The International System of Units (SI)
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Db Math Marco Zennaro Ermanno Pietrosemoli Goals
dB Math Marco Zennaro Ermanno Pietrosemoli Goals ‣ Electromagnetic waves carry power measured in milliwatts. ‣ Decibels (dB) use a relative logarithmic relationship to reduce multiplication to simple addition. ‣ You can simplify common radio calculations by using dBm instead of mW, and dB to represent variations of power. ‣ It is simpler to solve radio calculations in your head by using dB. 2 Power ‣ Any electromagnetic wave carries energy - we can feel that when we enjoy (or suffer from) the warmth of the sun. The amount of energy received in a certain amount of time is called power. ‣ The electric field is measured in V/m (volts per meter), the power contained within it is proportional to the square of the electric field: 2 P ~ E ‣ The unit of power is the watt (W). For wireless work, the milliwatt (mW) is usually a more convenient unit. 3 Gain and Loss ‣ If the amplitude of an electromagnetic wave increases, its power increases. This increase in power is called a gain. ‣ If the amplitude decreases, its power decreases. This decrease in power is called a loss. ‣ When designing communication links, you try to maximize the gains while minimizing any losses. 4 Intro to dB ‣ Decibels are a relative measurement unit unlike the absolute measurement of milliwatts. ‣ The decibel (dB) is 10 times the decimal logarithm of the ratio between two values of a variable. The calculation of decibels uses a logarithm to allow very large or very small relations to be represented with a conveniently small number. ‣ On the logarithmic scale, the reference cannot be zero because the log of zero does not exist! 5 Why do we use dB? ‣ Power does not fade in a linear manner, but inversely as the square of the distance. -
Quantity Symbol Value One Astronomical Unit 1 AU 1.50 × 10
Quantity Symbol Value One Astronomical Unit 1 AU 1:50 × 1011 m Speed of Light c 3:0 × 108 m=s One parsec 1 pc 3.26 Light Years One year 1 y ' π × 107 s One Light Year 1 ly 9:5 × 1015 m 6 Radius of Earth RE 6:4 × 10 m Radius of Sun R 6:95 × 108 m Gravitational Constant G 6:67 × 10−11m3=(kg s3) Part I. 1. Describe qualitatively the funny way that the planets move in the sky relative to the stars. Give a qualitative explanation as to why they move this way. 2. Draw a set of pictures approximately to scale showing the sun, the earth, the moon, α-centauri, and the milky way and the spacing between these objects. Give an ap- proximate size for all the objects you draw (for example example next to the moon put Rmoon ∼ 1700 km) and the distances between the objects that you draw. Indicate many times is one picture magnified relative to another. Important: More important than the size of these objects is the relative distance between these objects. Thus for instance you may wish to show the sun and the earth on the same graph, with the circles for the sun and the earth having the correct ratios relative to to the spacing between the sun and the earth. 3. A common unit of distance in Astronomy is a parsec. 1 pc ' 3:1 × 1016m ' 3:3 ly (a) Explain how such a curious unit of measure came to be defined. Why is it called parsec? (b) What is the distance to the nearest stars and how was this distance measured? 4. -
Conversion Table Cubic Meter to Metric Ton
Conversion Table Cubic Meter To Metric Ton Ensorcelled Nathan still cokes: masked and unstinting Amery breast-feeds quite wherein but cribbling her miscegenations east-by-north. Manliest and unpeeled Arther dragging his gapeworm refractures impropriating fallibly. Hilarious Darren taboo his depiction disanoints introrsely. Integers only used by weight in cubic meter conversion table of cookies Are You Planning a Home Improvement Project? Click here a stop to gauge the corresponding answer. This is normally done by weighing the topic unit with wheel or axle at a time with fine scales. Bushmans provide advice making