Lab 13 Magnetic Potential Energy Lab

Student: Xavier Lomeli
Partners: Matthew Ibarra, Billy Justin
Date of Lab: 12 October 2016 

Lab 13 Magnetic Potential Energy

Mission Statement:To verify that conservation of energy applies to a system involving MPE (magnetic potential energy) and to find an equation to model MPE.

Theory: Every kind of calculation is in truth an approximation, and the tolerance of uncertainty depends on the application the calculation will be for. When multiple calculations are involved, then the uncertainty ripples, or propagates, through to the final result. Learning the method by which this kind of propagated uncertainty is determined is the essence of this lab.
Experimental Procedure:
First, we set up our apparatus to conduct our experiment as shown below.

We positioned books underneath the air track so that the glider would attain an angle θ, thereby obtaining GPE (gravitational potential energy) before beginning its descent. On the impact side of the glider, we attached a magnet of the same polarity as the fixed magnet on the bottom of the slope, shown below.

When the air track is activated, the glider was suspended on a cushion of air, ensuring that friction was negligible during its descent. During the descent, the glider gained KE (kinetic energy) up until the glider reached some equilibrium point some distance r from the bottom of the slope where the repulsion force between the magnets matched the force of gravity continuing to pull the glider down farther still, shown below.

We collected the appropriate data (r, h, θ) by tilting the track at different angles for different trials so that we could plot a relationship between the magnetic force F and the separation distance r. Before we plotted the graph, however, we first assumed that this relationship takes the form of a power law, namely A*e*r^n. Below is our graph. 

From our graph, the values for A and B were 0.0001863 and -0.1128,  respectively, and the appropriate function U(r) for the interaction between the magnets would thus appear to be 0.0001863*r^-1.872. 

Next, we set up our experiment such that we positioned a motion detector to record the position and velocity of the descending glider. Furthermore, we were supposed to determine the relationship between the distance the motion detector reads and the separation distance between the magnets, shown below. 

 The relationship to determine r is s-k, which we found with the help oft the motion detector and then proceeded to position the cart at the far end of the track, where we started the detector and gave the glider a light push, recording the data needed to verify conservation of energy for the time before, during, and after the collision. We then proceeded to make a single graph showing KE, MPE, and total energy of the system as a function of time, shown below.

Conclusion- From our graph above, we showed how the relationship between MPE and KE is fairly close. The behavior of the curves corresponds with the concept of conservation of energy since the KE and MPE curves seem to be inversely related as expected.
Predominant sources of error would include the overzealous application of too much 'pushing' force when the block is initially resting atop the elevated edge of the air track, thereby introducing an external force into our supposedly closed system, and furthermore the possibility of measurement errors in determining the distance r.