Solving for Magnetic Potential Energy

Purpose: The purpose of the lab was to use conservation of energy laws in order to solve for a function of magnetic potential energy for the magnet-cart system.

Procedure: In order to get the magnetic potential energy we first had to set up the air track and the cart on top of it. The air emitted from the air track allowed the system to remain as frictionless as possible. On one end of the air track we had a motion sensor so that we could measure how much the air cart will move. In order to get the actual distance of the magnet from the other magnet on the glider we had to get the track level for it to be in equilibrium. We then let the motion sensor read how far away the magnet on the track was and then we subtracted how far the glider was. This gave us the real distance from the magnet. Then we changed the angle at which the track was placed 8 times so that we could get different readings for the distance the magnets were from each other. This info would then be used to plot a graph of Magnetic Force vs Distance which would give us a value of force. Then we completed the lab by plotting kinetic energy, potential energy and total energy to see whether the system enforces the conservation of energy.

Below is a picture of how the whole set up looked like.

Data: The data we had to record included the angles and distances apart the magnets were.

Below is the data table we had gotten for the different angles and the different distances.

We also plotted the values into Logger Pro in order to get a force and an angle chart. Using the angles and Weight of the glider we were able to come up with the forces.We then used this to make a force and distance graph.

We did decide to get rid of the last point to increase the accuracy of our graph as shown below.

Calculations: The calculations we did were for finding the force of the magnets. In order to do this we needed the mass of the cart and by using its weight and the angle it was elevated with we were able to get the force on the magnets.

The graph below shows what the force vs distance graph looked like after plotting the points.

After plotting the points we took the integral of the curve given by the graph in order to get a function for the magnetic potential energy.

After that we calculated the remaining energies using the given equations.

 Finally, we graphed all the energies.

 Summary: Overall the lab was a success because we managed to find a function for the magnetic potential energy between two magnets and we were able to show that energy was conserved throughout meaning that there is a valid function for the magnetic potential energy. By finding the forces between the magnets and the angles in relation to the weight of the glider we were able to come up with a function for the magnetic potential energy by finding the area under the force vs distance curve. The total energy on the last graph though is not straight and this might have to do with the fact that there was still some friction between the glider and the track. The whole experiment was not also exactly level because of the location of the classroom which was another contributing factor.