Lab 13: April 17, 2017: Magnetic Potential Energy

Lab 13: Magnetic Potential Energy

Amy, Chris, and John

April 17, 2017

Today's lab is to verify that the conservation of energy applies to a system where a cart with a magnet on a friction less track hits a magnet of same polarity. 

Theory: When a cart is at the position closest to a fixed magnet, the carts' Kinetic Energy is momentarily zero, where the energy in the system is stored in the magnetic field of as magnetic potential energy, then rebounds back. Where the potential turns back to Kinetic Energy. 

Apparatus and Procedure: For this lab we use a glider on an air track as our cart on a friction less surface.We needed a glider cart, an air track, books to raise one end of the track, a phone, a caliper, and logger pro. First we had to level the air track in order to measure the angle as we raise the track more accurately. 

 

We raise one end of the track where the cart will end up at some equilibrium position, where the magnetic repulsion force between the two magnets will equal the gravitational force component on the cart that is parallel to the track. We got the angle that we raised the track by downloading and app on our phone and measured by resting it and then remeasuring the angle by holding the phone parallel to the track and perpendicular and got the average. We measured the distance between the magnet on the cart and the fixed magnet on the track.

As we raised the angle we continued to collect the data for the distance between the magnets (r). 

After collection various angles and separation (r) measurements, we plot a relationship between the magnetic force and the separation distance (F vs. r). For this lab we assumed the best fit for our graph was a power fit in the form F=Ar^n. We calculated A and n from the curve fit to the graph. After that we determined the appropriate function for our potential magnetic force to be:

Data:
For our data we measured the angle we raised the track and measured the separation between magnets: 

Angle (degree)	separation (m)
2.5	0.0239
3.8	0.0232
5.1	0.0212
6.4	0.0199
7.9	0.0183
9.1	0.0176
10.5	0.0163

Because we used an app on our phones to measure the angle, we measure the phone horizontally and vertically, we took both measurements and took the average +/- 0.1 degree.
By plotting the points we get our graph F vs. R

Here our function F(x)=(1.491x10^-5)R^-2.741
Although our uncertainty for our value A was very high +/- 7.149x10^-6 which divided by our calculated value produces an uncertainty of 47.9%.

That was our formula for the force, we integrated this formula in order to find the magnetic potential:


By creating columns that calculate kinetic energy, we notice that our graph shows that the energy is not constant.

Conclusion: Our results from deriving our function for the magnetic potential force were pretty inaccurate however we faced some issues. The equipment was a bit flimsy in a way, our magnets would not align properly every time we pushed the glider. The measuring of the angle was completely trusted upon a phone. We also used these digital calipers that did not really fit in the gap to really measure the separation between magnets properly. In this experiment we also introduced uncertainty with the speed we pushed the glider with and even how many books we stacked to raise the track by one degree.