Lab 2 _Experiment 3

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Northeastern University *

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1156

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Physics

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Dec 6, 2023

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Introduction: In this lab, we repeated the famous experiment of Galileo. He was one of the greatest experimentalists in physics from Italy. Due to the Galileo free fall experiment, the belief of a heavy object falls faster than a lighter one was challenged. With his results there was new information that came to the eye, complete motion is simply the vector sum of component motions. This experiment has to do with motion in one and two dimensions. Motion in one dimension implies motion along a straight line or in a single direction. An example of one dimensional motion is an object being tossed up in the air vertically and then watching it fall. Along with one dimension, there two equations that can best describe it, along the x- axis and . Similar are the equations for the y- axis, and Two dimensional motion means that it takes place in two different directions at the same time. Some examples of two dimensions are a gymnast on a balance beam or a clown being shot out of a cannon, also a very known one is a rollercoaster doing a loop. For two dimensional motion, the displacement , velocity and acceleration are all vectors. The goal for this experiment was to study the time of displacement, velocity and acceleration in both dimensions. As well as show the motion in one direction is independent of motion in a perpendicular motion. We did 4 investigations each of them being connected to each other. By find the uncertainty error in the first, to have the puck do different situation in both investigation 2 & 3, and plotting them on to a plot and find the slope equations from there. Its all connected to find the acceleration of free fall towards the end in investigation 4. Investigation 1 For this investigation, most of what we were doing was setting up the glass table and calibrating the video tracker software to analyze the random errors in the data that was given by the software. For the steps into setting up, the glass table needed to be leveled, so that the puck would be able to stay still mostly while it was turned on. Once the table was leveled the wooden block was placed under the leg farther away from us, creating an inclined plane so we are able to study the motion on the puck. Next came the software program being able to be set up on the computer. The program itself was called IPL Tracker. The program should have live video footage thanks to the camera on
top of the table, while making sure the camera is being able to focus, adjust the setting of saturation, brightness and contrast setting to have the puck as bright as possible. Once the camera settings are adjusted, the next step was to identify the outer corners of the table in live video by just clicking on the outer most corners of the table in the video. After finishing, moving on to color masking the puck so the only thing you're able to see is the pick and black everywhere else by experimenting with the saturation, brightness, and contrast. Once everything is set it is now time to record the first data. While keeping the puck turned off and in the middle of the glass table, press record for 10 seconds. With the data given by the software, we are able to copy and paste into Excel to create a table. Table shown at Appendix A. Once the data is located we are able to find the random error in the pucks position. By also making two separate histograms with y and x positions,
After we finished the histograms, we moved on to finding the standard deviation of the y and x values. By using the equation in excel for standard deviation, and δ? = . 0175 δ? = . 0279. With these errors we found, we now have the error for the rest of the remaining investigations by just multiplying each error by 10. The unaccounted sources of error in this lab that could have happened is the software registering the value consistently higher than it actually is. Investigation 2 For the next investigation, we were able to analyze the case of one dimensional motion. Something similar to the Galileo experiment. With the Camera Settings still the same as investigation 1, the puck is now turned on and placed in the middle of the table, making sure everything is in view. Next it's time to click on the recording, while waiting a second before releasing. The puck will be able to slide down and bounce and the bottom edge a couple of times, stopping the recording after around 8 seconds. Coping the data into excel is the same as in Investigation 1. Table shown in appendix A For the analysis portion of the investigation, we were going to calculate the pluck velocity using its position vs time data. With the equation given by the manual, where 𝑉? = ∆?/∆? and . While also calculating the average time with the equation ∆? = ?2 − ?1 ∆? = ?2 − ?1 . With these equations given to us by the manual, we added two new ? ??𝑔 = 1 2 (?1 + ?2) columns to our excel table, t avg and Vy, for us to calculate the average time and average velocity. Table is shown in Appendix A
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Once that is calculated we are able to calculate the error in Vy. With the equation from appendix a which we used . Once the error was calculated, we are δ𝑉 = (δ?) 2 + (δ?) 2 δ𝑉 = . 3947. able to make a scatter plot of Vy vs t avg. The behavior of Vy is very constant in the beginning ( 0 secs to .8 secs) of the graph and towards the end ( 5 secs to 7.5 secs) but when it gets towards the middle (.9 secs to 1.8 secs) and ( 2 secs to 3.1 secs ) it happens to turn into a linear equation. With the graph data being plotted we are able to have two straight portions, and are able to determine their slopes,by using separate data series. While also adding the R^2 value. R^2 meaning that all the data points are exactly on the trendline. Each equation is shown on the graph, orange trend line has the equations of and the ? = − 51. 469? + 42. 04 𝑅 2 =. 972 gray trend line has an equation of These two ? = − 60. 033? + 150. 01 𝑅 2 = 0. 992 slopes represent how the velocity changes over time. For the last part of this investigation we are able to put these same numbers into the IPL Straight Line Fit Calculator to compare the values of both. I did expect both the values to be close, i did not infact believe they were going to be basically the same points. As for the first equation the calculator was able to give me, , the only different in the both ? = ( − 51. 469 ± 6. 026)? + (42. 04 ± 9. 308) 𝑅 2 =. 078 equation was the statiscal measuse was lower in the calculator than the plot equation. 𝑅 2 Meaning that the points on the graph are closer to the trendline.
