Work and kinetic energy theorem: Jose Rodriguez: Lab completed: 4/10/17: Lab partners: Philip, John.

The focus of this lab was to try to show that work is equal to kinetic energy of an object during acceleration due to a force.

To try to prove this relationship we did several experiments and recorded data.  The experiments were based on capturing the values of force vs. distance of a cart that rides on a metal platform.  Then, the values for the forces and the displacement were entered into LoggerPro so we could make a graph that allowed us to integrate the area under the slope of the graph that in return gave us the value for the work done at any given point of the graph.  With this information, we then made a graph of kinetic energy vs. position and superimposed it onto the force vs. position graph and used a tool that allowed us to integrated both graphs at the same time to see the respective values at a specific point.  Lastly, the main techniques that were used for this lab were physics, a computer program, and some sensors.

To begin with, we had to set up a metal ramp that allowed a small cart to travel a short distance while being pulled by the tension of a string tied to hanging weight.  The distance and time the cart took for this displacement was captured with the use of a motion sensor, and the force was captured with a force sensor that was connected to the cart which all was recorded by a computer with the application logger pro.  Once the trial was completed, we used the all that data to make a graph of force vs. distance and imposed one of kinetic energy vs. position so we could use a tool that allowed us to integrate the area in between both graph so we could see the values for work and kinetic energy at the same time during any point on the graphs.  Ultimately, to confirm our findings we did the same type of experiment with the use of a spring instead of string to supply the force measured during the displacement of the cart.  We locked the spring in between the force sensor and the cart during displacement and repeated the same process that resulted in similar result.

This is an image of the cart and the hanging mass.  Notice the sensors that are all connected to the computer so we could record data.

This image shows the initial recordings of the experiment of the cart with the hanging mass.  Notice that we needed the time in all the graphs so we could link all of them together.

This image already shows the slopes of the force and velocity graphs are similar.  For instance force slope value is .389 and  velocity is .314; the absolute is 0.075.

This image shows the superimposed graphs of force and kinetic energy for the first part of the experiment.  Notice that work .1705 n*m is very close to kinetic energy 0.155 J.  The absolute difference is only .0155.

This image shows the graphs for the part of the experiment that involved the spring as the intermediate.  Again, notice the the slope values of force and kinetic energy are very close to one another.  The absolute difference is 0.0108.

In conclusion, the experiments did prove to show that there is a definite similarity between work and kinetic energy of an object during displacement. Although the values did not match, they were very close in value.  One reason that we didn't get a 100% match may have been because the motion sensor was not positioned the way it should have been so it didn't capture the distance traveled properly.  This error will throw off the kinetic energy because it measures velocity which is dependent of displacement. Another reason may be because the force sensor was not properly calibrated.  My lab partner calibrated it a way that was not recommended so the force sensor never read the exact force that is showed have sensed.  In return, the force values were never exact so work and kinetic energy were never going to be equal.  Although, the similarity and theorem were proven in my eyes because the values had such a small absolute error as mentioned in the image descriptions of the graphs.