Lab #0 Report (1)

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University of Texas *

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105M

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Physics

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Feb 20, 2024

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5

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Lab #0 Report: Jake (John) Lorimer / Greyson Wong Part 1 Initial Measurements with Tape Measure Blue Marble: 1.4 +/- .05 cm Red Marble: 1.4 +/- .05 cm Yellow Marble: 1.4 +/- .05 cm Goal : To test whether the marbles are spherical or not. To do this, we will take several measurements of the marble’s diameter, and compare them. If the measurements are the same, we can say that the marble is a perfect sphere. Prediction : I predict that the marble may not be exact spheres, but they will come very close. It’s likely that imperfections occurred during the manufacturing of the marble, or that inconsistencies in the marble's diameter have been created over time by wearing down and being used for previous experiments. Variables: The only variable that should change is the point of the marble that is being measured. The same caliper will be used to measure each diameter of the marble. Measuring Device: Use a caliper to measure the diameter of the marbles. Primarily because we were told that it was easier to use than the micrometer, also there literally was not a micrometer in our box, so it was not much of a choice anyway. Method : Select a random point on the marble, and measure the diameter using the caliper. Repeat three times. Do so for each of the three marbles. Compare each marble’s three measurements together to see if it is a true sphere.
* Caliper measurements made in inches Uncertainty: The systematic uncertainty for each measurement was 0.00005 inches. Standard deviation for Blue: 0.018288520989954 Standard deviation for Red: 0.0029816103031751 Standard deviation for Yellow: 0.00017320508075687 Conclusion : The caliper measurements showed that the blue marble was not very close to a sphere, as the measurements varied within a fairly large range. The standard deviation for the blue marble’s diameter was 0.018288520989954 inches. The red and yellow marbles produced measurements that were very close to each other, suggesting that they were nearly perfect spheres. The measurements of the yellow marble were especially consistent. The standard deviation for the yellow marble was a very small 0.00017320508075687 inches. Improvements : One possible way to improve the experiment would have been to increase the number of trials. That way there would have been more samples to use in the data collection. Also perhaps a method of measuring the diameter that is even more precise than the caliper.
Uncertainty due to limited trials, imperfect measurements. Final Question : What explains why some marbles would be more spherical than others? Would the use of the marbles in previous experiments affect the shape of the marbles, as they were used in ramp experiments, and possibly chipped after being dropped.
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Part 2 Goal : To test the speed at which each marble rolls down a ramp. Prediction : Since the marbles are all very similar in size, I predict that the recorded times for each marble will be relatively similar. The color of the marble will not affect the marble’s recorded times, but unknown variables like the marble’s mass could have an impact. Relevant Variables : Marble size, Marble shape, marble mass, friction, angle of ramp, air resistance. Manipulated Variable: The color of the marble being tested Choice Measurement: A stopwatch will be used to measure the time it takes for the marble to fall down the ramp. There is probably going to be significant human error, but it is the only option for measuring that is available. Method: Place marble at a marked spot at the top of the ramp. One experimenter will count down from three, and then release the marble. Another experimenter stands at the bottom of the ramp and starts the stopwatch once the marble is released. Once the marble falls off the ramp, the second experimenter will stop the stopwatch. We conducted enough trials (40 for blue, 25 for red & yellow) so that the random uncertainty was lower than the systematic uncertainty of 0.01. Blue Marble Measurements: Random Uncertainty: 0.01030613148 Systematic Uncertainty: 0.01 Yellow Marble Measurements:
Random Uncertainty: 0.01066722971 Systematic Uncertainty: 0.01 Red Marble Measurements: Random Uncertainty: 0.05802298395 Systematic Uncertainty: 0.01 Conclusion: We conducted 40 trials for the blue marble, and 25 for both the red and yellow marbles. The results were consistent with the prediction that there would not be a significant difference between the average times of the three different marbles. The mean times were all between 1.903 seconds and 1.914 seconds with a random uncertainty of .01 seconds. As we predicted, the color of the marble did not impact the recorded times. The mean times of each marble are within the systematic uncertainty of each other. Uncertainty due to human error while using stopwatch Improvements: Using the stopwatch meant there was significant opportunity for human error, especially when trying to time such a short and precise event. Some sort of camera or laser timing system would have improved the consistency and accuracy of the recorded measurements. Questions: How large is human error for timing an event that was on average, less than two seconds long. Between my eyes and my fingers, I’m not sure how accurate I could be in timing the marble.