1Experiment 1 Measurement, Analysis and Graphing “All knowledge begins with experience.” From Metaphysics by Aristotle, 384-322 B.C.E. Preparation Prepare for this week's quiz by studying: the metric system, significant digits, and units. Be sure you have the required items such as lab notebook, ruler, and calculator. Principles All experiments are based on measurements. No matter how elegant the theory or how complex and beautiful the analysis, poor measurements guarantee worthless results. All the measurements and calculations you do this quarter depend on three basic quantities. These are mass, length, and time. All other units are derived from these three. The SI, or International System of Units, uses the kilogram, meter, and the second. The SI is not inherently more accurate than the English system, but it is a lot easier to work with because it is based on powers of ten. Sometimes this is called the MKS system. Sometimes it is more convenient to use the cgs system- this stand for centimeters, grams, and seconds. Usually your lab instructions specify the units and precision you should use for your data. There are some very important points that you must always keep in mind when you are doing experiments. The first is that each measurement, sample calculation, and answer must be clearly labeled and accompanied by the correct unit. A number without the right unit is meaningless. Your grade will suffer greatly if you do not keep proper track of your units. The second point is that you must use significant digits correctly. Many people think that the number of significant digits is the same as the number of digits to the right of the decimal point, but this idea is wrong. The number of significant digits in a measurement is determined by the precision of the measuring instrument and the size of whatever is to be measured. For example, suppose you are measuring time intervals with a stopwatch that is precise to the hundredth of a second. A short interval, say 6.43 s is a number with three significant digits. 10.62 s and 100.45 s have four and five digits, respectively. The value 15.20 s also has four significant digits; the final zero is an indicator of the precision of the measurement. However, 0.02 s has only one significant digit. The number of significant digits in a measurement is not affected by your choice of units. For example, suppose you measure a length of 3.64 cm. This is the same as 36.2 mm or 0.0362 m. In each case, the value has three significant digits.2Procedure This week you are going to make measurements of length using a Vernier caliper. Meter sticks can be used to measure lengths to the nearest millimeter (thousandths of a meter) and you can estimate tenths of millimeters fairly well. With the type of Vernier caliper used in these physics labs one can precisely measure lengths to the nearest tenth of a millimeter. When you use a meter stick it is a good idea to place the object to be measured directly against the scale. This way the reading is not affected by parallax, which is the apparent shift in the relative positions of two objects due to their different distances from the observer. Don't use the end of the meter stick; lab students (and instructors) lean on them, use them as pointers, fence with them, and generally chew up and abuse the ends. Use the one centimeter or ten centimeter mark for a reference and subtract that value from your measurement. Get a Vernier caliper and study it. It has a fixed scale that is marked in centimeters and millimeters just like a meter stick. It also has an attached sliding scale. This is the Vernier scale (named after a French mathematician, Pierre Vernier, ca. 1580-1637). This scale has eleven lines etched on it and the distance between then first and the last is 0.9 cm or 9 mm. Close the caliper and look at the sliding scale. Notice that the zero mark on the sliding scale and the zero mark on the fixed scale line up against each other. Now clamp the caliper around the object to be measured. Look at the sliding scale again. It will have moved a distance along the fixed scale equal to the length being measured. Read the centimeters and millimeters from the fixed scale where the zero on the sliding scale crosses it. Now look at the lines on the sliding scale. One of the lines will line up, or nearly line up with on of the lines on the fixed scale. The value of the line on the sliding scale gives you the last digit of your measurement, the tenths of millimeters. Reading the Vernier takes some practice. Sometimes it helps to hold the scale under a lamp to make the scale clearer. Refer to the diagram in the manual and ask your instructor for help if you have trouble.3Before you start to record measurements spend some time getting familiar with your instruments. If you've not used the metric system before, try to develop a sense of the magnitude of the different units. Spend some time looking at your meter stick. Try to get a sense of how long a meter and a centimeter are. Measure the length of your fingers, your, knuckles, the distance from your waist to the floor. Frequently during the term you will be asked if a measured or calculated value seems reasonable. You will need to have a clear idea of various metric lengths. 1. If your instructor doesn’t assign lab partners, find one or two other students to work with. Since there won't be enough equipment for group to have a complete set, only take the objects you need and don’t hog equipment. You are encouraged to discuss the experiment and work together, but each person must make some of each type of measurement, record his or her own set of measurements and write his or her own report. You may make the measurements in any order. 2. You should have with you a bound quadrille ruled lab notebook. If you don't have a notebook you will have to go get one before you can proceed. No, you may not write your data on scratch paper and copy it over later. 3. Make a data table in your notebook for each set of measurements. Use a ruler. You may use pencil for drawings, lines for tables and for making graphs, but everything else must be written in ink. Measurements recorded on scrap paper will be ruthlessly seized and destroyed. This means that you get one shot at recording data accurately and neatly. Think about each set of measurements before you start; a little thought and preparation