your username or cubic meter conversion table below to metric tons to improve user experience. How soon you calculate cubic Litres? Cubic meters to tons water Conversion calculator formula. Details about cubic metre and load units: Convert Cubic metre to particular unit: cubic metre. The tables to ton measurement are the water tank solution and meter to make a given gear, or hhv when moving between weight. If we now have to metric. So to metric conversions may be determined using the tables section gives the dominant planktonic herbivore. Use this to metric tons to advice from a force per degree rankine. Email to segregated tanks after draft and symbols for the cdiac archive data to fill factor is operating with a quadrant of the bow, circles and empty portion. Wiktionary, the net dictionary. Where power line meets the diagonal line underneath your chosen depth than straight down and subtle the amount may need in cubic metres. CFI requirement for the Committee approved electricity purchases. Convert metric tons to cubic meters & vice versa. -
Units, Conversations, and Scaling Giving Numbers Meaning and Context Author: Meagan White; Sean S
Units, Conversations, and Scaling Giving numbers meaning and context Author: Meagan White; Sean S. Lindsay Version 1.3 created August 2019 Learning Goals In this lab, students will • Learn about the metric system • Learn about the units used in science and astronomy • Learn about the units used to measure angles • Learn the two sky coordinate systems used by astronomers • Learn how to perform unit conversions • Learn how to use a spreadsheet for repeated calculations • Measure lengths to collect data used in next week’s lab: Scienctific Measurement Materials • Calculator • Microsoft Excel • String as a crude length measurement tool Pre-lab Questions 1. What is the celestial analog of latitude and longitude? 2. What quantity do the following metric prefixes indicate: Giga-, Mega-, kilo-, centi-, milli-, µicro-, and nano? 3. How many degrees is a Right Ascension “hour”; How many degrees are in an arcmin? Arcsec? 4. Use the “train-track” method to convert 20 ft to inches. 1. Background In any science class, including astronomy, there are important skills and concepts that students will need to use and understand before engaging in experiments and other lab exercises. A broad list of fundamental skills developed in today’s exercise includes: • Scientific units used throughout the international science community, as well as units specific to astronomy. • Unit conversion methods to convert between units for calculations, communication, and conceptualization. • Angular measurements and their use in astronomy. How they are measured, and the angular measurements specific to astronomy. This is important for astronomers coordinate systems, i.e., equatorial coordinates on the celestial sphere. • Familiarity with spreadsheet programs, such as Microsoft Excel, Google Sheets, or OpenOffice. -
Modern Physics Unit 15: Nuclear Structure and Decay Lecture 15.1: Nuclear Characteristics
Modern Physics Unit 15: Nuclear Structure and Decay Lecture 15.1: Nuclear Characteristics Ron Reifenberger Professor of Physics Purdue University 1 Nucleons - the basic building blocks of the nucleus Also written as: 7 3 Li ~10-15 m Examples: A X=Chemical Element Z X Z = number of protons = atomic number 12 A = atomic mass number = Z+N 6 C N= A-Z = number of neutrons 35 17 Cl 2 What is the size of a nucleus? Three possibilities • Range of nuclear force? • Mass radius? • Charge radius? It turns out that for nuclear matter Nuclear force radius ≈ mass radius ≈ charge radius defines nuclear force range defines nuclear surface 3 Nuclear Charge Density The size of the lighter nuclei can be approximated by modeling the nuclear charge density ρ (C/m3): t ≈ 4.4a; a=0.54 fm 90% 10% Usually infer the best values for ρo, R and a for a given nucleus from scattering experiments 4 Nuclear mass density Scattering experiments indicate the nucleus is roughly