October 5th, 2016: LAB 11: Work-KE Theorem Activity

Michell Kuang
Lab Partners: Charles, Anthony
Date performed: 10/05/16

Our goal in this experiment is to understand how work and kinetic energy relate to help explain the work-kinetic energy theorem. To do this, we measured the work done while stretching a spring to a specific distance (about 0.6m) on a track. On the track we have a cart with which we pulled the spring. A white square is attached to the cart magnetically so that the force sensor can more easily detect the motion. In addition, we placed a book under the spring so that we could lay it out flat and make sure that it was unstretched.

Setup of cart and track with which we stretched spring; force sensor on one end

We first had to calibrate the force sensor to 4.9N. Then, we had to zero the force sensor so we could set an initial "x=0" position. With the force sensor connected to a laptop, we collected data on Logger Pro. This produced a graph of force vs. position. To determine the spring constant of our spring, we did a linear fit on the resultant graph, and our spring constant came out to be 29.39 N/m. To find the work done, we used the integration routine function on Logger Pro. Our work done was 2.755 Nm.

Logger Pro view: Graph of force vs. position

For the second part of the experiment, we did the same thing again by pulling the cart along the track, but this time we created a column on Logger Pro to calculate the kinetic energy of the cart. We first had to measure the mass of the cart, which was 0.714kg. Then, using the same spring (so we could use the same spring constant that we calculated in the first part), we again pulled the cart a distance of 0.6m. This time, we made a graph of both force vs. position and kinetic energy vs. position.

Logger Pro view: Graphs of force vs. position and kinetic energy vs. position

Automatically, the kinetic energy vs. position graph should have a data box that tells us the kinetic energy at any point on the graph. Using this, we found the kinetic energy for a few different positions, and then found the corresponding work done at that same position. Once again, we used the integration routine function to determine that. We picked four points, and recorded this data onto an excel sheet.

Excel sheet of work and kinetic energy at certain positions

If done right, the experiment should produce values for work and kinetic energy that are almost the same. Our values are fairly similar. One definite source of error in our lab was that we didn't read the manual carefully, and ended up switching our springs because our first one was difficult to work with. As you can see in my lab's third image, we got a different spring constant doing the experiment the second time around (the slope from the linear fit). Another reason for the discrepancy in our values may be that we didn't calibrate or zero the force sensor correctly. 

All in all, our lab was more or less successful. One can see that work and kinetic energy are definitely related. Since energy cannot be created nor destroyed, the work done on an object converts energy from one kind to another. Initially, all the energy in the spring is elastic potential energy. Then, when we pull the spring, kinetic energy increases (is gained) an amount equal to the work done.