7-Oct-2014: Spring Collision

Purpose:
The purpose of this lab is explore the conservation of energy in magnetic forces. Also, to find the equation of forces between two magnets.
Apparatus:
There are two parts to this experiment. The first part is to find an equation for the forces between the magnets. By tilting the track up at the other end of the track, we find the cart moves closer to the track, and with the force coming from the mass of the cart, we can find the force exerted on the magnets, and plot a force vs. position graph to find the equation. The second part of this lab is to determine if the energy throughout the experiment was conserved. To do this, we leveled the track and attached a motion detector at one end of the track. We then pushed a frictionless cart with a magnet at one end of the cart to the end of the track with a magnet attached to that end. With the magnets pushing off each other the cart should move the other direction.
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Explanation:

For the first part of the lab, we raised the track at several different heights. For each certain heights we can observe the distance between the magnets decreases as the height of the cart increases. We took eleven different measurements, and with the mass of the cart, we can measure the force of the magnets by using the angle between the track and table. With the measurements forces and distances, we graphed a force vs distance chart, and found the equation of the forces, 1.285x10^-7r^-4.893. We had to cross-out four points to obtain a perfect logarithmic curve.

For the second part of this lab, we leveled the track and placed the motion detector at one end of the track. With Logger Pro set up, we pushed the cart, with a magnet in the front of the cart, towards the magnet where the motion detector is. The cart starts with an initial velocity; once the magnets come close to contact, the frictionless cart slows down and eventually, for an instance, hit zero velocity before moving in the opposite direction. Once the magnets exert force off each other, potential energy increases and kinetic energy decreases. To find the kinetic energy, we used the equation 1/2mv², and for potential energy, we integrated the equation we found in part one of this experiment, which gave us -3.3x10^-8r^-3.893. We plot the kinetic energy, potential energy, and the total energy on one graph and the results were as expected. The total energy should show close to a linear line while the kinetic energy and potential energy shifts at the point were the magnets come close together. With these results, we can assume that energy was somewhat conserved. But the point were the magnets almost meet, there was a lost in energy and this was recorded by Logger Pro. We believe that the lost in energy was due to how the cart lifts a little.

Conclusion:

To assure that the system of this apparatus has conserved energy, we first found an equation for the magnetic potential energy. To do this, we raised on end of the track and found the distance between the track; the higher the track was lifted, the smaller the distance was between the magnet. With this equation we were able to confirm that some energy was lost but most of the energy was conserved.