As for the second equation, the equation the calculator was able to give me was, . Again I did expect it the values ? = (− 62. 525 ± 3. 416)? + (156. 89 ± 7. 157) 𝑅 2 = . 028 to be close and I was correct while this time the values are not the same just in the same range. The is the same thing as the first straight portion equation, it seems to be more accurate on 𝑅 2 the plot. Investigation 3 For this next investigation we are goign to be using the same set up and analysis portion except this time the puck will start at the bottom left corner. One you click record you will throw the puck so it makes a parabola so it comes back down on on the right corner with out it touching any of the sides. Once it hits the bottom edge of the table you can stop recording. Again copying the data into excel, table can be seen in appendix A. For the analysis portion we are calculated the same values of as shown ? ??𝑔 , 𝑉 ?, , δ𝑉 ? , 𝑉 ? , δ𝑉 ? on the table. After we were able to calculate the values, were told to make a scatter plot the same as in Investigation 2. Doing the same thing of finidng the equation and the value of the 𝑅 2 straight portions. The slopes are representing the velocity change of the pucks it continuous through a parabola. As instructed the same data was put in to the IPL Straight Line Fit Calculator for the first equation giving us , these two ? = (− 9. 734 ± 5. 451)? + (37. 322 ± 10. 652) 𝑅 2 = . 497
equation are basically the same having the same slope and b value. The is a little bit smaller 𝑅 2 in the plot diagram making the point from the calculator be closer to the trendline. For the second equation we did the same as the first and entered into the calculator, , I predicted that both of the ? = (−. 986 ±. 073)? + (− 25. 052 ± 1. 427) 𝑅 2 = 703. 323 equation would be closely similar but i was proven wrong as the calculator gave us something completely different. Investigation 4 In this investigation we were able to calculate the acceleration due to gravity using our results from investigation 2 and 3. We were first told to draw a diagram based on the setup of the glass table we used for the investigations, finidng the heignt on both of the table as well as the angle and the hypotenuse as show in the picture below.. After were done finding the basics of the diagram it was now time to derive a formula for g, which was . Once we found this equation it was time to calculate the acceleration of 𝑔 = ? ?𝑖?θ free fall in each of the investigations (2 & 3). 𝑔 1 = − 867. 849 𝑔 2 =− 1012. 252 𝑔 3 =− 925. 448
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After we calculated the acceleration of free fall, we calculated the uncertainties using the absolute error come front the uncertainty of the IPL straight line fit δ𝑔 = ????𝑙??𝑒???? 𝑔 equation. . Finally to obtain the final result we average g δ𝑔 1 = . 0069 δ𝑔 2 =. 0033 δ𝑔 3 =. 0058 which is . The did not fall nowhere near the theoretical value gravity of 9.8 𝑔 ?? =− 935. 183 𝑔 ?? m/s^2. Most likely do to systematic error when calculating the distance of the glass table or the puck. Conclusion We did 4 investigations each of them being connected to each other. By find the uncertainty error in the first with standard deviation, and To have the puck do δ? = . 0175 δ? = . 