1-Oct-2014: Potential Energy of Spring cart

Purpose:
The purpose of this lab was to determine the relationship between the work and change in kinetic energy of a cart attached to a spring.

Apparatus:
The apparatus, as pictured below, consists of a track, a cart, a spring, a motion sensor, and a force sensor. Two wooden blocks were added onto the cart in order to increases its mass, also another wooden block was placed under the spring to increase the data's accuracy.

Experiment:
In order to begin the experiment we first had to open logger pro on the laptop and setup the force and motion sensors so that the data could be digitally recorded on the program. Once completed we proceeded to conduct the actual experiment by moving the cart a good distance so that the spring was extended to an effective length. An effective length would be one that could record a decent change in the potential energy of the spring without causing the cart to accelerate at a speed that could cause the data to be unreliable and/or damage the apparatus when the cart is released. Once found the cart was then stretched to that position and let go. As a result a force vs. position graph was constructed by logger pro depicting the amount of force experience at each position.

The next step requires the construction of a kinetic energy vs position graph using the data recorded by logger pro. By creating a "New Calculated Column" and using the data recorded, the computer was able to compute values for kinetic energy:

KE = 1/2 * mass * velocity^2

Once the two graphs were constructed we proceeded to determine the relationship between the work done and the amount of kinetic energy at each position. By finding the area of the work graph between two defined position point we were able to find the total amount of work done from one point to another. We compared these values with the amount of kinetic energy at each point and observed that the values were very similar

Conclusion:
As seen in the graphs above our values for work and kinetic energy are slightly off but there are entities that can effect the values retrieved from this experiment the first being the looseness spring which caused a friction effect between it and the wooden placed below it. Second are our values for the mass of the cart because we do not have and exact value, only an estimated one which can slightly effect our value for kinetic energy. Disregarding the errors it is clear that the work done by is system is equal to the kinetic energy it sustains.