Lab partners:
Lab performed: 09/07/16
With this experiment, we try to understand the relationship between mass and periods of oscillations by varying the masses with which we use to create a rate of oscillation. The periods are recorded with an inertial balance and photogate.
Instead of using the conventional balances, we used an inertial balance to measure masses of various objects. In doing so, we can find the inertial mass of an object, instead of the gravitational mass, and notice the type of relationship that is formed between mass and period. Additionally, through this method, we can record oscillation periods with which we can form a power-law equation. With that equation and our known variables, we can solve for an unknown mass.
Inertial balance setup; photogate apparatus on left to record data onto computer
We start by varying the masses we set on the tray (0g, 100g, etc.) and recording each of the oscillation periods with Logger Pro. This proves that there is, in fact, some kind of relationship between mass and period.
On the left: Recorded data of all our runs with varied masses
On the right: Logger Pro view- run with 800g of mass on tray
Given in the lab manual is the equation: T= A(m+ Mtray)^n. By taking the natural log of each side, we get: lnT= nln(m+ Mtray). We plug in our known data into Logger Pro (mass and period), and create equations for the unknowns. In the end, our only unknown variable is Mtray, whose parameter we vary in attempt to find a correlation coefficient as close to 1 as possible (this will result in a nice straight line for the linear fit of the corresponding graph). Since it would be very tedious and difficult to find an exact value of Mtray, we instead find a range for what it could be. We find that our Mtray must be between 325g and 375g. The corresponding values of y-intercept and slope are recorded for later use of the power-law equation.
On the left: Logger Pro view- Data of several variables and corresponding graph with linear fit
On the right: Recorded values of Mtray min and max, along with corresponding A and n values
With our newly found data, we are able to move on to the extension of the lab in which we must find the masses of two unknown objects (we chose a partially empty water bottle and a cellular phone). In this part of the experiment, we record the oscillation periods for the two objects in order to calculate the inertial mass. Using our equations, we find a range of values for the inertial masses of the objects. We then record the gravitational masses of the objects (obtained by measurement on a scale), and compare those values with the ones we calculated.
In the center: Logger Pro view- run with unknown object #2 (cellular phone) on tray
On the right: Recorded data of both unknown objects
On the top: Calculations of min and max inertial masses of unknown object #2 (cellular phone)
On the bottom: Calculations of min and max inertial masses of unknown object #1 (water bottle)
The comparison of our results with the measured gravitational mass show that there was some error produced during the process of this lab. I believe this could have been an error in data collection or calculation. The calculated values of mass for the unknown objects are negative, which is immediately incorrect because our objects can't have negative masses. I initially thought that it was simply a syntax error because my results for the masses of the water bottle created a range that the value of the measured gravitational mass would have fit if the numbers were just positive. However, after completing the calculations for the masses of the cellular phone, I saw that there must have been a greater error somewhere else because my values for this object were almost identical to the values calculated for the water bottle. By looking at the numbers, it seems as though this may have been avoided with different values of Mtray.
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