Our project is a science exhibit that shows the concept of instantaneous velocity. It shows that as a disc rolls, the instantaneous velocity at the very top point of the disc is twice the velocity of the center of the disc. (Figure 1)
To illustrate this concept, the exhibit has two parts. The first part will measure the speed of the top and the center of the disc as it rolls past the sensors. This speed is then shown on a computer screen to show that the speed at the top is twice the speed at the center. The second part will attempt to show this difference in speed visually. A disc with light emitting diodes (LEDs) on the top, center and bottom will be rolled. In a dark room, observers will see a longer trail of light corresponding to the LED on the top and a very short trail of light corresponding to the LED on the bottom.
Learning physics is both an intuition-building process and a modeling process. Using these two themes, we wanted to produce an exhibit that would delve into the broad yet simple subject of instantaneous velocity and, in our case, with special emphasis on rotating disks. The concept in question centers around the fact that the velocity of a rolling disk at its center is 1/2 the instantaneous velocity at the point on top. Also, and just as interesting, is the fact that the point in contact with the ground has zero velocity. To add factors into the equation, we decided to roll this disk on a slope, perhaps one that could be changed, to illustrate some concept of gravity. Or perhaps just to make the disk roll faster, as everyone knows that faster is good.
In reality, the design process was nowhere near as clean-cut or predictable as the previous paragraph would like you to believe. We were initially inspired by an exhibit in the ITLL where a "square wheel" rolled smoothly along a surface perfectly tailored to it. We tried to conceive of some mechanism for making the wheel arbitrary shapes and a way to dynamically modify the surface to keep it going. Even very basic ideas of how to do this seemed far too difficult to do in the few weeks we had available. More brainstorming began to revolve around rotating things. Mike Eisenberg (our esteemed and brilliant professor with whom we take no shame in attempting to suck up to) came up with an idea of showing the unintuitive physics concept described earlier. Things rolled along from there.
Our first idea was to use some sort of visual trails on the disk to show relative speeds. We decided we wanted to use LEDs in a dark environment. Optimally, they would blink at intervals exactly synchronous with the turning of the wheel to remove the light trails at the front and back (which would distract the viewer from the concept). Other options we decided not to pursue included using some sore of drawing device that would map out the relative speeds. This didn't seem as promising because it would be best implemented without computation. Even disregarding the fact that we would be bypassing the whole point of the project, it didn't strike us as especially intuitive, or, to make up a word, as intuition-grabbing. Besides, it wouldn't have cool looking colored LEDs. While we did seem to focus on visual phenomena, there are other ways to influence intuition. For example, if you have ever rolled down a hill in a tire, you probably felt something related to our concept in the change of acceleration. You were probably also too disoriented by vertigo and/or on the edge of nausea to appreciate the phenomena. One possibility for a museum environment is to present our exhibit (after paying us mega-bucks to build it for you) followed by an area where children and adults alike could actually try rolling down a hill in a tire. In the best scenario, there would be a chilidog stand right before the ride.
To actually implement the visual part, we connected 3 LEDs of different colors to the top, middle and bottom of a wooden disk. We used two AA batteries and enough resistors to avoid burning out the LEDs. Blinking would have been nice, but it was deemed unnecessary and thus dropped to "if there's time" status. For the ramp and rolling area, it was constructed by putting wood strips together. A stop was added at the end and guides were needed to keep the disk on track. A hinge was also added to the end to make the entire assembly configurable by height. Check out figure 2 and all will be revealed.
While intuition may be a guide, quantification is how you actually get there. We wanted to provide a mechanism for experimentation in a real, numerical situation. Our vision was to build sensor equipment that would approximate the instantaneous velocity at the top, middle and bottom of a rolling disk. We planned on using infrared sensors to measure the passage of the disk. The data would be transmitted to a PC over a parallel port, then processed and displayed on a screen. Users would be able to roll the disk and see the readings displayed automagically with other useful representations of the data such as graphs or pictures. In this type of situation, it would be best to have several sets of data, so the readings could be taken on different parts of the ramp. One would hope that users could experiment and get a better sense of the concept.
