Set Up:
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| Cart and Air Track on Left Motion Detector on Right |
In this system, when the cart was at its closest approach to the fixed magnet, the carts kinetic energy was momentarily at zero. All of the energy in the system is stored in the magnetic field as magnetic potential energy.
Potential energy U is caused by an interaction force F. The relationship is
In this case, x=r, and we are trying to find the equation of force to find the equation of potential energy.
The set up shows a glider on our air track which is like our cart on a frictionless surface.
In the example above and just like the picture of our set-up, we raised one end of the air track so that the cart would end up at some equilibrium position.
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| The track is raised, but the air was not on which explains why the cart was not closer to the other magnet. In the experiment, the cart fell until there a small distance r between the cart's magnet and the magnet at the end of the air track. |
This equilibrium position is where the magnetic repulsion force between the two magnets would equal the gravitational force component on the cart parallel to the track.
We then used an app on my phone to get a measure of the angle lifted (instead of using height h to calculate the angle).
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| The angle is being measured on the phone |
We then collected the appropriate data by tilting the track at various angles to plot a relationship between the magnetic force F and the separation of distance r. The data was plotted onto a graph shown below:
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| The Power Fit is Shown in the Box |
We then did a power fit to the graph to find the equation F = Ar^B. We then found the integral to determine the potential energy function.
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| Data is on the left and U = (3.825x10^-7)*x^-2.213 |
Once we found the formula to the potential energy, we wanted to verify it by checking the conservation of energy.
To verify the conservation of energy:
1. We separated the car from the magnet, turned on the air track and then pushed the cart, recording its speed as it went toward the magnet and got repelled.
2. We needed to make sure the distance r recorded was correct in scale so that when we plugged r in for potential energy U we got more accurate data.
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| r = "position" -.703m |
3. Now that we could accurate graph the potential energy, we then needed to be able to graph the kinetic energy which was 1/2*m*"velocity". Since velocity was recorded, we had to find the mass show below:
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| mass = .343 kg |
4. Lastly, we graphed the potential energy, kinetic energy, and total energy all in one graph to see if energy was conserved using our magnetic potential energy equation and data collected.
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| Graph of Energy: Total energy is in blue |
As shown the total energy of the system is almost constant in the blue line. Although we could have had human error in recording the distance of r or in not having an accurate enough recording of the angle, we still managed to find the potential energy of the magnet where energy was mostly conserved providing a successful experiment.
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