The first experiment of the course will be a measurement of the speed of sound, which everyone will do together. We will use this experiment to discuss ways to analyze experimental data and to introduce the ideas of measurement error. At the same time, you will be reading the first four chapters of Error Analysis by Taylor and taking on-line quizzes.
Error Analysis Quizzes
A quick word on the quizzes. Last year students were allowed to take these quizzes as many times as necessary to pass them with 85% or better. Some people seemed to pursue a "gaming" strategy of guessing and then trying to learn from the answers. Ultimately, they learned that this was an unsuccessful strategy, but they wasted a fair amount of time figuring this out. Let their experience be a guide to you: read the book first, then do your best each time you attempt a quiz. You'll need a calculator and some paper. You are allowed only five attempts at each quiz.
During the second portion of the course, two experiments will be set up: the simple pendulum and projectile motion. You and a partner will investigate one apparatus for four sessions and then switch to the other. The pendulum experiment will be evaluated with a formal written report, called a "technical report". The projectile experiment will be assessed orally.
Towards the end of the sixth week of the semester, the other experiments will be set up and you will conduct two further investigations. These are the Cavendish experiment to measure the gravitational constant (1 setup), the speed of light (1 setup), an investigation of statistical mechanics using Squiggle balls (1 setup), standing waves on a string (2 setups), an anharmonic oscillator using a glider on an air track (2 setups), and the oscillations of one or more masses connected to springs. You will have four laboratory periods for each of these experiments.
During the final portion of the semester you will work on a project of
your own choosing, in collaboration with two other students. It may be
theoretical or experimental. Look for more details on the Projects page.
Your work on the speed of sound experiment will be kept in a laboratory notebook, which will be turned in at the end of third day. You should keep track of all your work, including "scratch" calculations, in your notebook. We find it helpful to use the following conventions:
- Make chronological entries on the right-hand page.
- Date each page.
- Use lists and short phrases to explain your procedure
- Use tables to record data
- Use sketches to show the apparatus and how it is set up for your experiment. Make these large enough to show all relevant detail. Label distances symbolically, and tabulate dimensions near the sketch.
- If you prepare a graph using Kaleidagraph or other program, print it out, cut it out, and tape it into the notebook right away. Make sure to explain where the data for the graph may be found, what the graph shows, and what it means.
Computer Files
An account for this course has been created on the file server KATO and you all have access privileges for this account. Most of your experimental work will be done in pairs, and each partner will need access to the data. Please use the course account for all your work in the course. Inside the Physics 23A directory create a directory with your name. Within that directory, create a directory for each experiment you do, and place all files pertaining to that experiment in this directory.
- Please use a sensible naming scheme for your files. It is useful to use names that make clear the order in which the corresponding data were obtained.
- If the data files are in your partner's directory, you should make copies into your own directory.
- It is an honor code violation to look through or copy files in anyone else's, with the exception given immediately above.
On Conducting Experiments
In this course you will conduct experiments with at least five different sets of apparatus. Each experiment will be performed with a different partner. These experiments will extend over several laboratory sessions. We are fortunate this semester that this class is the only one using Keck B127; you may assume, therefore, that the apparatus will not be disturbed between experimental sessions.
Notebook
To make the most of this opportunity, it is vitally important for you to keep careful notes of your activities. If you perform a calibration of the equipment on the first day of an experiment, but misplace the results, you will have lost most of the benefit of that first day’s efforts. An Avery Dennison model 43-648 Computation Notebook for keeping these notes is required material for the course; you must bring it to the lab each meeting. Keep notes as you go; if you prefer, you can also keep notes on the computer. Be sure to save often, and to print out the notes at the end of the day. Tape the printed version into the laboratory notebook as a permanent record of your activities, thoughts, and conclusions.
Analysis and Conclusions
The goal of most experimental work in physics is to measure one or more quantities as accurately and precisely as possible, and to compare the measurements to a theoretical model of the phenomenon under study. The quality of an investigation hinges on the successful suppression of extraneous influences and the size of the remaining uncertainty in the results. The uncertainty arises from both systematic flaws in the apparatus or methodology and in the random fluctuations that accompany nearly all measurements.
During the Watergate saga, the $64,000 question became, “What did the President know, and when did he know it?” In your experimental work, the questions are,
- “What did you measure, and how well did you measure it?”
- “What did you establish, and how well did you establish it?”
- “What did you conclude, and how well did you conclude it?”
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To make this more concrete, consider an experiment to measure the
acceleration due to gravity, g, in which you throw Furbies off the
roof of Sprague and time how long it takes them to thud satisfyingly on the
pavement below. From the times and the known height of the library, you
deduce a value of g. Let’s say you get
What are we to think? On the one hand, the textbook says you should get 9.80 m/s2, so your result is "wrong." On the other hand, this is not the easiest way to measure g accurately, and it turns out that you estimate the uncertainty in your measurement is 1.0 m/s2. Since the book’s value is well within your estimated uncertainty, you conclude that your value and the book’s value are in agreement. Meanwhile, your buddy has used a pendulum to measure g in a different way. She reports a value of g = 9.8004 ± 0.0008 m/s2. Is her result better or worse than yours? Well, it certainly is more precise. She is confident to 0.008% in her value for g. In this respect, her value is vastly superior to yours, which has a precision of only 10%. On the other hand, the value of g in Claremont turns out to be 9.7959 ± 0.0001 m/s2 (see Gravity). Her value is 0.0045 m/s2 off the true value, which is more than 5.5 times her estimated uncertainty. Her value, therefore, is in absolute disagreement with the accepted value, even though it is much closer in an absolute sense. Moral: It’s not just what you know but how well you know it.
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The course text by Taylor discusses how to assess experimental error. Reading assignments in this text are posted on the "Introduction to Error Analysis" page, as are WebQuiz assignments to assess your progress. You must take and pass these quizzes following the schedule discussed on that page.
Working Together
Henry Ford revolutionized mass production with the invention of the assembly line. By assigning to each member of the production team a single task to be performed on the cars as they pass by slowly down the assembly line, Ford realized a tremendous gain in efficiency compared to traditional assembly methods.
Without question, division of labor is crucial for efficient teamwork. However, I want to caution you against patterning your partnership’s division of labor on the Ford model. It is tempting to let one partner make all the measurements while the other types them into the computer. It is even efficient in one sense — it gets the numbers in the computer quickly. All too often, however, one or more members of the team haven’t the foggiest idea what the numbers really mean. Computers invite the unfortunate garbage-in-garbage-out syndrome.
The best way to avoid this is by making sure that both partners are as actively involved in the measurement process as possible. Before sitting down to record vast columns of data, make sure that each partner understands how the measurements will be taken, how points should be spaced, what the units of the measurement are, what the uncertainty of the data points is, or how it will be assessed after the data are taken, etc. Then take turns with the roles of "doer" and "scribe".
Sometimes students don’t listen well to one another. If you feel that your partner is taking things over and not sharing the tasks of the experiment, please speak to one of the course instructors. We will be glad to facilitate constructive teamwork in the partnership.
Updated 8/25/00 by Peter N. Saeta .