Magnetic Potential Energy

Purpose:

For this lab, we are trying to find a relationship between a magnet and its potential energy, which does not fit Hooke's law for a spring.  In order to calculate this, we need to measure force vs. separation distance.

Experiment:

For the first part, we will be using an air track with a cart to make a near friction-less surface for the cart to glide upon. This will ensure we record accurate measurements and the separation distance is not influenced by friction. We also attach magnets to one end of the cart and on the other end of the track which were set to repel each other. Below is a picture of the setup with the cart and air pump.

In order to get data points for a graph, we had to create a greater force on the cart. We used large physics books to elevate one end of the track to various angles and decrease the separation distance, thus giving us different distances. We also used an equation to calculate the force of the cart

Force = mgh * Cos(x), where x is the measured angle

Once we had out data points, we could plot them on a graph and let Logger Pro calculate a power fit for us which would give us values for A and B. Using these values we could establish an equation for the potential energy of the magnets we were using.

Now that we have our equation for the potential energy of the magnets, we leveled the track and used a motion sensor to track the position and velocity of the cart as we pushed it towards the end of the track where the other magnets were.

We then made a graph to show the potential, kinetic and total energy in the system.

The final graphs show position vs time in the top and total energy on the bottom
The red line shows total energy, which was conserved, while the purple shows potential energy of the magnet and the orange shows kinetic energy of the cart