0279. different situation in both investigation 2 & 3, and plotting them on to a plot and find the slope equations from there. Its all connected to find the acceleration of free fall towards the end in investigation 4 and finding the average of g, , finding out that it was not near 𝑔 ?? =− 935. 183 the actual value of g. Questions 1. Find the time for the puck to reach the bottom of the air table starting from the top for Investigations 2 and 3. Are these times all the same, as shown in the picture of the cannon? Why or why not? No there are not the same because while the equation for time is time= distance/ speed. The distance for the cannon ball are tow differnt making the time being completely different. 2. If the acceleration of a puck falling down an incline of angle ( where is , θ θ < 45 ◦ ) ? θ what is ? 2θ ? ? 2θ = 2? θ ???θ 3. You determined the acceleration from the slope of your plot of v vs. t. What is the meaning of the intercept of your line with the v-axis? Do you expect this value to be close to the origin? The intercept of the line v axis mean the change in the acceleration goes from positive to negative. I dont expect this value to be close to the origin. 4. If you performed Investigations 2 and 3 again with an incline of = 0 , what would the θ trajectories look like in each case? They would all look the same because there is no force of gravity pulling the puck down Like it is in this lab. 5. In Investigation 3, you launched the puck so that it goes all the way up and comes back down in the right corner of the table. Since the table is a square, the puck goes up the
same distance in the y direction as it travels in the x direction. Calculate the theoretical angle that is required for this. θ = ????𝑖?( ?? 2 2?(𝑉 ? −𝑉 ? ) Appendix A. Investigation 1 Table. t(s) x1(cm) y1(cm) 0.0333 31.584 34.031 0.0667 31.557 33.88 0.1 31.551 34.019 0.1333 31.546 33.871 0.1666 31.564 33.946 0.2 31.549 33.903 0.2333 31.553 34.031 0.2667 31.554 33.913 0.3 31.547 34.015 0.3333 31.56 33.939 0.3666 31.543 33.949 0.4 31.578 33.931 0.4333 31.553 34.013 0.4666 31.594 33.865
0.5 31.538 33.991 0.5333 31.539 33.911 0.5667 31.564 34.023 0.6 31.555 33.924 0.6333 31.536 34.023 0.6666 31.563 33.946 0.7 31.552 33.986 0.7333 31.543 33.898 0.7667 31.551 33.978 0.8 31.56 33.924 0.8333 31.571 33.974 0.8666 31.54 33.955 0.9 31.555 33.949 0.9333 31.549 33.93 0.9666 31.56 33.972 1 31.55 33.94 1.0333 31.539 33.889 1.0667 31.519 33.905 1.1 31.549 33.974 1.1333 31.557 33.884 1.1666 31.553 33.976 1.2 31.552 33.914
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1.2333 31.547 33.991 1.2667 31.534 33.96 1.3 31.538 33.974 1.3333 31.545 33.966 1.3666 31.548 33.993 1.4 31.57 33.952 1.4333 31.595 33.993 1.4666 31.558 33.894 1.5 31.551 33.956 1.5333 31.559 33.949 1.5667 31.556 33.994 1.6 31.539 33.954 1.6333 31.546 33.974 1.6666 31.539 33.958 1.7 31.592 34.005 1.7333 31.551 33.909 1.7667 31.562 33.97 1.8 31.522 33.926 1.8333 31.535 33.957 1.8666 31.559 33.929 1.9 31.537 33.962 1.9333 31.539 33.964
1.9666 31.552 33.992 2 31.535 33.975 2.0333 31.548 33.942 2.0667 31.579 33.997 2.1 31.55 33.939 2.1333 31.546 33.931 2.1666 31.55 33.942 2.2 31.555 33.913 2.2333 31.545 33.944 2.2667 31.54 33.957 2.3 31.515 33.956 2.3333 31.535 33.931 2.3666 31.553 33.973 2.4 31.555 33.943 2.4333 31.563 33.974 2.4666 31.541 33.932 2.5 31.557 33.934 2.5333 31.572 33.901 2.5667 31.525 33.968 2.6 31.522 33.904 2.6333 31.538 33.952 2.6666 31.538 33.948
