15 April 2015. Magnetic Potential Energy Lab.

Purpose

Part 1
Deriving an equation for magnetic potential energy of the system described in the section apparatus through several experiments.

Part2
Using the equation found in part 1, we are going to prove that the conservation of energy is indeed true once again.

Apparatus:

1. Air track glider. This apparatus is designed to have a moving mass (the glider) in horizontal motion without friction. On the track there are holes that emit air from the reversed vacuum cleaner connected to the system.

2. Magnets. We are going to measure the force between these two magnets.
3. Some books. These are used to varies angle of the track.
4. Angel Measurement. Your phone.
5. Motion detector.

Base Theory

• What do we know about Force and Potential Energy that we get from that force? We recall that there is no relationship whatsoever between them. We just memorize the formula. Turns out, there is indeed a relationship between them! (see picture)

• Yay! The relationship is:
• F = - du/dx
• Note that this is true for potential energy of any kind.

Procedure and Data analysis

for this lab blog, the procedure and data analysis will be described individually under one part section. Since there are two parts of this experiment.


Part 1 (determining the equation of the Potential Magnetic Energy between magnets)

Procedure

1. Set up the air track on a horizontal table. Make sure that it is really level out, meaning the glider stays still unless we give it a push (when the vacuum is on).
2. Attach a magnet at the end of glider, and another magnet with the same polarity at the end of air track as well. It is important to check whether the magnet works since it will affect the entire calculation later.

3. Connect the other end of air track to the reversed vacuum system
4. Measure the mass of the air track glider.

0.343 kg

5. Use books or blocks to create at least five different angle, so that the air track glider will have five different forces of gravity acting. Record each angle.

6. Measure the Separation Distance (the distance between two magnets) created by each angle each time. Record it.

Data Analysis

• Now, we have five different separation distance. What affect these lengths to be different? Yes! It's the gravitational force acting on the air track glider.

• Now, if we plot this Force vs the Separation Distance. We will get points that seem to match a power fit. Thus, Lets do a power fit in logger pro and see what we got.

F = 8.464 x 10^-7 times R^-2.213

• Now, we basically got the equation of the Force of the Magnetic.

• What do we do with it? In the Base Theory section, we know that F = - du/dx. This means that to get U (potential energy), we need to integral force over dx. Lets do this!

• Yes. Now we got our equation for Potential Energy between Magnets.

Part 2 (Conservation of Energy: PE magnet and KE)

Procedure

1. We use the same set-up as part 1 and plus we add a motion sensor behind the magnet to record the velocity of the glider. This later will be used as Kinetic Energy.
2. Place the glider on the air track, reasonably close to fixed magnet. Run the motion detector. Determine the relationship between the distance the motion detector reads and the separation distance between the magnets. Record.
3. Give the air glider a push and record the whole motion on logger pro.

Data Analysis

• Now, we need to understand that the conservation of energy playing in the system is the Kinetic Energy of the glider and the Potential Energy of the Magnets.
• Our goal is to add up these Energy and expect a constant value of the Total Energy.
• The motion detector will gives us these data: Time, Velocity, and Position.
• We need to determine the formula for KE and PE.
• For PE, the formula we got from part 1 is: F = 8.464 x 10^-7 times R^-2.213. The separation distance (R) is the distance between magnet, which we acquire by the procedure number 2. (see picture)

• So the PE magnetic is:

• And the KE is:

• Thus, total energy is:

• Plotting all of these together, we got:

• Yes. we got the total energy to be "almost" constant with some error.

Conclusions

• We manage to get the Potential Energy of Magnet from taking the integral of the forces playing in the system. And this actually works!
• We prove that the conversation of energy is indeed true. The KE and the PE magnet sums up to be a constant value with, we admit, quite a huge error=29.5%
• These errors are from:
• When we acquire the distance measure and the angle, we have our uncertainties (0.5 cm and 0.1 degrees).
• This lead into a bigger uncertainties in our Force model, and thus our Potential Magnetic Energy.
• There are some air resistance that we do not calculate over the system.
• There are some human errors in measuring the distance etc
• But, beside these errors, we find the PE from integrating the force, and actually manage to get a quite good result!