Units of Weights and Measures Knowledge Probe (Pre-Quiz) Primary Knowledge Unit Activities (2) Participant Guide

www.scme-nm.org

Southwest Center for Microsystems Education (SCME) University of New Mexico

MEMS Fabrication Topic

Units of Weights and Measures Learning Module This booklet contains five (5) Sharable Content Objects (SCOs): Knowledge Probe (Pre-Quiz) Units of Weights and Measures Primary Knowledge (PK) Research Activity Conversion Activity Assessment

Target audiences: High School, Community College, University Support for this work was provided by the National Science Foundation's Advanced Technological Education (ATE) Program through Grant #DUE 0902411.

Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and creators, and do not necessarily reflect the views of the National Science Foundation.

Copyright © by the Southwest Center for Microsystems Education and The Regents of the University of New Mexico Southwest Center for Microsystems Education (SCME) 800 Bradbury Drive SE, Suite 235 Albuquerque, NM 87106-4346 Phone: 505-272-7150 Website: www.scme-nm.org

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Units of Weights and Measures Knowledge Probe (Pre-Quiz) Participant Guide The purpose of this knowledge probe is to determine your current knowledge of weights and measures history, the content of the International Standards of Units, and your ability to convert from one unit of measurement to another. Answer the following questions to the best of your knowledge 1. In what country is it believed that the first units of weights and measures were standardized? a. Egypt b. England c. France d. Italy e. United States 2. Which of the following measurement systems is the International Standard of Units? a. English system b. Metric system c. Roman system d. British system 3. How many base units are in the International Standard of Units (SI)? a. 14 b. 10 c. 7 d. 5 4. Which of the following BEST describes one of the first standardized units – the cubit? The length of an average… a. person’s arm from elbow to the outstretched fingertips b. person’s thigh from the hip joint to the front of the knee c. person’s single stride d. work horse’s face from the tip of the nose to the crown of the head 5. What was one of the main factors that influenced the standardization of units? a. Population growth b. Increase in commerce and trade c. The fall of the Roman empire d. World War I Southwest Center for Microsystems Education (SCME) Int_Scale_KP10_PG_072313

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6. When was the original metric system developed? a. 1910’s b. 1940’s c. 1870’s d. 1790’s 7. Which of the following industrial countries has NOT adopted the metric system as its standard measurement system? a. Germany b. England c. United States d. China 8. Which of the following is NOT one of the seven fundamental units of the SI? a. Meter b. ampere c. Second d. Centigrade 9. The metric system is the standard unit of measure for science and technology. Which of the following micro-sized devices would use the metric units µliters/sec? a. Thickness of gold thin film on a micro-sensor b. Output of an inkjet printer nozzle c. Tensile strength of a micro-spring d. Resonance of an oscillating microcantilever 10. Micro is _______ and nano is __________. a. 103, 10-6 b. 10-3, 10-6 c. 10-6, 10-9 d. 10-6, 10-12 11. How many meters is 6.5 feet? (Hint: 1 in = 2.54 cm) a. 1.73 meters b. 1.98 meters c. 2.27 meters d. 2.43 meters 12. How many ounces in 32 kg? (Hint: 1 lb = 0.453 kg) a. 1130 ounces b. 466 ounces c. 232 ounces d. 7.25 ounces

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13. How many kg in 1200 grams? a. 1,200,000 kg b. 120 kg c. 1.2 kg d. 0.12 kg 14. How many millimeters (mm) in 0.05 km? a. 0.00005 mm b. 50 mm c. 5,000 mm d. 50,000 mm 15. How many micrometers (µm) in 10,700 nanometers (nm)? a. 0.0107 µm b. 1.07 µm c. 10.7 µm d. 10,700,000 µm

Support for this work was provided by the National Science Foundation's Advanced Technological Education (ATE) Program. Southwest Center for Microsystems Education (SCME) Int_Scale_KP10_PG_072313

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Southwest Center for Microsystems Education (SCME) University of New Mexico

MEMS Introduction Topic

Units of Weights and Measures Primary Knowledge (PK) Shareable Content Object (SCO)

This SCO is part of the Learning Module

Scale

Target audiences: High School, Community College, University Support for this work was provided by the National Science Foundation's Advanced Technological Education (ATE) Program through Grants #DUE 0830384 and 0902411. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and creators, and do not necessarily reflect the views of the National Science Foundation. Copyright © by the Southwest Center for Microsystems Education and The Regents of the University of New Mexico Southwest Center for Microsystems Education (SCME) 800 Bradbury SE, Suite 235 Albuquerque, NM 87106-4346 Phone: 505-272-7150 Website: www.scme-nm.org

