Experiment 1 The Metric System Measurement Tools and Graphing Preparation Prepare for this week s quiz by reading about the metric system in your textbook Read the introduction to the manual the appendix and the first experiment carefully Principles Making measurements is the basis for all science experiments But measurements only have meaning under certain circumstances First everyone has to agree on a system of units Second these units have to be standardized and tools have to be calibrated Third everyone has to use measuring tools correctly Units In all of the physics experiments you will make measurements using the metric system This is standard for all science The metric system is not any more accurate than the English system but since it is based on powers of ten it is much more convenient to manipulate mathematically It is also used for common measurements in the everyday world in all nations of the planet except the United States and Libya In this country more and more products are labeled in both English and metric units and eventually the United States will convert to the metric system Each of you will need to learn the basic units of the metric system Every measurement that you make will have a unit associated with it A number without its unit is essentially meaningless and for our purposes will be wrong Almost everything you measure this semester will end up with units depending on three basic quantities length mass and time In the SI system the basic units are the meter the kilogram and the second This used to be called the mks system In the Gaussian or cgs system the basic units are the centimeter the gram and the second These basic units are not always the most convenient to use The kilogram is too large a unit to use for the size of a vitamin C tablet the meter is too small to use for the distance from here to New Jersey The SI units can be modified by adding standard prefixes which give the powers of ten by which the unit is multiplied Some common prefixes their powers of ten and symbols are Prefix Power Symbol nano 10 9 n micro 10 6 milli 10 3 m centi 10 2 c kilo 103 k 6 mega 10 M Many people just starting in physics have problems in their lab work because they don t have a clear idea of the size of various metric units If your ruler told you the lab table was four inches across 1 you would immediately suspect a problem because you know about how big an inch is Everyone can estimate weight in pounds but most people raised in American can t estimate mass in kilograms It is therefore important that you get a sense of various metric measurements so that you can tell if your measurements are reasonable or not In this week s experiment you are going to use two tools to measure length the meter stick and the Vernier caliper Then you will plot your data and find the slope The Meter Stick The meter stick is one meter m long and is divided into one hundred centimeters cm Each centimeter is in turn divided into ten millimeters mm Therefore you can precisely measure an object to the nearest millimeter It is also possible to estimate tenths of millimeters fairly accurately The meter stick is said to be precise to the nearest millimeter It is a good idea to start measuring from the 1 cm or the 10 cm mark on a meter stick since the ends of the sticks tend to become worn and inaccurate Also whenever it is possible place the object to be measured on the meter stick and look straight down at it This reduces errors induced by parallax which is the apparent shift of one object compared to another caused by their different distances from the observer The Vernier Caliper The Vernier calipers in the physics labs can be used to precisely measure length to the tenth of a millimeter If you look at a caliper you will see that it is just like a meter stick but with a movable scale attached This sliding scale has eleven lines etched on it and the distance between the first and the last is exactly 0 9 cm or 9 mm The lines represent values from 0 to 10 When the jaws of the caliper are closed the zero on the sliding scale will line up with the zero on the fixed scale When the jaws are spread the distance between the zero marks will be the same as the distance between the jaws To use the caliper first clamp it around the object to be measured Then look at the zero line on the sliding scale and see where it crosses the fixed scale Read the first two numbers cm and mm from the fixed scale just as you would from a meter stick To find the last digit tenths of a millimeter look at the lines on the sliding scale One of the lines will line up exactly or nearly so with one of the lines on the fixed scale The lines on the sliding scale are numbered from zero and the number of the line on the sliding scale that lines up with a line on the fixed scale is the value of the final digit of your measurement see the diagram Learning to use a caliper takes practice your lab instructor will help you if you have trouble 2 Accuracy Precision and Tolerance The smallest difference that you can detect with a measuring tool is called its precision A meter stick is precise to the nearest millimeter the caliper we use in our labs is precise to the nearest tenth of a millimeter The precision of your instrument determines how many significant digits your record in your data The instructions for the experiments you do this semester usually specify the precision of your measurements by telling you the smallest unit to measure This does not mean that those are the units to use when you record the data For example the instructions might tell you to measure to the nearest millimeter This does not mean that you should record your lengths in millimeters Read the directions and use common sense to decide what unit to use If you have doubts ask your instructor The calibration of the tool and the skill and care of the person using it determine its accuracy For example if your triple beam balance is out of calibration you may measure something to the tenth of a gram but the measurement would not be accurate If you don t position the Vernier calipers correctly or misread the scale your answer will be precise to the tenth of a millimeter but the answer will not be accurate All things don t need to be measured to the same precision For example you would want to know the distance to the next town on the road to within a few kilometers If you buy a pair of shoes you want the length to be …