Copy of Lab-1 Report

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Temple University *

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1061

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Aerospace Engineering

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Apr 3, 2024

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Lab 1 Motion in 1 Dimension Goals: - The purpose of this lab is to demonstrate/explore some real world applications of motion, specifically acceleration, velocity, and time using the photogate sensor. Moreover, this lab helps to familiarize us with the Capstone and Excel applications. Procedure: - In part 1, we dropped a ﬂagged ruler through the photogate sensor to record the time between each ﬂag. The data was placed into a table which recorded time (seconds), position (m), and velocity(m/s). This procedure was repeated by 6 teams which was documented in excel. Some discrepancies that were found between tests were that depending on the drop height of the ruler the position and times recorded varied and in some cases did not exist. Error and precautions: - An error that could have occurred was the picket fence not clearly going through the photogate. The measurements would have been off or if the red light on the back of the stand never went off that would mean no data was collected and the run would have to be restarted. - Another error would be conversions and putting in incorrect ﬂag spacing measurements. The computer would collect incorrect values for the picket fence position, which would affect the measured velocity. Results:

Trial Acceleration m/s 1 4.8418 2 0.0929 3 0.1171 4 0.0966 5 0.2425 6 0.0841 avg 0.9125 stand dev 1.75805969 Questions: Question 1 . Looking at the data, you should notice that the time difference between successive data points is smaller and smaller the farther the picket fence falls. Why is this? - The difference between the successive points getting smaller and smaller is the result of acceleration. The photogate sensor is recording the times between the subsequent lines on the ruler. As the ruler accelerates and gains velocity or overall displacement, naturally the times between the next dash will shorten. Question 2 . How does the computer know the velocity when all it is measuring is time? Hint: what is the other part of the equation for average velocity? - The other part of the equation for average velocity is displacement, so the computer knows the velocity when measuring time because the photogate is also recording the position of the picket fence and the ﬂag spacing is recorded as well to give accurate results when the the black strips on the picket fence are blocking the red beam. Question 3 . If we want the slope to be the acceleration, which variable, velocity or time, goes on the x-axis? Why? - If we want the slope to measure acceleration then we would need to measure the x-axis using time. This is because the slope is measured as rise over run or y/x and if we want to measure acceleration which is velocity/time; Thus, time would have to be in the denominator.

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Question 4. Describe in words the shape of the velocity vs. time graph. (Does the slope stay constant? Is the y-intercept zero?) - The difference between velocity and a time graph, is the difference between a graph f(x) and f’(x). Unlike time, velocity measures direction, or rather, factors it in. In the case where you sometimes drive a total 3 hours and 300 miles from Philadelphia to Pittsburge, a time graph would express just that, you traveled 300 miles in 3 hours moving a x mpx. However, a velocity graph would indicate that your overall displacement is zero because you started and ended at the same location. Question 5 . Describe in words the shape of the distance vs. time graph for the free fall. How should this look (linear, quadratic, etc.)? - The shape of the distance vs. time graph is linear and starts at (0,0) and gradually increases on both the x-axis and y-axis, making it go diagonal. Question 6 . Look at your list of 6 slope values (i.e. acceleration values) and, in one or two qualitative sentences, report how reproducible your acceleration results appear (e.g. very similar values, widely varying from one trial to the next, etc.). - Our values for most of the trials were similar. However, runs one and five seemed to be outliers compared to the rest of the data. I think that some of our data would be reproducible, considering the similarity of the numbers, but I do not believe our results are reproducible overall. Question 7 . Is your standard deviation low when compared to the value of your average? As a rough guideline, a standard deviation less than 10% of your average is OK (but the lower the better!). Does this standard deviation seem reasonable with what you put for your quantitative description of reproducibility in Question 6? This shows how standard deviation is a measure of reproducibility. - Our standard deviation was higher than our acceleration values. As mentioned above, we believe that the data is not reproducible, and the standard deviation being higher than the average acceleration instead of lower supports that idea. Question 8 . Looking at this equation, what would the standard deviation be if all of your measured values were the same? Explain. - The standard deviation would be close to 0. Looking at the data, it can be seen that the first run is the outlier in regards to acceleration. This caused our standard deviation to be higher than the average. So, if the values were all the same, the standard deviation would be close to or zero.

Discussion: The final result of this lab did not result in us getting the expected value of 9.8 m/s 2 , ending up with 0.9125m/s 2 . This is likely due to significant measurement errors. As outlined in our error and precautions this lab was prone to a great deal of deviation from the desired outcome as a result of human and equipment error. There were two primary errors that we suspect contributed to the discrepancies in our data. This first, which almost certainly happened and is supported by the presence of a standard deviation in the first place, is that the photogate sensor is inaccurate to some degree. The second discrepancy we suspect occurred during the execution phase of this project. While recording that data we record the data in cm instead of meters and convert the units twice. This would make sense given that our final result was 0.9125m/s 2 which is off by a degree of 100. If this hypothesis is accurate, it would make our final result 9.1m/s 2 which is much closer to the expected value of 9.8 m/s 2 .

Copy of Lab-1 Report

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