Kevin Tran
Lab Partners: Kevin Nguyen, Jose Rodriguez
22 April, 2017

Magnetic Potential Energy Lab

Purpose: This experiment was set up to verify the conservation of energy applied to an apparatus. In order to verify the conservation of energy that is applied to the apparatus, we needed to create an equation for magnetic potential energy.

In the picture below:

r= distance between the magnet in the end of the trash and the magnet on the glider.

h= height of air track from the ground

mass of cart: 0.344 kg

First, we set up our apparatus similarly to the model above. We made our air track as level as possible to make sure we get an angle of 0.0 degrees. We tilted the air track at 5 different angles to find the relationship between magnetic Force (F) and separation distance (r). We plotted a graph of magnetic force (y-axis)/ separation distance (x-axis). Since we assume that the relationship takes the form of a power law: F= Ar^n, we created a power line fit of the graph. We created a magnetic force/ separation distance because integrating the magnetic force in respect to separation distance will give us the magnetic potential energy. By finding the magnetic potential energy, we were able to verify the conservation of energy applied to the apparatus. 

-Above is the magnetic force/ separation distance graph.

-The uncertainty of the "A" parameter is plus or minus 4.62*10^-6

-The uncertainty of the "B" parameter is plus or minus 0.08493

After finding the equation from the box, we integrated the equation of magnetic force in order to find the magnetic potential energy equation. The magnetic potential energy equation that we got was  U(r) = (8.76756*10^-6)r^-1.566.

After finding the equation for magnetic potential energy, we were able to verify the conservation of energy. We attached an aluminum reflector on top of the air track cart in order to record the speed of the cart accurately with a motion detector. We placed the cart close to the magnet and ran the motion detector. By doing so, we are able to determine the relationship between the distance the motion sensor reads and the separation distance of the magnets.

We created a new column that allowed us to get the separation between the magnets from the position measured by the motion detector. We made our motion detector capture 30 samples per second. We also created additional columns in order to find the kinetic energy, the magnetic potential energy, and the total energy. We set the cart at the far end of the air track and gave it a small push. After, we made a single graph that displays kinetic energy, magnetic potential energy, and total energy in the same time frame.

Data

    angles                            "r"                        Force

1.8 degrees                    32 mm                  0.106 N

3.0 degrees                    25 mm                  0.176 N

3.6 degrees                    23 mm                  0.212 N

5.3 degrees                    20 mm                  0.312 N

8.2 degrees                    17 mm                  0.481 N

Calculated Data

Below is a graph that represents kinetic energy, potential magnetic energy, and total energy.

Kinetic Energy= purple

Potential magnetic energy= red

Total energy= blue

We created this graph in order to help us verify the conservation of energy by determining if the total energy is a linear line. If the total energy is a linear line, conservation of energy does apply to this apparatus.

Below is a picture of calculating magnetic potential energy.

Conclusion:

By using the graph that contains kinetic energy, magnetic potential, and total energy, we found out that the total energy line was not linear; therefore the conservation of energy does not apply to the apparatus. But when we we adjusted the separation distance from .257 to .254 meters, the total energy line became straight. The uncertainty in the separation distance affects our results tremendously.