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Units of Weights and Measures Primary Knowledge Participant Guide Unit Description This unit provides information on the evolution of the current systems of weights and measures and an overview of the International Standards of Units and metric system. A strong foundation in weights and measure, an understanding of the units used in the metric system, and the ability to convert within the metric system and between systems is fundamental when working with MEMS Technology. This information is needed in order to understand how MEMS are used, how they work, how they are made, how they are designed and how they are marketing. Estimated Time to Complete Allow approximately 15 minutes Introduction

Units for pressure, weight / mass, distance and temperature How many pounds of pressure do car tires require? How much does the average person weigh? What is the temperature? How far is it to the nearest gas station? What do all of these questions have in common? All of the answers require a "unit of measurement".

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A unit of measurement is a standardized quantity of a physical property, such as length, weight, time, and temperature. Some of the first units of measurement were units of length, many of which were derived from the length of a body part. For example, by 2500 BC the cubit was the standard unit for length. It was derived from the length of an average person's arm from the elbow to the outstretched fingertip. Throughout history, the standards for units of weights and measures have continued to change. Different standards have been used by different countries and at times, within the same country. These factors have created the need for continuous conversion from one standard to another, from one unit to another. Today there is a global standard, the International System of Units (SI), which is the current metric system. As of 2007, the SI standard has been adopted by all but three countries: United States, Liberia, and Myanmar (Burma). It is universally recognized as the standard for science and technology. 1 This unit will provide a brief history on units of weights and measures, and a review of the International System of Units (SI). Objectives   

State two problems with the systems of weights and measures which led to the development of the metric system. Discuss the importance of an international standardized system of weights and measures. List the seven basic SI units of physical quantities.

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First Units of Weights and Measures

The cubit with close-up [Photo courtesy of and by Jon Bodsworth] The earliest known units of weights and measures were developed in Egypt around 3000 BC. Most of these units were derived from the human body or the natural surroundings. One of the first standardized units was the "cubit". By 2500 BC the Egyptian cubit was standardized as the length of an average person's arm from the elbow to the outstretched fingertips (52.3 cm). The Egyptian shekel became the standard unit for weight. It was defined by 180 grains of barleycorn (8.33 grams). Grains of wheat were also used for weight measurements. The conversion due to size differences was three barleycorns to four wheat grains. Over the centuries, the original units of weights and measures were altered by different civilizations. The Royal Egyptian cubit (see figure), which was originally divided into 28 digits (the width of a finger), was later divided into 24 digits or 6 palms (width of the hand) of 4 digits. The Roman cubit was 16 palms. The number of grams in a shekel ranged from 8.5 to as high as 17 grams which is not surprising considering the fact that there are variations in weight among the grains of barleycorn. Subsequent units, such as the foot and pound, were eventually derived from these original units of length and weight.

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Commerce and Trade

Ancient Stones used as Standards for various weights [From Materials Evaluation, Vol. 64, No. 10. Reprinted with permission of The American Society for Nondestructive Testing, Inc.] As commerce and trade spread across countries, it became necessary to have more consistent representation of units. Materials such as stone and metal were used to produce exact units of weight and length, creating a standard for the trade market. Larger quantities such as the yard, mile or pound were based on multiples of these smaller units. As commerce and trade spread across countries, it became necessary to have more consistent representation of units. Materials such as stone and metal were used to produce exact units of weight and length, creating a standard for the trade market. Larger quantities such as the yard, mile or pound were based on multiples of these smaller units. English Units of Measurements

One Pace = 5 feet The English units of measurement were derived from the base-12 system developed and standardized during the Roman Empire (510 BC – 476 AD). This system divided both the foot and the pound into 12 equal parts (inches and ounces). The Romans established the "pace" equal to five feet and the mile equal to 1000 paces or 5000 feet. 2 In 1595, under the reign of Queen Elizabeth I, the Roman mile was changed from 5000 feet to 5280 feet or 8 furlongs. (The furlong is equal to 220 yards. It was derived in the Middle Ages as a "furrow long," the length of a plowed strip of land in the English open field system). Both the Imperial System, used in the United Kingdom (UK), and the US System were derived from the English units of weights and measures. Southwest Center for Microsystems Education (SCME) Int_Scale_PK10_PG_072213

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Systems of the US and the UK

