaged to account for human reaction time.
Mass (grams) |
50 |
150 |
250 |
350 |
450 |
550 |
Average Time (seconds) |
1.63 |
1.68 |
1.76 |
1.77 |
1.81 |
1.78 |
Trial 1 |
1.65 |
1.65 |
1.79 |
1.66 |
1.78 |
1.78 |
Trial 2 |
1.65 |
1.73 |
1.74 |
1.83 |
1.83 |
1.76 |
Trial 3 |
1.58 |
1.66 |
1.76 |
1.82 |
1.81 |
1.80 |
Example Calculation: (1.65+1.65+1.58)\3 = 1.63
Plotted in Logger Pro, a linear fit for the data give the equation:
Time = 0.000329 seconds/gram * Mass + 1.64 seconds
Time = 0.000329 seconds/gram * Mass + 1.64 seconds
Considering the small slope of the graph, there is more likely no relationship between a the mass of a mass of a pendulum and its period. A manually fit line with a slope of zero provides close to equally as good of a fit to the data:
The fact that the period time only deviated by a maximum 0.25 second difference while the mass of the pendulum increased by a factor of 11 suggests that the positive slope of the linear fit is only a result of the uncertainty of the data. In addition, the last data point did not match the linear fit while still being consistent with the other trials in the experiments. This proves that even if the relationship between a the mass of a pendulum and its period is linear, the data could not reasonably determine the slope with its level of uncertainty.
The two most significant sources of uncertainty in the experiment were human reaction time and the level precision when letting go of the pendulum. Because the length of the pendulum's period is so short, reaction time could influence the result immensely. this source of uncertainty prompted the use of three trials of each pendulum mass, but reaction time can result in similar errors across multiple trials. Another source of uncertainty came from the act of releasing the pendulum to time it. When pulling it back, the pendulum was held by the end of end of the string, allowing the rack to remain perpendicular to the ground. As the pendulum was released, the rack swung back and forth on at the end of the pendulum as it was swinging. this double pendulum effect introduced unwanted vibrations into the systems, which grew as more mass was added.
A solid pendulum with a wood or metal component in place of the string would hold the rack in line with the rest of the pendulum at any angle, eliminating the risk of creating a double pendulum effect. Using automatic sensors to detect the pendulum t the end of its period would also eliminate any uncertainty due to reaction time.
The two most significant sources of uncertainty in the experiment were human reaction time and the level precision when letting go of the pendulum. Because the length of the pendulum's period is so short, reaction time could influence the result immensely. this source of uncertainty prompted the use of three trials of each pendulum mass, but reaction time can result in similar errors across multiple trials. Another source of uncertainty came from the act of releasing the pendulum to time it. When pulling it back, the pendulum was held by the end of end of the string, allowing the rack to remain perpendicular to the ground. As the pendulum was released, the rack swung back and forth on at the end of the pendulum as it was swinging. this double pendulum effect introduced unwanted vibrations into the systems, which grew as more mass was added.
A solid pendulum with a wood or metal component in place of the string would hold the rack in line with the rest of the pendulum at any angle, eliminating the risk of creating a double pendulum effect. Using automatic sensors to detect the pendulum t the end of its period would also eliminate any uncertainty due to reaction time.