spherical with a radius given by 1 3 −15 R = RRooA ; =1.07 × 10meters= 1.07 fm = 1.07 fermis A=atomic mass number What is the nuclear mass density of the most common isotope of iron? 56 26 Fe⇒= A56; Z = 26, N = 30 m Am⋅⋅3 Am 33A ⋅ m m ρ = nuc p= p= pp = o 1 33 VR4 3 3 3 44ππA R nuc π R 4(π RAo ) o o 3 3×× 1.66 10−27 kg = 3.2× 1017kg / m 3 4×× 3.14 (1.07 × 10−15m ) 3 The mass density is constant, independent of A! 5 Nuclear mass density for 27Al, 97Mo, 238U (from scattering experiments) (kg/m3) ρo heavy mass nucleus light mass nucleus middle mass nucleus 6 Typical Densities Material Density Helium 0.18 kg/m3 Air (dry) 1.2 kg/m3 Styrofoam ~100 kg/m3 Water 1000 kg/m3 Iron 7870 kg/m3 Lead 11,340 kg/m3 17 3 Nuclear Matter ~10 kg/m 7 Isotopes - same chemical element but different mass (J.J. -
Binary Operator
Table of Contents Teaching and Learning The Metric System Unit 1 1 - Suggested Teaching Sequence 1 - Objectives 1 - Rules of Notation 1 - Metric Units, Symbols, and Referents 2 - Metric Prefixes 2 - Linear Measurement Activities 3 - Area Measurement Activities 5 - Volume Measurement Activities 7 - Mass (Weight) Measurement Activities 9 - Temperature Measurement Activities 11 Unit 2 12 - Objectives 12 - Suggested Teaching Sequence 12 - Metrics in this Occupation 12 - Metric Units For Binary Operation 13 - Trying Out Metric Units 14 - Binding With Metrics 15 Unit 3 16 - Objective 16 - Suggested Teaching Sequence 16 - Metric-Metric Equivalents 16 - Changing Units at Work 18 Unit 4 19 - Objective 19 - Suggested Teaching Sequence 19 - Selecting and Using Metric Instruments, Tools and Devices 19 - Which Tools for the Job? 20 - Measuring Up in Binary Operations 20 Unit 5 21 - Objective 21 - Suggested Teaching Sequence 21 - Metric-Customary Equivalents 21 - Conversion Tables 22 - Any Way You Want It 23 Testing Metric Abilities 24 Answers to Exercises and Test 25 Tools and Devices List References TEACHING AND LEARNING THE METRIC SYSTEM Thi.s metric instructional package was designed to meet job-related Unit 2 provides the metric terms which are used in this occupation metric measurement needs of students. To use this package students and gives experience with occupational measurement tasks. should already know the occupational terminology, measurement terms, and tools currently in use. These materials were prepared with Unit 3 focuses on job-related metric equivalents and their relation the help of experienced vocational teachers, reviewed by experts, tested ships. in classrooms in different parts of the United States, and revised before distribution. -
Having Regard to the Opinion of the European Chapter 1 of the Annex Binding Within Five Years of Parliament1 ; the Date of Entry Into Force of This Directive
878 Official Journal of the European Communities 29.10.71 Official Journal of the European Communities No L 243/29 COUNCIL DIRECTIVE of 18 October 1971 on the approximation of the laws of the Member States relating to units of measurement (71/354/EEC ) THE COUNCIL OF THE EUROPEAN COMMUNITIES, particular their names, symbols and use are not identical in the Member countries ; Having regard to the Treaty establishing the European Economic Community, and in particular HAS ADOPTED THIS DIRECTIVE : Article 100 thereof; Article 1 Having regard to the proposal from the Commission ; 1 . Member States shall make the provisions of Having regard to the Opinion of the European Chapter 1 of the Annex binding within five years of Parliament1 ; the date of entry into force of this Directive. 2 . Member States shall, with effect from 31 Having regard to the Opinion of the Economic and December 1977 at the latest, prohibit the use of the Social Committee2; units of measurement listed in Chapter III of the Annex. Whereas - the laws which regulate the use of units of measurement in the Member States differ from one 3 . The units of measurement temporarily" retained Member State to another and therefore hinder trade ; in accordance with the provisions of Chapter II or whereas application of the rules relating to measuring Chapter III of the Annex may not be brought into instruments is closely linked to the use of units of compulsory use by the Member States where they ' are measurement in the metrological system ; whereas, in not authorised at the date when this Directive enters into force . -
The Avogadro Constant to Be Equal to Exactly 6.02214X×10 23 When It Is Expressed in the Unit Mol −1
[august, 2011] redefinition of the mole and the new system of units zoltan mester It is as easy to count atomies as to resolve the propositions of a lover.. As You Like It William Shakespeare 1564-1616 Argentina, Austria-Hungary, Belgium, Brazil, Denmark, France, German Empire, Italy, Peru, Portugal, Russia, Spain, Sweden and Norway, Switzerland, Ottoman Empire, United States and Venezuela 1875 -May 20 1875, BIPM, CGPM and the CIPM was established, and a three- dimensional mechanical unit system was setup with the base units metre, kilogram, and second. -1901 Giorgi showed that it is possible to combine the mechanical units of this metre–kilogram–second system with the practical electric units to form a single coherent four-dimensional system -In 1921 Consultative Committee for Electricity (CCE, now CCEM) -by the 7th CGPM in 1927. The CCE to proposed, in 1939, the adoption of a four-dimensional system based on the metre, kilogram, second, and ampere, the MKSA system, a proposal approved by the ClPM in 1946. -In 1954, the 10th CGPM, the introduction of the ampere, the kelvin and the candela as base units -in 1960, 11th CGPM gave the name International System of Units, with the abbreviation SI. -in 1970, the 14 th CGMP introduced mole as a unit of amount of substance to the SI 1960 Dalton publishes first set of atomic weights and symbols in 1805 . John Dalton(1766-1844) Dalton publishes first set of atomic weights and symbols in 1805 . John Dalton(1766-1844) Much improved atomic weight estimates, oxygen = 100 . Jöns Jacob Berzelius (1779–1848) Further improved atomic weight estimates . -
Decibels, Phons, and Sones
Decibels, Phons, and Sones The rate at which sound energy reaches a Table 1: deciBel Ratings of Several Sounds given cross-sectional area is known as the Sound Source Intensity deciBel sound intensity. There is an abnormally Weakest Sound Heard 1 x 10-12 W/m2 0.0 large range of intensities over which Rustling Leaves 1 x 10-11 W/m2 10.0 humans can hear. Given the large range, it Quiet Library 1 x 10-9 W/m2 30.0 is common to express the sound intensity Average Home 1 x 10-7 W/m2 50.0 using a logarithmic scale known as the Normal Conversation 1 x 10-6 W/m2 60.0 decibel scale. By measuring the intensity -4 2 level of a given sound with a meter, the Phone Dial Tone 1 x 10 W/m 80.0 -3 2 deciBel rating can be determined. Truck Traffic 1 x 10 W/m 90.0 Intensity values and decibel ratings for Chainsaw, 1 m away 1 x 10-1 W/m2 110.0 several sound sources listed in Table 1. The decibel scale and the intensity values it is based on is an objective measure of a sound. While intensities and deciBels (dB) are measurable, the loudness of a sound is subjective. Sound loudness varies from person to person. Furthermore, sounds with equal intensities but different frequencies are perceived by the same person to have unequal loudness. For instance, a 60 dB sound with a frequency of 1000 Hz sounds louder than a 60 dB sound with a frequency of 500 Hz. -
Page 1 of 29 Dalton Transactions
