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| What is Metrology? |
| Metrology |
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Measurement
What is measurement? |
| What can be measured? |
| International System of Units (SI) |
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What is a knot? What is a nautical mile? What is a nautical mile, and how does it differ from a normal mile and a kilometer? Knots and Nautical miles are good old navy terms. The nautical mile was based on the circumference of the earth at the equator. Since the earth is 360 degrees of longitude around, and degrees are broken into 60 so-called "minutes", that means there are 360 * 60 = 21,600 "minutes" of longitude around the earth. This was taken as the basis for the nautical mile; thus, by definition, 1 minute of longitude at the equator is equal to 1 nautical mile. So the earth is ideally, by definition, 21,600 nautical miles (and 21,600 "minutes" of longitude) in circumference at the equator. If anyone ever asks you how far is it around the earth, you can quickly do the math in your head (360 degrees * 60 minutes per degree) and answer "about 21,600 nautical miles!" In fact, even modern navigators use the "minute of latitude" on charts to measure distance; this is what you see them doing when they use their compass spreaders while they are hovering over their nautical charts (maps). [For geometrical reasons, we use the minute of latitude on charts to correspond to a nautical mile rather than the minute of longitude. Minutes of longitude shrink as they move away from the equator and towards the poles; minutes of latitude do not shrink. Take a look at a globe with longitude and latitude lines marked on it to understand why.] Using the definition of a nautical mile for distance at sea, the challenge was to measure speed -- i.e. what is the ship's speed in nautical miles per hour? (By the way, the nautical mile is about 1.15 larger than the "statute" mile used by land lubbers.) Since [speed] = [distance] divided by [time], if we measure a small distance (or length) in a small time we can do the math and figure our speed. The device that sailors used to make their speed measurement was called the "chip log." Chip as in chip of wood, and log as in to record in a log. What is Density? How is Density Measured? How do they get ships made of iron and steel to float? Density is a property of matter that is unique to each substance. It is a measure of the mass of the substance in a standard unit of volume. Sometimes density is easy to sense. If two objects have exactly the same size and shape, the denser one may feel heavier. But if their densities are very close together, it will be hard to tell a difference. It gets really tough if you are dealing with materials that have very different sizes and/or very different shapes. The only way to decide the density of a substance is to measure its mass and its volume, then divide. Density = Mass � Volume Units for density g/cm3 Mass vs Volume Pre-Test Questions Name: ____________________________ Period: ___________ Date: ___________ 1. Mass is measured with which instrument listed below? a. thermometer b. triple beam balance c. ruler d. graduated cylinder 2. What is formula for finding density of an object? a. volume � mass b. mass � volume c. volume x mass d. mass x volume 3. What is a correct unit for volume? a. centimeter 3 b. kilogram 2 c. seconds -1 d. pound 4. Which of the following is a formula for finding volume of an object? a. density � mass b. mass � density c. density x mass d. mass x density Densities: Balsa: 0.13 g/cm 3 Iron: 7.9 g/cm 3 Gold: 19.3 g/cm 3 Aluminum: 2.7 g/cm 3 Formulas: Sphere: 4/3 x π x radius x radius x radius Cylinder: π x radius x radius x height Cube: length x length x length Cone: 1/3 x π x radius x radius x height 5. Using the information in the charts above, calculate the mass of an aluminum cone with a radius of 2 cm and height of 7 cm. a. 79.1 grams b. 277 grams c. 39.7 grams d. 712.3 grams 6. Using the information in the charts above, calculate the mass of an gold sphere with a radius of 17 cm. a. 397 grams b. 23.2 kilograms c. 397 kilograms d. 1.4 kilograms 7. You have 4 spheres all with an equal radius. One is made of iron, one of gold, one of balsa, and one of aluminum. Which sphere is the least massive? a. iron b. gold c. balsa d. aluminum 8. What is the fewest number of aluminum spheres it would take before their total mass is greater than one gold sphere with the same radius. a. 2 b. 4 c. 8 d. 16 9. Can two objects with the same volume have different masses? a. No, objects with the same volume always have the same masses. b. Yes, objects with the same volume will have different masses if they have different densities. c. Yes, objects with the same volume will have different masses if they are in different locations (like on the moon) . d. Yes, objects with the same volume will only have the same mass if they have the same shape. 10. You have an elementary balance with three iron spheres, each with a radius of 1 cm. on one side. The other side of the balance you have an empty container with a mass of 10 grams. What volume of water will need to be added to the container to make the balance level? a) 99 cm 3 b) 33 cm c) 10 cm 3 d) 89 cm 3 Mass vs Volume Pre-Test Answers 1. B 2. B 3. A 4. B 5. A 6. C 7. C 8. C 9. B 10. D Mass vs Volume Post Test Questions Name: ____________________________ Period: ___________ Date: ___________ 1. Volume of a box is measured with which instrument listed below? a. thermometer b. triple beam balance c. ruler d. graduated cylinder 2. What is a correct unit for mass? a. centimeter b. kilogram c. milliliter d. pound 3. What is a correct unit for density? a. grams � cm 3 b. grams x cm 3 c. cm 3 � grams d. cm 3 x grams 4. Which of the following is a formula for finding the mass of an object? a. density x volume b. volume x density c. density � volume d. volume � density Densities: Balsa: 0.13 g/cm 3 Iron: 7.9 g/cm 3 Gold: 19.3 g/cm 3 Aluminum: 2.7 g/cm 3 Formulas: Sphere: 4/3 x π x radius x radius x radius Cylinder: π x radius x radius x height Cube: length x length x length Cone: 1/3 x π x radius x radius x height 5. Using the information in the charts above, calculate the mass of a balsa wood cylinder with a radius of 3 cm and height of 0.5 cm. a. 0.61 grams b. 1.8 grams c. 18.4 grams d. 30.6 grams 6. Using the information in the charts above, calculate the mass of an iron cube with all edges equal to 4 cm. a. 505.6 grams b. 126.4 grams c. 31.6 grams d. 7.9 grams 7. You have 4 spheres all with an equal radius. One is made of iron, one of gold, one of balsa, and one of aluminum. Which sphere is the most massive? a. iron b. gold c. balsa d. aluminum 8. You have a gold cube. Which of the following is more massive? a. A balsa wood cube with triple the gold cube�s edge length. b. A gold cone with radius that is equal to half of the gold cube�s edge length and a height of twice the gold cube�s edge length c. An aluminum cube with double the gold cube�s edge length. d. An iron sphere with a radius of 1.5 times the gold cube�s edge length. 