6-April-2015: Work-Kinetic Energy Theorem Activity

Purpose: To measure the work done when one stretches a spring through a measured distance.

First we set up a ramp with a cart, motion detector, force probe and a spring shown below.

The force probe was actually put on after this picture. It was set on the bar and attached to the spring to measure the force of the spring. 

We then opened LoggerPro zeroed the probe and motion detector, a verifying motion was in "reverse direction" so that we could find the slope of a positive graph that represented F against distance. 

To collect data, we stretched out the cart and starting taking data as soon as we let go. After receiving the distance and force data from the probes, we created a graph of Force times distance.

We then graphed Kinetic Energy versus position by finding the mass and plotting (1/2)m"velocity"^2. 

We then put both graphs onto the same graph as shown in the examples below:

As one can see, next we took the integral of the Force times Position graph, which equals the work done by the cart. When compared to the kinetic energy of the KE graph at the end of the increment, one can see in the multiple examples above that the kinetic energy and work are the same but inverse of each other. 

Part 2: 

After looking at a Force vs. Stretch of the rubber band (m) i.e. position graph of a machine, we found the work under the graph to be closely related the kinetic energy calculation. The readings varied with the graph so that our estimated calculations of the area under the integral were off of the real value of kinetic energy.