To try to prove this goal, we took the approach that says for any system that has non-constant potential energy the potential energy is caused by an interaction force (F). Hence, we used a glider with a magnet attached to one end (on an air track) and had it glide towards a magnet at one end of the track at various angles and recorded the distance (r) between the magnets when the glider stopped by itself so we could get enough data to make a graph that gave us a relationship between the force (F) and the distance (r). The force in this case was calculated with gravitational potential energy (mgh), since we assumed that this was the only force acting on the glider on its way towards one end of the track. To get the relationship we used a power fit curve that calculated the slope values for two variables that would complete the formula for our assumed potential energy of the system. Last, to test that our formula was correct we did an experiment where we gave the cart a gentle push and measured its kinetic energy with the help of a motion sensor that recorded the distance and time of the cart during the trial so we could obtain the velocity of the cart. That data allowed use to get a value for kinetic energy that had to match the simultaneously recorded values for potential energy and total energy of the system. The potential energy of the system was calculated with the use of our formula the was obtained earlier in the experiment, and the use of the motion sensor that calculated the distance (r) that we had to plug into our formula for potential energy.
To begin this experiment, we had to level the track that the glider would glide on and measure the mass of the glider. To level the track, we used a program on Kevin's iphone called "bubble level" and to measure the mass we used a digital balance. Next, we did several trials that involved tilting the track and turning on the power source of the air track (so the glider would glide) and let the glider travel towards the end of the track until it stopped by itself so we could measure the distance between the magnet ends and the angle of the track for further use. The calculations for the gravitational potential energy of each trial were then calculated with the formula (mgh) were "h" was the value of sin(angle) and entered into loggerpro so we could make a graph of the force per each trial vs. the distance (r) between the magnets per each trial. Note that the angle per each trial was also measured with an application on Kevin's iphone. After that, the slope of the graph that we had just made allowed us to obtain a power fit formula for the potential energy of the system in relationship to the distance (r) per each trial. Lastly, to test the formula we did another experiment in which we calculated the kinetic energy of the glider by giving it a gentle push towards the magnet end of the track with the use of logger pro and a motion sensor and compared it to the potential energy and the total energy of the system during that experiment. The potential energy graph was given the formula that involved the distance (r) which the motion sensor measured during the trial to complete the graph, and the total energy graph was given the formula of total energy= kinetic energy+ potential energy.
This is an image of the air glider and its' track. Note the motion detector at the same end of the track as the magnet.
This is another image of the track set-up.
This is an image of the Force vs. radius graph that we used to get the unknowns for our power law formula for the assumed potential energy formula. Note, the values for A and B on the slope box were the ones we used for our calculations.
This is the power law formula format that we tried to get with our data: F=Ar^n.
This is an image for the proof that our formula for potential energy was correct because the graphs show that the energy of the system was conserved during the experiment. Hence, the kinetic energy all turned into potential energy when the glider stopped and the total energy (in blue) was conserved during the total experiment. Note that the distance (r) between the magnets changed, but that both of the graphs still showed the energy was conserved leading towards the proof that our formula for potential energy was correct.
In conclusion, we did gather enough energy to show that potential energy is a cause of some force before the measurable value of potential energy. For example, the graphs showed that the energies were conserved because once the kinetic energy went to zero then the potential energy increased to the last value of the kinetic energy; also, the total energy of the system (that is seen through the graph) was at a constant total value of energy throughout the experiment. As far as errors for this experiment, not many were noticed by me because my interpretation of the graph that displayed the three energies is that the total energy that was in the system was conserved throughout the experiment. Although, I do believe frictional force was involved during the experiment (but I can't prove it) and that the measurements for the distance (r) during the entire experiment were slightly off so that caused the experiment to have some incorrect results that I can't explain with the given results. The reason I think there was frictional force is because the air track that we used was very old so I think there were areas in the track with less air flow that caused some friction; and the reason I think there were distance measurement errors is because we used a simple ruler that is not 100% accurate. Lastly, even though there were likely errors we were still able to see a clear relationship that lead me to conclude that we did prove there is a conservation of energy for a system.
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