The purpose of this lab was to develop an equation that showed the relationship between the mass of an object and the oscillation period of the object on an inertial balance clamped to the table.
Equipment used:
The picture is of the clamp and inertial balance set up, and the device that is at the end of the balance is the photogate instrument. With the setup, the oscillation period of the balance was timed by the photogate which uses a light sensor.
Logic behind the Numbers:
First an understanding of what data was actually collected is needed. The oscillation period of various weights on the tray of the balance were measured. The experiment started by measuring the oscillation of only the tray at the end of the balance then adding a 100 gram weight to the balance and measuring the oscillation of the balance again. This was repeated until 800 grams total were on the balance.
 |
| The periods collected for each weight |
There wouldn't be a reliable relationship if only the weight added was compared to the oscillation period, so the equation T = A(mass of object + mass of Tray)^n, where T is the period, A is a constant, and n is the order of the equation, had to be manipulated. The end result will be a graph of the natural log(T) versus the natural log(mass of the object and the mass of Tray).
 |
| Graph of the natural log of the data collected |
 |
| Expansion of text in box |
 |
| The table of the value used for the graph |
A parameter, which was an estimation at first, was used for the mass of the tray. When the parameter was changed, either increasing or decreasing the mass of the tray, the correlation of the best fit line change as well. The parameter was changed until the correlation was as close to 1 as it could be, .9991 was the closest that could be achieved for the set of data that was collected. Once the parameter, the mass of the tray, was adjusted, then the manipulated equation yielded the value for n and the value of the natural log(A), which are both constants. The mass of the tray = .251 kilograms, the natural log(A) = -.4159, and n = .5996. The new equation could now be used to find the mass of an object placed on the tray if the oscillation period is known.
Finding Unknown Masses:
Using the equipment and equation from above, the masses of two phones were found by measuring the oscillation periods when each phone is individually placed on the inertial balance. The first phone had an oscillation period of .3613 seconds and the mass calculated from the equation was .115 kilograms but when the phone was weighed the true mass was .118 kilograms. The second phone had an oscillation period of .3857 seconds and the mass calculated from the equation was .158 kilograms but when the phone was weighed the true mass was .164 kilograms.
Conclusion:
The percent error for the first phone was -2.54% and for the second phone the percent error was -3.66%. Both percent errors are fairly high considering the simplicity of the lab and the expected accuracy. The most probable cause of the error was the fact that multiple trials weren't performed for timing the oscillation period of each 100 gram weight increment. Since the data that would be used to create the equation was not very precise and accurate it created the high amount of error.
 |
| Manipulated equation, isolating mass of object |
Finding Unknown Masses:
Using the equipment and equation from above, the masses of two phones were found by measuring the oscillation periods when each phone is individually placed on the inertial balance. The first phone had an oscillation period of .3613 seconds and the mass calculated from the equation was .115 kilograms but when the phone was weighed the true mass was .118 kilograms. The second phone had an oscillation period of .3857 seconds and the mass calculated from the equation was .158 kilograms but when the phone was weighed the true mass was .164 kilograms.
Conclusion:
The percent error for the first phone was -2.54% and for the second phone the percent error was -3.66%. Both percent errors are fairly high considering the simplicity of the lab and the expected accuracy. The most probable cause of the error was the fact that multiple trials weren't performed for timing the oscillation period of each 100 gram weight increment. Since the data that would be used to create the equation was not very precise and accurate it created the high amount of error.
Sincerely,
Swaggy C
