Velocity Measurements

Counting is a simple operation for digital systems. As a result, it's often desirable to be able to convert the physical quantity you want to measure into an interval of time and use counters and a reliable clock to digitally measure that time interval. Hence any quantity easily converted into either a frequency or a period can be measured almost trivially by counting. Perhaps the simplest example of this is measuring velocity, where the connection between time and distance allows simple time measurements to give fairly high resolution measurements of speed. For example, by measuring the time required for an object to travel a fixed distance, the average speed can be extracted easily. This lab will involve making timing measurements on one of two systems. One timing problem is to measure the time-of-flight of a projectile (specifically a BB) shot from a gun over a fixed distance. The other system consists of timing the duration of the contact between a thin metal rod dropped onto a heavy steel block as the rod bounces back. The duration of contact in the bouncing process can be related to the speed of sound in the rod. The counting system developed in Physics 3061 (the one you used to measure your reaction time) serves as the foundation for the measurements to be made in this experiment. As a clock source in this lab, you will use a pre-packaged crystal oscillator with a frequency of 1 MHz that produces TTL compatible levels and requires a +5 V supply. Crystal-based oscillators constitute a stable, convenient fixed frequency source. Once your circuit is running you will be able to measure precisely the frequency of your particular oscillator with a commercial frequency counter. Your report should contain a complete circuit diagram of your system and a full description of its operation, as well as the data collected and analysis carried out.

BB Experiment: The basic idea is quite simple: detect when the BB passes a known reference point, start counting clock pulses, and stop when the BB passes a second reference point. This clearly requires several components. Most of the essential components should already be ready from the previous lab. You should also be sure your existing counting circuit can be started and stopped in a manner compatible with the the rest of your system. You may need to modify your start/stop circuit (clearly the push-button of the previous lab is not suitable for this application). The most difficult aspect probably involves designing a suitable mechanism for detecting the arrival of the BB at the start and stop points and ensuring that your measurements will not be significantly affected by switch bounce. The counting, display, and debouncing aspects can be taken care of largely without detailed knowledge of the switching mechanism, but rather just a general idea. Attack the problem in a modular fashion. Choosing a switch mechanism is the most troublesome aspect of the problem. A couple of varieties have been used in the past. The simplest method is to rely on the BB to break a thin strip of aluminum foil as it passes each of the two reference points and incorporate the aluminum foil as a switch, initially closed (continuous) and then open (broken) (similar to the scheme described in a problem in chapter 8 of Horowitz and Hill). This method can be tedious but is simple to implement. Proper positioning of the aluminum strips can be accomplished by first placing thin sheets of paper in the path of the BB at the measuring points to locate the proper foil position based upon holes left by a trial shot. A more elegant (and more difficult to implement) scheme uses an optically driven transistor (photo-transistor) and an infrared-emitting LED or a red laser (c.f. the discussion of optical interrupters in Horowitz and Hill). The BB breaks the beam of light to the photo-transistor (the base is photo-sensitive) and momentarily turns the transistor off. Once again, one can use the transistor as a switch and detect the change in state. This method requires careful alignment of the source and detector pair and for truly reliable operation requires an AC coupled op-amp-based amplifier plus a comparator at the front end. The aluminum foil method, while tedious, is at least straightforward, using a minimum of additional components. You should carry out at least five complete, reliable measurements, compute the velocity of the BB, and estimate the uncertainties in your results based upon careful consideration of your measurement methods and the precision of your measured values.

Contact time: If you allow a piece of material to be dropped onto another, the falling piece will usually bounce one or more times. Upon first contact, both it and the piece underneath are momentarily compressed before the falling piece returns to the air. The situation here is a thin metal rod dropped onto a heavy steel plate. The objective is to measure how long the rod remains in contact with the plate during the first bounce. You will need to invent an appropriate “switch” circuit to carry out this measurement. To do the necessary counting make use of as much of your circuit from the preceding lab as possible. Then, after thinking about the physics of the bounce, determine the speed of sound in the metal rod. In thinking about the bouncing process, you'll need to be able to explain exactly how it is that the rod is made to move upwards after contact with the plate, and when the bottom end of the rod is made to leave the plate. Since this experiment is supposed to yield a speed of sound, the fact that the rods are stiff but not perfectly rigid must in some way be relevant. You should carry out measurements (at least ten, since the measurements themselves will take very little time) for three rods of different materials. For (at least) one rod you should also investigate how the contact time depends on initial height the rod is dropped from. For each material tested report an average speed of sound deduced from your measurements as well as an uncertainty in that calculated value. Compare your measured value to values reported in handbooks (e.g. CRC Handbook of Chemistry and Physics). If you discard any measurements during your data analysis, suggest reasons or mechanisms why they can be discarded in analyzing your data.