Physics 201/207 Lab Manual Mechanics, Heat, Sound/Waves

R. Rollefson, H.T. Richards, M.J. Winokur

August 29, 2001

Contents

Forward 2

Introduction 4

I Mechanics 8

MC-1 Errors & Motion 8 MC-1a Measurement and Error . . . . . . . . . . . . . . . . . . . . . . . . 8 MC-1b Errors and the Density of a Solid . . . . . . . . . . . . . . . . . . . 12 MC-1c Motion, Velocity and Acceleration . . . . . . . . . . . . . . . . . . . 15

II Appendices 19

A. Precision Measurement Devices . . . . . . . . . . . . . . . . . . . . . . . . . 19 B. The Travelling Microscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 C. The Optical Lever . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 D. PARALLAX and Notes on using a Telescope . . . . . . . . . . . . . . . . . 25 E. Notes on Radiation Dosage, Dosimetry, and the Radon Problem . . . . . . 27 F. PASCO\begin{matrix}c \\ ◯ \end{matrix} Interface and Computer Primer . . . . . . . . . . . . . . . . . . . 30

Forward

Spring, 2001

We are gradually revising the manual to improve the clarity and interest of the activities. In doing this, we have discovered the tremendous amount of work that M.J. Winokur and M. Thompson did in order to bring the manual into its current electronic form. I speak for the students and Physics Department when I say: Thankyou!

M. Briggs J. Sylvester B. Grogan

In reference to the 1997 edition

Much has changed since the implimentation of the first edition and a major overhaul was very much in need. In particular, the rapid introduction of the computer into the educational arena has drastically and irreversibly changed the way in which information is acquired, analyzed and deseminated. To reflect these changes in the introductory laboratory we have endeavdored to create a educational tool which utilizes this technology to its fullest extent; hopefully while enhancing the learning process and the understanding of physics principles. Thus, when fully deployed, this new edition will be available not only in hard copy but also as a fully integrated web document so that the manual itself has become an interactive tool in the laboratory environment.

The introductory student will find a wealth of learning resources to be available while the laborary is being performed. Too many times students have questions during these lab sessions which could be answered if the student could access additional information. In the past the teaching assistant has been the only source of this additional information and, if already occupied, too often these questions went unanswered. There are also instances in which a student may inadvertently stumble and produce a lab write-up containing a major error. Too often this mistake is only seen at a latter time when the instructor is correcting the lab reports. Students do not always have the opportunity to go back and make it right and so the misunderstanding is never satistisfactorily resolved. By making an interactive lab manual we hope to provide students with immediate feedback so that if they do stray from the straight and narrow, a timely course correction is provided.

M.J. Winokur M. Thompson

From the original edition

The experiments in this manual evolved from many years of use at the University of Wisconsin. Past manuals have included “cookbooks” with directions so complete and detailed that you can perform an experiment without knowing what you are doing or why, and manuals in which theory is so complete that no reference to text or lecture was necessary.

This manual avoids the“cookbook” approach and assumes that correlation between lecture and lab is sufficiently close that explanations (and theory) can be brief: in many cases merely a list of suggestions and precautions. Generally you will need at least an elementary understanding of the material in order to perform the experiment expeditiously and well. We hope that by the time you have completed an experiment, your understanding will have deepened in a manner not achievable by reading books or by working ”paper problems”. If the lab should get ahead of the lecture, please read the pertinent material, as recommended by the instructor, before doing the experiment.

The manual does not describe equipment in detail. We find it more efficient to have the apparatus out on a table and take a few minutes at the start to name the pieces and give suggestions for use. Also in this way changes in equipment, (sometimes necessary), need not cause confusion.

Many faculty members have contributed to this manual. Professors Barschall, Blanchard, Camerini, Erwin, Haeberli, Miller, Olsson, Visiting Professor Wickliffe and former Professor Moran have been especially helpful. However, any deficiencies or errors are our responsibility. We welcome suggestions for improvements.

Our lab support staff, Joe Sylvester and Harley Nelson, have made important contributions not only in maintaining the equipment in good working order, but also in improving the mechanical and aesthetic design of the apparatus.

Likewise our electronic support staff (Mike Murrary, Jerry Glowacki, and Art Webb) not only maintain the electronic equipment, but also have contributed excellent original circuits and component design for many of the experiments.

R. Rollefson H. T. Richards

Introduction

General Instructions and Helpful Hints

Goals

Physics 201/202 and 207/208 are introductory calculus-based physics courses which introduce the undergraduate student to a broad spectrum of fundamental physical laws spanning from mechanics to heat and thermodynamics to electricity and magnetism to waves and light. To help develop a meaningful understanding of these physics principles the beginning student is presented with a variety of resources: textbooks, lectures and demonstrations, problem solving, discussion sessions and the laboratory.

Of these, the laboratory component furnishes a unique opportunity for demonstrating physical principles in both a qualitative and quantitative hands-on fashion. An inseparable aspect of this laboratory experience should be the realization that physics is, first or foremost, an experimental science in which the limitations of the instrumentation and the technique of the experimenter can heavily impact the scientific process. Hence this laboratory experience is intended to provide the student with a diverse set of experiences including: a realistic feeling for the origin and limitations of physical concepts; an awareness of experimental errors, of ways to minimize them and how to estimate the reliability of the result in an experiment; an appreciation of the need for keeping clear and accurate records of experimental investigations.

Throughout this laboratory experience there is one crucial step for achieving these stated goals in an enduring way: Simply put, a clearly written laboratory notebook in which each of the aforementioned components is documented and recorded. This lab notebook, at a minimum, should contain the following:

1. Heading of the Experiment: Copy from the manual the number and name of the experiment. Include both the current date and the name(s) of your partner(s).

2. Original data: Original data must always be recorded directly into your notebook as they are gathered. “Original data” are the actual readings you have taken. For example if you know that each in a series of distance measurements is in error by a constant offset of 0.006 mm, then you should record the actual readings (containing this error) and then, afterwards, either correct each data point or the average. In this way it will always be clear that you have made appropriate corrections. Also, when you take 5 or 6 successive readings of a measurement, record each reading, not just the average. From the scatter of the readings, you can estimate the precision of the measurement. Both partners should record data, so that errors of recording show up. (Complete trackability, say if you were producing a part for the space shuttle, would require that you record serial numbers of equipment. You could then find the same equipment to check results later.) Arrange data in tabular form when appropriate, and properly label each item or table.