2.7 31.568 33.949 2.7333 31.534 33.939 2.7667 31.56 33.95 2.8 31.535 33.911 2.8333 31.56 33.91 2.8666 31.554 33.894 2.9 31.604 33.972 2.9333 31.552 33.912 2.9666 31.542 33.964 3 31.534 33.927 3.0333 31.538 33.906 3.0667 31.549 33.91 3.1 31.548 33.891 3.1333 31.537 33.938 3.1666 31.56 33.938 3.2 31.543 33.908 3.2333 31.542 33.948 3.2667 31.549 33.942 3.3 31.534 33.971 3.3333 31.55 33.927 3.3666 31.547 33.943 3.4 31.51 33.925
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3.4333 31.592 33.995 3.4666 31.535 33.876 3.5 31.568 33.941 3.5333 31.511 33.951 3.5667 31.505 33.897 3.6 31.52 33.977 3.6333 31.551 33.935 3.6666 31.562 33.963 3.7 31.49 33.988 3.7333 31.54 33.987 3.7667 31.528 33.96 3.8 31.562 33.947 3.8333 31.567 33.949 3.8666 31.544 33.964 3.9 31.561 33.945 3.9333 31.552 33.957 3.9666 31.55 33.929 4 31.577 34.002 4.0333 31.522 33.936 4.0667 31.533 33.965 4.1 31.534 33.939 4.1333 31.575 33.943
4.1666 31.549 33.968 4.2 31.569 33.97 4.2333 31.548 33.963 4.2667 31.575 33.935 4.3 31.55 33.938 4.3333 31.555 34.015 4.3666 31.535 33.977 4.4 31.548 33.942 4.4333 31.565 33.957 4.4666 31.556 33.956 4.5 31.523 33.962 4.5333 31.545 33.979 4.5667 31.497 33.954 4.6 31.552 33.929 4.6333 31.556 33.947 4.6666 31.55 33.932 4.7 31.547 33.947 4.7333 31.537 33.969 4.7667 31.568 33.966 4.8 31.549 33.995 4.8333 31.552 33.948 4.8666 31.555 33.955
4.9 31.542 33.971 4.9333 31.506 33.955 4.9666 31.535 33.951 5 31.575 33.933 5.0333 31.577 33.993 5.0667 31.544 33.938 5.1 31.523 33.949 5.1333 31.54 33.998 5.1666 31.542 33.945 5.2 31.501 34.015 5.2333 31.567 33.948 5.2667 31.579 33.935 5.3 31.553 33.937 5.3333 31.538 33.971 5.3666 31.526 33.943 5.4 31.566 34.023 5.4333 31.543 33.941 5.4666 31.547 33.948 5.5 31.548 33.965 5.5333 31.546 33.968 5.5667 31.556 33.957 5.6 31.544 33.971
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5.6333 31.55 33.928 5.6666 31.547 33.912 5.7 31.564 33.957 5.7333 31.529 33.943 5.7667 31.556 33.951 5.8 31.55 33.95 5.8333 31.521 33.923 5.8666 31.524 33.954 5.9 31.545 33.926 5.9333 31.569 33.934 5.9666 31.561 33.959 6 31.544 33.939 6.0333 31.544 33.933 6.0667 31.526 33.934 6.1 31.526 33.976 6.1333 31.556 33.941 6.1666 31.552 33.951 6.2 31.541 33.987 6.2333 31.531 33.934 6.2667 31.517 33.917 6.3 31.555 33.936 6.3333 31.54 33.939
6.3666 31.546 33.934 6.4 31.563 33.96 6.4333 31.538 33.958 6.4666 31.55 33.962 6.5 31.57 34.027 6.5333 31.543 33.963 6.5667 31.551 33.935 6.6 31.561 33.987 6.6333 31.547 33.914 6.6666 31.552 33.911 6.7 31.537 33.958 6.7333 31.566 33.946 6.7667 31.557 33.939 6.8 31.569 33.943 6.8333 31.534 33.984 6.8666 31.549 33.967 6.9 31.552 33.933 6.9333 31.555 33.959 6.9666 31.554 33.958 7 31.545 33.93 7.0333 31.576 33.932 7.0667 31.567 33.977
7.1 31.529 33.954 7.1333 31.499 33.928 7.1666 31.571 33.937 7.2 31.511 33.973 7.2333 31.553 33.946 7.2667 31.551 33.962 7.3 31.533 33.957 7.3333 31.55 33.927 7.3666 31.553 33.913 7.4 31.563 33.962 7.4333 31.557 33.94 7.4666 31.545 33.97 7.5 31.549 33.989 7.5333 31.54 33.944 7.5667 31.541 33.939 7.6 31.565 34.011 7.6333 31.519 33.972 7.6666 31.538 33.954 7.7 31.537 33.948 7.7333 31.572 33.97 7.7667 31.551 33.96 7.8 31.55 33.973
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7.8333 31.558 33.922 7.8666 31.558 33.967 7.9 31.571 33.955 7.9333 31.568 33.944 7.9666 31.554 33.955 8 31.527 33.958 8.0333 31.524 33.972 8.0667 31.542 33.926 8.1 31.547 33.956 8.1333 31.544 33.961 8.1666 31.571 33.962 8.2 31.567 33.94 8.2333 31.542 33.965 8.2667 31.531 33.971 8.3 31.544 33.965 8.3333 31.545 33.947 8.3666 31.554 33.934 8.4 31.536 33.973 8.4333 31.555 33.958 8.4666 31.551 33.947 8.5 31.543 33.964 8.5333 31.543 33.91
