Magnetic Potential Energy Lab & Impulse-Momentum Activity
Annemarie Branks
Professor Wolf
Experiment 1:
Objective: Determine the relationship between the the separation distance of two magnets and their potential energy.
Procedure:
1. Set up your vacuum and air track so when you place a cart on it, it ends up at equilibrium. Record the angle at which the track is equilibrium. "The magnetic repulsion force should equal the gravitational force component on the cart parallel to the track."
2. Set the air track at various angles with the vacuum blowing out air. Measure the distance between the two magnets for each trial. Our mass of the cart is 0.354 kg +/- 0.001 kg. We want to know the Force of the magnets so we can find their potential energy equation. In the Free Body Diagram below, we can see that the Force of the magnets is equal to mgsinθ.
This is our measured data. The angles have an uncertainty of +/- 0.1 degrees and the separated distance have an uncertainty of +/- 0.001 meters.
3. Using LoggerPro, make an x and y column. The x will be the distance between the magnets, and the y will be the Force of the magnets which was mgsinθ. Generate a graph with these new columns along with a PowerFit.
4. Since our data points are in a curve, we can assume the function is in this format: F=A*r^B. A and B have a error margin of +/- 10%. Our Function is F=0.0002380r^(-1.848). Since Potential Energy is the negative integral of Force, we can come up with an equation for Potential energy.
5. Set up a motion detector on the stationary magnet side. Give the cart a push and begin collecting data on a Position vs. Time graph. Columns for time, position, and velocity should be made by LoggerPro. Create columns for the separated distance (which in our case was "position" - 0.20m), Kinetic energy, Potential Energy of the magnets (which we figured out in Step 4; r = "separation distance"), and Total Energy (KE + U). Generate a graph to include all of these columns in relation to time.
Conclusion: We really want to just focus on the part of the graph where we see good data that proves Conservation of Energy. The change in direction of the cart is around two seconds. We can see how, just like in spring problems we have done, that the magnets posses a potential energy that goes to zero when the mass reaches its max velocity.
We now know that the smaller the separation distance between the two magnets, the larger the potential energy is. The graph tells us that when there is a very small separation distance the force is very big. You can visually see from pushing the cart toward the stationary magnet and it slowing down and flying back that there is a noticeable potential energy.
Experiment 2:
Objective: Prove the Impulse-Momentum Theorem using a cart and spring.
Procedure:
1. Calibrate a force sensor, and set up your system with the force sensor on top of your cart so that it will horizontally push into the spring you have set up with a clamp and rod. Use an L-shaped bracket and screws to secure your force sensor to the cart. Weigh the new mass of the cart. Our mass was 0.677 kg. You will also have a spring for the cart to run into. A motion detector should be placed on the opposite end of the track from the spring. For our experiment we set the motion detector to detect at 100 data points per second.
2. Using LoggerPro, collect data of your moving cart for a Velocity vs Time graph and a Force vs Time graph. The dramatic change in the graphs are where the collision occurred. Highlight and integrate the area under the curve on the Force vs. Time graph to find Impulse. Impulse should equal to the change in momentum, so find the final and initial velocity of the collision which are indicated by the vertical rectangle below. Multiply your change in velocity by the mass to get the change in momentum. Your change in momentum theoretically should equal to your impulse.
LoggerPro gave use an impulse of 0.4231 s*N and for the change in momentum we got -0.315 s*N. The final velocity was -0.237 m/s and the initial was 0.228 m/s. The difference of those velocities times 0.677 kg gave us our momentum. I believe the Force graph is upside down and give us a negative value.
3. Repeat the experiment with added masses. We added 400 grams for a total mass of 1.077 kg.
Generate another graph like the one made in Step 2.
LoggerPro gave use an impulse of -0.4523 s*N and for the change in momentum we got -0.402 s*N. The final velocity was -0.176 m/s and the initial was 0.197 m/s. The difference of those velocities times 1.077 kg gave us our momentum.
Conclusion: The first trial gave us an impulse that was supposed to be negative, but if it were then the value would be close to the change in momentum. We got even better results for the second trial where the impulse and the change in momentum were even closer. It possible to attribute these values to errors in system, measurements, and human discrepancies. The spring wasn't at a perfect angle, LoggerPro can only capture so many frames per second, and we may have been slightly off when picking the initial and final velocities of the cart. With all this in mind, the results were fairly good in demonstrating that Impulse and momentum are equal in a system.
Experiment 3:
Objective: Prove the Impulse-Momentum Theorem using an inelastic system.
Procedure:
1. Set up your system similar to how you did in Experiment 2, but replace the spring with a piece of clay attached to a wooden block. Make sure someone is holding down the block during the experiment so it doesn't move. At the end of the Force sensor there is a hook. Put the hook in one end of the a stopper and a nail in the other end of the stopper. Place the clay/block so the nail will stab directly into it. Make sure to get rid of any holes made in the clay before starting or repeating the experiment.
2. Give your cart a push and collect data to make a Velocity vs Time graph and a Force vs Time graph. Here are our results:
3. Just as you did in Experiment 2, find the Impulse and change in momentum by finding the change in velocity and the Integral of the Force vs. Time graph. There was "shakiness" when the nail penetrated the clay. so we highlighted all of the graph where that occurred so we didn't exclude any energy transfer. LoggerPro gave us an Impulse of -0.3564 s*N. Our final velocity is 0 m/s and our initial velocity is 0.277 m/s. The difference between the two multiplied by the mass 1.077 kg gives us a momentum of -.0298 s*N.
Conclusion: We wanted to reconfirm that Impulse and Momentum are equal even in an inelastic system. We focused on the part of the graphs where the collision occurred and found that the Impulse and Momentum calculated are fairly close in value. There are still errors, as mentioned in Experiment 2, that could attribute to the difference in the numbers. Still, this is a fairly good demonstration of the Impulse-Momentum Theorem.
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