3. Housekeeping deletions: You may think that a notebook combining all work would soon become quite a mess and have a proliferation of erroneous and superseded material. Indeed it might, but you can improve matters greatly with a little housekeeping work every hour or so. Just draw a box around any erroneous or unnecessary material and hatch three or four parallel diagonal lines across this box. (This way you can come back and rescue the deleted calculations later if you should discover that the first idea was right after all. It occasionally happens.) Append a note to the margin of box explaining to yourself what was wrong.

We expect you to keep up your notes as you go along. Don’t take your notebook home to “write it up” – you probably have more important things to do than making a beautiful notebook. (Instructors may permit occasional exceptions if they are satisfied that you have a good enough reason.)

4. Remarks and sketches: Avoid, when possible, “pictorial” sketches of apparatus. On the other hand, a simple diagrammatic sketch is useful and is sometimes the simplest and clearest way to define the various quantities indicated in a table of data; a phrase or sentence introducing each table or calculation is essential for making sense out of the notebook record. When a useful result occurs at any stage, describe it with at least a word or phrase.

5. Graphs: There are three appropriate methods:

A. Affix furnished graph paper in your notebook with transparent tape.

B. Affix a computer generated graph paper in your notebook with transparent tape.

C. Mark out and plot a simple graph directly in your notebook.

Show points as dots, circles, or crosses, i.e., ·, ∘, or ×. Instead of connecting points by straight lines, draw a smooth curve which may actually miss most of the points but which shows the functional relationship between the plotted quantities. Fasten directly into the notebook any original data in graphic form (such as the spark tapes of Experiment M4).

6. Units, coordinate labels: Physical quantities always require a number and a dimensional unit to have meaning. Likewise, graphs have abscissas and ordinates which always need labeling.

7. Final data, results and conclusions: At the end of an experiment some written comments and a neat summary of data and results will make your notebook more meaningful to both you and your instructor. Note that perfect results are not essential when making a quantitative measurement. “Good” results occur when your value agrees, within appropriate limits of error, with the expected result. “Bad” results occur if the measured value falls outside the range given by uncertainty. This latter result may be perfectly acceptable if a satisfactory explanations (i.e., a legitimate error) for the failure can be forwarded. In fact, most people seem to learn more from their failures rather than their successes.

INTRODUCTION 6 PARTNERS

Limitations of space and equipment usually require that one works with a partner. In addition, discussing your work with someone as you go along is often stimulating and of educational value.

Independent calculations; checks: If possible both partners should perform completely independent calculations. Mistakes in calculation are inevitable, and the more complete the independence of the two calculations, the better is the check against these mistakes. Poor results on experiments sometimes arise from computational errors. CHOICE OF NOTEBOOK

We recommend a large bound or spiral notebook with paper of good enough quality to stand occasional erasures (needed most commonly in improving pencil sketches or graphs). To correct a wrong number always cross it out instead of erasing: thus 3.1461 ////// 3.1416 since occasionally the correction turns out to be a mistake, and the original number was right. Coarse (1/4 inch) cross-ruled pages are more versatile than blank or line pages. They are useful for tables, crude graphs and sketches while still providing the horizontal lines needed for plain writing. Put everything that you commit to paper right into your notebook. Avoid scribbling notes on loose paper; such scraps often get lost. A good plan is to write initially only on the right-hand pages, leaving the left page for afterthoughts and for the kind of exploratory calculations that you might do on scratch paper. COMPLETION OF WORK

Plan your work so that you can complete calculations, graphing and miscellaneous discussions before you leave the laboratory. Your instructor will check each completed lab report and will usually write down some comments, suggestions or questions in your notebook.

Your instructor can help deepen your understanding and “feel” for the subject. Feel free to talk over your work with him or her. Using the Computers: Printing You will want to avoid printing two copies in rapid succession. Wait for your computer to finish “spooling” before sending your next print job, or you risk crashing your computer and thereby loosing all your data.

Part I

Mechanics

MC-1 Errors & Motion

MC-1a Measurement and Error

OBJECTIVES:

The major objectives of this first, short (est. 1 hr) computer lab are to begin to develop an understanding of what it means to make an experimental measurement and provide a methodology for assessing random and systematic errors in this measurement process. In addition this lab will also give you a minimal framework in which to introduce you to the PASCO\begin{matrix}c \\ ◯ \end{matrix} (page 30) interface hardware and software.

THEORY:

By now you should have had numerous opportunities to become familiar with time and the concept of a time interval. The increment of one second will be used as an intuitive reference point. In this lab you will test your ability to internalize this one second time interval by making and recording a repetitive flicking motion with your finger. By flicking your finger back and forth you will move it though an infrared beam sensor (i.e. the PASCO photogate) and each full cycle (back and forth, approximately 2 seconds) will be simultaneously recorded, plotted and tabulated by the PASCO interface software.

Your goal in this experiment is to assess the size of systematic and random errors in your data set and learn a simple methodology for distinguishing between the two. SYSTEMATIC ERRORS: These are errors which affect the accuracy of a measurement. Typically they are reproducible so that they always affect the data in the same way. For instance if a clock runs slowly you will make a time measurement which is less than the actual reading. RANDOM ERRORS: These are errors which affect the precision of a measurement. A process itself may have a random component (as in radioactive decay) or the measurement technique may introduce noise that causes the readings to fluctuate. If many measurements are made, a statistical analysis will reduce the uncertainty from random errors by averaging.

APPARATUS:

⇒ Computer with monitor, keyboard and mouse. ⇒ A PASCO photogate and stand: This device emits a narrow infrared beam in the gap

and occluding the beam prevents it from reaching a photodetector. When the beam is interrupted the red LED should become lit. (Plugged into DIGITAL CHANNEL #3.)

⇒ A PASCO Signal Interface (CI-700) monitors the photodetector output vs time and can be configured to tabulate, plot and analyze this data.

PROCEDURE:

To configure the experiment you should refer to Fig. 1 below. Adjust the photogate so that one member can easily and repetitively flick his/her finger through the gap. The phone-jack cable from the photogate should be plugged into the DIGITAL CHANNEL #3 socket. Ignore the other sensors which may already be plugged into other sockets. It is important that the PASCO interface be turned on before the computer. If not the computer will not recognize it and, therefore, it must be rebooted to properly communicate with the PASCO module.

Figure 1: A schematic of the M0C components.

