13-Apr-2015: Magnetic potential energy

PURPOSE

The purpose of this experiment was to practice conservation of energy problems in a real-life situation.

PROCEDURES

Figure 1: Initial set-up of air track and cart

Figure 2: Air generator

We commenced this experiment by constructing the set-up shown in Figure 1. The set-up consisted of a track connected to an air generator (Figure 2) with a tube at the location marked by the red circle. The air produced from this generator allowed the cart (circled in green) to move on a virtually frictionless surface. In addition, there were magnets at the end of the track and on the front of the cart. There was a magnetic potential energy between these magnets that was inversely related to distance.

Figure 3: Altered set-up with track at an angle

Figure 4: Books were used to place the track at an angle

After constructing the set-up, we proceeded to place the track at an angle by using books (Figures 3 and 4). We then turned on the air generator and allowed the cart to stabilize before we turned it off. We measured the resulting distance between the magnets. We repeated this process four more times, increasing the angle of the track each time. The angles and their corresponding separation distances are listed below in Figure 5.

Figure 5: Data table

Figure 6: Newton's second law

From the gathered data, we were able to find the force between the magnets (F_m) by applying Newton's second law in the x-direction as shown in Figure 6. Then, we plotted F_m with respect to the separation distance (Figure 7). We applied a Power Fit to this graph to get a function for the magnetic force. We integrated this function with respect to the separation distance in order to find the potential energy between the magnets. This process is displayed in Figure 8 below.

Figure 7: Magnetic force vs separation distance

Figure 8: Function of magnetic potential energy

Once we found a function for the potential energy between the magnets, we removed the books from under the track and made sure the track was level. Moreover, we set up a motion sensor to track the cart's velocity and the distance between the magnets. Then, we turned on the air generator and gave the cart a push. From the measurements we made with the motion sensor, we were able to create calculated columns for the kinetic energy of the cart and the potential energy between the magnets. From these energy values, we also found the total energy of the system. We plotted these three energies with respect to time (Figure 9).

Figure 9: Energy vs time

Based on our knowledge on the conservation of energy, we expected to see a constant total energy throughout the cart's motion. As it can be seen from Figure 9, our experiment was a moderate success since the total energy was mostly constant with the exception of two parts in the graph. Furthermore, the shapes of the kinetic energy and potential energy graphs were very close to what we expected. We expected the energies to essentially be inverses of each other, which is pretty much what we saw.

CONCLUSION

As discussed earlier, this experiment was somewhat successful as the graphs of the energies with respect to time had shapes that were similar to what we expected. There are several factors that could have contributed to the graphs not having the exact shapes that we expected. One possible reason is that the cart was not completely stable throughout its motion, especially when it reached the magnet at the end of the track and bounced back. This could have affected the data that we gathered on the cart's velocity, which in turn would have affected the values we found for the kinetic energy of the cart. This makes sense because the dips in the total energy graph that we saw in the Figure 9 were due to the kinetic energy graph. Another reason why the results were a hundred percent accurate was the measurements we made on the separation distances. Since we used a ruler to make these measurements, we could not make measurements that were very accurate.