April 14: Lab 13 Magnetic Potential Energy

Lab 13 

Magnetic Potential Energy

Ricardo Gonzalez and Peter

April 17, 2017

1. Objective

We have equations for both gravitational and elastic potential energy, yet we don't have an equation for that of magnetic potential energy, so we must somehow show that the conservation of energy applies to a magnetic-system. 

2. Procedure

We  first had the apparatus set up for us by the Lab-Tech Maria. The apparatus was set up by having a glider placed on an air track. On One end of he air track, a magnet was placed and similarly a magnet was placed on the glider. The air track was leveled as much as possible.

The air track system was turned on, we lifted one side (the opposite side of he air track where the magnet is placed) at a small angle. At that angle, the glider would be a distance x between the two magnets. By increasing the angle , the x distance between the magnet on the glider and the magnet on the air track decreases. We found a total of 6 distances x with angles θ.

With the aluminum deflector on the glider (as it was on for part 1), we placed a motion sensor just behind the air track. The motion detector was connected to our laptop for the Logger Pro software. We placed the glider 0.01 meters from the magnet on the air track and the magnet on the glider. We hit collect on the logger pro software and measured a total distance x(1) as the glider was not moving with the magnets 0.01 m away from each other which helped us find the "separation" from the two magnets. We set up the motion detector so that it would record 30 measurements per second. We set a new calculated column for "separation" which would be our "position" minus "the distance behind the magnet om the air track to the motion sensor." 

The distance in cm between the two magnets

3. Measured Data

4. Calculated Data
 

The force exerted from the magnet is equal to the force of gravity pushing the cart down the air track.

 

Example calculation

F(mag) = (0.339 Kg)(9.81 M/s^2)sin(14.3°)= 0.821 N

Velocity before impact = -0.44 m/s^2
Kinetic energy before the impact = 0.5(0.339 kg)(-0.44 m/s^2)^2 = 0.033 J

Velocity after impact = 0.40 m/s^2
Kinetic energy before the impact = 0.5(0.339 kg)(-0.40 m/s^2)^2 = 0.027 J

"separation" = "position" -total distance from motion sensor to glider - distance between two magnets
"separation" = "position" - 0.373 m - 0.100 m
"separation" = "position" - 0.273 m

5. Graphs

Graph showing the F(mag) vs r

The position graph of the glider with the magnets set a distance 0.01 m apart

Graph showing the velocity of the glider.

Graph 1: When the "separation" =is set to "position" - 0.273 m

Graph 2: When the "separation" =is set to "position" - 0.272 m

Graph 3: When the "separation" =is set to "position" - 0.271 m

6. Analysis

We set up another calculated column for the Kinetic energy, Potential energy, and total energy of the system as functions of time. The potential energy calculated column used the equation we derived where R is our "separation," Lastly we made a calculated column for the total energy in the system which is the Kinetic energy + the Potential magnetic energy. In the last three photos above, we can see the KE, PE(mag) and total Energy under the same graph.

We initially were given graph 1 and as we can see the potential energy of the magnet looks like it is nearly double the value of the kinetic energy of the glider resulting in a large total energy. We do know that the potential energy of the magnet is dependent of the "separation" value. So if we can assume we were not precise when we measure our distance between the two magnets, we can change the 0.273 m to 0.272 m (27.3 cm). What we can see from graph 2, our magnetic potential energy has decreased but if we change the separation to a tenth less of a centimeter, we can see that in graph 3, our value of Total energy is much  more linear than before.

7. Conclusion
In our objective, we stated that we were not given an equation for the magnetic potential energy, however we can measure it as we have shown. Although this experiment was not perfect, we made minor adjustments in our "separation" which yielded a better fit for our total energy curve in respect to the potential energy of the magnet and the kinetic energy of the glider. In theory, energy is not conserved and as as we can see in the graphs 1-3, the total energy before the collision was larger than the total energy after the collision. One source of error in our measurements was clearly the distance between the two magnets when we had to set up the "separation" calculated column. the magnets were taped onto the glider and the air track using tape which covered the front faces of the magnets. Air resistance was ignored but probably shouldn't have been. When we gave the glider an initial velocity, the aluminum deflector may have had a surface area large enough to present a reasonable opposing force to the motion of the glider.