UK versus US Pint Through the years each country, the United States (US) and the United Kingdom (UK) working independently, continued to develop their respective standards for weights and measures. As a result, the differences between these two systems increased. For example, the US pint was defined as 16 ounces and the UK pint as 20 ounces. The US wine-gallon was defined as 231 cubic inches and the UK wine-gallon as 277 cubic inches. The Origin of the Metric System To complicate matters even more, in 1790 the French Academy of Sciences was charged by the National Assembly of France to "deduce an invariable standard for all of the measures and all weights." 3 The outcome was the metric system. The metric system attempted to reduce the existing conflicting and confusing units of measure to a few fundamental units. Common multipliers (powers of 10) were developed to enable each unit to be expressed in larger and smaller quantities. Treaty of the Meter In Paris on May 20, 1875, an agreement referred to as the Treaty of the Meter (Convention du Mètre), was signed by 17 nations. Fifty-one nations have since signed this treaty, including all the major industrialized countries as well as the United States. 3 Two of the major outcomes of the Treaty of the Meter were the formation of the General Conference on Weights and Measures (CGPM, Conference Generale des Poids et Mesures), an intergovernmental treaty organization, and the creation of the International Bureau of Weights and Measures (BIPM, Bureau International des Poids et Mesures). The CGPM meets every four years and remains the basis of all international agreements on units of measurement.

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International System of Units (SI) Since the original metric system of 1791, several variations have evolved. Countries around the globe began replacing their traditional systems of weights and measures with the French metric system or slight variations of it. At the 9th CGPM conference in 1948, the BIPM was instructed to conduct an international measurement requirements study of the scientific, technical, and educational communities. The data from this study led to the adoption of the International System of Units or Système International d'Unités (commonly referred to as SI) at the 11th CGPM conference in 1960.3 All systems of weights and measures, metric and non-metric, are linked through a network of international agreements supporting the International System of Units (SI). The Seven Base Units of the SI The SI replaces all traditional units of measurement (except for those used for time) with seven base units for seven physical quantities assumed to be mutually independent. The table shows the basic units and the physical quantities they represent. Physical Quantity length mass temperature (absolute) amount of substance electric current luminous intensity time

Unit of Measure Meter Kilogram Kelvin mole ampere candela second

Unit Symbol m k K mol A cd s

Table 1: Seven Base Units of SI

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Derived Quantities Other quantities, called derived quantities, are derived algebraically in terms of the seven base quantities. The SI units for these derived quantities are derived from these algebraic equations and the seven SI base units. The table shows some of these derived quantities. Derived quantity area volume speed, velocity acceleration wave number mass density specific volume current density magnetic field strength amount-of-substance concentration luminance

Name square meter cubic meter meter per second meter per second squared reciprocal meter kilogram per cubic meter cubic meter per kilogram ampere per square meter ampere per meter mole per cubic meter candela per square meter

Symbol m2 m3 m/s m/s2 m-1 kg/m3 m3/kg A/m2 A/m mol/m3 cd/m2

Table 2: Derived Quantities of SI Challenge Write an algebraic equation for each of the following. Your answer should result in one of the derived units of the SI. 

The volume of a cube 3.5 m x 2 m x 6.3 m



The speed of a car that traveled 88 km in 45 minutes

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Defining the Seven Base Units As with most units of measurement, the official definitions for the seven base units of SI have changed through the years. The most current definitions are those established by the International Bureau of Weights and Measures (BIPM). These definitions and other aspects of SI are updated every four years at the CGPM. The Meter The meter was originally defined by the French Academy of Science as one ten-millionth (10-7) of the distance from the equator to the North Pole. The meridian that was used was the one that goes through Paris. In 1983 the General Conference on Weights and Measures (CGPM), replaced this definition with the following: The meter is the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second.3 Meridian used for the Original Meter Derivation The Kilogram The kilogram was originally defined as one thousand times the absolute weight of a volume of pure water equal to the cube of the hundredth part of a meter, and at the temperature of melting ice. This definition was later changed to the mass of a cubic decimeter of water at standard pressure and temperature. In 1889, the CGPM sanctioned the international prototype of the kilogram, made of platinum-iridium, and declared "This prototype shall hence forth be considered to be the unit of mass." This prototype is kept at the International Bureau of Weights and Measures (BIPM). In 1901, the CGPM redefined the kilogram: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. 3 To learn the historical derivation of the other base units of SI, complete the Unit of Weights and Measures Activity.

