ELEMENTARY LABORATORY MEASUREMENTS

Transcription

1 ELEMENTARY LABORATORY MEASUREMENTS MEASURING LENGTH Most of the time, this is a straightforward problem. A straight ruler or meter stick is aligned with the length segment to be measured and only care in matching the segment's boundary points to ruled marks (estimating between marks) is necessary. VERNIERS AND MICROMETERS Greater precision, if the distances are not more than a few centimeters, is afforded by a caliper (see Fig. 1), which can be set to match the distance in question. The distance is in effect memorized by the instrument, which can then be removed to an area where it can be read with ease. The caliper method has a very large application in length measurements. The vernier caliper in Fig. 1 can be used to measure both inside and outside diameters, and even depths, by using the different sets of jaws or the probe at the end. (a) 3cm on the fixed caliper 0.22mm on the vernier mm on the fixed caliper Total measurement: =33.22mm Fig. 1 (b)

2 A vernier scale (see Fig. 1b) provides a better method of reading between the ruled lines of a main scale than simply estimating by eye. To read a vernier scale, first note how many divisions on the vernier are equal to an integral number of main scale divisions. In the ordinary metric vernier, ten vernier divisions are equal to nine main scale divisions. Hence the least count, or smallest value that can be read directly from a vernier scale of this type, is one-tenth of a division. The caliper divisions are millimeters, so that the least count would be one-tenth of a millimeter. The sketch in Fig. 1b shows the reading of a vernier. Sleeve reads full mm: Thimble reads: 0.368mm 35 Sleeve reads 1/2 mm: 0.50 Fig. 2 Total measurement: =11.868mm Micrometer calipers (Fig. 2) are used to measure diameters quite precisely. Turning a handle moves a rod forward, by a screw thread, until the object to be measured is clamped very gently. In the usual metric instrument, one turn of the handle advances the rod a half-millimeter. A circular scale around the handle reads fiftieths of this halfmillimeter, or thousandths of a centimeter. One more figure is estimated between scale marks. Exactly the same kind of screw, rod, and scale are often incorporated into other measuring instruments. Both vernier and micrometer calipers should always be tested for zero readings when fully closed (so of course should any other instrument). MEASURING MASS Several types of balances for weighing objects exist. With any kind, a zero reading (no load and no weights) should be taken first. Care should be taken not to overload any balance or to spill any corrosive materials on them. The trip balance, or pan balance is used for heavy objects, and for general weighing. The unknown goes in the left pan, the standard masses in the right pan. Beam balances are available in comparable size; there are also more sensitive ones for weighing small objects. In using a beam balance, the unknown is placed in the pan and a weight is arranged to slide along a calibrated beam

3 OHAUS TRIPLE BEAM BALANCE The range of this general laboratory mass balance is increased over the simple single beam form by the use of several beams (see Fig. 3). One beam is for the largest mass increment -- the movable mass on this beam can be placed, in the balances used here, in five positions besides zero. Each corresponds to an increment of 100 gm. Another beam contains a weight that can be placed in any of ten non-zero positions corresponding to increments of 10 gm. In using these two beams, each movable weight must be placed definitely in the appropriate notch. The front beam contains a weight that can slide continuously along a marked scale to a maximum corresponding to 10 gm. The maximum mass that could be measured without additional features would be gm = 610 gm. The least count of the scale is 0.1 gm, and the weight can be estimated to fractions of this smallest division. Before measuring, a zero adjustment check is made with no mass on the pan, and all sliding beam masses at their left-most positions. A thumbscrew under the pan at the left is turned in either direction until the pointer indicates zero. Recheck the zero for each use of the balance. A measurement is made by placing the mass to be measured on the pan, then moving the largest scale-mass (or poise ) to the highest position that does not cause the pointer to change position. Then the second poise is similarly adjusted so the scale reads within ten grams less than the unknown. Finally the front poise is moved until the scale returns to the zero, or balanced, position. The unknown mass will have been determined to within the smallest subdivision of the front scale, a tenth of a gram. Accurate to 0.1g, tiered beam scales read up to 610g 100g 10g 500g 100g 10g 0.1g Fig

4 OTHER BALANCES The chemical balance for weighing very small objects has two pans suspended below a light see-saw truss. Again the unknown goes on the left (except in the special technique of double-weighing ). The standard masses for such balances should be handled only with forceps, lest perspiration etch them away. The surrounding glass case is closed while judging a result, so that drafts cannot cause errors. Correct balance is determined by watching the swing of a pointer, not by waiting for it to come to rest (friction may hold it off center). There are also electrically operated balances which give readings of mass directly upon dials, after prescribed settings have been made. For most applications in our lab, the triple beam balance is adequate. Measurement of Elapsed Time: Electronic Time-Measuring Units Note: The following discussion is based on the Pasco Scientific electronic system. An alternate system (Daedelon timers) can sometimes serve in specific limited applications. The manual mode of operation of an electronic timer is identical to that of a digital stopwatch. The Pasco Model 8025 Timer (Fig. 4b) accumulates time in 6 microseconds (1 s 10 seconds) in the timer mode, and when used in the split timer mode, it becomes two separate timers which independently record the time elapsed in milliseconds (more on this later). It also contains provisions for the use of external oscillators instead of the internal circuitry for special applications. Please note that two different Pasco models exist in the laboratory: most are the newer system, based on the Model 9215 Timer but the older Model 8025 is still often used. You can find the lab equipment manuals through the following link

