Physics Lab 1: Sphere Geometry and Marble Rolling Study

Question: Is a given object a sphere? Goal: The goal of this portion of this experiment is to determine if the given objects are spheres. This experiment is conducted to test the geometry of the spheres against the geometric model. In order to answer this question we used two different measuring devices. Using the tape measure, we measured the red and green marble twice. Then, we chose to use a caliper. We measured the red, green, and large marble in three different orientations to get three different diameters. The differences in our measurements can be assumed to be the systematic uncertainty. Prediction: Using the tape measure the marble does not appear to be spherical because the diameters of the two spheres do not fall within the uncertainty level. However, with increased precision we predict that marbles are spherical. Quick Check: Measure diameter of a marble with tape measure Red marble: 1 +/- 0.005 mm Green marble: 1.3 +/- 0.005 mm Method: Using a tape measure is an inefficient method of determining the diameter of marble because the uncertainty level is not especially small. With that being said, there was an option to measure the marble using either a Micrometer or dial Caliper, which both have lower levels of uncertainty. In the following experiment, a dial caliper was used to measure the diameters of red marble, green marble, and a large marble. A dial caliper was used over a micrometer as members of the group had more experience with the caliper. Additionally, for each marble, three trials were conducted that all have a systematic uncertainty of 0.01 mm. Each marble differed in color and size, which made all three trials independent of each other so there can be a conclusive result. However, using the dial caliper for every trial on every marble stayed the same. Table 1: Marble Diameters calculated with Dial Caliper (mm) Marble Trial 1 Trial 2 Trial 3 Average Red Marble 10.0432 +/- 0.01 mm 10.0428 +/- 0.01 mm 10.0420 +/- 0.01 mm 10.0427 mm Green Marble 10.0590 +/- 0.01 mm 10.0594 +/- 0.01 mm 10.0584 +/- 0.01 mm 10.0589 mm Large Marble 30.142 +/- 0.01 mm 30.143 +/- 0.01 mm 30.141 +/- 0.01 mm 30.142 mm Statistical Analysis: To determine the level of certainty with the measurements, we must also calculate the random uncertainty of our measurements to determine if there is a random source of error that can influence the validity of our results. Calculating Random Uncertainty: Random uncertainty: 0.0007 mm Systematic uncertainty: 0.01 mm Since the random uncertainty is less than 0.01 mm, the systematic uncertainty is used as the source of uncertainty. Check In: One difference is that the other group used a micrometer as opposed to a caliper. One similarity is the other group also conducted multiple trials and measured each of the marbles: red, green, and large. Conclusion: It can be concluded that the marbles that were investigated are spheres because the measurements of diameters are the same. This was concluded due to an experimental trial measuring 3 different marbles, with different average diameters, with a dial caliper. More specifically, when looking at the average of a red marble, 10.0427 mm with a random uncertainty of 3.46 x 10^-4mm . However, since the systematic uncertainty is bigger, the average falls within the diameters of all the other trials, 10.0432 mm and 10.0428 mm, indicating that all the diameters are the same. Thus, using the systematic uncertainty, all of the diameters are the same which indicates the marbles are spherical in shape. However, it must be noted that manufacturer companies play a role in the production of each marble. Thus, depending on the manufacturer companies, some marbles are not spherical. This can be improved to include more trials and to compare with additional measuring devices to confirm that our data is both accurate and precise. Part 2: Question: does the time it takes a marble to roll down a ramp depend on color? On which marble we’re using? Quick Check: Trial with red marble: 1.74 +/- 0.01 s Influences that affect marble rolling time: - Friction of surface - Air resistance - Height and angle of ramp - Mass of marble - Human reaction time Trial with green marble: 1.82 +/- 0.01 s There is no reason to believe that marble rolling time depends on color and the second trial does not support the idea that rolling time depends on color despite having different times. This difference in time could be due to the many different confounding variables aforementioned. Materials: - Ramp - Block under ramp - Stopwatch - Green, red, large marble Method: The experiment consisted of measuring the rolling times of three marbles, red, green and large. Each lab member was given a role while running this