PES 1160 Data Analysis Report

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University of Colorado, Colorado Springs *

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1160

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Statistics

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Feb 20, 2024

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UNIVERSITY OF COLORADO – COLORADO SPRINGS Data Analysis Name: Braden Baker Lab Partners name: Benjamin Keyston Objective The goal of this lab is to understand the relationships between distance, velocity and acceleration. To interpret the meaning within graphs of distance, velocity and acceleration vs. time. To analyze the motion of a student walking across the room using the graphical information collected. Uncertainty will be explored as well as the methods needed to find the uncertainty in a calculated result. To apply statistical analysis to a series of identical measurements in an attempt to discern a value for the uncertainty of an experimental result and to narrow in on its source of error. Data and Calculations Part I: Position vs. Time Graph Matching Position #1

P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I +  Describe how you had to walk to reproduce each section of this graph. To yield these results on the graph, we simply had to sit still in front of the device.  Are your graphs different than the target graphs you had to reproduce? Why? Our graphs are ever so slightly different from the target graphs due to our slight movement during the testing. Position #2  Describe how you had to walk to reproduce each section of this graph. To yield these results, we had to start close to the device, move further away, then move closer.  Why are your graphs different than the target graphs you had to reproduce? The difference in graphs was mostly due to the amount of space we had to work with, and replicating the exact position was near impossible without hitting a wall or table to prevent the replicated movement. Data Analysis - 2

P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I Position #3  Describe how you had to walk to reproduce each section of this graph. For this graph, we had to move further away rather quickly, wait, then slowly move back, until we came to a stop.  Why are your graphs different than the target graphs you had to reproduce? Our graph is different due to a lack of space. Near the end, we reached the table, and the device could not properly pick up our position due to how close we were to it. Data Analysis - 3

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P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I Part II: Velocity vs. Time Graph Matching Velocity #1  Describe how you walked for each of the graphs that you matched. To create our graph, we had to constantly move away from the device, and maintain a speed whilst doing so.  Why are your graphs different than the target graphs you had to reproduce? This one was rather difficult to recreate, as maintaining an exact constant speed was difficult with our limited space. Data Analysis - 4

P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I Velocity #2  Describe how you walked for each of the graphs that you matched. To create this graph, we had to slowly move away from the device, then closer, then back away.  Why are your graphs different than the target graphs you had to reproduce? We were able to generally follow the line of the path, but it was quite difficult to create the intended arc of the graph. Data Analysis - 5

P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I Velocity #3  Describe how you walked for each of the graphs that you matched. For this one, we had to slowly accelerate away from the device.  Are your graphs different than the target graphs you had to reproduce? Why? There is a point where when we reached too far or too close to the device, it wouldn’t read our position consistently, so we had to replicate our initial planned movement extremely slowly to create the graph. Data Analysis - 6

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P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I Velocity #4  Describe how you walked for each of the graphs that you matched. To create this graph, we had to start close to the device, quickly move away, then slowly accelerate back towards the device.  Why are your graphs different than the target graphs you had to reproduce? This one was by far the most difficult one to create, as moving away to the exact distance where the device would still detect our movement then immediately accelerating back without reaching the device proved practically impossible. Part III: Ball Drop Data Analysis - 7

P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I 1.) Describe how your histogram graph compares to the theoretical gaussian distribution. What would you need to take to get a smoother distribution? 2.) Calculate the mean of your data set. The mean is 0.36, rounded to the hundredth. Data Analysis - 8

P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I To reach the mean of the data set, I added together all the values, then divided the total by the amount of values I put in. (Sum of the 19 values was 6.82, divided that by 19.) 3.) Using the mean and the table below calculate the standard deviation (  ). So, the standard deviation would be .06214. Data Analysis - 9 Trial # (i) Time (sec.) deviation ( δx i = x i - { ¯ x ¿ ) (  x i ) 2 1 .37 .1 .01 2 .41 .5 .25 3 .36 0 .0 4 .35 .1 .01 5 .36 0 .0 6 .39 .3 .09 7 .39 .3 .09 8 .41 .5 .25 9 .34 .2 .04 10 .47 .11 .0121 11 .37 .1 .01 12 .38 .2 .04 13 .39 .3 .09 14 .36 0 .0 15 .34 .2 .04 Sum total = 0.932 1

