10-Oct-2016: Magnetic Potential Energy

Lab 13: Magnetic Potential Energy
Name: Andrew Martinez
Lab Partner: Richard Mendoza

Statement: To verify that conservation of energy applies to this lab

Introduction: To find an equation for magnetic potential energy. To find the magnetic potential energy for a non-constant potential energy one must recognize the relationship between potential energy and force. The relationship appears as U(r)= - (integral ^r _infinity) F(r)dr.

Apparatus: Air track (Friction less surface), glider, magnets, air pump, books

Books were used to raise the air track to multiple angles to plot the separation distance

Procedure
- Level the air track to measure the variable h.
- From h this will be the position the experiment is done at.
- Collect data from various angles to plot a relationship between magnetic force F and the separation distance r.
- Plot F vs r graph. The relationship in this graph is a power law F = Ar^n. Find A and n from the curve fit performed on the graph
- Verify conservation of energy
- Attach an aluminum reflector
- Weigh the cart
- Determine the relationship between the distance the motion detector reads and the separation distance between the magnets
- Make a single graph showing KE, PE, and total energy of the system as a function of time.

Measured Data:
Using books we take the angle of the air track at different points and measuring the separation distance between the glider and the magnet. (+/- .1 degrees, +/- .2 mm).
1. .6 degrees, 22.2 mm
2. 2.1 degrees, 18.2 mm
3. 4.0 degrees, 14.1 mm
4. 5.2 degrees, 12.9 mm
5. 8.3 degrees, 10.6 mm
Convert mm to meters

Using this data we can use the equation F_mag=sin(theta)mg to find the force of the magnet
1. .03456 N
2. .210554 N
3. .2304 N
4. .299 N
5. .477 N

Graphed Data:
Using the measure data we plot a Distance(r)(x-axis) vs. Forces(F)(y-axis)

Using graph we perform a curve fit to find the A=2.363*10^-6 (+/- 1.368*10^-6) and n=-2.690 (+/- 0.1301) to plug into a power law (F=Ar^n)

Using the graphs we can verify that conservation of energy applies to this system

The bottom graph represents the single graph of KE, PE, and total energy as a function of time. As can be seen the graphs come together at a single point.

Conclusion: Despite knowing that conservation of momentum does apply to this experiment based on our graphs results it can not be proven with the data provided. Their are a number of reasons why the graphs fails to show the conservation of energy but one must likely answer is due to systematic error where the human element may have miscalculated or used a wrong equation.