10/2/2014 Work-Energy Theorem

Purpose:
Today we looked at the Work-Energy Theorem which is the work is equal to the total kinetic energy.

Experiment:
We are going to attempt to show this relationship in our lab by taking a spring attached to a rolling cart  and attached to force sensor on the other side of the spring and start the car at rest to zero the distance of our motion detector. We also had to make sure our force sensor was zeroed and was measuring close to a known mass. So now we have a cart attached to a spring at rest pointing to location zero. We then stretch the spring out and hold the cart in position and tell our motion sensor that towards the resting position which is zero is our positive axis. So the cart is pulled away from the resting position show an increase of distance not a negative distance. We pull the cart back again turn on the sensor to collect data and let the cart go.

Here is a picture of our setup.

Calculations:

 Now we have all the data collected into our logger pro program from our motion sensor and force sensor we have force, time, position, and velocity, so all we need now is the Kinetic Energy which we add a calculated variable into logger pro using the formula KE = (mv^2)/2. Which our kinetic energy now calculated we plot a graph with kinetic force vs position and also plot a separate graph on the same graph for kinetic energy. We then select a portion of our graph for force vs position to get the area by using the integral of the selected portion of our graph which should give us the the same kinetic energy for the same time. It is no perfect but we feel our data is has a reasonable error.

Results:
Here is our graph red is force vs position and purple is kinetic energy. You can also see our integral compared to the kinetic energy for that time.