8.5667 31.53 33.927 8.6 31.515 33.913 8.6333 31.542 33.959 8.6666 31.537 33.959 8.7 31.548 33.936 8.7333 31.558 33.961 8.7667 31.548 33.981 8.8 31.605 33.992 8.8333 31.537 33.97 8.8666 31.541 33.933 8.9 31.601 33.965 8.9333 31.534 33.968 8.9666 31.53 33.954 9 31.551 33.947 9.0333 31.554 33.944 9.0667 31.536 33.955 9.1 31.538 33.955 9.1333 31.541 33.961 9.1666 31.551 33.969 9.2 31.599 33.963 9.2333 31.539 33.95 9.2667 31.565 33.94
9.3 31.577 33.937 9.3333 31.548 33.964 9.3666 31.558 33.932 9.4 31.563 33.945 9.4333 31.556 33.957 9.4666 31.555 33.943 9.5 31.563 33.966 9.5333 31.584 33.971 9.5667 31.55 33.94 9.6 31.542 33.936 9.6333 31.515 33.942 9.6666 31.524 33.969 9.7 31.542 33.96 9.7333 31.542 33.96 9.7667 31.547 33.965 9.8 31.559 33.96 9.8333 31.548 33.91 9.8666 31.543 33.922 9.9 31.534 33.949 9.9333 31.517 33.959 9.9666 31.525 33.966 10 31.539 33.937
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Investigation 2 Table. t(s) x1(cm) y1(cm) t avg Vy(cm/s) 0.0333 31.665 36.198 0.05 -0.2994 0.0667 31.626 36.188 0.08335 -0.06006 0.1 31.621 36.186 0.11665 -0.06006 0.1333 31.611 36.184 0.14995 -0.12012 0.1666 31.623 36.18 0.1833 -0.1497 0.2 31.631 36.175 0.21665 0.45045 0.2333 31.627 36.19 0.25 -0.05988 0.2667 31.63 36.188 0.28335 0.27027 0.3 31.624 36.197 0.3167 -0.05988 0.3334 31.632 36.195 0.35005 0.3003 0.3667 31.632 36.205 0.38335 -0.54054 0.4 31.631 36.187 0.41665 1.051051 0.4333 31.612 36.222 0.45 -1.01796 0.4667 31.628 36.188 0.48335 0.09009 0.5 31.621 36.191 0.51665 -0.12012 0.5333 31.636 36.187 0.55 0.209581 0.5667 31.63 36.194 0.58335 -0.21021 0.6 31.637 36.187 0.61665 0.24024 0.6333 31.647 36.195 0.64995 0.21021 0.6666 31.645 36.202 0.6833 0.598802
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0.7 31.662 36.222 0.71665 -0.72072 0.7333 31.666 36.198 0.75 0.419162 0.7667 31.637 36.212 0.78335 -0.45045 0.8 31.633 36.197 0.8167 0.179641 0.8334 31.655 36.203 0.85005 -0.96096 0.8667 31.723 36.171 0.88335 -1.83183 0.9 31.764 36.11 0.91665 -4.17417 0.9333 31.828 35.971 0.95 -5.35928 0.9667 31.808 35.792 0.98335 -7.83784 1 31.776 35.531 1.01665 -9.90991 1.0333 31.918 35.201 1.05 -14.3114 1.0667 31.881 34.723 1.08335 -14.3544 1.1 31.956 34.245 1.11665 -13.9339 1.1333 31.983 33.781 1.14995 -20.6006 1.1666 32.291 33.095 1.1833 -12.4251 1.2 32.12 32.68 1.21665 -28.1682 1.2333 32.094 31.742 1.25 -22.2455 1.2667 32.147 30.999 1.28335 -23.7237 1.3 32.232 30.209 1.3167 -26.7964 1.3334 32.221 29.314 1.35005 -25.5255 1.3667 32.423 28.464 1.38335 -29.8799 1.4 32.49 27.469 1.41665 -32.4925
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1.4333 32.546 26.387 1.45 -35.2695 1.4667 32.587 25.209 1.48335 -30.3003 1.5 32.683 24.2 1.51665 -38.4985 1.5333 32.772 22.918 1.55 -37.6647 1.5667 32.892 21.66 1.58335 -40.2102 1.6 32.911 20.321 1.61665 -39.8498 1.6333 33.039 18.994 1.64995 -43.1832 1.6666 33.08 17.556 1.6833 -43.9521 1.7 33.222 16.088 1.71665 -46.997 1.7333 33.307 14.523 1.75 -47.3653 1.7667 33.468 12.941 1.78335 -47.3273 1.8 33.551 11.365 1.8167 -51.6766 1.8334 33.697 9.639 1.85005 -53.964 1.8667 33.795 7.842 1.88335 15.46547 1.9 33.97 8.357 1.91665 37.17718 1.9333 34.118 9.595 1.95 0 1.9667 34.118 9.595 1.98335 62.79279 2 34.54 11.686 2.01665 31.29129 2.0333 34.722 12.728 2.05 25.53892 2.0667 34.944 13.581 2.08335 26.63664 2.1 35.13 14.468 2.11665 20.54054 2.1333 35.304 15.152 2.14995 24.14414
