Lab 0 PHY105

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Feb 20, 2024

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Crystal Zimmermann (crz369) Lauren McKay (lam6934) Eshal Maredea (ezm233) Lab 0 Part 1: Method: The goal of this experiment is to test whether a marble is a sphere or not. The experimenters predict that the marble is a sphere because marbles are manufactured with precise measuring instruments to ensure the product is mathematically a sphere with equal diameter across the sphere. For our experiment, we chose one person to measure the diameters of the marble while another person read the measurements and the third person recorded the data into an Excel sheet. The experimenters chose to use the dial caliper to measure the diameter of the marble as it was the most accurate tool to measure the diameters. We also chose to use the dial caliper because it was easy to learn, use, and read measurements. The experimenters chose to use Excel to record the data collected from measuring the diameters of the marble. After measuring the diameter at three different points of the marble, we recorded the data into an Excelel table. We made sure to record and take into account the standard error when recording the measurements to allow the experimenter to later analyze if the marble is in fact a sphere by checking if the system uncertainty errors were in the allowable range of error to classify the marble as a perfect sphere. The experimenters chose to use the measuring device, the dial caliper, to measure the diameter of the marble. The measuring device was held constant through the three trials as we

only used the dial caliper to measure the diameter and did not change measuring devices. All three trials to measure the diameter of the marble were used by the dial caliper. Another variable we held constant in the experiment was the person measuring the different diameters. The same person held the dial caliper and measured the 3 diameters across the marble. A variable that was not held constant or was varied was the points along the sphere at which we measured the diameters. The experimenter moved the marble to change the points across the marble at which they were measured. • Overall clarity of method Data: Table 1: The table shows the measurement of three diameters in inches with uncertainty being +/- 0.0005 inches. These measurements pertain to the diameter of the marble on its x, y, and z axes. Equations: D 1 = D 2 = D 3 Conclusion: The conclusion of our experiment is that the marble is a sphere, as this data aligns within the uncertainty range. After analyzing the data, the marble is a sphere as D1, D2, and D3 are all statistically the same as the measurements fit within the range of uncertainty. D1, the first diameter reading, was measured at 1.067 inches with a standard error of +/- 0.0005. D2, the

second diameter reading, was measured at 1.066 inches with a standard error of +/- 0.0005, and D3 was measured 1.067 inches with a standard error of +/- 0.0005. Therefore, by considering the diameters of each marble with its uncertainty error, the experimenter can conclude that our prediction was correct because the marble was mathematically classified as a sphere. In other words, our experiment proved that the marble statistically had the same diameter across all three points we measured and thus, the marble can be deemed a sphere. For the next iteration of this experiment, we would use a more accurate measuring tool, such as an electronic measuring device, that eliminates the uncertainty of human error. This would ensure our measurements were, in fact, correct and would make the experiment more precise and accurate. By using a better measuring tool to eliminate human error in our next iteration of this experiment, our prediction that the marble was a sphere could either be proved or refuted based on these more accurate results. To summarize, the experimenters measured the diameters of a marble across three different points along the same marble using a dial caliper. We then recorded these measurements in Excel and calculated the standard error of the measurements. Then. we analyzed the results and concluded that our prediction was correct as the marble was, in fact, a sphere following the mathematical system of error. The lab manual asks, “You likely found that, given the increased precision, at least one of your marbles wasn‘t a sphere. But is it totally wrong to describe the marbles as spherical? Should we sue the manufacturer?”. In our results, we concluded that our marble was a sphere, but if we were to run the experiment multiple times with more marbles, we would most likely find that at least one marble is statistically not a sphere. However, the manufacturer should not be sued because the marbles are not advertised as spheres. They are advertised as marbles. Even though the manufacturer intends for the marble to be a sphere, if the

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marble can work properly and act as a marble in the ways the manufacturer intended it to be, they should not be sued. Part 2: Method: In Part 2, our goal was to measure whether the factor of color impacts the time it takes a marble to roll down the ramp. Gravitational force, friction on the ramp, force used to initiate the roll, and ramp angle can all impact the time in seconds it takes for a marble to roll down the ramp. Because none of the factors listed above include color, we predicted that, on average, there would be no difference in the time (seconds) it takes for the different colored marbles (yellow and white) to roll down the ramp. We used an analog stopwatch to measure the time it takes for different colored marbles to roll down the ramp because it was the most precise tool we had access to. Additionally, we used a tape measure to measure the ramp length. Our constants for this experiment were the person rolling the marble, ramp length, ramp height, and the starting position of the marble on the ramp. We completed ten trials for each marble. Next, the experimenters will calculate the average and standard deviation of the mean meausuments. When we compared our methods to another’s, we found that both groups agreed to have a single person consistently recording with a stopwatch. However, a key difference emerged in the starting point of the ramp: our group initiated measurements from a marked point, whereas the other group started theirs from the top. Data:

Table 2: The table shows the time it took the white and yellow marble to roll down a ramp with an uncertainty of +/- 0 .021489015 s. There were ten trials for each marble with mean, standard deviation, and random uncertainty calculated. Sample Calculations: Mean (Average): x̄ = ∑x / n Ex: Average of the time (seconds) it took for the white marble to roll down the ramp X ̄ = (1.61 + 1.54 + 1.65 + 1.56 + 1.45 + 1.50 + 1.44 + 1.55 + 1.47 + 1.51) / 10 X ̄ = 15.28/10 X ̄ = 1.528 Standard Deviation:

Ex: The standard deviation of the white marble’s time (seconds) to roll down the ramp. Random Uncertainty: δ ɴ = σ N / 𝑁 Ex: Random uncertainty of the white marble’s time (seconds) to roll down the ramp. δ N = 0.067954233/ √10 δ N = .021489015 Since random uncertainty ( δ N ) is 0 .021489015, and the system uncertainty ( δ 0 ) is 0.01, you can see that δ N is greater than δ 0 (0 .021489015 ≥ 0.01). This means the chosen uncertainty for Experiment 2 is δ N, which is +/- 0 .021489015 seconds. Conclusion: Based on our experiment, the experimenters found that color does not impact the time it takes the marble to roll down the ramp. Because the uncertainty in seconds it takes for the marbles to roll down the ramp overlaps, we can say that, on average, it took the same time for the different colored marbles to roll down the ramp. For example, the experimenters found that the yellow marble had a rolling time of 1.505 0.019 seconds while the white marble had a rolling ±

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time of 1.528 seconds. The experimenters found that in both cases for our ± 0. 021 δ𝑁 ≥ δ0 experiment were 0.021 and 0.019 was greater than 0.01. For the white marble, the average time for rolling the yellow marble was 1.505 0.019 seconds. On the other hand, the average time for ± rolling the white marble was 1.528 seconds. ± 0. 021 In the future, the experimenters could repeat the trials with different colors, different ramp angles, and use a more precise way to measure the time it takes the marbles to roll down the ramp. Additionally, the researchers could standardize the initial rolling force by using an automated machine for consistency.

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