Physics 4A (5/10/16)
Work and kinetic Energy
Brett Mccausland
Lab Partners: Luis Diaz, Bimaya Jayaratne
Purpose
Calculate experimentally kinetic energy and work by a non constant spring force, and model the relationship between work and kinetic energy.
Procedure Experiment 1
As seen in the apparatus we placed a steel cart on a steel track and attached a force sensor to the top of it as well as a plate. we attached steel bar to the end of the table with a clamp and attached a spring which we also attached to the force sensor and placed a motion sensor at the opposite side of the track. We zeroed are instruments at the point where the cart sat with no tension in the spring. We connected all are instruments to logger pro . We wanted to find work and the spring constant so we dragged the cart to the opposite side of the track and using the data on the force from the force sensor and the distance traveled from the motion sensor we created a force to position graph. The slope of this graph was are spring constant and the area under the curve was the work done on the spring.
Procedure Experiment 2
For the second procedure we used the same apparatus and we zeroed the cart at the end of the track in which the cart was attached to the spring and pulled the cart all the way to the opposite side of the track. We measure the mass of the cart and entered the data into logger pro. we released the cart, and using the motion sensor tracked its velocity along its path, and displacement. The motion sensor gave us a data point every 30th of a second. To make sure that the motion sensor was able to track the movement of the cart down the track we placed a square plate to the side of the cart that the motion sensor was directed at as in the first experiments procedure.
Calculations Exp 1
For the first procedure we pulled the cart as mentioned in the procedure exp1 section of this report and using a force sensor connected to logger pro and motion sensor we were able track force to position and graph it as seen below. Since we know that work = F*∆d the area under curve yields the total work done pulling the cart attached to the spring the length of the track. We found this area by using an integral capability on logger pro. Additionally the linear fit of the slope of this curve gave us are spring constant.
Calculations Exp 2
Are goal was to model both kinetic energy of a system and work of a system and show that they are equivalent . As mentioned in the procedure Exp 2 section of this report we dragged the cart that had the force sensor attached to it to the opposite side of the track and then gathered the data following the release of the cart. This data gave two graphs the top graph is our position to kinetic energy graph, let's talk about it a little. Logger pro calculated the kinetic energy by using the following formula KE= 1/2mV^2. Obviously logger pro didn't know are mass so we measured the mass of are kart and manually entered it into logger pro. The only other variable is velocity, logger pro used the ∆position/∆time gathered from the motion sensor to calculate the velocity. Then using this information logger pro plugged in the values it was gathering into the equation for Ke and graphed it relative to position yielding the top graph.For the Bottom graph logger pro used the data from the force sensor and ∆x from the motion sensor to yield the force to position graph. As I might have already mentioned the work at any given position is the area under the graph to that position and this should be equal to the kinetic energy which is why we placed these two graphs on top of each other to make comparisons and test this theory experimentally. I will discuss these results in the data analysis and conclusion section. 
Conclusion and Data Analysis
The data from are two graph from exp 2 as can be seen in the data analysis boxes do not perfectly match as we would predict, for one position , the closets positional match we had the kinetic energy was .685 J and are work was 0.8473 J .There is several reasons some from random error and 1 systematic that I would like to discuss that might be the cause of these less than convincing results. The first is that while the motion sensor is very precise and creates a data point every 30th of a second the experiment entire length of time is only approximately 0.4s yielding only around 13 data points to track the position and use this to also calculate the velocity. With a more precise device we might see a slight improvement in the difference between these two graphs. One other problem is that we were trying to compare the results for work and kinetic energy at the same point on both graphs however, as can be seen, we could not exactly match the position for both graphs do to a lack in data points in the exact same position on both graphs and had to settle with a difference in position of 0.002 s not a big difference however remember this is a small measurement to begin with so it affects a larger percentage of error than previous experiments. Had I had more control over the experiment there are a couple of ways that the experiment could be made to be more accurate. The easiest two solutions is extend the track maybe by connecting two tracks thus reducing the percentage error from the instruments and also using springs with smaller constants thus lengthening the time and yielding more data points from the motion sensor. Overall despite the fact that we were not able to make a perfect match with are data from are graph for work and for kinetic energy we can still see that even under very small instances kinetic energy is directly connected to work hence the work done on the cart by the spring causes a direct change in its kinetic energy.
