This laboratory work examines the patterns of water droplet accumulation on the surface of a penny. When a certain amount was reached, water was spilled from the money, which was equivalent to the end of the test. Since the experiment requires static validity, a series of control experiments were performed to establish ideal conditions. This was followed by a test experiment, which confirmed the initial hypothesis. This report aims to summarize the results of the laboratory work on counting water droplets on the penny surface.
Given the average size of a water droplet and a penny’s circumference area, it is reasonable to assume that the working number of droplets placed on one side before spilling is approximately seven. On the contrary, in a series of five control tests, the average number of drops was found to be 10, and although successive results were not always repeated (10, 8, 11, 11, 10), there was little deviation from the average.
Such a discrepancy could have been influenced by several critical factors, the discussion of which is necessary for the construction of the hypothesis. First of all, it should be recognized that the instruments (coin and medical pipette) were not changed, and therefore did not affect the result. In addition, the same tap water was used, so its viscosity was also not essential for the experiment. On the other hand, the angle at which the pipette was tilted to the surface of the penny did not always remain constant. The sharper the angle, the larger the droplet size: consequently, fewer droplets accumulated on the penny. Moreover, the force with which the experimenter pressed on the plastic body of the dropper mattered. It was measured that the stronger the pressure exerted on the pipette, the smaller the size of the droplet that came out. It follows that in the third and fourth line of control experiments, the pressure force may have been the largest.
The identified sources of error were eliminated, and the series of control experiments were repeated to evaluate the reliability of the newly obtained data. As expected, the use of only one pipette angle (90°) coupled with an average pressure force on the plastic body resulted in more homogeneous results. In the new series of five control lines, the distribution of the number of droplets on the surface of the penny was as follows: 10, 10, 9, 10, 10. At the same time, the calculated deviation from the mean was even lower, indicating that an effective model of the experiment had been found. Successful completion of this phase and achievement of better experimental conditions allows us to proceed to the stage of setting the working hypothesis and testing.
The average number of drops accumulated on the surface of a penny using a medical pipette before water is spilled is ten.
Results and Discussion
A series of four test trials were conducted to confirm or disprove the initial hypothesis. The results of each test are shown in Table 1.1. First of all, it should be noted that some discrepancies are noticeable compared to what was shown in the near-perfect control test. Although all identified sources of error were eliminated and clear instructions were followed, there was still a difference in the results. In this case, it can be assumed that random and unpredictable factors may have influenced the test experiment.
|Trial #||# of drops|
The average was calculated according to the equation : the estimated number practically coincided with the one found in , which indicates very reliable results. Nevertheless, the average itself is an insufficiently weighty statistical metric, as it reflects only the superficial trend of the data set (Luellen, 2018). Instead, it is appropriate to utilize a standard deviation model to calculate more convincing statistics. Thus, based on equation , it can be concluded that each of the numbers of drops in a given test trial deviates from the mean by 0.96 on average.
It is noticeable that this value is about twice as high as that obtained in the ideal control test. This might indicate less reliable data even if the overall trend in the number of drops was maintained. In other words, the average number of drops was indeed ten, as predicted by the initial hypothesis. However, since the standard deviation was higher than for the control trial, it is appropriate to conclude that there were additional quality-impeding factors in the experiment. A comprehensive analysis of such sources might conclude that experimenter fatigue, excitement, air flows, and reducing the test series to four might have been causes of the discrepancy.
In summarizing the outcome of this laboratory work, it should be said that the result obtained coincides with the predicted number of droplets. Indeed, on average, exactly as many drops as expected, namely ten, were placed on the surface of the penny. A series of test trials were preceded by control lines, which allowed to calibrate the conditions and to obtain more reliable results. Thus, it was shown that the angle of the dropper in relation to the penny and the force of the pressure on the plastic body were essential to the experiment. Finally, although the final number of droplets matched the hypothesis, some slight discrepancies and variability were noticeable. This could indicate additional factors that hindered quality.
Luellen, E. (2018). Why averages are often wrong. Towards Data Science.