Unit 2 Lab Report

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Apr 3, 2024

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Yagmurov 1 Roman Yagmurov Prof. Tuero PHY2048L January 10, 2024 Unit 2 Lab: Photographic Analysis of a Falling Object Abstract: I looked a spliced frame-by-frame picture on my computer and then measured the distance the ball was falling using “mouse units.” I then converted the “mouse units” to meters and used those, along with one of the modified kinematic equations to experimentally find the acceleration due to gravity. As you may have expected, I wasn’t very successful in getting a value close to the accepted value because of different reasons. However, this lab did require me to use unit conversion and calculations. The free fall acceleration that I found turned out to be 13.68 m/s 2 which is around 3.88 m/s 2 off from the commonly accepted value of 9.8 m/s 2 . The reason for this may be because I mismeasured the “mouse units” or maybe because I set up the virtual experiment incorrectly.
Yagmurov 2 Introduction: The purpose of this lab is to find out if it is possible to accurately find out the value of the acceleration due to gravity experimentally. In this lab, I will be employing different techniques, such as unit conversion, kinematic equations for free fall, and percent error to see how close I am to the accepted value. I expect to find the value somewhat accurately for the free fall acceleration although I do believe I will be off by a significant amount because of the type of experiment this is. General Principles: The general principle of this lab is finding acceleration of a free-falling object. This can be done because objects that are falling near the surface of the Earth and are small enough to not have air resistance reasonably affect them, should usually have an acceleration due to gravity of 9.8 m/s 2 . In other words, one can also say that g is the measure of the gravitational field strength at Earth’s surface, which is found using the general equation for gravity. However, if we did not know the value of g, we could also find it through experimental means, which is the goal of this lab. This is possible because a free-falling object that is only moving in the vertical direction will only accelerate towards Earth’s surface and that would give us a good opportunity to find the acceleration due to gravity as no other force (except negligible air resistance) would be acting on the object. To find the acceleration, one would need to find the total displacement and the time interval that the displacement occurred in. This is because of one of the big 3 kinematic equations that was modified for free fall. Having calculated the acceleration due to gravity, I could then compare it to the actually accepted value and see by how much I was off percentagewise. Methods: The method I’m using for this lab is, first, to convert the “mouse units” on my screen to actual meters (through the use of the metersticks in the photo) and then to find the displacement in meters, rather than “mouse units.” Then, I’m using one of the modified
Yagmurov 3 kinematic equations, y = 1 2 > ¿ , to find g. Then I will compare the result with the accepted scientific value using percent error which will tell me how far off I was in my estimate. Results: Here are my findings for the conversion between “mouse units” and meters 516 67mu = 449mu = 2meters 1mu = 2 449 = 0.0045meters With this conversion, I can now find the differences in position in “mouse units”: Time (s) "Mouse Units" Difference from 0.1 0.1 81 0 0.2 112 31 0.3 166 85 0.4 245 164 0.5 345 264 0.6 461 380 Let’s take the difference between t=0.1 s and t=0.6 s and use it to find the acceleration due to gravity: y = 380 mu = 1.71meters y = 1 2 gt 2 g = 2 y t 2 = 2 ( 1.71 ) 0.25 = 13.68 m s 2 The percent error is 39.6% according to: δ = | v A v E v E | × 100 δ = | 13.68 9.8 9.8 | × 100 = 39.6% These findings, as well as the percent error, tell me that something went wrong in the calculations; these findings contradict free fall acceleration. Conclusion: In this lab I have shown that it is possible to calculate free fall acceleration with only knowing displacement and time. However, what I saw during my calculations is that there must have been some errors that I made, be it in measuring mouse units, converting them, or during the actual calculations. The error may have also come from my equipment not being set up correctly. Wherever the error may have come from, this lab shows that, while it is possible to
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Yagmurov 4 calculate the free fall acceleration, it would be inaccurate due to the many things that can affect it, ranging from wrong set up to even air resistance.
Yagmurov 5 Works Cited Moebs, William, Samuel J. Ling and Jeff Sanny. University Physics Volume 1 . 2016.