The document describes an experiment that measured the relationship between the distance between two magnets and the distance the magnets repel each other. Data was collected with the distance between magnets ranging from 0-9 cm and the repelling distance measured. The results showed an inverse relationship, with shorter distances between magnets producing longer repelling distances. While the data fit the relationship well overall, some outliers were observed. The conclusion is that repelling force and distance repelled are directly proportional, with less distance between magnets producing more force and greater repelling distance. However, uncertainties exist due to experimental limitations.

1. Distance between Magnets and Distance being Travelled <br /> Eunice Lee<br />Introduction<br />A magnet is an object that produces magnetic force. The space around magnet, in which a magnetic force is exerted, is filled with a magnetic field. The shape of the field is revealed by magnetic field lines. Magnetic field lines spread out from one pole, curves around the magnet, and return to other pole. All magnets have both a north and a south pole. On one end of the magnet, there is North Pole of the magnet and on the opposite end, is South Pole of the magnet. They are similar to electric charges, for they can both attract and repel without touching one another. When opposite poles are brought together, attraction occurs and when same poles are brought together, repel occurs. <br />In this experiment, two magnets of same poles are put together in varying distance and they distances that they travel away from each other are being measured. Since magnetic with same poles will repel each other, the repelling force will cause them to travel in opposite direction. The purpose of this experiment is to find out the relation of distance between two magnets and repelling distance between two opposite poles. <br />According to coulomb’s law, the force between magnetic force is defined by the following, <br />19050125730<br />[eqa 1]<br />whereis the forceis the permeability of free space, , are the magnetic pole strengthis the distance separating the polesis the unit radial vector<br />In this equation, the “r”, which represents the distance of two poles, is in denominator thereby, is in inverse relationship with the force. The stronger force is, farther the cart will roll back. This theory can be applied to this experiment and predict that the longer the distance is, less cart wheel repels. However, no specific mathematical relationship between force and the rolling distance is established. Therefore, the equation of rolling distance and distance between two magnets may not follow this model. <br />Procedure<br />Repelling forceDistance being rolled because of repelling forceFigure 1. The experimental set up-52387567310The experiment is set up as shown in the diagram. One magnet is taped to the wall, and the other magnet is taped to a cart wheel. The two magnets have the same pole facing each other in order to repel each other. They are placed in varying distances and distances which the cart wheel rolls backwards are being measured. These data will be used to figure out relationship.<br /> In this experiment, the independent variable is the distance between magnets ranging from 0 to 9 centimeters. The data was collected with six different variables with three trials for each variable. The dependent variable is the rolling distance. The original force of magnet, type of wheel cart and floor are the controlled variables. For the magnets, magnet taped to the wall and the magnet taped to cart wheel were used throughout the experiment without change. The experiment was set on same location, in the same part of the floor, therefore was controlled. <br />Design<br />[Table 1.] The distance between magnets and rolling distance<br /> Distance Between Magnets (±0.1cm)Rolling Distance (±1cm)Trial 1Trial 2Trial 3Average 9.03.33.43.83.57.06.16.56.66.45.08.88.69.58.93.011.612.012.111.91.038.838.936.4380108.1108.7109.2108.6<br />The above table shows the collected data from the experiment. It is shown that the shorter the distance between magnets are, the longer repelling distance becomes. The uncertainty of the rolling distance is the uncertainty of the ruler. <br />[Fig. 2] The distance between magnets and rolling distance<br />The above graph shows that distance between magnets and repelling distance. Overall, the data fit with the graph. The data, especially on 5cm of distance and 7cm of distance are not stable but generally, fit with graph. However, the data on 0cm distance between magnets do not fit with the curve. This is because there is uncertainty on the measurement of distance. The two magnets had to be placed, touching each other before being released, however, the two magnets were keep pushing each other, so the magnets could not placed exactly on 0cm distance. Thus, the data would be more accurate if it is moved a bit right from its position and it may fit the curve graph. <br />Conclusion<br />According to the figure 2, an equation of rolling distance is found. The equation turned out to be <br />Distance rolled= 38.80/x^1 – 0.1481<br />From the equation, the relationship between distance of two magnets and rolling distance can be seen. Farther distance of magnets is, the shorter cart wheel traveled. Therefore, the prediction was right. Mathematically, the two variables are inverse relationship. <br />In the previous theory, [equ. 1] showed that the distance between two magnets and magnetic force has inverse relationship. If applied in this result, it can show the relationship of repelling force, distance between magnets and travelling distance. Since force increases as distance between two magnets decrease, and travelling distance increases as distance between two magnets decrease, it can be concluded that force and distance being travelled have proportional relationship. When the distance between two magnets gets shorter, the repelling force increases and thus the distance travelled by the cart increases. <br />This rule can be applied to all magnets. All magnets, when in greater distance will have greater force therefore will have more powerful repelling distance. Generally, the conclusion is reliable because the data stably fit the graph but there are still uncertainty regarding this experiment. Moreover, the distance that travels may vary not only by the distance of magnets but the size, type and original magnetic force of magnets. So, it is important to remember that there are uncertainty and variance to this specific equation on the graph although relationship of distance travelled and distance of magnets can be applied to all magnets. <br />Evaluation<br />The position of magnets, which was placed to face each other directly, kept repelling each other to move side ways. This may have decreased the precision because if they are not facing each other directly, the force may slightly change, causing different rolling distance. A path that prevents cartwheel from moving sideways can be used for next experiment. The border between wall and floor was slightly curved, and may have been source of uncertainty. Next time the cart wheel can be rolled in sharp edged floor. Lastly, when the data from 0cm of distance was being collected, the two magnets were keeping pushing each other, so it could not be kept at exact 0 distances. This would have caused uncertainty. This could be improved by using magnets with weaker force. <br />Citations<br />http://physics.bu.edu/~duffy/py106/Charge.html<br />