LAB 13 - Magnetic Potential Energy
Tony Wu
October 13, 2016
Experimental Procedure: We first leveled the airtrack and also recorded the mass of the cart. The cart was 0.348 kg. With every test run, we measured the angle of the track and the distance between the magnets when the cart was at the bottom the track. By tracking these two values, we can associate the magnetic force F and the separation distance r. We then created a graph of F vs. r, with the assumption that the relationship takes the form of a power law, F = Ar^n.
The next part of the lab is to verify the conservation of energy. We attached an aluminum reflector to the top of the cart. With the air turned off, we placed the cart reasonably close to the fixed magnet. Using the motion detector, we determined the relationship between the distance the motion detector reads and the separation distance between the magnets. This gives us a way to measure both the speed of the cart and the separation between the magnets at the same time. We had a position distance of 0.0453 m and a separation distance of 0.020 m.
We had to make sure that we gave the cart an appropriate push towards the stationary magnet. A push that is too strong will result in the cart colliding with the end of the track. This would not give good results as some of the kinetic energy would not be transferred into magnetic potential energy. The cart could end up tilting on the airtrack if we did not push it evenly, causing the cart to come in contact with the track. This would cause a loss of energy due to friction.
Data and Calculations:
Conclusions: We created a graph of single graph showing kinetic energy, magnetic potential energy and total energy of the system. Unfortunately, we saved it on the classroom laptop and did not email it to ourselves. From that graph, we saw that the cart had a certain amount of kinetic energy, as it traveled closer to the fixed magnet, the cart slowed down and its kinetic energy was momentarily transferred into magnetic potential energy. For a moment, all the energy in the system is stored as magnetic potential energy. The cart is then pushed away by the magnets, converting its magnetic potential energy back into kinetic energy. The total energy of the system was maintained through the whole run. The energy is not perfectly maintained as the system is not a perfectly ideal, frictionless setup. There are a number of things that could affect the final values for our magnetic potential energy equation, U_mag. A likely cause of error is simply from measurement inaccuracies. We measured the distance of each magnet by hand, using only a caliper.
Lab Goal: To verify that conservation of energy applies to this system. We examine conversion of kinetic energy into magnetic potential energy and then back into kinetic energy. We will find an equation for the magnetic potential energy.
Theory/Introduction: We used an air track that has a frictionless cart with a strong magnet on one end. The cart approaches a fixed magnet of the same polarity. When the cart is at the position of closest approach to the fixed magnet, the cart's kinetic energy is momentarily zero and all of the energy in the system is stored in the magnetic field as magnetic potential energy. The cart then rebounds back and the magnetic potential energy is transferred back to kinetic energy. We did multiple test runs with the air track at different angles. By changing the angle of the airtrack, the cart ends up at different equilibrium positions. This is the point where the magnetic repulsion force between the two magnets is equal to the gravitational component on the cart parallel to the track.
Apparatus: The cart is sitting on an air track. We used a leveling application on a phone to measure the angle of the track.
Theory/Introduction: We used an air track that has a frictionless cart with a strong magnet on one end. The cart approaches a fixed magnet of the same polarity. When the cart is at the position of closest approach to the fixed magnet, the cart's kinetic energy is momentarily zero and all of the energy in the system is stored in the magnetic field as magnetic potential energy. The cart then rebounds back and the magnetic potential energy is transferred back to kinetic energy. We did multiple test runs with the air track at different angles. By changing the angle of the airtrack, the cart ends up at different equilibrium positions. This is the point where the magnetic repulsion force between the two magnets is equal to the gravitational component on the cart parallel to the track.
Apparatus: The cart is sitting on an air track. We used a leveling application on a phone to measure the angle of the track.
Experimental Procedure: We first leveled the airtrack and also recorded the mass of the cart. The cart was 0.348 kg. With every test run, we measured the angle of the track and the distance between the magnets when the cart was at the bottom the track. By tracking these two values, we can associate the magnetic force F and the separation distance r. We then created a graph of F vs. r, with the assumption that the relationship takes the form of a power law, F = Ar^n.
The next part of the lab is to verify the conservation of energy. We attached an aluminum reflector to the top of the cart. With the air turned off, we placed the cart reasonably close to the fixed magnet. Using the motion detector, we determined the relationship between the distance the motion detector reads and the separation distance between the magnets. This gives us a way to measure both the speed of the cart and the separation between the magnets at the same time. We had a position distance of 0.0453 m and a separation distance of 0.020 m.
We had to make sure that we gave the cart an appropriate push towards the stationary magnet. A push that is too strong will result in the cart colliding with the end of the track. This would not give good results as some of the kinetic energy would not be transferred into magnetic potential energy. The cart could end up tilting on the airtrack if we did not push it evenly, causing the cart to come in contact with the track. This would cause a loss of energy due to friction.
Data and Calculations:
Time vs. Position and Time vs. Velocity Graphs
Power Fit for the Force due to Gravity vs. the Separation Distance of the Magnets
Using the power fit from above, we calculated the magnetic potential energy by integrating the force.
Total Energy in the System
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