Units and Measurement Physics 40 Lab 1: Introduction to Measurement One of the most important steps in applying the scientific method is experiment: testing the prediction of a hypothesis. Typically we measure simple quantities of only three types: mass, length, and time. Occasionally we include temperature, electrical charge or light intensity. It is amazing, but just about everything we know about the universe comes from measuring these six quantities. Most of our knowledge comes from measurements of mass, length, and time alone. We will use the standard used by the international scientific community for measuring these quantities: the SI metric system. A measurement without a unit is meaningless! For more information, check out these websites: SI Base Units: http://physics.nist.gov/cuu/units/units.html Metric prefixes: http://physics.nist.gov/cuu/units/prefixes.html Commonly used metric prefixes Often it is necessary to convert from one unit to another. To do so, you need only multiply the given quantity by a conversion factor which is a ratio equal to 1, derived from definitions. For example, there are 100 centimeters in a meter. You can make a conversion factor out of that definition so that if you need to convert 89cm to meters, simply multiply by the conversion factor, which is equal to 1: 1m 100cm=1m =1 100cm 1m 89cm = 0.89m 100cm You can make conversion factors out of the definitions listed in the tables above and in your book. Please always have leading zeros on decimals!! (0.89 and NOT.89)
Precision & Accuracy By their nature, measurements can never be done perfectly. Part of the error in making measurements may be due to the skill of the person making the measurement, but even the most skillful among us cannot make the perfect measurement. Basically this is because no matter how small we make the divisions on our ruler (using distance as an example) we can never be sure that the thing we are measuring lines up perfectly with one of the marks. Therefore the judgment of the person doing the measurement plays a significant role in the accuracy and precision of the measurement. Accuracy: Accuracy describes the nearness of a measurement to the standard or true value, i.e., a highly accurate measuring device will provide measurements very close to the standard, true or known values. Example: in target shooting a high score indicates the nearness to the bull's eye and is a measure of the shooter's accuracy. Precision: Precision is the degree to which several measurements provide answers very close to each other. It is an indicator of the scatter in the data. The lesser the scatter, the higher the precision. Ideally, we want to make measurements that are both accurate AND precise. However, we can never make a perfect measurement. The best we can do is to come as close as possible within the limitations of the measuring instruments. Uncertainty Since we can never make a perfect measurement, every measurement is approximate. Therefore it is important to always report the amount of confidence we have in our measurements, what we call experimental uncertainty. For example, you may estimate the length of the lab bench to be 5 meters give or take a meter. The give or take part is an expression of your confidence in your estimate. In scientific measurements we say plus or minus but it means the same as give or take. We write that our measurement of the length, represented by L is : L 5 m /-1m If you are using a scale such as a ruler to measure the length of an object, then your uncertainty is usually estimated to be one tenth the smallest division. For example, this bug has a length between 1.54 and 1.56 in or L 1.55 in /-0.01in. The 1.55in is the average measure and the 0.01in is the uncertainty. Error An experimental error is not a mistake! It is the difference between a measurement and an accepted value of something. For example, if you determine from an experiment that the acceleration due to gravity is 10 m/s 2 then the error is the difference or DISCREPENCY between that value and the accepted value of 9.8m/s 2, or 0.2m/s 2. The error can also be expressed as a percent: 10 9.8 % error 100% 2% 9.8
Physics 40 Lab Section 1 2 3 4 Print Names: Lab 1: Measurement Worksheet Equipment: ½, 1 and 2 meter rulers, digital caliper, various small metal objects Part I: Units, Metric Prefixes & Unit Conversion Show calculations. NEATNESS COUNTS!! 1. Convert 32 kilometers to nanometers. 2. If 1 light year = 9.46 x 10 15 m and 1 mile = 1.6 km, how many miles are in a light year? 3. Explore the Universe in powers of 10! http://micro.magnet.fsu.edu/optics/tutorials/java/powersof10/ Step through the animation in manual mode. What is the power of 10 for each of the following? Milky Way Galaxy: Stars in the Milky Way Galaxy: Solar System: Earth and the Orbit of the Moon: Southwest Tallahassee: Oak Tree Branch: Cells on a Leaf: DNA Strand: Nucleus of a Carbon atom: Quark: By what power of 10 is the Milky Way Galaxy larger than the Nucleus of a Carbon Atom? Show your calculation. Box your final answer. Part 2. Precision and Accuracy Identify the following as either being Precise and Accurate, both or neither, by circling the words. Precise Precise Precise Precise Accurate Accurate Accurate Accurate
Part 3. Measuring Length & Uncertainty Make a thumb ruler by marking the size of your thumb starting on the left line and across the strip below. You will use the thumb ruler to measure the length of the computer screen but first GUESS the length in thumbs by eye balling it. Be sure to include +/- uncertainty in your guess and measurement. Guesstimate: Measurement: How close was your guess? How many thumbs off were you? Measuring with a metric ruler. When using a metric ruler, your uncertainty to the nearest one tenth of the space between the smallest scale divisions. Here are two metric rulers. Write the measurement in standard form with +/- uncertainty. Don t forget the units! Ruler on Left: Ruler on Right: Now measure the computer screen with a metric ruler. Again, first GUESS the length in cm by eye balling it. Be sure to include +/- uncertainty in your guess and measurement. Guesstimate: Measurement: How close was your guess? By what percent was your guess off? Measure the length of the metal object with a metric ruler. Write the measurement in standard form with +/- uncertainty. Don t forget the units! Metric Ruler Length: Measure the length of the metal object with a digital meter. In general, when using a digital meter, the uncertainty is ½ the digit not shown. What is that for your digital meter? Digital Meter Uncertainty: Write the measurement in standard form with +/- uncertainty. Don t forget the units! Digital Meter Length: