13th April 2015: Magnetic Potential Energy

Lab 12: Magnetic Potential  Energy with a Cart

Purpose: To prove that there is conservation of energy within the system of an unknown magnet and a glider that is on an air track. By proving an equation for magnetic potential energy then we can prove that the system does have conservation of energy.

Procedure: The materials consisted of a large frictionless air glider and an air track. Attached to the air track was an inverted vacuum which allowed the gilder to be frictionless(almost). We also used books in order to give an angle to the the air glider. On top of those materials we also used magnets which we put at the end of the air glider and the opposite end of the track in order to have a repulsion as the glider glided down the track. We also used logger pro in order to set up a motion sensor that we used to measure the displacement of the glider as it moved closer to the magnet on the opposite side.

These are the materials we used in the experiment the motion sensor is not visible in the picture but is off to the right. 

After we had our track set up and running. We ran several trials which consisted of different angles and each time we moved the angle up we measured the force. Newtons second law of F=(Mass)(acceleration), was used to solve the force of the glider moving on the track, we derived an equation of f=mgsin(ø). We then used logger pro and used the five different forces from the five new angles to create a calculated column, then we compared it to the distance the magnets repulsed. This separation distance vs. force graph was carefully examined, by finding the curve fit of the graph using a power equation, we were able to establish an equation for the magnetic potential force of our contraption. 

Our trial with several books
so that we can increase the angle of our mechanism,

This is the power curve fit to our force vs. separation
equation. Power-fit= y=Ar^B

After we had found the magnetic potential energy equation we made more calculated problems so we could try to prove the conservation of energy. First we calculated a column for the the total energy, which consisted of the two new calculated columns we made for both potential and kinetic energy. We know that the initial potential energy and the final kinetic energy is equal to the total energy of the system. And in our case we are trying to solve for the magnetic potential which we did and to prove it has conservation of energy we had to set our magnetic potential energy equal to the total energy which is potential initial energy plus final kinetic energy. 

This is a graph of all of the calculated columns.
The top is total energy, red is potential, and orange is kinetic.

When examining and analyzing our results we find that there is an error in our data, with the total energy being equivalent to .095 jules approximately, we find that our data is off. For one, it should have the same position as the kinetic energy graph and mirror its every curve. There was most likely an error when we first ran the trial and did the power fit. The most reasonable answer to the error in our graph was the power fit curve which was not perfectly fit to our data because the surface wasn't perfectly frictionless. And the force which we applied to the glider in order for it to come into repulsion contact with the magnet may have been a different applied force every time causing our data to be inaccurate. All in all mathematically we found that energy was in fact conserved, but we could have ran better trials to assure that our data came out to be more sufficient. All in all we had a successful experiment in proving magnetic potential energy does in fact have conservation of energy.