October 1 2014: Finding the kinetic energy of a cart being pulled by a spring system

Purpose: To find the work done  by the spring on the cart during the execution of the experiment.

This is the spring-cart system that we used to perform our lab. There is a motion sensor on one the ends to calculate the data needed to create a graph of this system. Attached to the string there is also a force sensor to calculate the force which the spring in pulling the cart.

Explanation: We are going to calibrate the force sensor, so that the data obtained is more accurate. From that, we are going to pull the cart with certain force and release it. This will allow the force sensor and the motion sensor to calculate our data information such as force, position, time, velocity, etc... By using the graphs that the computer will give us, we plan to the graph force vs. position and calculate random areas to know the work done by the spring on the cart.

This is the data table for our graph, it contains information such as Force, time, position, velocity, and kinetic energy.

These are the graphs that we got when performing the experiment. The first graph is position vs. time, the second is velocity vs. time, and the third is Force(blue) and Kinetic Energy(purple) vs. time.

This is the 1st area that we calculated the integration to find the work done, it gave us a value of  0.79m*N

This is the 2nd area for the integration, it gave us  0.896m*N.

This is the 3rd area for integration, it gave us 0.625m*N.

 This picture is a hand-made drawing by the professor to explain how the system should work. Our experimentation was similar to the one expected.

This is an expectation of what the graph Force and Kinetic Energy vs Position should look like. The fact that our  sensor had reference to the opposite way made our graph have the Force reaching zero as the position increased, but the integration gave us a good expectation for the work done, it did not affect the process at all.

Summary: First we created a system where the cart could be dragged by the string force without any problems. Then we calibrated the force sensor, so that our graphs would be accurate. We then, perform the experiment, letting the cart go from a certain distance and have the spring force drag the cart. With the force and motion sensor in position, they provided us data information from which graph could be generated. By analyzing the graphs, specifically the Force and Kinetic Energy vs Position graph, we were able to find the area of the graph at random points to calculate the work done by the spring on the cart at specific positions.