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2.1666 35.554 15.956 2.1833 16.79641 2.2 35.731 16.517 2.21665 18.64865 2.2333 35.878 17.138 2.25 15.23952 2.2667 36.105 17.647 2.28335 13.24324 2.3 36.29 18.088 2.3167 10.71856 2.3334 36.518 18.446 2.35005 8.828829 2.3667 36.682 18.74 2.38335 7.057057 2.4 36.835 18.975 2.41665 5.165165 2.4333 37.056 19.147 2.45 2.48503 2.4667 37.202 19.23 2.48335 1.981982 2.5 37.374 19.296 2.51665 -3.75375 2.5333 37.586 19.171 2.55 -1.28743 2.5667 37.801 19.128 2.58335 -6.81682 2.6 37.955 18.901 2.61665 -7.86787 2.6333 38.149 18.639 2.64995 -9.72973 2.6666 38.302 18.315 2.6833 -11.2275 2.7 38.46 17.94 2.71665 -14.0841 2.7333 38.601 17.471 2.75 -16.5269 2.7667 38.759 16.919 2.78335 -16.006 2.8 38.903 16.386 2.8167 -19.8204 2.8334 39.084 15.724 2.85005 -22.3724 2.8667 39.213 14.979 2.88335 -20.3904
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2.9 39.337 14.3 2.91665 -28.8889 2.9333 39.466 13.338 2.95 -25.1198 2.9667 39.6 12.499 2.98335 -28.1682 3 39.701 11.561 3.01665 -29.6697 3.0333 39.829 10.573 3.05 -32.5449 3.0667 39.937 9.486 3.08335 -34.5946 3.1 40.04 8.334 3.11665 -27.3273 3.1333 40.144 7.424 3.14995 0 3.1666 40.144 7.424 3.1833 0 3.2 40.144 7.424 3.21665 0 3.2333 40.144 7.424 3.25 0 3.2667 40.144 7.424 3.28335 0 3.3 40.144 7.424 3.3167 0 3.3334 40.144 7.424 3.35005 133.0931 3.3667 40.377 11.856 3.38335 10.36036 3.4 40.369 12.201 3.41665 7.957958 3.4333 40.406 12.466 3.45 6.377246 3.4667 40.363 12.679 3.48335 4.804805 3.5 40.375 12.839 3.51665 3.423423 3.5333 40.35 12.953 3.55 1.946108 3.5667 40.341 13.018 3.58335 -2.25225 3.6 40.321 12.943 3.61665 -3.84384
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3.6333 40.265 12.815 3.64995 -5.37538 3.6666 40.212 12.636 3.6833 -5.83832 3.7 40.171 12.441 3.71665 -9.51952 3.7333 40.114 12.124 3.75 -10.2994 3.7667 40.042 11.78 3.78335 -14.0841 3.8 39.962 11.311 3.8167 -13.7126 3.8334 39.877 10.853 3.85005 -16.4264 3.8667 39.79 10.306 3.88335 -18.3183 3.9 39.721 9.696 3.91665 -21.1111 3.9333 39.607 8.993 3.95 -22.0958 3.9667 39.494 8.255 3.98335 -24.3844 4 39.379 7.443 4.01665 13.003 4.0333 39.29 7.876 4.05 0 4.0667 39.29 7.876 4.08335 28.40841 4.1 39.107 8.822 4.11665 0 4.1333 39.107 8.822 4.14995 0 4.1666 39.107 8.822 4.1833 0 4.2 39.107 8.822 4.21665 32.67267 4.2333 38.589 9.91 4.25 0 4.2667 38.589 9.91 4.28335 0 4.3 38.589 9.91 4.3167 0 4.3334 38.589 9.91 4.35005 0
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4.3667 37.993 9.91 4.38335 -5.73574 4.4 37.819 9.719 4.41665 -6.3964 4.4333 37.66 9.506 4.45 -8.47305 4.4667 37.538 9.223 4.48335 -10.991 4.5 37.348 8.857 4.51665 -11.7117 4.5333 37.141 8.467 4.55 -15.4192 4.5667 37.001 7.952 4.58335 -13.7538 4.6 36.719 7.494 4.61665 6.396396 4.6333 36.605 7.707 4.64995 9.57958 4.6666 36.443 8.026 4.6833 6.467066 4.7 36.257 8.242 4.71665 5.405405 4.7333 36.059 8.422 4.75 0 4.7667 36.059 8.422 4.78335 3.993994 4.8 35.62 8.555 4.8167 -1.16766 4.8334 35.388 8.516 4.85005 0 4.8667 35.388 8.516 4.88335 -7.02703 4.9 35.019 8.282 4.91665 -6.18619 4.9333 34.778 8.076 4.95 -9.01198 4.9667 34.597 7.775 4.98335 0 5 34.597 7.775 5.01665 -3.003 5.0333 34.133 7.675 5.05 5.688623 5.0667 33.899 7.865 5.08335 2.882883
