Kinetic Energy and Spring Relationships

Purpose: The purpose of the lab was to find the work done by the spring-cart system by using the kinetic energy and force with the position of the cart.

Procedure: The lab consisted of a spring attached to a force sensor and a cart on top of a track. On the other side of the track there is a motion sensor that measure position of the cart on the track. First, we calibrated the force sensor so that we could get accurate readings. Then we moved the cart a certain position back so that when we let go so that we could gather data and plot the data into graphs. Then we would find the area under the graphs in order to get the work.

Below is the set up of how the experiment looked like.

Below is a picture of how the force sensor looked like. 

Below is a picture of how the motion sensor looked like.

Data: All the data was input into Logger Pro in order to get the graphs.

Below is the chart for the different types of data we recorded. It has the force, position, velocity, acceleration an kinetic energy which was a calculated column, meaning that we used different values to come up with the kinetic energy column.

Below are the graphs of position vs time, velocity vs time and force and kinetic energy vs time. We mainly focused on the force and kinetic energy vs time for it was the one that we used to calculate work.

Calculations: In order to find the work done we had to take the integral from a certain point on the graph to the other.

Below is one of the integrals taken of the force and kinetic energy vs position in order to find work. The value was 0.896 Nm.

The next graph is another area of integration which was 0.790 Nm.

The last graph shows the last integral we did for the graph. The value was 0.625 Nm.

Below are just instructions on what the professor expected us to do in the lab.

Summary: Overall the lab was a success because we were able to get a result for the force by integrating the force vs position portion of the graph. Since the work-kinetic energy theorem states that the change in kinetic energy is equal work and the values we got for both were about the same, the lab proved to be successful. The only thing that was weird was the position of the graphs because they were supposed to look like they were increasing but we did not inverse the position and it made the graphs look like the inverse of what they were supposed to be.