# Data Analysis

Determining Energy Loss

The ball's bounces become smaller as time goes on and the ball eventually stops moving. This is because the ball is lossing energy to its surroundings (the floor and air). Let's determine how much energy the ball as at the peak of each of its bounces (including when it is at its peak at t=0.0s) and examine how much energy is loss with each bounce.

Deliverable #6: Turn in a plot of bounce number of the x-axis and energy on the y-axis. Submit a short analysis of how much energy is loss due to air resistance and impact with the floor. The y-axis should be scaled such that 1.0 is the energy of the ball at t = 0.0s. There should be four plots on the graph: the average of the Arduino runs (or the best one, your call), the manual object detection with Logger Pro, and the automated object detection without machine learning. Make sure your graph includes a legend.

Determining the "Spring Constant" of the Ball

Note: the following may be difficult to accomplish. You may consider taking a second video to analyze of just the ball on the final few centimeters of its descent at the highest frame rate you have available (slow motion equates to a high frame rate). If you are unable to get a sastifactory answer for this part, write a short analysis as to how the experimental design could be changed to achieve this. You could also try to tune "k" in the numerical model to make the experimental data and report the value(s) from this process.

When the ball is registering as closer to the ground than either (A) its radius if you are measuring from the center or (B) its diameter if you are measuring from the top of the ball, then the ball is being compressed due to its impact with the ground. Using this data we should be able to extract the "spring constant" of the ball described in Section 7.5 of Elementary Mechanics with Python (linked in the Theoretical Modeling section).

Do this with as many of the data sets as it seems feasible to do so and update the numerical model to the average of these experimental spring constants.

Deliverable #7: Report the process used to extract the spring constants and the spring constants from the different data sets. Submit an updated version of the graph from the Theoretical Modeling section with the new k value.

Determining g (the Near Earth Gravitational Constant)

When the y-position is plotted as a function of time, we should be able to extract the gravitational constant, g, from our data. For each bounce of your data set, use a curve fitting function to extract an approximation of g. Average all of the approximations to find the experimental g for each data set. For the Arduino data set, average all of the g predictions together and provide an average and standard deviation.

Deliverable #8: Create a bar graph or line plot with the experiment name on the x-axis and the percent error on the experimental g on the y-axis. Provide a short analysis of your results.