Title: Finding the Stopping Distance of An Elephant
Name: Ray Arellano
Lab Partners: David Hwang & Jesus Hernandez
Date: 3/8/17
This lab consisted of finding the distance it took for an elephant riding frictionless roller skates to stop. The elephant rode down a hill and rolled on a flat surface for a certain amount of time. Attached to the elephant was a rocket that provided a force in the direction opposite of the elephant's motion; this helped stop the elephant.
This problem could be done using calculus. Given to us were the equations for the mass of the elephant and the elephant's acceleration. The acceleration function could be integrated to find the velocity function, and the velocity function could be integrated to calculate the position function. Setting the velocity function equal to zero in order to find the time it took for the elephant to stop could help. This time, t, could be used in the position function so that we can calculate the distance it took for the elephant to stop. When functions are easy to integrate, problems like these are easy to solve. However, the acceleration functions might not always be simple to integrate. In cases like those, it is useful to use a spreadsheet in order to calculate what we solved for numerically.
This image shows how the spreadsheet was used to calculate the information we want numerically. The approach here was to use a set of formulas that would provide information about the elephant's motion during each time interval.
This image shows that when t= 19.7 seconds, the elephant reached the farthest distance it was going to go. The value given in the spreadsheet agrees with the answers Professor Wolf derived analytically.
Sometimes it is not that difficult to calculate the stopping distance, or when an object stops with some given equations. One could use calculus to find the answers needed. However, it is somewhat difficult to do this when the integration process involves tedious work. Therefore, it's worth knowing that these same answers could be derived numerically.
Initially, my group struggled to develop the appropriate equations to put into the cells. If it weren't for the guidance provided to us by our instructor, our calculations would not have matched the analytic results.
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