Facsimile of the International Prototype of the kilogram [Photograph is reproduced with permission of the BIPM, which retains full internationally protected copyright.] Southwest Center for Microsystems Education (SCME) Int_Scale_PK10_PG_072213

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SI Prefixes To represent smaller and larger quantities of the fundamental units, the SI established a system of prefixes based on powers of 10. Factor Name Symbol Factor Name Symbol 1024 yotta Y 10-1 deci D 21 -2 10 zetta Z 10 centi C 18 -3 10 exa E 10 milli M 1015 peta P 10-6 micro µ 12 -9 10 tera T 10 nano N 109 giga G 10-12 pico P 6 -15 10 mega M 10 femto F 103 kilo K 10-18 atto A 2 -21 10 hecto H 10 zepto Z 1 -24 10 deka Da 10 yocto Y Table 3: SI Prefixes Using the Prefixes Examples of the prefixes with base units: 2000 meters = 2 kilometers or 2 km 0.005 meters = 5 millimeters or 5 mm 0.025 amperes = 25 milliamperes or 25 mA Since the kilogram already uses a prefix (kilo), smaller and larger values are based on the gram (100). 0.015 kilograms = 15 x 10-3 kg = 15 grams

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Importance of a Standardized System5

Mars Climate Orbiter [Created by and courtesy of NASA] On September 23, 1999, NASA's Mars Climate Orbiter probe was lost after a 286-day journey to Mars. Upon its approach, the probe fired its engines to move into orbit. The firing brought it to within 60 km (36 miles) of the planet's surface. This was 100 km (60 miles) closer than planned and about 25 km (15 miles) beneath the level at which the Orbiter's engines could properly function. As a result, the probe's propulsion system overheated and was disabled. The Orbiter fell deep into the planet's atmosphere and possibly burned up, or "continued out beyond Mars and now could be orbiting the sun" (Frank O'Donnell, spokesperson for NASA's Jet Propulsion Laboratory). After a thorough investigation it was discovered that the loss of the $125 million Orbiter was due to the use of two different units of measurement. NASA and other project teams used the metric system; however, one lone engineering team was using the English system. It was this team that provided the thruster information in English units of pound-force-seconds rather than the metric unit of Newton-second which was being used by the Orbiter programs. This simple unit of measurement resulted in a very costly mistake. Summary Since 3000 BC units of weights and measures have been derived, defined, redefined, replaced and evolved into an international quagmire. Through the years, this has created many problems with international communication and commerce. In 1790 the French Academy of Sciences developed the metric system. In 1960 the General Conference on Weights and Measures (CGPM) declared the modern metric system as the international standard of units (SI). The SI consists of seven fundamental units and additional derived units each of which use common multipliers (powers of 10) to represent smaller and larger quantities.

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Food For Thought Other than science and technologies, the US system of weights and measures is still used by the citizens of the United States. We still drive mph rather than km/hr. We still weigh ourselves in pounds rather than kilograms. How do you feel about the United States' conversion to the SI? What do you see as the biggest road block to converting to the SI? References 1 The World Factbook. Appendix G – Weights and Measures. https://www.cia.gov/library/publications/the-world-factbook/appendix/appendix-g.html 2

"Measurement: Wrestling the mother of all nonstandards", Kenneth Holladay. InTech: Control Fundamental. August 1998.

3

The NIST Reference on Constants, Units, and Uncertainty. http://physics.nist.gov/cuu/Units/current.html

4

Facsimile of the international prototype of the kilogram kept at the BIPM. http://www.bipm.org/en/scientific/mass/prototype.html

5

Mars Climate Orbiter Website. http://mars.jpl.nasa.gov/msp98/orbiter/

Disclaimer The information contained herein is considered to be true and accurate; however the Southwest Center for Microsystems Education (SCME) makes no guarantees concerning the authenticity of any statement. SCME accepts no liability for the content of this unit, or for the consequences of any actions taken on the basis of the information provided.

Support for this work was provided by the National Science Foundation's Advanced Technological Education (ATE) Program.

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Units of Weights and Measures Research Activity Participant Guide Description and Estimated Time to Complete This activity provides three separate discussion points that allow you to gain a better understanding on  the current International Standard of Units (SI),  the United States’ resistance to adopting the SI and  the use of metrics within MEMS technology. This activity will help you to better understand the factors affecting design, fabrication, and commercialization of microsystems. It should open your eyes to the problems faced by scientists, engineers and technicians in educating the general population on micro and nanotechnology. Estimated Time to Complete The instructor may choose to have you complete all three discussions, two discussions or one discussion. Allow approximately 3 hours for completion of each discussion problem.