To initiate the PASCO (page 30) interface software you will need to click the computer mouse on the telescope icon in the “toolkit” area below. Fig. 2 below gives a good idea of how the display should appear. Note that, while you are able to reconfigure the display parameters, the default values that are specified on start-up will allow you to do most of this experiment without necessitating any major changes.

You will note that a “dummy” first data set already exists on start-up showing a typical data run. In the table you can view all 35 data points and the statistical analysis, including mean and standard deviation. In addition there should be a plot of this data and a histogram.

SUGGESTED PROCEDURE:

1. Start the preliminaries by CLICKing on the MONitor icon and practice “flicking” a finger back and forth so that a two second interval appears in the window. CLICK on the STOP icon when done. (The upper left window is configured like a tape player). The same person need not perform both operations. The purpose of the “monitor” function is to permit adjustments and trials without storing the results in memory.

2. Start the data run by CLICKing on the RECord icon and stop it by CLICKing on the STOP icon. Each run gets its own data set in the “Data” display window. (If there are any data sets in existence you will not be able to reconfigure the interface parameters or sensor inputs.)

3. With the REC option on, cycle a finger back and forth fifty times and STOP the data acquisition. DO NOT watch the time display while you do this, since you want to find out how accurately and precisely you can reproduce a time interval of 2 s using only your mind.

Figure 2: The PASCO SCIENCE WORKSHOP display window

4. What is the mean time per cycle? What is the standard deviation? The mean \overline{t} and standard deviation σ are given by:

\overline{t} = ∑_{i=1}^{N} t_{i}/N and σ = \sqrt{∑_{i=1}^{N}(t_{i} − \overline{t})^{2}/[N − 1]} .

Questions to consider: I. Is your mean suggestive of a systematic error? II. Does your data qualitatively give the appearance of a normal distribution (i.e. a Gaussian bell curve.)

5. For analyzing and quantifying random errors, you need to asses how a data set is distributed about the mean. The standard deviation σ is one common calculation that does this. In the case of a normal distribution approximately 68% of the data points fall within ±1σ of the mean (90% within ±2σ). Is your data consistent with this attribute?

6. Assessing the possibility of systematic behavior is somewhat more subtle. In general σ is a measure of how much a single measurement fluctuates from the mean. In this run you have made fifty presumed identical measurements. A better estimate of how well you have really determined the mean is to calculate the standard deviation of the mean \overline{σ} = σ/\sqrt{N}. After recording \overline{σ} in you lab book, can you now observe any evidence that there is a systemic error in your data? Answer this same question with respect to the first “sample” data set.

7. OPTIONAL: Systematic errors can sometimes drift over time. In the best-case scenario they drift up and down so that they hopefully average out to zero. (Clearly it would be better if they could be eliminated entirely.) With respect to \overline{t} and \overline{σ} for the first 25 and second 25 cycles do you observe any systematic trends? Use the “region of interest” feature of the statistical analysis software by using the mouse and highlighting (in black) a data subset (through a CLICK and drag motion) over the rows of interest.

MC-1b Errors and the Density of a Solid

OBJECTIVES:

To learn about systematic and random errors; to understand significant figures; to estimate the reliability of one’s measurements; and to calculate the reliability of the final result.

NOTE: This experiment illustrates the earlier sections on Errors and Significant Figures. The actual density of the metal is incidental. However, the accuracy of your estimate of reliability will show whether you have mastered the material in the earlier sections.

APPARATUS:

Metal cylinders of varying sizes, micrometer and vernier calipers, precision gauge blocks, precision balance. Precautions: Avoid dropping or deforming in any other way the metal cylinders. Avoid damage to the precision screw of the micrometer by turning only the friction head to open or close the caliper jaws. Be sure to disengage the caliper lock before using. (The caliper lock lets you preserve a reading.) \underline{Improper weighing procedures may damage the precision balance.} Consult your instructor if in doubt. In handling the gauge blocks avoid touching the polished surfaces since body acids are corrosive.

INTRODUCTION:

First read the material on Errors and Significant Figures in the Manual Introduction??). Since density is the mass per unit volume, you must measure the mass (on a balance) and compute the volume (hπr^{2} = hπd^{2}/4) from measurements of the cylinder’s dimensions where d is the diameter and h is the height. Any one of three length measuring devices may be used. These include a micrometer, a vernier caliper and/or a simple metric ruler. The micrometer will permit the highest precision measurments but using one can be cumbersome, especially when reading the vernier scale. All methods will demonstrate the aforementioned objectives. Your instructor will give you guidance in choosing an appropriate measurement device.

THE MICROMETER:

Record the serial number of your micrometer. Then familiarize yourself with the operation of the caliper and the reading of the scales: work through Appendix A. on the Micrometer. Note that use of the “friction” head in closing the jaws insures the same pressure on the measured object each time. Always estimate tenths of the smallest division. Some micrometers have verniers to assist the estimation.

THE VERNIER CALIPER: Work through Appendix A. on the Vernier Caliper. You should also try the java vernier at java vernier http://webphysics.davidson.edu/. Experiment with one of the large verniers in the lab until you are sure you understand it. Note that verniers need not be decimal: for many inch scales the vernier estimates 1/8’s of the 1/16 inch division, i.e. 1/128’s of an inch. However vernier calipers divide the inch into 50 divisions and the vernier estimates 1/25 of the 1/50 inch divisions, i.e. 1/1000 inch or 1 mil. The vernier was invented 1631 by Pierre Vernier.

Precautions on use of the calipers:

1. Unclamp both top thumbscrews to permit moving caliper jaws.

2. Open caliper to within a few mm of the dimension being measured.

3. Close right thumbscrew to lock position of lower horizontal knurled cylinder which executes fine motions of caliper jaw. Never over tighten!

CALIBRATION OF THE MICROMETER (or VERNIER, ETC.):

1. OPTIONAL: Wipe the micrometer caliper jaws with cleaning paper. Then determine the zero error by closing the jaws. Make and record five or six readings. The variation of these repeated readings gives you an estimate of the reproducibility of the measurements. (For those using the micrometers they have been given a small zero error. Thus a zero error correction is necessary.) In general any measurement device can have a zero error.

2. Measure one or four (OPTIONAL) calibration gauge blocks (6, 12, 18, and 24 mm): Set the gauge blocks on end, well-in from the edge of the table, and thus freeing both hands to handle the caliper. Record the actual (uncorrected) readings and take several readings (3 to 5) of each gauge block used. If measuring only a single block choose one with a thickness intermediate to the diameter and height of the metal cylinder.

