The purpose of this lab was to find a relationship between the mass and period for an inertial balance. This is done by using an inertial balance with varying masses and timing each period with a photogate.
Experiment
This experiment is set up with a inertial balance clamped to the table with a photogate on the other side of the inertial balance. Then with the photogate connected to to a laptop, logger pro is used to record the different periods corresponding with the different masses. To make sure that the photogate picks up the motion of the inertial balance, we used a piece of tape at the end of the inertial balance to so make sure that the photogate picks up the movement. Various masses is then placed onto the inertial balance and the periods are recorded.
The experiment is then conducted starting off my measuring the period of the inertial balance without anything on it, then gradually increasing the mass placed on it by 100 grams each time. This is in turn all collected by logger pro and recorded down by hand ourselves. Next the process is repeated again with two objects of unknown mass, in our case a phone and motion sensor
The data of the mass and period is then graphed into logger pro so physically see the relationship between them. The graph is generated excluding the two unknowns because we won't know the actual mass of the unknowns until later. As we observed the graph we saw that the relationship between the mass and the period is that of a power-law, more specifically the relations is T=A(m+Mtray)^n.
To make better use of the data to figure out the unknowns within the power-law equation we changed it into a linear form along with the graph. By rearranging the original equation similar to y =m x + b, giving us lnT= n ln(m+Mtray) + lnA we were able to find out what our unknown variable were. However, the Mtray variable was found by arbitrarily picking a mass until we got a correlation of 0.9999, and this was done until we had a range that in which the correlation was 0.9999. For us that range was from 282 grams to 311 grams.
We then used the unknown found, the lowest and highest values of the Mtray, and the period of the unknown masses, to find a out what the mass of our unknown was. Seeing that the theoretical masses that we calculated is very close to the actual mass of the unknown above it can be seen that the the relationship we found between the mass and period is a good match.
One of the errors that affected the this experiments that caused the theoretical to differ from the actual are how far we pulled back each time for each trial varied. Another would be data collection was not started on the oscillation for each trial.
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