Lab Partners: Charles, Anthony
Date performed: 10/10/16
In this lab, our goal was to verify that energy is conserved. Our setup consisted of a frictionless glider with a magnet on an air track. On either ends of the air track are magnets to which the cart's magnet opposes (because they're the same polarity). This, along with the air from the track, keeps the glider in motion back and forth across the track. With this setup, we tested and verified that conservation of energy applied to the system.
Setup of air track and glider with aluminum reflector attached onto glider
To start, we had to tackle the problem of not having an equation for magnetic potential energy. Since this is so, we had to find an equation for it, and to do that, we had to find the interaction force F(r).
First, we weighed our glider (0.352kg) and leveled the air track. Then, we found our value for r, the separation between the glider, more specifically the aluminum reflector that sits on top of the glider (attached so that the motion sensor can better detect the motion of the glider), and the magnet at the end of the air track. To do this, we used a digital vernier caliper to measure the distance between the magnet at the end of the track and the magnet on the glider. Then, we used a ruler to measure the distance between the motion sensor and the square piece. We then subtracted the first value from the second, and got the value 0.168m. This number, however, is not our r. Our separation r is the position of the glider minus this value (since the glider will be moving positions).
Once we determined how to find our r values, we collected data while tilting the track up at different angles. We used an iPhone app to measure the angle.
Data of track at different angles and the corresponding r values
Now using Logger Pro, we plotted a graph of F vs. r, assuming a relationship in the form of a power law: F=Ar^n. On Logger Pro, our A and n variables will be shown as A and B, respectively.
Logger Pro view: Graph of F vs. r with curve fit; values of A and n shown in data box
F=0.0004724r^-2.004
Once we had that equation, we were able to verify the conservation of energy. To do this, we set the motion sensor to record 30 measurements per second. Then, starting at the end of the track, we gave the cart a push to get it moving. Using our function for r that we derived earlier, we created a new calculated column to calculate the separation at various different positions.
Logger Pro view: Graphs of Position vs. Time and Velocity vs. Time
These graphs show the point at which the glider began to go backwards once it was pushed back by the same-polarity magnet. We then created three more calculated columns, one for KE, one for Umag, and one for the total energy, Etotal. We also plotted a graph for all three of those vs. time.
Logger Pro view: Graph of KE, Umag, and Etotal vs.Time
As you can see, as potential energy increases, kinetic energy decreases. This makes sense if energy is actually conserved. Looking at the total energy, it is also consistent with the conservation of energy principle.
I see lots of placeholders for diagrams and graphs. The only "picture" that shows up when I look is the data table for the separation angles and distances.
ReplyDeleteIf you can see the pictures when you log into your blog, let me know.