10/05/2016 : Work-Kinetic Energy Theorem

Lab #11: Work-Kinetic Energy Theorem 

Name:    Charles Xu,

Partner: Anthony, Michell

Date:    10/05/2016

Statement:

In this experiment, we comparing the measurement of work that was done and kinetic energy that recorded, and find the relationship between this two sets of datas.

Theory:

This experiment was divided by two parts. We need to find the relationship between work and kinetic energy using force sensor and motion sensor.

Summary:

In the first part of the experiment, we pulled a cart on the track, which was attached to the spring. Then we use force sensor to measure the force when the spring was stretched to a certain amount of distance. Then plot the Force vs. Position graph using LoggerPro. Then used linear fit to find out the function for the graph. The slope of the function is the spring constant we looking for. In our experiment, which is 13.64 N/m. Then using the integration routine in the software, we were able to find the work done by stretching the spring 60 cm. We got 2.248mN as result.

This is the set up for the Experiment

For the set up, we have a cart with a force sensor on it. On one end, there is a white board that attached on the cart by magnet. It allows motion sensor detects the cart easier. On the other side, a spring is attached on the force sensor. The book beneath the spring is to reduce experimental error by keeping the spring not stretched. 

The analysis graph in LoggerPro

For the second part of the experiment, we use the same spring so that we have the same spring constant that we have measured in part one. We pull the cart to the same spot as part one, which is 60 cm apart from the initial position. This time we release the cart and let motion sensor to measure the datas. From the collected data, we plot Force vs. Position graph and Kinetic Energy vs. Position graph. In order to have beautiful graphs, we use strike through data cells method to remove useless data points on the graphs. 

Force vs. Position graph and Kinetic Energy vs. Position graph

Here are the Force vs. Position graph and Kinetic Energy vs. Position graph. This two graphs look like opposite to each other from looking at the graphs. Furthermore, we select a portion of datas and use examine feature of the software to compare two datas.

Examine 

We select a data point on the graph, for the first graph, we have the area as 1.64mN; for second graph,

we have kinetic energy as 1.535J. Comparing this two numbers, there are almost identical.

Conclusion:

From this experiment, we could say that the work done by pulling the spring almost identical to the kinetic energy that the cart has after releasing. In my opinion, the work done by pulling the spring converts to elastic potential energy of the spring, then elastic potential energy converts to kinetic energy and heat. The little difference between the Work and Kinetic Energy is converted to heat produced by friction.