Lab#13: Magnetic Potential Energy

Magnetic Potential Energy

Samuel
Ellis
Mia
10-12-2016

Purpose:

  Verify that conservation of energy applies to this system.

Theory:

According to Laws of Conservation, all energy must conserve if no additional force is apply to the system. We can determine the energy applied by calculating before and after energy. In addition, by tilting the system, we can turn it into gravity potential energy. With different angles, We can find the relationship between magnetic energy and kinetic energy by measuring the distance it oppose by magnetic force.

Procedure:

1. Level air track (this way you know where to be measuring h from. This is the position the track will be in when you actually do your experiment.)

2. Collect the appropriate data by tilting the track at various angles so that you can plot a relationship between the magnetic force F and the separation distance r.

3. Plot a graph of F vs. r. We'll assume that the relationship takes the form of a power law: F = Ar^n. Get the appropriate values of A and n from a curve fit to your graph. Record the uncertainties in your fit equation. 

4. Determine the appropriate function U(r) for the interaction between the magnetic. 

5. Attach an aluminum reflector to the top of the air track cart.

6. With the air turned off, place the cart on the air track, reasonably close to the fixed magnetic. Run the motion detector. Determine the relationship between the distance the motion detector reads and the separation distance between the magnetic.

7. Now you have a way to measure both the speed of the cart and the separation between the magnetic at the same time. 

8. Set the motion detector to record 30 measurements per second. Under the data menu in the LoggerPro create a New Calculated Column that will let you get the separation between magnetic from the position as measured by the motion detector.

9. Start with the cart at the far end of the track. Start the detector, then give the cart a gentle push.

10. Record whatever the other data you need to verify conservation of energy for the time before, during and after the collision.

11. Make a single graph showing KE, PE, and total energy of the system as a function of time.

Data:

Theta(degree) /Separation(mm):

2(degree)/18.5(mm)

6(degree)/11.9(mm)

13(degree)/8.9(mm)

14(degree)/7.2(mm)

18(degree)/6.5(mm)

Mass of cart: 337.1 grams

Motion detector: 0.399 m

Separation: 46.9 mm 

Graph/Calculated Result:

(Above is graphs of Position vs Time, Velocity vs Time and (Kinetic, Magnetic Potential and Total energy) vs Time. First graph, it shows around 5 seconds there's a reverse direction of where the cart is traveling. That's where the cart got different force from magnet. Second graph shows that at exact moment where position reverse, the velocity became 0 and start increase its speed. Which is correct since magnet push it to other direction. On third graph, total energy vs Time, it shows energy is conserved. Since it is equal to each other, it become 0 when cancelling out with different energy.)

(We plot the points from measuring the angle and separation from the experiment, and used power fit in LoggerPro to find the curve of magnetic force. The curve above is to measure the separation with given angle)

Conclusion:

Overall, the data we got are pretty precise on when and where the change in energy occur(it match up with other graph). In this experiment, we first tilt the track to form potential energy and when cart moves down the ramp and bump into magnetic force then turn that energy into kinetic energy. From that, we turned off the air so we can know the distance it had travel. However, there are still some error during this experiment. First, the ramp angel we measured, it has only 2 significant figure and we average it from 3 different cellular devices. Second, the weight of cart and separation from magnet are measured with 4 significant figure device. Although it is highly precise, there might still have human or mechanical error involve in.