3. If using a single precision block obtain a correction factor you will use to minimize systematic measurement errors. Otherwise, plot a correction curve for your micrometer, i.e. plot errors as ordinates and nominal blocks sizes (0, 6, 12, 18, and 24 mm) as abscissa. Normally the correction will not vary from block to block by more than 0.003 mm (for the micrometer). If it is larger, consult your instructor.

DENSITY DETERMINATION:

1. Make five measurements (should be in millimeters) of the height and five of the diameter. Since our object is to determine the volume of the cylinder, distribute your measurements so as to get an appropriate average length and average diameter. Avoid any small projections which would result in a misleading measurement. If not possible to avoid, estimate their importance to the result. Record actual readings and indicate how you distributed them.

2. Calculate the average length and average diameter reading, and then use your correction value (curve) to correct these average readings. If you were to use the uncorrected values, how much relative error would this introduce?

3. Calculate the standard deviation for your length and diameter averages.

4. Weigh the cylinder a few times on the electronic balance; estimate to 0.1 mg.

5. From the average dimensions and the mass, calculate the volume and density. Make a quantitative (refer to Section ??) estimate of the uncertainty in the density. You should use, as your starting point:

Density(ρ ± Δρ) = ρ(h ± Δh, d ± Δd, m ± Δm) = \frac{m}{π(d/2)^{2} h}

6. Compare the density with the tabulated value. Tabulated values are averages over samples whose densities vary slightly depending upon how the material was cast and worked; also on impurity concentrations.

7. In your notebook or lab form summarize the data and results. Also record your result on the blackboard. Is the distribution of blackboard values reasonable, i.e. “normal” distribution (refer to Section ??, pg. 9)?

OPTIONAL: To test how accurately you can estimate a fraction of a division, estimate the fractions on the vernier caliper before reading the vernier. Record both your estimate and the vernier reading.

Related facts and URL links:

Question: Why are there are exactly 25.4 mm in 1 inch?

Answer(not verified): The Treaty of the Meter (Convention du Metre) in the late 19th century established the first centralized international system of metrology. This defined the meter.

In 1959, the countries of the world that were using Imperial units defined them uniformly based on the metric units. The inch was simply defined that way and agreed to by all. Before 1959, different countries related inches to meters in other ways. Among them was the United States. The Metric Act of 1866 defined the meter in terms of inches (i.e., before the Treaty of the Meter), and that relationship had continued to been used even after the Treaty fixed the length of the meter.

Changing the definition in the U.S. in 1959 caused very little problem, except for the U.S. Geological Survey. When you deal with things 10^{5} meters big (like the sizes of the states), even 1 part in 10^{5} changes affect the specifications of boundary lines in significant ways. So, to this day the U.S. has two different systems of inches, feet, and yards (in the ratio of 36:3:1, for both). There’s the usual inch, foot, and yard; and there’s the survey foot (and inch and yard), which is based on the pre-1959 definition. (The ambiguity goes away, of course, when metric specification is used. Newer USGS maps are metric.)

Links to metrology site(s): National Institute of Science & Technology at http://www.nist.gov/

MC-1c Motion, Velocity and Acceleration

OBJECTIVES:

The major objectives of this exploratory computer lab are two-fold. Since you will be using computer based data-acquisition throughout this course, we expect you to become familiar with the PASCO\begin{matrix}c \\ ◯ \end{matrix} (page 30) interface hardware and software. Our second objective is for you to develop an intuition for Newtonian mechanics by experimenting with 1-D motion. There is no extensive write-up in this lab, but only a series of recommended experiments and the requirement to write down your observations in your lab book/form.

THEORY:

The motion of an object is described by indicating its distances x_{1} and x_{2} from a fixed reference point at two different times t_{1} and t_{2}. From the change in position between these two times one calculates the average velocity (remember that direction is implied) for the time interval:

average velocity ≡ \overline{v} = \frac{x_{2} − x_{1}}{t_{2} − t_{1}} = \frac{Δx}{Δt} m/s

The acceleration of an object is found by finding its velocity v_{1} and v_{2} at two different times t_{1} and t_{2}. From the change in velocity between two different times one calculates the average acceleration for the time interval:

average accelation ≡ \overline{a} = \frac{v_{2} − v_{1}}{t_{2} − t_{1}} = \frac{Δv}{Δt} m/s^{2}

FUNDAMENTAL CONCEPTS:

1. The equation that describes the motion of an object that moves with constant velocity is: x = A + B · t. If you make a plot of x versus t, you find that it describes a straight line. The letter A indicates the position of the object at time t = 0. The letter B is the slope of the line, and is equal to the velocity of the object. So we can rewrite this x = x_{0} + v · t.

2. The equation that describes the motion of an object that moves with constant acceleration is: x = x_{0} + v_{0} · t + \frac{1}{2}at^{2} and v = v_{0} + at. So we can rewrite this as: x = A+Bt+Ct^{2} and v = B +2Ct. The letter A indicates the position of the object at time t = 0. The letter B is the the velocity of the object at time t = 0, and is the slope of the graph at this time. The letter C is equal to half the acceleration.

PRECAUTIONS:

In order for the position sensor to work properly it must be pointed in such a way that it “sees” the vane, and doesn’t identify the front of the cart; that means that it must be pointed slightly upwards. The sonic ranger tends to “see” the closest reflecting surface. In addition the minimum range is approximately 40 cm. Make sure you do not drop the carts or allow them to roll off the table, because it damages the bearings and they begin to suffer too much friction. Try to arrange to keep the cart on the track all the time.

APPARATUS

⇒ Computer with monitor, keyboard and mouse.

⇒ A PASCO position sensor; this device emits a series of short pulses of sound, and receives the echo of the sound reflected by a nearby object. The length of the time interval between the emission and the reception of the sound pulse depends on the distance to the reflecting object. This method of locating an object is the same as the one used by bats to find flying insects or by navy ships to locate submarines.

⇒ A PASCO Signal Interface converts the time interval between the emission and reception of the sound pulse to digital form , i.e., numbers that can be then plotted on the monitor.

⇒ PASCO dynamic track with magnetic bumpers; cart with reflecting vane; meter stick; one or two steel blocks.

PROCEDURE:

Your instructor will demonstrate how to configure the experiment. To initiate the PASCO(page 30) interface software you will need to click the computer mouse on the telescope icon in the “toolkit” area below. The Fig. 1 below shows how the display should appear. Note that, while you are able to reconfigure the display parameters, the default values that are specified on start-up will allow you to do this experiment without necessitating any changes. All three measured quantities, position, velocity, and accelation, are displayed simultaneously. Since velocity is determined from the position data and acceleration from the velocity the “scatter” in the data will become progressively more pronounced.

