Purpose
To find the length of static string needed to get a falling weight connected to an elastic string to fall within a certain range. Additionally, considering most other people's failures with the testing, describe a reason as to why this occurred.
Theory
For the lab, we are given a set of variables that are to be determined by Mr. Bowman prior to the lab testing. For the setup, a mass connected to an elastic cord of a length of our choosing -- which in turn is connected to a hanging static string, is dropped.
The lab follows suit by using the idea of Energy Conversion, as the mass goes from a set amount of total Potential energy before the drop to a state of complete Elastic energy at the very bottom of the drop. Using this idea, we can derive an equation for normal terms.
Additionally, as seen in the Data section below in the image, we are able to set equal the distances of the strings before & after the drop, giving another equation to derive.
Finally, to find the value for k, we can use Hooke's Law to make a relationship between the force of the elastic string being stretched and the distance at the corresponding area to find k using k = F/x.
The lab follows suit by using the idea of Energy Conversion, as the mass goes from a set amount of total Potential energy before the drop to a state of complete Elastic energy at the very bottom of the drop. Using this idea, we can derive an equation for normal terms.
Additionally, as seen in the Data section below in the image, we are able to set equal the distances of the strings before & after the drop, giving another equation to derive.
Finally, to find the value for k, we can use Hooke's Law to make a relationship between the force of the elastic string being stretched and the distance at the corresponding area to find k using k = F/x.
Experimental Technique
~ Draw out the problem
~ Derive the equations and set equal to the length of the static string (s)
~ Stretch string to remove any error of changing values for k
~ Find relation of Force (F) and distance (x) by using DataStudio force sensor for stretching string
~ Graph results in form of F/x to find value for k
~ Solve equation with parameters of values set by Bowman
~ Derive the equations and set equal to the length of the static string (s)
~ Stretch string to remove any error of changing values for k
~ Find relation of Force (F) and distance (x) by using DataStudio force sensor for stretching string
~ Graph results in form of F/x to find value for k
~ Solve equation with parameters of values set by Bowman
Data & Graph
DataStudio graph of F/x, data taken and used in Excel
Excel graphs of data for k1 (left) & k2 (right), respectively. For purposes, k1 is the correct value while k2 is the incorrect one.
Analysis
To left side, variables controlled & decided on by Bowman on day of testing. In middle, drawn data and original & derived equations for the experiment. To right, list of values of F and x for the graph in Data section.
Conclusion & Why It's Incorrect
Looking at the 2 values I had given k, it may come to wonder as to why the higher value of k is the correct one. Well, it all has to do with the form of Hooke's Law. Hooke's Law, as stated, is F = kx, the equation that was used to find k in the graph. If we look at the graph to the right, we can see why this is false.
This graph shows the correct value for k with the black line, while the red line is for the incorrect value. While we can see that the line is relatively straight for the first 4 values in the graph, the values begin to increase as it gets to the 5th and 6th. So what does this mean? It means that the value of k isn't constant. As more and more force is put on the string, the value of k increases, making the relation of it being more quadratic than linear, thus making the linear form of k = F/x incorrect. Using the correct k constant, I got my mass to drop in the 5 range, making my experiment a success. However, for Bowman's drop where he only got into the 2 range, judging by how the data went, his drop most likely did not drop low enough and landed above the intended mark. Overall, this was a success. |