8-Oct.-14: Magnetic Potential Energy

Purpose:

To verify that conservation of energy applies in a magnetic energy/air-track system.

Note: The idea we are applying is that at every point, the sum of the PE_magnet and the KE_cart is constant.



Apparatus:

Equipment -
 - A nearly-frictionless track (achieved with an air-track),
 - a cart (m=0.351-kg) that fits comfortably on the air-track,
 - two magnets (one for the cart, and one for the end of the track)

The two fixed magnets have the same polarity and are both at the same height perpendicular to the track - This force is very effective since the track is nearly without friction.
By raising one end of the air-track 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 parallel to the track.

Track and Air Source:

   

Leveling the track:

   


The two magnets repelling each other:






Experiment:

1. We began the experiment by leveling the air-track which was accomplished by adding individual pieces of paper under one side of the air-track, while simultaneously monitoring the angle (using a smartphone app.)
   This was done so we know where we'd be measuring h from.
2. We let "r" represent the distance between the two magnets and "h" be the height of one end of the track. This relationship helps us find the values for potential energy.
   It's assumed that the relationship between the F_magnet and r takes the form of a power law: F=Ar^n.
3. We stacked books beneath one end of the track to change the slope of the track and measured the separation distance "r" at that angle.
   This step was repeated for a total of 8 measurements
4. Calculating the values for F_magnet required finding the component of the cart's weight parallel to the track. Which led to the equation: F_magnet =mgsinθ
5. Plotting our data allowed us to find the unknown variables A and n in the power law.
   A = 0.0003785, n = -1.792
6. We then attached a motion sensor at the end of the track where one of the magnets was fixed.
7. Recording the position of the cart gave us the velocity of the cart. From the velocity we find the kinetic energy of the cart.
8. We added the PE and KE to find the total Energy.
9. Finally, on the same graph we plotted the potential, kinetic, and total energy to determine if energy is conserved.

Conclusion:

The energy in magnetic system is conserved.

A Great Day for Physics.

(10/8/14, 7:06am)