Figure 1: The PASCO scientic workshop display format Experiment I, Basic Operation and Sonic ranger calibration:

1. To start the data acquisition CLICK on the REC icon. To stop it CLICK on the STOP icon (the upper left window is configured like a tape player). Each run gets its own data set in the “Data” display window. If there are any data sets in existence you will not be able to reconfigure the interface parameters or sensor inputs, unless you clear (delete) all data.

2. With the REC option on move the cart to and fro and watch the position, velocity and acceleration displays.

3. STOP the data acquisition.

4. CLICK once (or twice) on the AUTOSCALE icon. CLICK on the MAGNIFY icon and move to one of graph regions and CLICK again. CLICK on the CROSSHAIR icon and move about on the various graphs. Change the plot display region be manual adjusting the x-min, x-max, etc. values. To do this CLICK in the various scale (time, position,etc.) areas. CLICK on the STATISTICS icon once and then again. Make sure that all three members of the team have an opportunity to test these components. It is imperative that the basic operations on the software interface are understood by everyone!

5. DELETE the data set by a CLICK on the RUN #1 item in the “Data” window and then striking the “Delete” (<DEL>) key.

6. Start the data acquisition and observe the closest distance to the sonic ranger at which it still functions. This value is supposed to be close to 40 cm. If it is much larger, re-aim the position sensor.

7. Configure the distances so that when the cart nearly touches the near magnetic bumper the sonic ranger still records accurately.

8. Measure the position at two distances approximately 1 m apart and compare the printed centimeter scale with the position sensor readout. By how much do the readings differ?

Experiment II, Inclined Plane and Motion:

1. Raise the side of the track furthest from the position sensor using one of the supplied blocks. Hang the 500 g weight off the other side to weigh the front end down and prevent unwanted slippage of the track (See the demonstration set-up to see how the weight should be positioned.)

2. Find an appropriate release point that allows the cart to roll down the track without striking the magnetic bumper.

3. CLICK the REC button and release the cart letting it bounce three or four times and the CLICK the STOP button.

4. Qualitatively describe the shape of the three curves: position, velocity and accelation and discuss how they evolve with time.

5. Obtain a hard copy of this data by simultaneously pressing the Alt-p keys.(Only one copy is made even if you ask for more.) Repeat this step to get additional copies.

6. Label/identify the various key features in the various curves by writing directly on the hard copies. Paste the graphs in your note bood.

QUESTIONS: (to be discussed as a group)

1. Does the velocity increase or decrease linearly with time when it is sliding up or down the track?

2. When the velocity is close to zero can you observe any discrepancies in the data? Can you think of a reason for any deviations from linearity?

3. Why does the maximum of the position readout fall with each subsequent bounce?

4. Is the collision with the magnetic bumper or the residual friction in the bearing the most likely source of loss?

5. Can you think of a method using your data to determine which of these two proposed

mechanisms is the most likely culprit? Experiment III, Reproducing Expt. II manually:

1. Remove the block so that the cart is no longer raised.

2. Start a new data set (by clicking the REC button) and try to move the cart back and forth at constant velocity using your hand from the side. Alternatively have one team member aim the position sensor at another member holding a book waist-high and walk towards the sensor or away from the sensor.

3. Using the cross hair estimate your velocity in either m/s or cm/s.

4. Repeat step 3. but now try to obtain a region of constant accelation. Experiment IV, Accelation at g (9.8 m/s^{2}):

1. Have one member of the group stand carefully on a chair and hold the position sensor facing downward above another member’s head while he or she is holding a notebook on their head.

2. Start a new data set and have the student holding the notebook jump up and down a few times.

3. Stop the recording and determine whether free-fall yields a constant accelation close to the accepted value.

4. You may wish to try the statistical analysis module to measure your acceleration. Ask you lab instructor for a demonstration.

5. Fini.

Part II

Appendices

A. Precision Measurement Devices

Vernier Calipers:

Figure 1: The vernier caliper

A Vernier consists of a fixed scale and a moving vernier scale. In a metric vernier the fixed scale is marked in centimeters and millimeters, the vernier scale is nine millimeters long, and is divided into ten parts each 0.9 millimeters long. The distances of each line from the first are therefore 0.9, 1.8, 2.7, …,mm or generally: d_{i} = 0.9×i, where d_{i} is the distance between the zero line and the i^{th} line of the vernier scale. If the vernier caliper is closed, so that the two jaws touch each other, the zero of the fixed scale should coincide with the zero of the vernier scale. Opening the jaws 0.03 cm = 0.3 mm will cause the fourth line (the three line which is a distance of 2.7 mm from the zero line of the of the vernier scale) to coincide with the 3 mm line of the fixed scale as shown below.

Figure 2: The vernier reads 0.03 cm

Below is another example of vernier reading; the arrow shows which mark on the vernier scale is being used.

EXERCISES:

A. Close the vernier and observe that the first vernier mark coincides with the zero of the centimeter scale.

B. Open the jaws of the vernier very slowly and observe how the different vernier marks coincide successively with the millimeter marks on the fixed scale: the first mark

Figure 3: The vernier reads 9.13 cm

coincides with the 1 mm mark on the fixed scale; then the second mark coincides with the 2 mm mark on the fixed scale; then the third mark coincides with the 3 mm mark on the fixed scale and so on.

C. Estimate the dimension of an object using a meter stick and then Use the vernier caliper to measure the dimension precisely.

D. In the four examples of Fig. 4 determine the actual reading.

Figure 4: Test cases

Micrometer:

A micrometer can measure distances with more precision than a vernier caliper. The micrometer has a 0.5 mm pitch screw, this means that you read millimeters and half millimeters along the barrel. The sleeve is divided into 50 divisions corresponding to one hundredth of a millimeter (0.01 mm) or 10 μ each. The vernier scale on the micrometer barrel has ten divisions, marked from 2 to 10 in steps of two. The “zero” line is not marked ‘0’, but is longer than the others. The vernier allows you to read to the nearest thousandth of a millimeter, i.e., to the nearest micron (0.001 mm = 1 μ).

