Lab 11 Work-Kinetric Energy Theorem Activity

Student: Xavier Lomeli
Partners: Matthew Ibarra, Billy Justin
Date of Lab: 5 October 2016 

Lab 11 Work-Kinetric Energy Theorem Activity

Mission Statement:To determine the relationship between kinetic energy and work done. .

Theory: Every kind of calculation is in truth an approximation, and the tolerance of uncertainty depends on the application the calculation will be for. When multiple calculations are involved, then the uncertainty ripples, or propagates, through to the final result. Learning the method by which this kind of propagated uncertainty is determined is the essence of this lab.
Experimental Procedure: This experiment actually consists of three different experiments, listed below, using the apparatus shown below.

Experiment 1: For the first segment, we measured the work done by stretching a spring accross a measured distance. We collected data for the force applied by a stretched spring verses the distance the spring is stretched an approximate distance of 0.6 meters, calculating the work done by finding  the area under the force v. distance graph, shown below. 

From our graph, we were able to identify
(a) our spring constant, which we  from the slope of the curve-fit line, here shown to be 5.794 Newtons/meter, which is reasonable.
(b) the work done, obtained through the integration routine of our function, which returned the result of 0.6455 Newtons*meter, or 0.6455 Joules.
Experiment 2

For the second experiment,  we weighed the cart, and then inputted the kinetic energy formula into our file. Conducting the experiment again, we obtained the graph below.

From the above graph, we determined that, from the 0.17 meter mark to 0.51 meter mark, the total work done was equal to 0.6316 Joules while the change in kinetic energy (shown in the above graph as the point corresponding to the 0.17 mark) was recorded as 0.825 Joules, which is just under 25% higher than the supposed work done. We proceeded to find the corresponding values of work and kinetic energy for two other position intervals, shown below.

For the above interval from x = 0.311 to x = 0.51, the work done is  0.4491 Joules and the kinetic energy is 0.595 Joules, which shows that our value for kinetic energy is 26.1 % higher than our work value. 

From the above interval from x = 0.420 to x = 0.51, the work done is  0.2323 Joules and the kinetic energy is 0.294 Joules, which shows that our value for kinetic energy is 21.2 % higher than our work value.
Below is a table of our collected data. 

Conclusion- The very significant percent difference between our work and kinetic energy likely has to do with inadequacies in our setup and/or equipment. Furthermore, we were supposed to stretch the spring by 60 cm, which we perhaps slightly overshot or undercut. Nevertheless, for our three different intervals, the percent difference stayed approximately consistent in the mid-twenties.
Regardless, what was supposed to happen is to show how the work done by the cart and spring system is equal to the change in kinetic energy of the cart and spring system.