Physics 10 Lab 1: Introduction to Measurement Units and 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: 100cm=1m → 89cm× 1m =1 100cm 1m =.89m 100cm You can make conversion factors out of the definitions listed in the tables above and in your book. 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 = 5m + /-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 = 1.55in + /-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/s2 then the ‘error’ is the difference between that value and the accepted value of 9.8m/s2, or 0.2m/s2. The error can also be expressed as a percent: % error = 10 − 9.8 ×100% = 2% 9.8 Physics 10 Print Name: ________________________________ Lab 1: Measurement Worksheet Lab Partner: ________________________________ 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. 15 2. If 1 light year = 9.46 x 10 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 Go to this website and shoot the bulls’s eye and test your understanding of accuracy and precision: http://www.utas.edu.au/sciencelinks/exdesign/EE3B.HTM Then, identify the following as either being Precise and Accurate, both or neither, by circling the words. Precise Accurate Precise Accurate Precise Accurate Precise 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: _________________________ Part 4: Measurement and Perception Our eyes and minds can deceive us and produce errors in our measurements and perceptions! Using observation only, answer the questions in the column on the left. Then measure the objects to the nearest tenth of a millimeter. Then answer the questions in column on the right. Can you trust your own eyes? Be honest!!