Figure 5: The micrometer calipers

Precaution: Great care must be taken in using the micrometer caliper; A ratchet knob is provided for closing the caliper on the object being mea- sured without exerting too much force. Treat the micrometer with care, ALWAYS close the calipers using the ratchet knob, this pre- vents tightening the screw too strongly. Closing the calipers too hard damages the precision screw.

Below are two examples of micrometer reading; the arrow shows which mark on the vernier scale is being used.

Figure 6: The micrometer reads 20.912 mm

Figure 7: The micrometer reads 3 μ

In Fig. 7 the zero line on the barrel is barely visible, and the vernier reads 0.003 mm = 3 μ; the zero error is ϵ_{0} = 3μ. A negative zero error, as shown below requires a moment of thought.

Figure 8: The micrometer reads -4 μ

In Fig. 8 the zero line on the barrel of the micrometer is obscured by the sleeve, (the “zero” line on the sleeve is above the “zero” line on the barrel) this corresponds to a reading of -0.5 mm; the vernier reads 0.496 mm the zero error is then ϵ_{0} = −0.5 + 0.496 = −0.004mm = −4 μ.

B. The Travelling Microscope

The sliding carriage of the traveling microscope rides on carefully machined ways, pushed by a nut under the carriage which rides on the micrometer screw. The nut must not fit tightly on the screw or it will bind; hence there is always some slack built into the mechanism.

When the nut is being pulled to the right (dial being turned toward larger numbers), the screw threads will press against the threads in the nut as shown in Fig. 1, with the screw threads in contact with the back side of the threads on the nut. When the direction of turning reverses, the screw threads then push on the front side of the nut threads.

Figure 1: Blacklash in screw mechanism.

For the microscope set initially on the same line for both directions of motion, the readings will differ by distance S, the backlash (slop) in the mechanism.

One way to avoid trouble with this slack is always to make settings after turning the screw more than the slack in one direction, say the direction of increasing readings. If one overshoots on a reading, go back by more than the slack and then turn forward again. The screw will then always press on the same side of the nut and no error arises.

A much better experimental technique is to take readings both ways. Suppose one wants to measure the distance between two lines, 1 and 2. Call the reading turned toward larger readings on line 1, D_{1} and when turning in the reverse direction, R_{1}; similarly for D_{2} and R_{2}. Then the distance between the lines will be D_{2} − D_{1} and also R_{2} − R_{1} so that one has immediately two independent readings to compare. More important, D_{1} − R_{1} is the slack in the mechanism; it should equal D_{2} − R_{2} and should be the same for all pairs of readings. If D − R changes by more than the experimental error in setting, you know immediately you have made a blunder in either setting or reading and can immediately repeat the measurement. The constancy of D - R is actually an excellent measure of the uncertainty in the measurements you are taking.

C. The Optical Lever

An optical lever is a convenient device to magnify a small displacement and thus to make possible an accurate measurement of the displacement. Experiment M-11, Young’s modulus, uses an optical lever to magnify the extension of a wire produced by a series of different loads.

The plate P carries a mirror M. The mirror mount has two points resting in a fixed groove, F, and at the other end has a single point resting on the object whose displacement one is measuring. Raising the object through a distance ΔL will tilt the mirror through an angle θ or ΔL/d radians (approximately) but will turn the light beam through an angle 2θ.

Figure 1: Schematic of the optical lever.

Hence

θ = \frac{ΔL}{d} ∼ \frac{\frac{1}{2}(y_{1} − y_{0})}{D}

if θ is small so that θ ∼ tan θ. Therefore

2θ = \frac{2ΔL}{d} = \frac{y_{1} − y_{0}}{D} , and Δl = (y_{1} − y_{0}) [\frac{d}{2D} ] .

Note that with the telescope nearly perpendicular to the scale at the beginning then y_{0} is close to the telescope, and the difference between two elongations (ΔL_{2} −ΔL_{1}) is very accurately given by

ΔL_{2} − ΔL_{1} = \frac{y_{2} d}{2D} − \frac{y_{1} d}{2D} = \frac{(y_{2} − y_{1})d}{2D}

where y_{i} is the scale reading. This relation holds so long as 2θ is small enough that tan 2θ ∼ 2θ.

D. PARALLAX and Notes on using a Telescope

1. PARALLAX:

To do quantitative work in optics one must understand parallax and how it may be eliminated. PARALLAX is defined as apparent motion of an object caused by actual motion of the observer.

When the observer’s eye is in position 1, objects 1 and 2 are in line and may appear to coincide. If the eye is moved to the left to position two, object 1 (i.e. O_{1}) appears to move to the left with respect to object 2, (i.e. O_{2}). If the eye moves to the right to position 3, object 1 (O_{1}) appears to move to the right with respect to object 2 (O_{2}).

As object 1 moves toward position 2 along the dotted line, its apparent displacement with respect to object 2 caused by motion of the eye from 2 to 3 gets smaller until it vanishes when O_{1} and O_{2} coincide. When O_{1} gets closer to the eye than O_{2}, the direction of its apparent displacement reverses for the same eye motion. In short, the object farthest from the eye apparently moves in the same direction as the eye. Try this with two fingers.

Note that if O_{1} is an image and O_{2} a cross hair, the absence of parallax shows that the cross hairs are in the plane of the image.

2. Focusing a Telescope for Parallel Rays:

The eyepiece E slides back and forth in the tube T and one should first adjust the eyepiece to give a clear image of the cross hairs. Then move the tube T back and forth in the barrel B until the image of a distant object, formed by the objective O, falls on the plane of the cross hairs. The test for this is the absence of parallax between the cross hairs and image.

The rays from a distant object are nearly parallel. For viewing a distant object, use an open window if the window glass is not accurately plane. Otherwise poor image formation may result. You can check by trying it both ways. At night use a distant object in the hallway.

The telescope, now focused for parallel rays, will stay so as long as the distance between O and C is unchanged. One may still adjust the eyepiece position to suit the observer.

3. Finding an Image in a Telescope:

If you have trouble finding an image in a telescope, locate the image first with your unaided eye, and then pull the telescope in front of your eye, aligning it with your line of sight. With high magnification it is difficult to find the image in the telescope because the alignment must be nearly perfect before the image appears in the field of view. The eye has a rather large field of view so that the image will be visible over a range of positions.

E. Notes on Radiation Dosage, Dosimetry, and the Radon Problem

INTRODUCTION:

The biological effects of radiation arise from the absorption of the radiant energy to produce heat, electronic excitation and/or ionization.

