Kevin Nguyen
Lab Partners: Jose Rodriguez, Kevin Tran
Date of lab performed: 21-Apr-2017
Purpose: This lab was designed to verify that conservation of energy applied to the apparatus (pictured below).
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| "r" represents the distance between the magnet at the end of the trash and the magnet on the glider. "h" represents the height of air track from the ground. |
Summary of experimental procedure
First, we set up our apparatus like the picture shown above. We made sure to make the air track as level as possible (0.0 degrees). We then tilted the air track at different angles to find the relationship between magnetic force (F) and separation distance (r) (explanation in "List of Calculated Data" section). We then plotted a graph of magnetic force (y-axis) vs separation distance (x-axis). Since we assume that the relationship between magnetic force and separation distance takes form of the power law F = Ar^n, we made a power line fit of the graph.
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| This is a magnetic force vs separation distance graph, not force vs radius graph. The uncertainty of the "A" parameter is plus or minus 4.619*10^-06 The uncertainty of the "B" parameter is plus or minus 0.08493 |
"U(r) = (8.76756*10^-6)r^-1.566."
Since we solved the problem of finding the equation for magnetic potential energy, we could now verify the conservation of energy. we attached an aluminum reflector on top of the air track cart in order for the motion detector to accurately record the speed of the cart. After weighing the cart, we put it back on the track. We put the cart as close to the magnet as possible (without the magnets touching) and ran the motion detector in order to determine the relationship between the distance the motion sensor reads and the separation distance between the magnets.
After setting the motion detector to 30 samples per second, we created a new calculated column that allowed us to get the separation between the magnets from the position measured by the motion sensor. We also created other calculated columns that allowed us to find kinetic energy, magnetic potential energy, and total energy (graph below). We started with the cart at the far end of the track and, after starting the detector, gave it a small push. We made a single graph that showed kinetic energy, magnetic potential energy, and total energy in respect to time.
List of Measured Data
List of Calculated Data
After setting the motion detector to 30 samples per second, we created a new calculated column that allowed us to get the separation between the magnets from the position measured by the motion sensor. We also created other calculated columns that allowed us to find kinetic energy, magnetic potential energy, and total energy (graph below). We started with the cart at the far end of the track and, after starting the detector, gave it a small push. We made a single graph that showed kinetic energy, magnetic potential energy, and total energy in respect to time.
List of Measured Data
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| Angle between track and table/ separation between magnets/ magnetic force |
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| Solving for Magnetic Force |
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| Graph of Kinetic energy (purple), potential magnetic energy (red), and total energy (blue) |
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| Finding the separation distance |
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| Equation for kinetic energy |
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| Calculating magnetic potential energy |
Explanation of Graphs/ Analysis:
First we made a graph of magnetic force vs separation distance. We made this graph because integrating the magnetic force in respect to separation distance gave us the magnetic potential energy. Finding the magnetic potential energy helped us in verifying if conservation of energy applied to this apparatus.
We also made a graph for kinetic energy, magnetic potential energy, and total energy. We made this graph to help us verify the conservation of energy by checking if the total energy is a straight line. The total energy line needs to be a straight line since the conservation of energy suggests that the energy lost from kinetic energy was transferred to magnetic potential energy. If the total energy line is a straight line, then that means that conservation of energy does apply to this apparatus.
Conclusion:
Using the graph containing the kinetic, magnetic potential, and total energy, we found that the total energy line is not a straight line. Since the total energy line was not a straight line, it meant that the conservation of energy does not apply to the apparatus. But this was not the case. When we adjusted the separation distance from .257 meters to .254 meters, the total energy line became more straight. The uncertainty in the separation distance greatly affects our results since a small change in the separation distance will change the shape of the total energy line completely, which affects our answer of verification of the conservation of energy of the apparatus.
Another source of uncertainty was that the track was not completely frictionless. This fact affects the velocity of the air track cart since friction decreases the cart's velocity. A decreased velocity leads to a decreased kinetic energy (since velocity is directly proportional to kinetic energy). The decreased kinetic energy affects our answer of verification of conservation of energy of the apparatus.
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