5 (a) (b) Fig. 4 Manual Timing When the timer is turned on via the connected power unit ON-OFF switch, a random digital number may (or may not) appear on the display. A RESET button on the timer clears the display to zero. For the Model 8025 one may choose from the FREQUENCY, COUNTER, and TIMER modes. The first two choices are used in special applications involving an external oscillator and will not be further discussed at this time. After the TIMER mode has been selected, one must choose either the PULSE or GATE mode. If the GATE mode is used, depression of the START/STOP button will start the timer and release of this button will stop it. If the PULSE mode is used, the first depression of the button will start the timer and the second depression will stop it. Used in this stopwatch mode, a manually operated timer has another feature common to stopwatches if it is operated after one timing operation without clearing the timer by RESET, the display simply accumulates more counts which may or may not be what you want to do. Manual timing clearly has many applications in the physics laboratory. One of its obvious limitations is the human reaction time (characteristically, hundreds of

6 milliseconds) involved in recognizing the start and stop instants in a process of interest. TO AVOID THIS LIMITATION, WE CONSIDER A SENSING DEVICE THAT CAN MAKE THE PHYSICAL MOTION ITSELF SWITCH THE ELECTRONIC TIMER ON AND OFF AUTOMATICALLY. Photo Transistors The electrical properties of certain materials change drastically when they are exposed to light, compared to their behavior in its absence. Their ability to pass an electrical current is one such property. A phototransistor (used in the application of interest here) constructed of such material can be thought of as a light-actuated switch. It is automatically turned on when bright light strikes its sensitive surface and turned off when the bright light is removed. Ordinary room light does not affect it. Phototransistors have, among many other uses, an important application in the laboratory because they switch states very rapidly they can be used in measuring precisely even very short time intervals. When the light beam that switches the transistor on and off is mounted properly, across the path of a moving object, the object can turn this kind of switch on and off without disturbing its own motion. The following sections show how mechanical motion can be timed by causing the object itself to control the precision timer by its own motion through light beams. Further information can be found in the Pasco manual for the Model 8025 on the Brown Physics lab wiki : C+Frequency+Meter.pdf?version=1&modificationDate= To use the photocell (the mounted, powered phototransistor) effectively, it is made an integral part of a photobridge. The latter consists of both the photocell and the bright light source mounted in a frame that holds the two elements in careful alignment, and separated by a few centimeters. The shape of the bridge allows mechanical objects to pass between the source and photocell, interrupting the beam as they pass through. The standard photobridge unit is a common way to monitor many kinds of motion which involve a well-defined path in space, such as falling objects, or objects constrained to move along a track, or in a circle. When such constraints don't exist, the path an object will take cannot be known well enough beforehand to position a light beam across it, and other methods could be more effective (photographing the object, for example). When a photobridge is used as a monitor, the photocell connects directly to both the power supply and the timer to provide its signals to the HOLD circuits, thus performing the same functions as are performed to operate the timer in the manual mode. Timing with a Single Photobridge NOTE: ALWAYS TURN OFF THE MODEL 8000 POWER SUPPLY WHEN MAKING CONNECTIONS BETWEEN UNITS

7 When using the Model 8025 Timer, the model 9204 Photobridge (Fig. 5), which contains both source and detector, is connected by means of a stereo phone plug to socket A on the back panel of the timer. Its mode of operation is exactly the same as that of the photobridge described above. When the photocell is illuminated by the light source, this connection will cause the timer circuitry to be held in the off state so that counting will not take place. The photobridge now controls the counter circuits, suppressing timer operation until the light is masked from striking the photocell. Stereo phone plug The particular way that masking turns the timer on depends on the MODE switch setting: Clamp Source Detector In PULSE MODE, masking the light will start the timer, which will continue running even when the mask is removed. When the mask is restored, the second pulse will turn the timer off. In GATE MODE, the timer will start when the light is masked, and will turn back off when the light is restored. Fig. 5 Another way to describe the MODE settings is to say that PULSE alternately activates and deactivates the timer on successive transitions from light to dark, at the photocell, while GATE activates the timer only during the dark periods. These operations can be checked simply by turning on the Model 8025 power supply and using RESET 8025 timers to clear their displays. Use your finger, or a ruler, or a piece of paper to mask the light, and verify the behavior of the counter/timer for each of the two modes. Applications of single photobridge timing GATE MODE timing is useful for measuring the speed of a body passing through the bridge. The length of the body, (or of a mask attached to the body,) divided by the recorded time, gives the speed. If the speed is not constant, the average speed through the bridge is what is measured. When the photobridge is mounted appropriately it can monitor the speed of objects dropping vertically, swinging on a pendulum, moving along a track, and so on. In some arrangements, for example a swinging pendulum, the object will repeat its passage through the bridge over and over, and some thought must be given to the fact that successive passages will each generate a timer reading that adds to the