Implementing this aspect of the exhibit would prove to be very difficult. However, that was at least in part because of poor decisions made in the beginning. We had knowledge and access to several kits and systems that would do the job. The MIT crickets were one example. With a light sensor on input, two crickets could be used to transmit data to a computer. There would have been several problems with this. First, a single cricket didn't have enough input ports to even measure the velocity at the top and bottom of a disk at one moment in time. An attempt at using multiple crickets would bring up issues about how to get the data back to the computer. Even if we somehow managed to pull it off, the sensors were known to be somewhat inaccurate with low sampling rates. Other solutions were available in commercial form. There were several kits we looked into which either could either do what we wanted in terms of measuring the velocity of the disk or facilitate the data transmission the computer. However, the cost was prohibitive. In retrospect, these might have been one of our better alternatives, had we been willing to spend the money. A kit would have drastically cut down on technical problems will allowing us to focus on creating an informative and insightful exhibit.
Instead, we opted to attempt and build custom infrared sensors and interface. This would be our stumbling block and largest mistake. Neither of us had much experience in electronics while the little we did possess was from quite some time ago. We got bogged down in trying to get even the sensors working, let alone the parallel port interface. Had we used some sort of kit, this would have gone much quicker, leaving more time for other things. After blowing up three batteries, popping the fuse on a multimeter and generally exhibiting incompetence, we did get the sensor working to a degree. However, the final straw would be the realization that the infrared detector we chose was somehow getting readings even through the disk. It responded to infrared input in the form of an emitter circuit we built, as well as input from a remote control, yet even when blocked by 3/4" of wood, the detector functioned. At this point, we had wasted too much time getting the circuit to work in the first place and were without enough time to change the design. To be fair, it was less of a question of the time we were given, and more of a question of being overconfident in our ability to implement the sensors. Thus we continually worked on getting a sensor implementation instead of seeking other solutions. The circuit had seemed so close to working we just couldn't put it down, yet it had problem after problem (many of them due to builder error).
The exhibit still has merit, despite our inability to produce a working prototype this time around. Our problems were technical in nature, yet problems that have been solved before by other people. So perhaps the real problem was in planning and execution. The exhibit could be very insightful for those with no physics knowledge to those with some. Even for others who understand the phenomena reasonably well, it would be an interesting reinforcement of the concepts. In future classes, please emphasize the educational/computational aspects over the more technical aspects. To clarify, if students have a good idea for an exhibit or toy or whatever else, get them to focus on taking the easy paths for the technical ideas and concentrate on perfecting the educational parts. While we learned a lot about electronics, our project was far from a learning experience in how to build an exhibit. This is because we made mistakes in deciding what we wanted to do and weren't able to complete it. Thus, when a student or group comes up with an interesting exhibit that's also technically difficult, make sure they emphasize the educational aspects and take every advantage to simplify the technical aspects.
We did have a fallback plan in place, but it failed as well. The idea for us was that if we couldn't get multiple points on the ramp working, we would use a single point and forego attempts to measure acceleration of the disk or other quantities. If we couldn't get five sensors working to measure speeds at the top and bottom of the disk, we would fall back to one sensor and change the entire experiment into something concerning acceleration due to gravity. However, we couldn't even get one sensor working reliably. Thus we were left with a somewhat incomplete visual exhibit and little else; a disappointing exhibit to say the least.
In the end, we learned that one should be very careful when planning and even more careful when early decisions on incomplete data can be difficult to change later on. One would have hoped we would have learned to take the easy road from our last project, but it was not to be. We also learned to focus on the important things and not get derailed by the details. These seem like lessons we should have learned long long ago, but apparently not. If we hadn't learned them before, we know them now, so at the very least we come away a little wiser about how to plan and execute building projects.