experiment. One person was assigned to the stopwatch, one to release the marble, and lastly one to record data for each time. When the marble was released onto the ramp the stopwatch was started and was stopped when it reached the end of the ramp. With that being said, there was a minimum of 15 trials per marble as there were extra trials for the red and green marble so our random uncertainty would be less than or equal to the uncertainty of the stopwatch which was 0.01 seconds. We started the timer at the top of the ramp with the wedge also being under at the top of the ramp and we stopped the timer when the marble rolled until the very end of the ramp. Our independent variable in this experiment was the difference in marbles, red, green, and large. However, the angle of the ramp and method of measurement all remained constant so we can determine the effect on rolling times. With that being said, increased trial times may be needed in order to get a random uncertainty that is less than or equal to 0.01. Time Taken for Red Marble (Small Marble #1) To Roll Down Ramp Trial # Time (s) Trial 1 00:01. 74 +/- 0.01 sec Trial 2 00:01. 68 +/- 0.01 sec Trial 3 00:01. 79 +/- 0.01 sec Trial 4 00:01. 72 +/- 0.01 sec Trial 5 00:01. 84 +/- 0.01 sec Trial 6 00:01. 78 +/- 0.01 sec Trial 7 00:01. 76 +/- 0.01 sec Trial 8 00:01. 78 +/- 0.01 sec Trial 9 00:01. 79 +/- 0.01 sec Trial 10 00:01. 68 +/- 0.01 sec Trial 11 00:01. 80 +/- 0.01 sec Trial 12 00:01. 98 +/- 0.01 sec Trial 13 00:01. 89 +/- 0.01 sec Trial 14 00:01. 82 +/- 0.01 sec Trial 15 00:01. 71 +/- 0.01 sec Trial 16 00:01. 75 +/- 0.01 sec Trial 17 00:01. 65 +/- 0.01 sec Trial 18 00:01. 80 +/- 0.01 sec Trial 19 00:01. 72 +/- 0.01 sec Trial 20 00:01. 79 +/- 0.01 sec Trial 21 00:01. 64 +/- 0.01 sec Time Taken for Green Marble (Small Marble #2) To Roll Down Ramp Trial # Time (s) Trial 1 00:01. 82 +/- 0.01 sec Trial 2 00:01. 85 +/- 0.01 sec Trial 3 00:01. 76 +/- 0.01 sec Trial 4 00:01. 87 +/- 0.01 sec Trial 5 00:01. 96 +/- 0.01 sec Trial 6 00:01. 81 +/- 0.01 sec Trial 7 00:01. 79 +/- 0.01 sec Trial 8 00:01. 84 +/- 0.01 sec Trial 9 00:01. 82 +/- 0.01 sec Trial 10 00:01. 99 +/- 0.01 sec Trial 11 00:01. 77 +/- 0.01 sec Trial 12 00:01. 78 +/- 0.01 sec Trial 13 00:01. 85 +/- 0.01 sec Trial 14 00:01. 86 +/- 0.01 sec Trial 15 00:01. 86 +/- 0.01 sec Trial 16 00:01. 88 +/- 0.01 sec Trial 17 00:01. 91 +/- 0.01 sec Trial 18 00:01. 78 +/- 0.01 sec Trial 19 00:01. 81 +/- 0.01 sec Trial 20 00:01. 73 +/- 0.01 sec Trial 21 00:01. 84 +/- 0.01 sec Trial 22 00:01. 85 +/- 0.01 sec Time Taken for Large Marble To Roll Down Ramp Trial # Time (s) Trial 1 00:02. 10 +/- 0.01 sec Trial 2 00:02. 28 +/- 0.01 sec Trial 3 00:02. 14 +/- 0.01 sec Trial 4 00:02. 20 +/- 0.01 sec Trial 5 00:02. 22 +/- 0.01 sec Trial 6 00:02. 26 +/- 0.01 sec Trial 7 00:02. 12 +/- 0.01 sec Trial 8 00:02. 17 +/- 0.01 sec Trial 9 00:01. 98 +/- 0.01 sec Trial 10 00:02. 14 +/- 0.01 sec Trial 11 00:02. 03 +/- 0.01 sec Trial 12 00:02. 24 +/- 0.01 sec Trial 13 00:02. 22 +/- 0.01 sec Trial 14 00:02. 23 +/- 0.01 sec Trial 15 00:02. 23 +/- 0.01 sec Statistical Analysis: Random uncertainty was calculated in order to determine if there are any slight variations that occur that could influence the validity of our results, including user error. We found the mean, standard deviation, and used the formula for random uncertainty as shown below. Check in: Comparing our group to another group, the number of trials differed as they did 15 for all three marbles, but the methodology stayed the same, like using a stopwatch. When checking in with that same group once again, it was found that our results were similar because they also found a random uncertainty that is around 0.01. Additionally, since they had multiple trials their standard deviations were also similar to each other. Conclusion: Our results indicate that the large marble had a larger average rolling time compared to both the red and green marble. As an example, the mean rolling time for the large marble was 2.17 seconds while the red and red marble had averages under 2 seconds. The large marble was the third marble we measured, and that had the biggest difference in rolling times due to the mass of the marble. When comparing the mean rolling time of all three marbles, there are differences in the times but that is not likely due to color. Furthermore, since these marbles have different diameters that can influence the rolling time as increased diameters are associated with higher mass. Additionally, these differences were determined as significant using the uncertainty value of 0.01. One way to determine the influence of color on marble rolling speed is to find marbles with the same diameter and mass and find the times of those marbles as the independent variable would only be color.