The purpose for this Inertial Pendulum lab was to find a relationship between a mass and its period. In doing so, we created a model that will give an appropriate estimate of the mass of an object when its period is given or vice versa.
The picture above shows the setup that was used for this lab.
Materials: Inertial Balance, Photogate, LabPro, Masses 100g-800g
The procedure was fairly simple. As the balance would oscillate, the photogate recorded the period and the results would then show up on the computer. After setting everything up,as seen in the picture above, our job was to record the period,T (sec) for a set of given masses. First, we recorded the oscillation of the inertial balance without any additional mass on it. Afterwards we conducted 8 trials, increasing the mass by 100 grams after each trial. In total we recorded the periods for 9 different masses. This is shown in the data table below.
In addition to the masses seen in the data table. We recorded the periods for two distinct objects. An eraser weighing 19 grams, period (.298 sec) and a calculator weighing 148 grams, period (.375 sec).
We then inputted all of this information into the computer.
Up to this point our model looked like this: T=A(m+Mtray)^n. Next we took the natural log of both sides resulting in: lnT=n*ln(m+Mtray)+lnA. From here our model can turn into y=mx+b.
As seen below
This graph shows our data in a linear fit.
It will ultimately help us determine all of the unknowns from our model. Our job was to tinker with the mass of the tray until the correlation was as close as possible to 1. We succeeded in narrowing down the mass of the tray between a low of 290 grams and a high of 310 grams. The correlation in this range was .9999. Using the masses of 290g and 310g, we came up with the following two models, which will give us a range of the mass of an object.
Finally, we used our new models to appropriately estimate the mass of the calculator and eraser as mentioned above. To recall, the eraser has a mass of 19 grams and a period .298 sec, and the calculator has a mass of 148 grams and a period of .375 sec.
Unfortunately, we were not able to match the weight of the objects with our model. By inputting a period of .298 sec the model gave a range of 35-44 grams. With a period of .375 sec, the model gave a range of 89-99 grams. The calculations are below.
We suspect this is due to an error in the periods we measured for our masses. Due to either human or computer error, the periods for the eraser and calculator are not accurate.
Systematic Error: There was a systematic error in this lab. The measured periods for the different masses are not reliable because we did not verify the results with a stopwatch. Unfortunately, that part was overlooked in the lab handout. This explains why an object with a mass of 148 grams gives a result that is lower than the 100 gram used in the curve fit.
In all, we found a relationship between a mass and its period. In doing so, we also created a mathematical model that can estimate the mass of an object based on its period, under the right circumstances.
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