Radio, T.V., microwave, visible light, u.v. light, x-rays, γ-rays are all electromagnetic radiation and differ only in wavelength. Electromagnetic radiation may have both beneficial and harmful effects: e.g. u.v. light absorbed by the skin can supply needed vitamin D, but excess u.v. radiation accounts for much skin cancer. X-rays and γrays are more penetrating and so can affect tissue below the skin.

Besides electromagnetic radiation one has high velocity charged (and neutral) particles. From naturally radioactive materials, the charged particles are either high speed electrons (β’s, beta rays) or alpha particles (α’s, the nuclei of helium atoms). Both types are rather easily stopped by a small thickness of matter e.g. ∼ 1.8 mm Al stops 1.17 MeV β’s from RaE, and ∼ 0.06 mm Al stops 5.3 Mev α’s from Po. Hence natural radioactivities are normally of little concern unless the parent nucleus has been inhaled or ingested in the body. The biological effects of neutral particles (e.g. neutrons and neutrinos) from naturally radioactive materials are normally negligible.

Radioactivity unit: 1 becquerel (Bq) = 1 disintegration/s ≅ 27 pCi (picoCurie) Radiation dose is the radiant energy absorbed per unit mass.

Dose UNITS: 0.01 J of radiation absorbed/kg of mass = 1 rad

1 J of radiation absorbed/kg of mass = 1 gray (abbreviated

Gy)

Dose Equivalent: includes the long term relative biological effects of different types of radiation. The original unit was the rem (rad equivalent man), but the now recommended S.I. unit is the sievert (abbreviated Sv) with:

1 Sv = 100 rem = 10^{5} mrem and so: 1 mSv = 100 mrem

Federal laws on permissible doses are:

1. For workers, < 50 mSv/year for a whole body dose, but employer must follow the ALARA (As Low As Resonably Achievable) principle. For the hands alone, 750 mSv/yr are allowed.

2. For the general population < 5 mSv/yr whole body dose.

RADIATION SOURCES:

Besides the sun’s u.v. radiation, the natural environment contributes an unavoidable dose equivalent to ∼ 1.3 mSv/yr plus a variable dose from inhaled radon which often is several times larger: see The Radon Problem (below). Hence the average natural background radiation dose is ∼ 3 mSv/yr. About .25 mSv/yr of this dose comes from internal radioactivities in the body (chiefly ^{40}K which constitutes 0.0119% of natural K and has T_{1/2} ∼ 10^{9} years). The rest comes from external natural radioactivities in the earth (chiefly decay chains of uranium and thorium, T_{1/2} ∼ 4 × 10^{9} years and T_{1/2} ∼ 10^{10} years) and from cosmic rays. The cosmic ray contribution increases with altitude and is ∼ 30 mSv/yr at 40,000 feet elevation (jet airplane altitudes).

Brick and stone houses often have larger backgrounds. Living in Denver (elevation 5200 ft.) contributes an additional ∼ 0.7 mSv/yr. In the Kerala region of India and the Espirito Santo region of Brazil, natural sources give ∼ 30 mSv/yr with no obvious abnormality resulting to the indigenous population so the Federal regulations seem very conservative for the general population.

Man-made radiation exposure averages ∼ .7 mSv/yr and comes almost exclusively from medical and dental x-rays. A single dental x-ray may involve 7 mSv to the skin. Exposures from nuclear power generating stations are nearly zero. In fact, per KWH of electricity generated, the radioactivity released from coal fired plants is often high compared to that permitted from nuclear plants since many coals contain appreciable uranium and/or thorium plus the equilibrium decay products from these long-lived radioactive nuclei.

For perspective on radiation exposure, Prof. Cameron of the UW Medical Physics Dept. suggests translating doses into a natural unit, the BERT defined as the Background Equivalent Radiation Time. Thus a BERT equal to 1 yr would correspond to 3 mSv (see above discussion on average background dose).

THE RADON PROBLEM: Radon (an inert gas) from decay of naturally occurring U and Th in the earth continually diffuses into the atmosphere and may cause ∼ 10,000 lung cancer cases per year in the U.S. The radon content of outdoor air 1 meter above ground typically gives 4 to 15 becquerels/m^{3} The health effects come mainly from inhalation of ^{222}Rn (from U) since this radon isotope has a T_{1/2} of 3.82 days whereas the thorium radon isotope (^{220}Rn) has T_{1/2} of only 56 seconds. The indoor air concentration of radon (∼ 50 Bq/m^{3}) varies perhaps a factor of a thousand from location to location, depending upon the U content and physical characteristics of the soil, moisture content, building construction, winds, etc. (A house in Maine had a record ∼ 160,000 Bq/m^{3}!)

A radon concentration of 50 Bq/m^{3} may result in an annual dose equivalent to bronchial epithelium (site of most radiation induced lung cancer) of ∼ 2.5 mSv/yr. Perhaps 25% of Wisconsin houses have concentrations > 150 Bq/m^{3} which is the EPA guideline where action should be taken in a few years since the lung cancer risk may be comparable to smoking 3 to 10 cigarettes/day. (M.S. Blumenthal, Wisconsin Medical Journal, Vol. 87, May 1988, p.17) In fact 2% of U.S. homes have radon concentrations > 300 Bq/m^{3} and occupants should take action to reduce the concentration since they may be receiving an effective dose of >∼ 16 mSv/yr. (By contrast the EPA limit for off-site exposure from nuclear reactors or from nuclear waste depositories is only .25 mSv/yr!) (Bodansky, Physics and Society 16, No. 4, p. 6, 1987).

If a house has high radon levels, then the radon ingress usually is from air infiltration from soil beneath the house. Natural convection in the house (chimney effect) tends to pull in the radon contaminated air. A solution is to drive pipes through the basement floor and connect them to fans exhausting to the outside air. See A. V. Nero Jr. “The Indoor Radon Story”, Technology Review Vol.89, No. 1, p. 28, (1986); also A. Nero, “Earth, Air, Radon and Home”, Physics Today, Vol 42, No. 4, p.32, (1989).

A good general reference on the subject is “Radon and its Decay Products in Indoor Air” edited by William Nazaroff and A.V. Nero, Jr., John Wiley & Sons, 1988. Ground water supplies often contain high concentrations of radon from uranium decay in the aquifers. The radon concentration in public ground water supplies averages ∼ 5000 Bq/m^{3}, and is much higher in some of the New England states. The health hazard is apparently not from drinking the water, but from the water’s contribution to the indoor radon air problem: perhaps ∼ 5 Bq/m^{3}. Private wells often have high concentrations. Storage or aeration of the water provides effective control of the hazard.

