In order to check conservation of energy still applies in situations with magnets, we created a system that would directly test magnetic potential energy without other forces such as friction complicating things. We used an air track with a cart on it that was attached to a machine that would blow air through the holes in the track to lift the cart. Most importantly, we placed a magnet on both the cart and the end of the track so the magnets would repel each other. We then placed books and other objects beneath the track to raise it.
The reason we were lifting the track was to get the cart to be supported by the magnetic force parallel with the track. We would then use the component of gravity parallel to the track to equate it to the magnetic force. We need to find the angle that the track is making with the table which we will call our horizon. For this, we used our phones which were accurate to a tenth of a degree. After the cart settled in it's new elevated position, we used a ruler to measure the distance between each face of the magnets. Also important was the mass of the cart. Below is a table with all our findings for this part of the lab.
We then put all our data into Logger Pro. In Logger Pro, we graphed the component of the force of gravity that was parallel to the track, calculated from our recordings, against the distance we measured between the magnets. Below is a picture of the graph.
From here, we assume that the line is the graph of some power law and do a power fit on the line. From here, we find our constants A and B and plug them into the equation that states that the negative of a force integrated over a distance is equal to the potential energy. We now have an equation for magnetic potential energy for this system. Below is our computation.
Next, we wanted to see if energy was conserved in the system. We attached a motion detector behind the magnet attached to the now level track. We then turned on the air and gave the cart a modest push so that the cart would be bounced back by the magnets and our number would turn out nice. From the graphs below, you can see in the velocity vs time graph that velocity starts at a number then becomes it's negative after the magnets push each other away. From the KE, magnetic potential energy and total energy vs time graph above it, we can see our magnetic potential energy depicted by the red line and our kinetic energy as the light blue line become mirror opposites of each other after the magnets push against each other. Our total energy, dark blue, unfortunately spikes slightly and we see magnetic potential energy as being larger than kinetic energy.
In the end, my group and I were satisfied with the first part of the lab but wished our magnetic potential energy was more the mirror image of the kinetic energy. This problem could have spawned from the first part of our lab with our constants relying on measurements taken with a ruler. It could have been that I pushed the cart too hard and we got the magnets closer than we ever did in the first part of the lab and saw it respond with greater force than anticipated.
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