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5.1 33.727 7.961 5.11665 1.621622 5.1333 33.537 8.015 5.14995 0 5.1666 33.537 8.015 5.1833 -3.62275 5.2 33.103 7.894 5.21665 -4.26426 5.2333 32.894 7.752 5.25 -7.27545 5.2667 32.694 7.509 5.28335 0 5.3 32.694 7.509 5.3167 6.287425 5.3334 32.28 7.719 5.35005 0.810811 5.3667 32.088 7.746 5.38335 -0.48048 5.4 31.938 7.73 5.41665 -3.18318 5.4333 31.776 7.624 5.45 -1.82635 5.4667 31.569 7.563 5.48335 0.810811 5.5 31.349 7.59 5.51665 0 5.5333 31.349 7.59 5.55 0.628743 5.5667 31.059 7.611 5.58335 -2.46246 5.6 30.868 7.529 5.61665 0 5.6333 30.868 7.529 5.64995 0.720721 5.6666 30.524 7.553 5.6833 -2.60479 5.7 30.351 7.466 5.71665 1.411411 5.7333 30.208 7.513 5.75 -0.8982 5.7667 30.058 7.483 5.78335 0.39039 5.8 29.882 7.496 5.8167 0
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5.8334 29.882 7.496 5.85005 -1.44144 5.8667 29.493 7.448 5.88335 1.141141 5.9 29.416 7.486 5.91665 1.741742 5.9333 29.245 7.544 5.95 -0.71856 5.9667 29.116 7.52 5.98335 -0.51051 6 28.992 7.503 6.01665 -0.21021 6.0333 28.81 7.496 6.05 0.02994 6.0667 28.692 7.497 6.08335 0.03003 6.1 28.562 7.498 6.11665 -0.03003 6.1333 28.451 7.497 6.14995 -0.03003 6.1666 28.297 7.496 6.1833 0 6.2 28.297 7.496 6.21665 -0.21021 6.2333 28.04 7.489 6.25 1.766467 6.2667 27.961 7.548 6.28335 0 6.3 27.961 7.548 6.3167 0 6.3334 27.961 7.548 6.35005 0 6.3667 27.961 7.548 6.38335 0.810811 6.4 27.488 7.575 6.41665 -1.59159 6.4333 27.392 7.522 6.45 1.377246 6.4667 27.326 7.568 6.48335 0 6.5 27.326 7.568 6.51665 -0.63063 6.5333 27.139 7.547 6.55 0
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6.5667 27.139 7.547 6.58335 0 6.6 27.139 7.547 6.61665 0.33033 6.6333 26.837 7.558 6.64995 0 6.6666 26.837 7.558 6.6833 0 6.7 26.837 7.558 6.71665 0 6.7333 26.837 7.558 6.75 0 6.7667 26.837 7.558 6.78335 0 6.8 26.837 7.558 6.8167 0.479042 6.8334 26.319 7.574 6.85005 0 6.8667 26.319 7.574 6.88335 0 6.9 26.319 7.574 6.91665 0 6.9333 26.319 7.574 6.95 -0.95808 6.9667 25.925 7.542 6.98335 1.231231 7 25.847 7.583 7.01665 0 7.0333 25.847 7.583 7.05 0 7.0667 25.847 7.583 7.08335 0 7.1 25.847 7.583 7.11665 0 7.1333 25.847 7.583 7.14995 0 7.1666 25.847 7.583 7.1833 0 7.2 25.847 7.583 7.21665 0 7.2333 25.847 7.583 7.25 0 7.2667 25.847 7.583 7.28335 0
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7.3 25.847 7.583 7.3167 0 7.3334 25.847 7.583 7.35005 0 7.3667 25.847 7.583 7.38335 0 7.4 25.847 7.583 7.41665 0 7.4333 25.847 7.583 7.45 0 7.4667 25.847 7.583 7.48335 0 7.5 25.847 7.583 Investigation 3 Table x1(cm) y1(cm) t avg (s) Vx (cm/s) dVx Vy (cm/s) dVy 6.183 7.493 1.0166 -2.01807 0.248591 0.722892 0.394733 6.116 7.517 1.04995 -0.92537 0.895522 6.085 7.547 1.0833 -3.07229 0.331325 5.983 7.558 1.1166 -2.33533 0.568862 5.905 7.577 1.1499 -2.95181 3.012048 5.807 7.677 1.18325 -2.38806 2.567164 5.727 7.763 1.2166 -1.92771 2.710843 5.663 7.853 1.2499 1.976048 0.958084 5.729 7.885 1.2832 -1.86747 -0.03012 5.667 7.884 1.31655 -1.97015 1.701493 5.601 7.941 1.35 -0.41916 -0.02994