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Introduction A unit of measurement is a standardized quantity of a physical property, such as length, weight, time, and temperature. Some of the first units of measurement were units of length, many of which were derived from the length of a body part. Throughout history, the standards for units of weights and measures have continued to change. Different standards have been used by different countries and at times, within the same country. These factors have created the need for continuous conversion from one standard to another, from one unit to another. Today there is a global standard, the International System of Units (SI), which is the current metric system. As of 2007, the SI standard has been adopted by all but three countries: United States, Liberia, and Myanmar (Burma). It is universally recognized as the standard for science and technology. 1 The following discussion problems allow you to further explore the units of the SI, the United States efforts toward metrication, and the use of metrics in MEMS Technology. 1

The World Factbook. Appendix G – Weights and Measures. Update 1/1/07. https://www.cia.gov/library/publications/the-world-factbook/appendix/appendix-g.html

Activity Objectives and Outcomes Activity Objectives  Compare and contrast the metric system and the US system of weights and measures  Discuss the United States' efforts toward metrication  Discuss the use of metrics within MEMS Technology. Activity Outcomes Upon completion of these discussions you should be able to support your argument – one way or another – as to whether or not the United States should enforce the use of the SI at all levels, and phase out the current US System of Weights and Measures. Team It is recommended to complete these discussion problems in small groups (2-3 participants). This will allow for discussion that may consider various viewpoints. Such back and forth will help when completing the written documentation. Resources Be sure to record and report all references and resources that support your discussions and arguments.

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Discussion Problem I: Systems Comparison A comparison of the current United States (US) System of Weights and Measures with the current metric system adopted by the SI. Documentation The documentation for this discussion will consist of a written report that must include, but is not limited to the following:  A comparison of the current US System of Weights and Measures with the current metric system based on the seven base units of the SI and the SI prefixes.  A summary of how each system of measurement is used within the United States.  A discussion on problems that have emerged as a result of operating under two systems of weights and measures (if any exist).  Graphics (when needed to support discussion)  References for information, materials, and graphics  Answers to the Post-Activity Questions (Discussion Problem I) Procedure: Systems Comparison Description In this discussion you will compare and contrast the US System of Weights and Measures with the seven basic units of the current metric system adopted by the International Standards of Units. 1. Research the unit equivalent of each of the seven basic units of the SI metric system, applications of each system with the US, and any problems that have emerged due to the use of both systems. 2. Complete a written report fulfilling the documentation requirements. 3. Answer the Post-Activity Questions for Discussion Problem I. Post-Activity Questions 1. Which system (US or metric) do you find to be the simpler system to use? (Explain your answer) 2. Which system do you find to be the simpler system when converting to larger or smaller quantities of a unit? (Explain your answer) 3. Discuss the advantages of one system over the other.

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Discussion Problem II: US Metrication Process Discuss the United States' efforts toward metrication. Documentation The documentation for this discussion will consist of a written report that must include, but is not limited to the following:  A discussion on the current efforts of the United States toward metrication.  Your personal opinion of this process and its effectiveness.  Your personal opinion as to whether or not this conversion is needed. Why or why not?  Graphics (when needed to support the discussion)  References for information, materials, and graphics  Answers to the Post-Activity Questions (Discussion Problem II) Procedure: US Metrication Process Description Research the United States' efforts toward metrication. Discuss your personal opinion of this process and the need for this conversion. 1. Research the United States' efforts toward metrication. 2. Complete a written report fulfilling the documentation requirements. 3. Answer the Post-Activity Questions for Discussion Problem II. Post-Activity Questions 1. What do you feel is the most significant factor in preventing a total conversion by the United States to the metric system? 2. Most of us in the Science and Technology fields have to deal with both the metric and US system of weights and measures. How has dealing with two different systems affected you – both personally and professionally? 3. At what grade level should the metric system be taught? Justify your answer.

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Discussion Problem III: Metrics and MEMS Technology Research the use of metrics within MEMS Technology. Documentation The documentation for this discussion will consists of a written report that must include, but is not limited to the following:  A discussion on the use of metrics with MEMS Technology.  Graphics (when needed to support discussion)  References for information, materials, and graphics Procedure: Metrics and MEMS Technology Description Research the use of metrics within MEMS Technology. Identify common SI units used in various applications. Briefly discuss the advantages or disadvantages of metrics vs. the US units for MEMS Technology.

1. Research the use of metrics with MEMS Technology. Your research should include, but is not limited to the following: a. A brief discussion of metrics within MEMS Technology. b. Specific units used for specific applications (e.g. μm and nm for length, width and height of cantilevers) c. Advantages and disadvantages of metrics vs. the US units for MEMS Technology 2. Complete a written report fulfilling the documentation requirements

Summary Since 3000 BC units of weights and measures have been derived, defined, redefined, replaced and evolved into an international quagmire. Through the years this has created many problems with international communication and commerce. The current internationally adopted system (SI) attempts to correct these problems. The SI has been adopted and incorporated into the everyday lives of all but three of the world's countries, one being the United States (US). The US has made a legislative commitment but has yet to develop an effective process for change.

Support for this work was provided by the National Science Foundation's Advanced Technological Education (ATE) Program.

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Units of Weights and Measures Conversion Activity Participant Guide Description and Estimated Time to Complete This activity provides process, examples, and practice for converting units of weights and measures. You will practice converting metric units to larger and smaller quantities and converting between metric and US units. This skill is vital to understanding almost every concept (design, fabrication, commercialization) associated with MEMS devices and components. Estimated Time to Complete Allow approximately 1 hour Introduction Throughout history the standards for units of weights and measures have continued to change. Different standards have been used by different countries and at times, within the same country. These factors have created the need for continuous conversion from one standard to another, from one unit to another. Today there is a global standard, the International System of Units (abbreviated SI, after the French Système International), which is the current metric system. As of 2007, the SI standard has been adopted by all but three countries: United States, Liberia, and Myanmar (Burma) 1. It is universally recognized as the standard for science and technology. This activity will provide examples and exercises for practicing conversion within the metric system and between the metric system and the US system of units. Activity Objectives and Outcomes Activity Objectives  Convert at least three metric quantities to a larger or smaller quantity  Convert at least three metric quantities to the US equivalents  Convert at least three US units to the metric equivalents Activity Outcomes Upon completion of this activity you should be able to convert successfully within the metric system and between the metric and US systems.

Base Units of the Metric System The following three tables can be used for this activity.  Base Units of the Metric System  Derived Quantities of the Metric System  Metric Prefixes Physical Quantity length mass temperature (absolute) amount of substance electric current luminous intensity time

Unit of Measure meter kilogram kelvin mole ampere candela second

Unit Symbol m k K mol A cd s

Table 1: Base Units of the Metric System Derived Quantities of the Metric System The derived quantities are derived algebraically from the base units. Derived quantity Name area square meter volume cubic meter speed, velocity meter per second acceleration meter per second squared wave number reciprocal meter mass density kilogram per cubic meter specific volume cubic meter per kilogram current density ampere per square meter magnetic field strength ampere per meter amount-of-substance concentration mole per cubic meter luminance candela per square meter

Symbol m2 m3 m/s m/s2 m-1 kg/m3 m3/kg A/m2 A/m mol/m3 cd/m2

Table 2: Derived Quantities of the Metric System

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Metric Prefixes The metric prefixes are powers of ten and are used for all metric units when converting from smaller to larger quantities. Factor 1024 1021 1018 1015 1012 109 106 103 102 101

Name yotta zetta exa peta tera giga mega kilo hecto deka

Symbol Y Z E P T G M K H Da

Factor 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 10-21 10-24

Name deci centi milli micro nano pico femto atto zepto yocto

Symbol D C M µ N P F A Z Y

Table 3: Metric Prefixes

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Converting Units of Weights and Measures

Multiplication by "1" Converting from one quantity to another of equal quantity in a different unit is easy as long as you remember this basic idea: Multiplication by "1" or a fractional equivalent of 1 does not change the quantity. A fraction is equal to "1" as long as the numerator and the denominator are of equal values. For example, 1 yard = 3 feet; therefore, using this equality as a fraction allows one to convert from yards to feet and feet to yards. The equations in "Multiplication by 1" show how to convert 346 ft to its equivalent in yds and 25 yds to its equivalent in ft. Notice how the common units in the numerator and denominator cancel leaving the desired unit. When converting, if the cancellation of units does not yield the desired unit, then the fraction of 1 is set up incorrectly. Metric to US equivalents In order to convert between metric and the US system, you need to know the equivalents or conversion factor. The table "Metric and US Equivalents" provides some of the more common equivalents. US Unit Metric Unit 1 inch 2.54 centimeter 39.37 inches 1 meter 0.6 mile 1 kilometer 1.0567 quart 1 liter 1 pound 0.45 kilogram Table 4: Metric and US Equivalents

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Converting between Metric and the US System

Converting between Systems Following the same principle of "multiplication by 1 (or a fraction equal to 1)", one can easily convert from metric to US and from US to metric. Study the equations in "Converting between Systems". Notice that the equality 1 in = 2.54 cm is set up as a fraction equal to one. In the conversion equation, this fraction is set up so that the original unit cancels and leaves the desired unit. Converting within Metric

Converting within Metric

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To convert to larger or smaller quantities within the metric system, use the power of 10 for the respective metric prefix. You can apply the same system as demonstrated previously (setting up a fraction of 1). Study the equations in "Converting within Metric". With practice, you can simply use the exponent of the desired prefix to know how many places to move the decimal point and in which direction. In the equations "Converting within Metric" 10546 cm was converted to meters and kilometers. Since the meter is 100 or 102 times larger than the cm, the decimal point moved two places to the left (10546 cm = 105.46 m). The kilometer is 10,000 or 105 times larger than the cm; therefore, the decimal point moved five places to the left (10546 cm = 0.10546 km). When converting to a smaller quantity, the decimal point would move to the right the number of spaces defined by the power of ten. For example, 3 m is equal to 300 cm or 3,000 mm. Conversion of Derived Quantities

Conversion of Derived Quantities Again, the same method applies when converting derived quantities. It also is used to convert derived quantities between systems, such as mph to km/hr or even to m/s. Study the equations in "Conversion of Derived Quantities." These equations convert 643 miles/hour to its equivalent in meters/second.

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Activity: Units of Weights and Measures Conversion Complete the Worksheet: Units of Weights and Measures Conversion for this activity. Show all of your conversion steps for each conversion. Worksheet: Units of Weights and Measures Conversion (With Answers) Description Convert each of the following quantities to the unit(s) indicated. Show your work in the spaces provided.

1. Convert 8,500 kg to lb

2. Convert 889,300 m to mi

3. Convert 9.25 km to m

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4. Convert 31.5 gal to liters

5. Convert 55 oz to kg

6. Convert 925 km/h to mph

7. Convert 35 km/h to m/s

8. Convert 11,500 cm to km

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9.

Convert 628 in2 to m2

10.

Convert 47 lbs/in3 to kg/m3

MEMS Applications 11. Hydrophobic (water fearing) coatings are deposited on microdevices to keep water from adhering to the device surface. These coatings are called "thin films" because they have microscopic thicknesses. An engineer has set up a process to deposit 50 angstroms (Å) of this coating with a tolerance specification of ±10 Å. In other words, the thickness specification is 50 ±10 Å. You are a metrology (measurement) technician that works with a thin film measurement tool set up to measure in nanometers. What is the thin film specification in nanometers?

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12. A particular MEMS device includes a thin spring. It is very important for that spring to have a consistent width from device to device. If the spring is too wide, it will be too stiff and if it is too narrow, it will be too compliant. Below is an image from a scanning electron microscope (SEM) of a MEMS comb drive and its springs (in the center). The springs provide the restoring force, returning the electrostatic comb teeth to their original position. The detail on the right shows a close-up of the two layer springs.

MEMS Comb Drive and Springs [Image source and text courtesy of Sandia National Laboratories. http://mems.sandia.gov/galler y/images_microengines.html]

You are a technician that works with a scanning electron microscope (SEM) which measures in nanometers. The engineering specifications are 0.55 ± 0.07um in width. The SEM indicates the spring's width to be 610nm. Does the measurement pass? (Show your work) Solution

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13. An inkjet print nozzle and pump system can produce 5 picoliter (pL) droplets.

The graphic shows a inkjet print head with a close-up of a nozzle. This particular nozzle uses a piezoelectric crystal that moves up and down acting as a “pump” pulling ink from the reservoir and pushing it through the nozzle.

a. A 1 milliliter (ml) eyedropper typically produces a 0.05 milliliter droplet or 20 drops. How many inkjet droplets are in a 1 milliliter eyedropper? Solution

b. If the inkjet nozzle/pump can print out 10,000, 5pL droplets per second, how long does it take to use 1ml of ink? Solution

c. A typical large capacity cartridge has 42 ml. of ink, how many droplets can it produce? Solution:

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d. The typical printed page has about 5% coverage – that is to say, 5% of the page is black and 95% of the page is white. The same 42 ml. cartridge above will let you print 833 pages at this 5% coverage rate. i. How many drops per average page? Solution:

ii.

How long does it take for one nozzle to print a page? (Assuming it is spraying at an average of 10,000 droplets/second since an actual inkjet nozzle turns on and off as the cartridge moves across the page) Solution:

It will take over 15 minutes to print one page! Would you buy this? In reality, why do pages print so much faster?

iii.

How many nozzles are in an inkjet cartridge for a printer that claims to print 30 black pages/minute? Solution:

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14. Density is a physical property of matter that describes the degree of compactness of a substance. The more closely packed together the individual particles of a substance, the higher the density of that substance. The ratio between the mass and volume of a substance defines its density: Density (ρ) = Mass/Volume

ρ = m/v Mass (m) is the amount of matter contained in an object. Mass is measured in units of grams (g). Volume (v) is the amount of space occupied by a quantity of matter. Volume is expressed in cubic centimeters (cm3). Gold is a commonly used element in MEMS fabrication. It is used as a conductive layer, a reflective layer and a bonding layer (see graphic below). The density of gold is 19.3 g/cm3.

So just for fun, let's make a comparison of a couple of gold objects. Let's compare the mass of a gold bar to that of a gold MEMS layer. Gold bar The gold bars stored in the Federal Reserve Bank of 7" x 3.625" x 1.75". a. What is the mass (in pounds) of one gold bar?

b. What is the mass of a layer of gold 5 μm x 10 μm x 0.3 μm?

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Summary Since 3000 BC units of weights and measures have been derived, defined, redefined, replaced and evolved into an international quagmire. Through the years, this has created many problems with international communication and commerce. In 1790 the French Academy of Sciences developed the metric system. In 1960 the CGPM declared the modern metric system as the international standard of units (SI). The SI consists of seven fundamental units and additional derived units each of which use common multipliers (powers of 10) to represent smaller and larger quantities. The United States is one of three countries that has yet to adopt the metric system into common practice; therefore, conversion between metric and the US system is often required. For those in the science and technology fields, conversion within the metric system is required. Due to the current efforts of US metrication, converting between metric and the US system, and converting within the metric system are skills that everyone should acquire.

Support for this work was provided by the National Science Foundation's Advanced Technological Education (ATE) Program.

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Southwest Center for Microsystems Education (SCME) Learning Modules available for download @ scme-nm.org MEMS Introductory Topics

MEMS Fabrication

MEMS History MEMS: Making Micro Machines DVD and LM (Kit available) Units of Weights and Measures A Comparison of Scale: Macro, Micro, and Nano Introduction to Transducers Introduction to Sensors Introduction to Actuators NanoTechnology: The World Beyond Micro Wheatstone Bridge (Pressure Sensor Model Kit available)

Crystallography for Microsystems (Breaking Wafers and Origami Crystal Kits available) Oxidation Overview for Microsystems (Rainbow Wafer Kit available) Deposition Overview Microsystems Photolithography Overview for Microsystems Etch Overview for Microsystems (Rainbow Wafer and Anisotropic Etch Kits available) MEMS Micromachining Overview LIGA Micromachining Simulation Activities (LIGA Simulation Kit available) Manufacturing Technology Training Center Pressure Sensor Process (Three Activity Kits available) MEMS Innovators Activity (Activity Kit available)

MEMS Applications MEMS Applications Overview Microcantilevers (Dynamic Cantilever Kit available) Micropumps Overview

BioMEMS BioMEMS Overview BioMEMS Applications Overview DNA Overview DNA to Protein Overview Cells – The Building Blocks of Life Biomolecular Applications for bioMEMS BioMEMS Therapeutics Overview BioMEMS Diagnostics Overview Clinical Laboratory Techniques and MEMS MEMS for Environmental and Bioterrorism Applications Regulations of bioMEMS DNA Microarrays (GeneChip® Model Kit available)

Revision: 6/27/13

Nanotechnology Nanotechnology: The World Beyond Micro (Supports the film of the same name by Silicon Run Productions)

Safety Hazardous Materials Material Safety Data Sheets Interpreting Chemical Labels / NFPA Chemical Lab Safety Personal Protective Equipment (PPE)

Check our website regularly for the most recent versions of our Learning Modules.

For more information about SCME and its Learning Modules and kits, visit our website scme-nm.org or contact Dr. Matthias Pleil at [email protected]

www.scme-nm.org