Magnetic potential energy and Kinetic energy

Introduction:
The purpose of this lab is to verify the statement of the law of conservation of energy again. The isolated system we looked at this time was a cart with magnet  on an air track with magnet attached on one edge. If the law of conservation of energy is correct, the sum of magnetic potential energy and kinetic energy of the cart should be an almost constant value.

Apparatus:

The magnet on the cart and the magnet on the end of the air track has the same polar facing each other, so there exist an magnetic potential energy caused by repulsion. We placed the motion sensor on the end of the air track, and the cart would be moving toward it in the experiment. The air track can produce an almost frictionless surface, so the experiment could be most accurate. We collected the velocity, position and acceleration with the motion sensor, and these data could only help us find the kinetic energy in the cart. To find the magnetic potential energy, we need to first find out the force function of distance.











Data:
Part 1,
To determine the magnetic force by distance, we needed to find out the relationship between the distance and the force.
To do so, we leaned the air track at different angle, and measure and record the equilibrium distance when the cart stop.
The cart we used has a mass 0.351 kg.
To calculate the force, we used the following formula:
Force = (0.351kg)*9.81*sin(angle)

We then graphed Force(N) vs. distance(m) curve:

According to the graph, the force function of distance is F=3.168*10^(-5)*(distance)^(-2.690)
With force calculated, we can then calculate kinetic energy and potential energy, and make the following table:

The following is the energy curves relate to time:

As we can see, the total energy of this system always very close to 0.011 J, which obeys the law of conservation of energy.

Conclusion:
This lab was divided into two parts: in the first part of this lab, we lean the air track at different angle to determine the relationship between the magnetic force and the distance between the two magnet. Find out the force function is important because we needed the magnitude of the force to calculate the magnetic potential energy. On the other hand, using the velocity we got from the motion sensor, we could figure out the magnitude of the kinetic energy. We then graph curves of kinetic, potential and total energy as functions of time. By looking at such graph, we could see that the total energy of the system was almost always a constant value 0.011J. In conclusion, the statement of the law of conservation of energy is correct.