We know that a, non constant, magnetic force, that is dependent on the separation distance, is exerted, between two magnets in this case. This force can then be integrated to solve for the potential energy.
To setup this experiment we used a motion detector, an air track with glider, two fairly strong magnets, a leveling device, and something that could be stacked in order to change the angle of the track, we used a set of old encyclopedias. We first leveled the track and made sure that when turn on the glider could travel across smoothly. Then we started to change the angle of the track by small increments, which we recorded, and measured the separation distance. Below is an image with the setup of the experiment.
Below is a table of what we recorded that also includes the force exerted by gravity parallel to the track.
We then plotted the collected values on a graph and integrated to find the area under the curve.
Force = (mg)*sin(angle) = ma
The area under the curve represents a value equal to the total potential energy of the system. Next we used the motion detector to find values of velocity, once pushed on the leveled track the acceleration should remain at or near zero so we ignore it, and with velocity we can find kinetic energy. The system is made up of potential and kinetic energy so if we add them up we get a total value for energy which we plotted as you can see below.
We see from the above graph that the magnitude of velocity seems constant, on the lower graph, which is what we would expect on a leveled track without an external force applied. Then on the upper graph we see our energy graphs. Orange is potential, purple is kinetic, and red is total energy. Once again we see that we live in a not so perfect world but still we can be happy with our results as we see a semi constant total energy.
It seems odd to graphically integrate the F vs. r function.
ReplyDeleteYou could get U(r) by integrating the F(r) that you got from the curve fit.
How did you generate the U vs. r graph for the collision?