According to Newtonian Physics

Introduction:

According to Newtonian physics, an object present in a potential field will experience a force due to the field. In this experiment, a system of magnets is attached to a glider, which is placed in a magnetic field. Then another system of magnets is placed onto the end of the air track in an orientation where the magnets repel each other. For 5 different magnitudes, the experiment involves compressing the distance x between the glider and the end of the air track against the force of repulsion of the system of magnets. This process imparts a certain potential energy to the glider, and by releasing the glider, the potential energy is transformed into kinetic energy. In addition, a photogate is utilized to measure the final velocity of the glider. This velocity is then used to calculate the initial potential energy. After plotting the kinetic energy and displacement of the magnets on a KaleidaGraph, which generates m1 and m2 by the best-fit line, the force, which is the negative derivative of the potential, can be calculated in terms of dx. The potential, which shares an inverse of the cube of the displacement of the magnets, can be calculated by the equation. [pic 1]

Conclusion:

        The experimental values calculated support the hypothesis of the final kinetic energy, and consequently the initial magnetic potential energy, continually decreasing as the displacement between the magnets increased by a magnitude of 0.005 m, but then eventually level off. From a kinetic energy of 0.06750 J ± 0.0044 J at a distance of 0.01 m to a kinetic energy of 0.0087 J ± 0.0005 J at the distance of 0.03 m, the KaleidaGraph visually represents the trend on the graph of potential energy and displacement of magnets. The experimental force, 0.6921 N ± 0.0971, was very accurate compared to the theoretical force, 0.4943 N ± 0.00097 N considering the uncertainty of both values. Also, after calculating the experimental error of approximately 20%, the accuracy is validated given the resources during the experiment.

Although the accuracy of the experimental was in the range of the theoretical force, there are a couple of errors, through both speculation and observation, which could have potentially increased the accuracy of our experimental force and lowered our experimental error. First of all, air drag was an issue since even though the plane of the air track was leveled, the glider was observed to have lowered in velocity as it reached toward the end of the track, meaning that an external force was present. During the experiment, this would have decreased the velocity of the glider, and thus decreased the initial potential energy. Such an error would describe the potential energy found at x = 0.01 m. Secondly, as a speculation, the unequal dispersion of produced air caused tiny uneven bursts of acceleration, thus generating velocities that were circumstantially higher. Such a case would explain the higher calculated energy value at x = 0.015 m. Although these two cases provide insight on slight inconsistencies in the calculated data, the experiment successfully validates the conception of the theory.