Lab #2: Measurement and Metrics Lab
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1 Lab #2: Measurement and Metrics Lab INTRODUCTION Observations are an essential part of science. Measurements allow scientists to accurately describe the world around them, which enables others to comprehend the relative size of structures and better understand them. Moreover, one requirement of the scientific community is that results be repeatable. As numerical results are more precise than purely written descriptions, scientific observations are usually made as measurements. Sometimes a written description without numbers is the most appropriate way to describe a result. The metric system is a universal measurement standard used in all fields of science. In this lab, students will use the metric system to measure temperature, volume, mass, and length of various objects. Students will also learn to convert metric units and write in scientific notation. Scientific Notation In scientific notation, numbers are composed of three components: the coefficient (C), the base (10), and the exponent (E). C x 10 E Thus, the number 93,000,000 can be expressed as 9.3 x In this number the coefficient is 9.3, the base is 10, and the exponent is 7. Specific rules have been developed to express a number in scientific notation properly. The base always has to be 10, the coefficient has to be greater than or equal to 1 but less than 10, and the exponent has to reflect the number of places that decimal has to be moved to change the number to its standard notation. In writing scientific notation, numbers greater than 1 should be expressed in positive exponents and numbers less than 1 should be expressed in negative exponents. Example numbers: 9,000 can be expressed as 9.0 x ,000,000 can be expressed as 2.29 x x 10 5 can be expressed as 763, can be expressed as 8 x can be expressed as 4.52 x Performing Basic Operations In multiplying values expressed in scientific notation, multiply the coefficients and add the exponents. Always convert the answer to properly written scientific notation. In dividing in scientific notation, divide the coefficients and subtract the exponent of the divisor by the exponent of the dividend. Convert the resulting answer to a properly written scientific notation. Example calculations: (3.0 x )(6.0 x 10 3 ) = 18 x = 1.8 x (8.1 x 10 7 )(3.5 x 10-3 ) = 28 x 10 4 = 2.8 x 10 5 (6.4 x 10-5 )(2.4 x 10-3 ) = 15 x 10-8 = 1.5 x
2 (8.0 x 10 6 ) / (4.0 x 10 2 ) = 2.0 x 10 4 (5.25 x 10 8 ) / (2.75 x 10-3 ) = 1.91 x (7.64 x 10-7 ) / (3.22 x 10-4 ) = 2.37 x 10-3 When adding and subtracting values expressed in scientific notation, always convert the exponent to the same value before beginning the calculation. In many cases, this requires changing the decimal place of the coefficient as well. Add or subtract the coefficients, and leave the base and exponent the same. Convert the resulting answer to properly written scientific notation. Example calculations: 4.0 x x 10 8 = 4.0 x x 10 6 = 204 x 10 6 = 2.04 x x x10-3 = 6,400,000 x x 10-3 = 6,399,997.8 x 10-3 = 6.4 x x x 10-4 = 9.2 x x 10-5 = x 10-5 = -5.2 x 10-4 Measurements Using the Metric System Units in the ideal system of measurement should be easy to convert from one to another. The metric system meets such requirements and is used by the majority of countries, by all scientists, educators, and researchers in the world. In most non-metric countries, such as the US and England, their governments have launched programs to hasten the conversion to metrics. It is well recognized that any country that fails to do so could be at a very serious economic and scientific disadvantage. "In fact, the U.S. Department of Defense adopted the metric system in 1957, and all cars made in the United States have metric components." Thus, one of the greatest advantages of the metric system is the ease of conversions. Since all metric units are of multiples of ten, converting between units requires only the movement of decimals places. The metric units of length, mass, and volume are meters (m), grams (g), and liter (L); respectively. The same prefixes are used for all units. For example, the prefix Kilo denote 1,000; 1 Kilometer (Km) = 1,000 meters (m), 1 kilometer (Kg) = 1,000 grams (g), 1 Kiloliter (KL) = 1,000 liters (L). Prefix Symbol Value Exponent Value Tera T 1,000,000,000, Giga G 1,000,000, Mega M 1,000, Kilo K 1, Hecto h Deca da Unit no prefix (meter, m, g, L gram, liter) Deci d Centi c Milli m Micro µ Nano n Pico p