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P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I I have just started calculus, so I had to look this one up. I used these steps. Results and Questions Part I: Position vs. Time Graph Matching 1.) Explain the meaning of the slope of a position vs . time graph. Include a discussion of positive and negative slope. Data Analysis - 10

P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I A position graph essentially displays movement. A positive slope implies movement away, and a negative slope implies movement towards. 2.) What type of motion is occurring when the slope of a position vs . time graph is; a.) zero? No movement. b.) constant? No movement. c.) changing? Movement, either away or towards the device. 3.) What parts of the graph were easier to match? Why? The fact that the graphs slopes represent movement make it relatively easy to determine when the user was moving, and how they were moving. Movement is easily noticed via slopes. 4.) What parts of the graph were the hardest to match? Why? The difficulty in determining the movement is simply which way the person was travelling. The graph states position in decimals, so it may be difficult to interpret which way the movement is for someone without the context. Part II: Velocity vs. Time Graph Matching 1.) What is the difference between the parts of the graph with positive slope and the parts with negative slope? For the velocity graphs, it displayed how if we are moving away, it has a positive slope, and if we are moving closer, it has a negative slope. 2.) What type of motion is occurring when the slope of a velocity vs . time graph is not zero? Data Analysis - 11

P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I Velocity measures displacement. When the graph is not constant at 0, no velocity is detected by the device. Therefor, when the graph is not at 0, it is detecting movement of some sort. 3.) Explain the motion during the time when the slope of a velocity vs . time graph is zero? (a horizontal line) When the velocity is at zero, that means there isn’t any movement detected from the device. (No motion.) Part III: Ball Drop 1.) Does simply increasing the amount of data result in an increase in accuracy? Think back to the two types of uncertainty, Random and Systematic. While more data generally makes the data more thorough, more data also creates more possibilities for outliers. There is a point where more data doesn’t prove or disprove anything, as the rest of the data is proving the same result. 2.) Looking at the histogram plot you made earlier. How would this help you determine if a new measurement was valid or should be thrown out? Think about  . Any value that differentiates from the mean by more than .20 is probably an outlier, as many things can interfere with the correct timing. Seeing that one spot of data is far different from the others on the histogram makes it quite clear that that value probably isn’t relevant. 3.) Discuss problems and sources of error involved with the ball drop measurement and how they can be minimized. With our available materials, there wasn’t much to improve the accuracy other than to simply disregard outliers. Realistically however, the experiment could be made much more accurate by recording the ball drops, and looking at timestamps in the recording to find the exact moments the ball began and stopped moving. Data Analysis - 12

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P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I 4.) Can you use the consistency of your measurements to determine if an outlying measurement is suspicious? Yes. Any result greater than .5 or less than .2 was likely created due to a mistake. Conclusion (later in life this is what your boss will look at first!) Delete all this information in favor of you own discussion. Meant for guidance ONLY!  This closing paragraph is where it is appropriate to conclude and express your opinions about the results of the experiment and all its parts. Only the final result(s) needs to be restated. Since this is your first lab I will give you some extra guidance. Graph Matching:  Comment on your general impressions on your results of the position vs. time and velocity vs. time graphs. Include your impressions about their accuracy and limitations and how they affected your results. Ball Drop:  What are your final impressions of the ball drop experiment, particularly on the experimental method and any problems with the results?  How would you improve the process to gain better results?  Calculating the mean is time consuming, but what are its advantages? Data Analysis - 13

P E S 1 1 6 0 - A D V A N C E D P H Y S I C S L A B I In conclusion, our experiment helped us understand motion using graphs. The ball drop method was effective, but it could be made more accurate with automated tools. Even though calculating the mean takes time, creates a reliable average, and makes outliers more apparent. Overall, this lab covered the display of movement and velocity, highlighting the importance of accuracy for future experiments. Data Analysis - 14

PES 1160 Data Analysis Report

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