Lab 13 Magnetic Potential Energy

Purpose: The purpose of this laboratory is to verify that conservation of energy applies to a system with a glider being pushed by a magnetic force.

The apparatus that we used consisted of an air track connected to an air blower on one end and a glider on the track with magnets on the front and back and a motion sensor on the end of the track.
We use the apparatus to measure the distance between the magnet on one end of the track and the magnet on the glider.

Procedure:

The first thing we did was find an equation for the magnetic potential energy. Generally for a system that has a non-constant potential energy like this one the potential energy U is caused by an interaction force F and is given by the relationship U(r) = - integral from infinity to r of F(r)dr, where r is the separation distance. We assume the force is 0 when r = infinity. so what we have to do is find an equation for F(r) .

But first we had to find out a way to measure the distance "r" which was the distance between the magnet on the track and the magnet on the glider. We did this using the motion sensor to measure the distance between the aluminum plate on the glider and the motion sensor and subtracting that distance to the distance r between the magnet on the glider and magnet on the track. This gave a distance that we would always subtract from the distance the motion sensor read. Allowing us to find "r" at any position for the glider. 

To find an equation for F(r) we had to collect data for the Force and distance of r at different angles so we elevated the track at many different angles and measured the angles and the distance r.

To get the force from the data collected we figured that the force pulling the glider to the end of the cart was a horizontal force parallel to the cart and the only force that could be was the horizontal force of friction, since the track was frictionless, which was mgsin(theta). So to calculate the force we used the measured angle and the measured mass of the cart which was .346kg. And we already talked about how to get r at the top so using this information we plotted a Force vs distance r graph and used the power law fit F = Ar^n to get a trendline for the graph.

Next we had to verify the conservation of energy is true. So we made columns that we needed to calculate the magnetic potential energy and the kinetic energy.

We plotted the graphs for kinetic energy and magnetic potential energy to see if energy was conserved.

The fact that the graphs are opposite tells us that the energy is conserved because when the kinetic energy goes to zero it turns to magnetic energy. Ideally the magnetic potential energy peak is supposed to be higher to show that the kinetic energy lost completely transferred to magnetic potential energy, but there was error as there is in all cases. Maybe the collision between the magnets was not perfect or the track was not completely frictionless because of the air molecules its going through .