15. April. 2015: Magnetic Potential Energy Lab

Purpose: Show that conservation of energy applies even with our own made up equation (from our experiment of course no, you can't just choose any random equation)

Materials
Air track (one that if you turn it on the glider is barely moving), glider (with a magnet that repels to the end of the air track), angle measurement, logger pro, balance, ruler, books

Procedure:
BACKGROUND INFO: So first of all we do not have an equation for the potential energy of a magnet. So that's what we have to find. BECAUSE when our cart is moving towards the magnet we agree that there is some kinetic energy and when it reaches the magnet that repels each other it heads back in the same direction which is from the potential energy of the magnet. To do this we will look at the angle the cart is at and the distance of how close it gets to the magnet.

1. setup:

Okay, so first we started with a lower angle then measured the distance between the two magnets (one on the end of the air glider and the other on the end of the track). Each time we added around 4-5 books in order to get a higher angle which we wanted to be around 5 degrees more than the last data point. We put this data straight into our logger pro graphing page. Typically we want more than 5 data points. In our lab the book stacking got really high and one person was holding the air track so it might not fall off, one person was measuring, and one person was holding the books. 

What we got from our data was the angle and x (distance). We know that these equations like radians more than degrees so we should have calculated radians first but in the picture we did it after. From that we know how to find the force of the magnet by the equation m*g*sin(radians). And now you are ready to graph.

From our graph, we took the power fit and got ourselves an equation of the magnet. As you can see as the distance gets bigger the force between the magnet got smaller.Our power fit through the line gave us F= .000508x^(-1.721). Now that we had our force equation does not necessarily mean that we have our potential energy function. Keep in mind this is what we are trying to find.

So from common knowledge we know that potential energy is negative the force of the integral with respect to "R" we changed our x value to r. It's just a variable. So we calculated for our potential energy by taking the integral. This is the potential energy of the magnet. We have taken a random magnetic force that we did not know the equation of and made an equation.

BACKGROUND INFO: so now that we have the potential energy we should have some way of verifying that this is correct. So we will now take out a motion sensor and have it at the end of the magnetic side. This has to be kind of behind the motion detector by some distance. Which means we do have to find the "new" distance.

First: take all of the books under the air-track and have it leveled so that the glider is barely moving (in a perfect world it wouldn't move unless you give it a push). The motion detector should be set up like mentioned above. We will give the cart a little push and record on logger pro. The cart should edge up to the magnet but not touch and then it should start going back the way it came from. 

The graph should have a position v time and also a velocity v time. The position vs time should go down then slowly curve back up like a parabola. From this we get data points yay. 

Okay so the graph originally gives us time, position, acceleration, and velocity. We can calculate Kinetic Energy by the equation 1/2 * m * v^2. The new x from what I mentioned above. The Potential energy is the equation that we have calculated before. The total is the kinetic energy + potential energy. We want a graph of the kinetic, potential, and also total. 

the total is not as "constant" as we would like it to be. Our ideal graph is if the total energy was at least kind of constant. However, we realized that our potential energy spiked up a bunch so we messed with the power so if we kind of changed our power the potential energy spike would be lowered.

If I changed the power by .05 our potential energy lowered significantly. This is due to the error in the lab which is a lot. A little bit off can mean a significant change in our graph.

Conclusion: 

There was a huuuuuge room for error in our lab. We would change data by .05 and it would make a significant change in our graph. I assume this is from 1. the friction on the air track. (most of the gliders slid on the air track when it was ideally supposed to stay still) 2. the magnets were different which meant that the distances could have been different each time they were next to each other. 3. sometimes the glider would go past the magnet so the magnet would push the cart off of the track (we always tried to redo it if this happened. Although our lab did not come out as ideally as we wanted it too. It was close enough for us to see that even with a magnet conservation of energy still holds true and that the potential energy of the magnet was the (same-ish) as the kinetic energy. The kinetic energy went down as potential energy went up and as potential energy went down kinetic energy went up.