These are 3 pictures to help visualize what we were working with in the lab. The second picture helps to show how we used varying angles to find the force of gravity, which was also equal to the force exerted by the magnetic field. The 3rd picture helps to show how we recorded position and velocity of the cart by using a motion sensor. We then used the sensor to take a measurement from the sensor to the reflector, which read 0.340m on logger pro. We then measured with a ruler the actual separation distance between the magnets which was 0.0359m. We then took a difference of the two numbers and used the difference to apply a correction to logger pro when we created a new calculated column. The formula we set was the distance read by the sensor (minus) the difference we calculated. This formula gave us a table with all the actual separation distances that were then used to create the potential energy function.
Purpose: To create a relationship (mathematical model) between distance and potential energy for two magnets of same polarity that approach each other.
Apparatus: The setup that we used was an air-track with a glider cart that would "float" along. Air that was pushed through holes along the track kept the glider suspended in the air as it moved along the track. There was a magnet on the front of the glider, and another magnet at the edge of the track. They both had the same polarity so that they would repel each other.
Procedure:We turned on the track in order to make the track frictionless. We then lifted one end of the track to a fixed angle, which we wrote down. The angle was measured by a protractor application on my cell phone. We then turned off the track in order to measure the distance between the two magnets. We then increased the angle and repeated the measurement of distance by using digital calipers. As we increased the angle, the distance between the magnets decreased. We then used simple trigonometry, gravity, and the mass of the cart to figure out the force that the magnets applied. We then related each force at each angle with the corresponding separation distance between the magnets by inputting the values into a table, and generating a graph on logger pro. We then used the points on the graph to create a power fit which gave us an equation for the force between the magnets based on distance. We then integrated the equation to give us the equation for the potential energy(U(r)).
U(r)=(0.0001929/1.066)*r^(-1.066)
Mass of the cart was 0.351kg
We then created a calculated column using our new function. We then leveled the track. At the end of the track with the magnet, we placed the motion sensor by way of a ring stand. We then collected data and pushed the glider along the track until it "collided" with the magnet at the end of the track. We then used this newly collected data to generate a new calculated column which was kinetic energy. We then created yet another column called total energy which was a sum of the column with our function and the kinetic energy.
This was a table of our raw data from inclining the air track.
This was our original power-fit function. However, due to to the manner in which we pushed the glider along the track, we needed to remove some points that were too small in distance for the distance between the magnets. Had we collected data with having pushed the glider harder, those points would have been more appropriate.
This is our power-fit after we removed some points in order to better accommodate our collected data.
This is our graph of kinetic energy, magnetic potential energy, and total energy which is the sum of the first two. At first we were having trouble with our graph because our total energy graph was not very flat at the point where the MPE peaks. Then we had to go back and remove some points from our power fit and ended up getting a more appropriate fit. We did not change any data, rather we omitted data that was inappropriate which resulted in a better overall graph.
This is a picture of the above graph, alongside a position vs. time graph for our collected data, and also a velocity vs. time graph.
Conclusion: This lab served as a powerful example that not every knowledge in this world has to be handed down. There exists no laws for magnetic potential energy however, using new technology, we were able to create a model for this specific setup. The proof that our model for magnetic potential energy works is in the graph for total energy. The line for total energy is relatively flat, indicating that the two are equal. It is not perfect however, due to many factors such as air resistance, and the magnetic fields not being perfectly uniform. Although our model is not perfect, it is good enough and shows the importance of ingenuity.
My partner is Elliot Sandoval.
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