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5.587 7.94 1.3833 -0.60241 1.084337 5.567 7.976 1.4166 0.08982 8.113772 5.57 8.247 1.44995 5.705706 20.33033 5.76 8.924 1.4833 7.125749 22.63473 5.998 9.68 1.5166 5.993976 32.83133 6.197 10.77 1.54995 11.28358 47.8806 6.575 12.374 1.5833 17.43976 63.28313 7.154 14.475 1.6166 20.62874 64.19162 7.843 16.619 1.6499 21.80723 59.87952 8.567 18.607 1.68325 22.26866 57.61194 9.313 20.537 1.7166 22.8012 54.60843 10.07 22.35 1.7499 23.62275 53.56287 10.859 24.139 1.7832 19.81928 54.63855 11.517 25.953 1.81655 17.70149 50.29851 12.11 27.638 1.85 18.11377 51.97605 12.715 29.374 1.8833 17.16867 44.18675 13.285 30.841 1.9166 19.4012 49.46108 13.933 32.493 1.94995 18.01802 44.56456 14.533 33.977 1.9833 17.72455 43.89222 15.125 35.443 2.0166 19.36747 40.1506 15.768 36.776 2.04995 16.53731 39.34328 16.322 38.094 2.0833 15.90361 37.43976
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16.85 39.337 2.1166 19.4012 36.88623 17.498 40.569 2.1499 15.66265 33.64458 18.018 41.686 2.18325 0 0 18.018 41.686 2.2166 0 0 18.018 41.686 2.2499 0 0 18.018 41.686 2.2832 0 0 18.018 41.686 2.31655 0 0 18.018 41.686 2.35 0 0 18.018 41.686 2.3833 0 0 18.018 41.686 2.4166 0 0 18.018 41.686 2.44995 0 0 18.018 41.686 2.4833 0 0 18.018 41.686 2.5166 0 0 18.018 41.686 2.54995 0 0 18.018 41.686 2.5833 0 0 18.018 41.686 2.6166 0 0 18.018 41.686 2.6499 0 0 18.018 41.686 2.68325 0 0 18.018 41.686 2.7166 0 0 18.018 41.686 2.7499 0 0 18.018 41.686 2.7832 0 0 18.018 41.686 2.81655 0 0
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18.018 41.686 2.85 0 0 18.018 41.686 2.8833 0 0 18.018 41.686 2.9166 0 0 18.018 41.686 2.94995 0 0 18.018 41.686 2.9833 0 0 18.018 41.686 3.0166 0 0 18.018 41.686 3.04995 493.7612 180.597 34.559 47.736 3.0833 17.92169 -19.6988 35.154 47.082 3.1166 18.11377 -20.3593 35.759 46.402 3.1499 19.09639 -24.759 36.393 45.58 3.18325 20.86567 -28.3582 37.092 44.63 3.2166 17.92169 -26.3855 37.687 43.754 3.2499 18.9521 -30.0898 38.32 42.749 3.2832 21.80723 -35.6325 39.044 41.566 3.31655 17.16418 -31.8209 39.619 40.5 3.35 20.86826 -37.1257 40.316 39.26 3.3833 18.88554 -37.0181 40.943 38.031 3.4166 19.91018 -40.2994 41.608 36.685 3.44995 18.4985 -40.5405 42.224 35.335 3.4833 20.11976 -44.8503 42.896 33.837 3.5166 20.84337 -45.3313 43.588 32.332 3.54995 19.10448 -47.9403
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44.228 30.726 3.5833 18.8253 -48.1325 44.853 29.128 3.6166 19.79042 -50.6287 45.514 27.437 3.6499 19.87952 -51.1145 46.174 25.74 3.68325 20.77612 -56.3284 46.87 23.853 3.7166 18.70482 -54.8795 47.491 22.031 3.7499 20.83832 -60.479 48.187 20.011 3.7832 16.56627 -52.8012 48.737 18.258 3.81655 17.67164 -60.8955 49.329 16.218 3.85 21.01796 -68.2036 50.031 13.94 3.8833 21.4759 -57.9217 50.744 12.017 3.9166 19.64072 -65.0599 51.4 9.844 3.94995 20.42042 -57.0871 52.08 7.943 3.9833 13.20359 52.39521 52.521 9.693 4.0166 14.96988 43.5241 53.018 11.138 4.04995 13.40299 41.70149 53.467 12.535 4.0833 13.76506 38.28313 53.924 13.806 4.1166 12.45509 41.52695 54.34 15.193 4.1499 12.86145 38.94578 54.767 16.486 4.18325 14.14925 37.8209 55.241 17.753 4.2166 14.63855 34.15663 55.727 18.887 4.2499 13.41317 32.30539 56.175 19.966 4.2832 13.91566 28.61446
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56.637 20.916 4.31655 14.20896 26.14925 57.113 21.792 4.35 11.70659 24.91018 57.504 22.624 4.3833 12.43976 24.30723 57.917 23.431 4.4166 11.46707 21.28743 58.3 24.142 4.44995 10.84084 21.41141 58.661 24.855 4.4833 11.0479 16.67665 59.03 25.412 4.5166 11.68675 15.90361 59.418 25.94 4.54995 12.92537 11.46269 59.851 26.324 4.5833 5.783133 13.31325 60.043 26.766 4.6166 -8.86228 11.52695 59.747 27.151
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