OTHER ISSUES:

Is a Small Amount of Radiation Healthy - The Hormesis Effect

The following is from RADIATION DOSIMETRY by Prof. John R. Cameron, Department of Medical Physics, UW, Madison (1989):

“Studies on nuclear workers often show that they have less cancer than other member of the population and even of other workers with similar jobs. This is usually explained as the ’healthy worker’ effect. That is, for reasons not understood, radiation work attract healthy workers. An alternate explanation which is rarely mentioned is the possibility that a small amount of radiation is good for you. This is referred to as the ’hormesis’ effect. Since humans and all of our ancestors evolved in a sea of natural radiation, it is possible that mutations have occurred that produce the hormesis effect. Animal experiments have demonstrated the hormesis effect. Rats exposed to increased radiation have a longer survival than their controls.”

F. PASCO\begin{matrix}c \\ ◯ \end{matrix} Interface and Computer Primer

INTRODUCTION:

The PHYS207/208 laboratories now utilize a Web-browser based display format in combination, when necessary, computer controlled data acquisition interface (typically the PASCO CI-700 or 750). Various sensors are plugged into either digital I/O (phone jack style inputs 1 to 4) or analog I/O ports (DIN-9 style inputs A, B and C). To aid in the data acquisition and analysis PASCO module also requires use of a special purpose software package which can be easily reconfigured for the particular need of a experiment. In general all experiment starting configuration will be preset and launched through a Web-browser button at the appropriate place in the lab.

THE MOUSE

CLICKING: Most of the operations of your computer are controlled by locating the cursor on the appropriate symbol (icon) and by clicking (CLICK) or double clicking (DCLICK) the left button of the mouse.

If the operation you have to perform requires clicking the right button this will be shown by CLICK-R or DCLICK-R. Double clicking means pressing the mouse button twice in rapid sequence without moving the mouse. The image of an hour glass appears momentarily indicating that the computer is loading the program, that is, getting ready to do what you requested. It will not do this if you moved the mouse while double clicking.

WINDOWS

The monitor usually displays various “windows” with a title bar. If you CLICK anywhere inside the window, the title bar turns blue, and the window is “active” (i.e. the computer will respond to any clicks on the “icons” on the border of the window). BASIC OPTIONS:

I. CLICK on the head bar to “drag” the window to a different position. II. Enlarge the window by placing the cursor on the corner, a diagonal arrow will

appear, then CLICK and drag to change the size of the window.

Depending on which experiment you are performing you will see various windows. These will be discusses separately.

ICONS

The icons that appear at the top right of \underline{all} windows are (see Fig. 1):

1. EXIT: The window is removed permanently.

2. RESIZE: The size is changed from large to small, or vice-versa.

3. ICONIZE: The window disappears. Its title and icons 1, 2 and 3 appear at the bottom of the screen. THE GRAPH WINDOW ICONS: At the bottom left corner of the graph window you will find six icons:

Figure 1: The Graph Window

4. STATISTICS shows/hides statistics for all existing graphs. You must first select the area of the graph you want to analyze by dragging the cursor (CLICK and hold) diagonally across the graph to generate a rectangle that encloses the area chosen. A new box will appear that allows you to select the type of fitting that is suitable to the data. The meaning of “fitting” is discussed separately below.

5. CURSOR: Displays cross hairs which can be moved about using the mouse. Simultaneously the coordinates of the cursor position are displayed and this enables the coordinates of graph features to be measured.

6. MAGNIFY: Enlarges any part of a graph. To select the area of the graph you want to enlarge by first CLICKing this icon and then CLICK a point on the graph using a drag motion (click and hold) diagonally across the graph. This will generate a rectangle that selects the area chosen.

7. AUTOSCALE: Scales the y-axis and the x-axis so that all the data is shown

8. GRAPH SETUP: This icon allows for adding your name to the title of the window, select plot (e.g. connected points, select grid).

9. ADD PLOT: Add another graph; presents a menu of available channels.

At the top left corner of the graph window you find two more icons:

10. PLOT DATA: Displays various data options.

11. DATA MENU: Displays the list of all the data sets recorded. CLICK on the one you want to display; a check mark will appear and the corresponding graph will be displayed. CLICK on the one you do not want to display, the check mark will disappear.

THE SCALE OF EACH AXIS: In order to change the scale of an axis CLICK on any number on that axis; a menu will appear allowing you to enter the minimum and maximum values of the scale, CLICK at the end of the number you want to change, backspace, type the new number, CLICK “OK” in the appropriate box. An alternative way of changing the scale of a graph is to CLICK on the ⊕ or ⊖ at the bottom right corner of the graph window.

THE SETUP WINDOW ICONS: Usually you will find the setup window in its “minimized” form as shown below:

Figure 2: The Setup Window minimized.

10. RECORD: DCLICK and the computer begins taking data. The data is stored, and can be recalled.

11. MONITOR: DCLICK on this and the computer begins taking data. The data is not stored, and it disappears at the end of the run. This allows you to view what the data will look like when you RECORD.

12. STOP: Stops the run, the data is stored. The run cannot be restarted.

13. PAUSE: Stops taking data till you CLICK again and the run is restarted.

14. DATA BOX: This area contains the color coded list of all the runs. Delete a run by clicking on it, and using the back arrow at the top right corner of the keyboard.

15. SAMPLING: Allows for terminating a data run after a predeterminate time.

16. SIGNAL GENERATOR: Starts a built-in signal generator (e.g. sine or square waves) and allows control of both frequency and amplitude.

THE TABLE WINDOW ICONS:

17. STATISTICS: Calculates displays the minimum and maximum value of the data, displays also the mean, and the standard deviation. NOTE: Subsets of the full data set can be analyzed by using the mouse and highlighting (through a CLICK and drag motion) the rows of interest.

18. TIME INDEX: Alter the display to include time at which data was recorded.

19. DIGITS SETUP: Resets the number of significant digits displayed.

20. DATA MENU: Allows access to data of preceding runs.

Figure 3: The Table Window

THE STATISTICS WINDOW ICONS:

21. STATISTICS: the fitting menu is displayed; a mathematical expression that approximates the data or other option (e.g. histogram data, calculate the derivate of the curve) may be chosen. “Fitting” or regression is the procedure used to find a mathematical expression that matches the function form of the data being analyzed (linear, exponential, etc.).

Figure 4: The Statistics Window and Menu