PHYS 223 - Lab Report 2 (Acceleration of a Falling Body)

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Feb 20, 2024

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PHYS 223 Acceleration of a Falling Body Megan Cousins Tuesday-Thursday Objective Our goal is to measure the approximate acceleration of a falling mass, also known as gravity, through using laser imprinted marks on a line of paper as it falls with a weight attached. Introduction For this lab, a Behr free-fall apparatus was placed at our lab stations which creates a spark burn every 1/40 of a second. We then put a piece of paper through the top of the apparatus with a weight attached to the bottoms of the paper to create an easier effect to measure the acceleration. Through measuring the distance between the first spark burn and each one in succession, this will show our velocity (or change of position over time) and thus also the acceleration (or change in velocity over time). Questions 1. The curve in Graph 1 will not pass through the origin. Explain the significance of where this curve crosses the vertical axis. The significance to where the line crosses the vertical axis is within the idea the motion of free fall starts as soon as you release the weight and allow the paper to start falling, the distance that the paper falls within the first 1/40th of a second cannot be accurately recorded since the spark burn first appears 1/40th of a second after the detector detects the motion of the paper. This would be called initial velocity. 2. If the value for g varies from the accepted value for g, list the possible sources of error which will account for the differences. Our value for g does not vary greatly from the expected value of g of 9.8. With our value being 9.98 this could simply be chalked up to us not measuring the distance between spark burns correctly or the paper getting jammed within the apparatus which would alter where the marks were located by a small distance. 3. What type of curve is plotted in Graph 2? Defend your answer.
This graph is a polynomial curve since as the velocity increases at the same rate (the acceleration), it will eventually reach terminal velocity. Terminal velocity is the point where the velocity stays the same and the acceleration reaches 0, this would produce a flat line at the top of our curve for Figure 1. 4. Compare the accuracy of the results for g used in the two methods of steps E and H. For our acceleration calculated in step E, the result is a much more accurate value to the true gravitational force being as 9.98 is closer to 9.8 than 8.374 is. Discussion During this lab, though we know that gravity exists, it still is an interesting topic to be able to actually observe it through simple lab work. Our main goal was to take a given apparatus, the Behr free- fall apparatus, and record the displacement of each spark burn it made over the given interval because we know how frequent the spark burns were made (every 1/40th of a second). Recording the average velocity (the change in interval length over the change in elapsed time) vs the elapsed time, this gives us an approximate gravitational acceleration of 9.98. Though this value is close to the expected value of 9.8, it's not quite there which could be potentially explained by not measuring the distance between spark burns correctly, the paper getting jammed within the apparatus which would alter where the marks were located by a small distance, or the weight altering the acceleration as we are not conducting the experiment in a perfect vacuum. Seen in question 4, or comparing two different approaches to finding the acceleration of gravity, we realize something that we did not experiment with in our ‘Measurement and Error’ lab which is the impact of sample size on accuracy of results. To help our answers to be more statistically significant, we need a larger sample size as more values will increase both the precision and accuracy of our answer. Having 18 data points in comparison to 4 data points does make a difference in the final answer that we give in this lab in particular.
Appendix Figure 1. v 0 = 0.3425 Calculated Value for g = 9.9847 Accepted Value for g = 9.8 Percentage difference = 1.87% Figure 2. Average g = See Table 2.
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Table 1. Table 2.

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