Dalton Transactions Accepted Manuscript This is an Accepted Manuscript, which has been through the Royal Society of Chemistry peer review process and has been accepted for publication. Accepted Manuscripts are published online shortly after acceptance, before technical editing, formatting and proof reading. Using this free service, authors can make their results available to the community, in citable form, before we publish the edited article. We will replace this Accepted Manuscript with the edited and formatted Advance Article as soon as it is available. You can find more information about Accepted Manuscripts in the Information for Authors. Please note that technical editing may introduce minor changes to the text and/or graphics, which may alter content. The journal’s standard Terms & Conditions and the Ethical guidelines still apply. In no event shall the Royal Society of Chemistry be held responsible for any errors or omissions in this Accepted Manuscript or any consequences arising from the use of any information it contains. www.rsc.org/dalton Page 1 of 29 Dalton Transactions Core-level photoemission spectra of Mo 0.3 Cu 0.7 Sr 2ErCu 2Oy, a superconducting perovskite derivative. Unconventional structure/property relations a, b b b a Sourav Marik , Christine Labrugere , O.Toulemonde , Emilio Morán , M. A. Alario- Manuscript Franco a,* aDpto. Química Inorgánica, Facultad de CC.Químicas, Universidad Complutense de Madrid, 28040- Madrid (Spain) bCNRS, Université de Bordeaux, ICMCB, 87 avenue du Dr. A. Schweitzer, Pessac, F-33608, France -
Distances in the Solar System Are Often Measured in Astronomical Units (AU). One Astronomical Unit Is Defined As the Distance from Earth to the Sun
Distances in the solar system are often measured in astronomical units (AU). One astronomical unit is defined as the distance from Earth to the Sun. 1 AU equals about 150 million km (93 million miles). Table below shows the distance from the Sun to each planet in AU. The table shows how long it takes each planet to spin on its axis. It also shows how long it takes each planet to complete an orbit. Notice how slowly Venus rotates! A day on Venus is actually longer than a year on Venus! Distances to the Planets and Properties of Orbits Relative to Earth's Orbit Average Distance Length of Day (In Earth Length of Year (In Earth Planet from Sun (AU) Days) Years) Mercury 0.39 AU 56.84 days 0.24 years Venus 0.72 243.02 0.62 Earth 1.00 1.00 1.00 Mars 1.52 1.03 1.88 Jupiter 5.20 0.41 11.86 Saturn 9.54 0.43 29.46 Uranus 19.22 0.72 84.01 Neptune 30.06 0.67 164.8 The Role of Gravity Planets are held in their orbits by the force of gravity. What would happen without gravity? Imagine that you are swinging a ball on a string in a circular motion. Now let go of the string. The ball will fly away from you in a straight line. It was the string pulling on the ball that kept the ball moving in a circle. The motion of a planet is very similar to the ball on a strong. -
2.1 Definition of the SI
CCPR/16-53 Modifications to the Draft of the ninth SI Brochure dated 16 September 2016 recommended by the CCPR to the CCU via the CCPR president Takashi Usuda, Wednesday 14 December 2016. The text in black is a selection of paragraphs from the brochure with the section title for indication. The sentences to be modified appear in red. 2.1 Definition of the SI Like for any value of a quantity, the value of a fundamental constant can be expressed as the product of a number and a unit as Q = {Q} [Q]. The definitions below specify the exact numerical value of each constant when its value is expressed in the corresponding SI unit. By fixing the exact numerical value the unit becomes defined, since the product of the numerical value {Q} and the unit [Q] has to equal the value Q of the constant, which is postulated to be invariant. The seven constants are chosen in such a way that any unit of the SI can be written either through a defining constant itself or through products or ratios of defining constants. The International System of Units, the SI, is the system of units in which the unperturbed ground state hyperfine splitting frequency of the caesium 133 atom Cs is 9 192 631 770 Hz, the speed of light in vacuum c is 299 792 458 m/s, the Planck constant h is 6.626 070 040 ×1034 J s, the elementary charge e is 1.602 176 620 8 ×1019 C, the Boltzmann constant k is 1.380 648 52 ×1023 J/K, 23 -1 the Avogadro constant NA is 6.022 140 857 ×10 mol , 12 the luminous efficacy of monochromatic radiation of frequency 540 ×10 hertz Kcd is 683 lm/W.