8 existing reading. In this case, the memory unit in the Model 8025 Timer can store one previous measurement. PULSE MODE timing with a single photobridge is limited to cases where: a) Once the body moves through the bridge to start the timer, some other action will generate a pulse to stop it. An example is an arrangement that lets you drop an object through the bridge to hit a pushbutton kind of switch. The bridge would turn the timer on, and the button switch would stop it, giving the travel time between the two devices. An instructive example is to have someone start the timer by tripping the photobridge out of your line of vision. If you watch the display with your finger on a similar pushbutton, and turn the timer off as soon as you see it counting, the timer reading is a good estimate of your reaction time. b) Some other action starts the timer, and the photobridge pulse turns it off. In analogy with one of the previous examples, you could imagine holding an object against a push button switch, from which it will drop through the photobridge. Here the button turns the timer on, and the bridge pulse turns it off, giving the travel time of an object that starts from rest and falls through a specified distance. c) Repetitive motion brings the object back through the photobridge, such as the pendulum swinging back and forth. Notice that simply switching the mode of timing from the GATE MODE in which this example was first cited to the PULSE MODE changes completely the physical meaning of the registered time. One GATE MODE reading gives the travel time of the body through the bridge; one PULSE MODE reading is the time taken for the body to swing through the bridge to the end of its motion and to swing back through the bridge (which is a time known as the half-period of the oscillation). As described above, the memory units may also be used to record consecutive measurements in this mode. Timing With Two Photobridges and One Counter Possible applications of the Model 8025 timers and 9215A timers are considerably expanded when two photobridges are connected to the same timing unit. (REMEMBER, ALL CONNECTIONS ARE MADE WITH THE POWER OFF). As many as four photobridges may be hooked to the Model 8025 timer at one time. This may be effected by plugging two photobridges into both stereo phone jacks A and B by means of 1 x 2 stereo phone plug adaptors. In the Timer mode, all four of the bridges are connected to one timer with microsecond resolution. In the SPLIT-TIMER mode, the timer display is split into two four-digit segments marked A and B by a flashing colon. The photobridges on jack A are monitored by timer A, while those on jack B are monitored by timer B. The two timers, with their respective photobridges,

9 operate independently of each other and can be used to time two concurrent events with millisecond resolution. However, both timers must be used in the same mode (either GATE or PULSE), and the RESET button will reset both timers together. Applications of Double Photobridge Counting GATE MODE timing with multiple photobridges on the same counter is equivalent to having many velocity meters, according to the usage (cited for a single photocell) when a mask of known length is combined with the time to give the velocity. The complication that needs to be handled is that the physical arrangement should allow enough time for the first reading to be noted before the body passes through the second bridge, etc. This is necessary because the time generated at each successive bridge will add to the original time reading, and one has to know how to separate the total time. Notice that it is not necessary to RESET manually between timer activations; that only adds to the separation time required. It can be alleviated on the Model 8025 Timer by recording independent measurements in the SPLIT-TIMER mode and by using the Timer's internal memory, which can record and hold one previous reading while accumulating more counts. One area where the reading time requirement can usually be met easily is on an air track, where gliders move slowly compared, for example, to falling body experiments. Air track examples that the double configuration measures well in GATE MODE are recoil collisions and accelerations. The first example can even be done with one photobridge for certain kinds of collisions, but with two photobridges virtually all types of collisions can be monitored. The basic theme is to place the bridges on each side of the area where the bodies will collide. Then, by noting the first readings, which give the velocities before the collisions of two gliders, you can unravel the velocities after collision. The second example that the configuration handles, an accelerated glider, applies because constant acceleration can be deduced from the difference of two velocity measurements. Newton's second law of motion can be checked if the glider is connected via a pulley to hanging masses. If the track is inclined, a component of the gravitational force acts directly to accelerate the gliders, and this acceleration is also constant at any particular angle. In general, if the acceleration is not constant, it is the average acceleration that is measured. PULSE MODE timing with two photobridges has the additional sensing element that the single bridge examples lacked. With two bridges, one to start the count in PULSE MODE and the other to stop it, velocities over much longer paths can be measured than those of GATE MODE. This concludes the introduction to electronic timing with the Pasco Scientific modules, either in manual operation or with one or more photobridges. The configurations and techniques used as examples will be used frequently in the elementary laboratories. While four bridges is the maximum number that will drive a single timer,

10 the number of timers connected to a single experiment obviously can be increased as necessary. Each timer functions in one of the configurations discussed here