9. Can two objects with the same mass have different volumes? a. Yes, objects with the same mass will have different volumes if they have different densities. b. Yes, objects with the same mass will have the volumes if they are in different locations (like on the moon). c. No, objects with the same mass always have the same volumes. d. Yes, objects with the same mass will only have the same volume if they have the same shape. 10. You have an elementary balance with two gold cubes in one pan and three gold cubes on the other. All five gold cubes have an edge length of 2 cm. On the side of the balance with the two gold cubes, there is an aluminum object. What must the volume of the aluminum object be in order to keep the balance level? a) 154.4 cm 3 b) 308.8 cm 3 c) 463.2 cm 3 d) 57.185 cm 3 Mass vs Volume Post Test Answers 1. C 2. B 3. A 4. A 5. B 6. A 7. B 8. C 9. A 10. D How many micrograms (�g, ug or mcg) in a milligram (mg)? 1000 micrograms = 1 milligram, and 1000 milligrams = 1 gram. How can I convert from international units (IU) to milligrams or micrograms? Math in the News. How is math used in everyday news reports on television, in newspapers, and in magazines? Follow a particular news program and/or section of the newspaper for several days. Record how numbers are used in reporting. What kinds of math are referred to the most? Which stories generate the most mathematical analysis? Choose a story that uses math and follow it. Do your own mathematical analysis to share with the class. Time. How did we come to use the system of time that we use today? Does everyone measure time the same way? What are different units of time? How were modern (analog and digital) clocks invented? Include a historical discussion of time and culture. Describe your project idea. * Relevance: What is the purpose of your project? Why is your type of project important or special to you? * Content: What subject topics will you incorporate into your project? Please be as specific as possible. * Methods: How do you plan to develop and/or explore the content through working on your project? How do you plan to incorporate different methods of representation (symbolic, numerical, graphical, and verbal) into your project? State your plan for each. * Organization: How will the content be organized within the project? Also, for group projects, how will you organize the work to be divided equally among group members? * Discourse: How do you plan to share your project with the class? Also, how will you use critique on your project presentations to help guide you through revision and subsequent presentations? * Challenge: What do you think will be the biggest difficulty you will encounter in completing this project? How do you plan to meet that challenge? * What resources will you use for research? * What do you hope to learn through this project? * What other questions, comments, concerns, and/or suggestions do you have? Progress Presentation Outline Progress Presentations should be short (5 minutes maximum). * Explain your project o What project did you do? What mathematics did you use? o Briefly share what you have done symbolically, numerically, graphically, and verbally. o Share what you learned from the Internet. o Share your plans for your Display Board * What�s next? o What do you have left to complete? o Who is responsible for finishing each part? Relevance: Is this project interesting and/or meaningful? Content: Does the project include the appropriate information accurately? Methods: Does the project exhibit mathematical and/or scientific thinking? - Does the project clearly demonstrate their understanding SYMBOLICALLY? - Does the project clearly demonstrate their understanding NUMERICALLY? - Does the project clearly demonstrate their understanding GRAPHICALLY? - Does the project clearly demonstrate their understanding VERBALLY? Organization: Is the project exhibited in a clear, well-organized format? Discourse: Does the project incite discussion to promote learning? Challenge: Is this project challenging for the author(s)? Please take notes summarizing the discussion following the presentation. Remember that this is to help the presenters improve their project. Continue your notes on the back if necessary. Name: ___________________________________ Question/Comment: _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ http://mathforum.org/mathtools/sitemap2/ALL/ |
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Q. What is Industrial Mathematics? Q. What Kind of Problems do IMS Professionals Work On? The problems that applied mathematicians work on are very diverse. Some of the problems that applied mathematicians and statisticians in industry have faced and solved include: Aerospace Q. What should be the dimensions of an aircraft manufacturing industrial estate plant with the following capacity? Aircraft for 800 passengers Wing span 115.02 m (or ft-in) Length 105.22 m (or ft-in) Jets of two types, single- and two-storied Jumbo Q. How should an airline set ticket prices to ensure maximum revenue while allowing for no-shows and the aggravation and expense of overbooking? Automotive Tractor Q. What should be the dimensions of a plant with production capacity of 120 units per month? Q. An automobile production plant is falling far short of the capacity for which it was designed. Why? |