3 Measuring Length Length is the measurement of a real or imaginary line extending from one point to another. The standard unit is the meter. Some common related units of length are: Materials required per lab group: cm ruler with metric and American (English) standard units on opposite edges. 2. Non-mercury thermometer(s) with Celsius( C) and Fahrenheit( F) scales (about C) ml beaker made of heat-proof glass 4. Electronic Burner mL Erlenmeyer Flask 6. Boiling chips 7. Three graduated cylinders: 10-mL, 25-mL, 100mL. 8. Thermometer holder Materials per lab room: 1. Source of distilled water (ddh 2 O) 2. Metric bathroom scale 3. Source of ice 4. One 2 L plastic graduated beaker 5. One-piece plastic dropping pipet (not graduated) or Pasteur pipette and safety bulb or filling devise 6. Four electric balances 7. Two vortexes 8. Two hot plates 9. Two measuring tapes (ft and in) 10. Two yard sticks 11. Two electric balances 1 m = 1000mm = 100cm 1000 m = 1 km 1. Precisely measure the length of this page in centimeters to the nearest tenth of a cm. How long is this page in cm? a. What is the length of this page in millimeters, meters, and kilometers? mm m km 3
4 2. Measure the following using the appropriate metric units of length a. Select 3 small wooden blocks. Measure the length, width, and height of each block to the nearest millimeter and record these values below. Calculate the volumes of each block. Note: volume of blocks = length x width x height Block # Length Width Height Volume 1 x x = mm 3 2 x x = mm 3 3 x x = mm 3 b. What is the volume of block 1 in cm 3? c. What is the volume of block 2 in nm 3? d. What is the volume of block 3 in m 3? Measuring Volume Volume is a measure of the space occupied by an object. Volume can be measured in cubic meters (m 3 ) but is typically measured in units termed liters (L). In the lab, several glassware are used to measure volume, including flasks, beakers, graduated cylinders, pipettes, etc Note: 1 cubic centimeter (cm 3 ) = 1 milliliter (ml) 1. Using the data collected in the previous section, calculate the volume of each of the three blocks in ml and record the data below. Volume of block 1 ml Volume of block 2 ml Volume of block 3 ml 4
5 2. When water is placed into a glass graduated cylinder or other glass container, water curves due to the surface tension of the solution and adhesion of the solution to the sides of the glass. To read volume from a glass graduated cylinder, hold the cylinder at eye level and read the bottom of the curve. The bottom of the curve is called the meniscus. Observe the beaker and graduated cylinder containing water that had been set up by the instructor. a. What is the volume of water in the beaker?. b. What is the volume of water in the graduated cylinder?. 3. Volume of a block/cube-shaped object can be determined by measuring and multiplying length, width, and height. The volume of unusually shaped objects, like a screw, cannot be measured this way. Measuring volume using the water displacement method permits the volumes of irregular shaped objects to be calculated. a. Fill a 50mL graduated cylinder to the 25mL mark. Then place the screw in the graduated cylinder and record the water level. Subtract 25 from the new water level and that will be the volume of the screw in ml. Use water displacement to determine the volume of 3 objects. Volume of object 1 ml Volume of object 2 ml Volume of object 3 ml Measuring Mass and Calculating Density Mass is a measure of the amount of matter that an object has. Mass differs from weight in that weight is the force on an object due to gravity. Therefore, the mass of an object stays constant, but weight can change if gravity changes. For example, the moon's gravity is roughly 1/6 that of the Earth's. A person weighing 180 lbs. on earth would weigh 30 lbs. on the moon. Since mass is constant, a person with a mass of 82 kg would have that mass on Earth or on the moon. 1. Using an electric balance, precisely weigh the mass of the three blocks used in the previous section on length and record those values below. (Values can be found in the Measuring Length section). Block 1 g Block 2 g Block 3 g 5
6 2. Density is calculated by dividing the mass by the volume. Calculate the density of each of the three blocks. Pay close attention to the units that density is measured in! D = M/V Block 1 g/cm 3 Block 2 g/cm 3 Block 3 g/cm 3 Measuring Temperature Temperature is defined as a measure of the average kinetic energy of molecules. So, scientists measure temperature using the Celsius or centigrade scale, which is based upon the freezing and boiling points of water. Water freezes at 0 C (32 F) and boils at 100 C (212 F). Converting from Celsius to Fahrenheit or Fahrenheit to Celsius requires the following equations: F = 9/5 C + 32 C = 5/9 ( F-32) Using the provided thermometer, measure the temperature of the following in Celsius ( C). Then use the equation above to convert each into Fahrenheit ( F). Temp. in Celsius ( 0 C) Temp. in Fahrenheit ( 0 F) Room Temperature Surface of Skin Ice Water in Beaker Boiling Water Tap Water 6
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