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Summer 2018 Astron 9 Week 2 FINAL
ORDER OF MAGNITUDE PHYSICS RICHARD ANANTUA, JEFFREY FUNG AND JING LUAN WEEK 2: FUNDAMENTAL INTERACTIONS, NUCLEAR AND ATOMIC PHYSICS REVIEW OF BASICS • Units • Systems include SI and cgs • Dimensional analysis must confirm units on both sides of an equation match • BUCKINGHAM’S PI THEOREM - For a physical equation involving N variables, if there are R independent dimensions, then there are N-R independent dimensionless groups, denoted Π", …, Π%&'. UNITS REVIEW – BASE UNITS • Physical quantities may be expressed using several choices of units • Unit systems express physical quantities in terms of base units or combinations thereof Quantity SI (mks) Gaussian (cgs) Imperial Length Meter (m) Centimeter (cm) Foot (ft) Mass Kilogram (kg) Gram (g) Pound (lb) Time Second (s) Second (s) Second (s) Temperature Kelvin (K) Kelvin (K)* Farenheit (ºF) Luminous intensity Candela (cd) Candela (cd)* Amount Mole (mol) Mole (mol)* Current Ampere (A) * Sometimes not considered a base cgs unit REVIEW – DERIVED UNITS • Units may be derived from others Quantity SI cgs Momentum kg m s-1 g cm s-1 Force Newton N=kg m s-2 dyne dyn=g cm s-2 Energy Joule J=kg m2 s-2 erg=g cm2 s-2 Power Watt J=kg m2 s-3 erg/s=g cm2 s-3 Pressure Pascal Pa=kg m-1 s-2 barye Ba=g cm-1 s-2 • Some unit systems differ in which units are considered fundamental Electrostatic Units SI (mks) Gaussian cgs Charge A s (cm3 g s-2)1/2 Current A (cm3 g s-4)1/2 REVIEW – UNITS • The cgs system for electrostatics is based on the assumptions kE=1, kM =2kE/c2 • EXERCISE: Given the Gaussian cgs unit of force is g cm s-2, what is the electrostatic unit of charge? # 2 ! = ⟹ # = ! & 2 )/+ = g cm/ s1+ )/+ [&]2 REVIEW – BUCKINGHAM’S PI THEOREM • BUCKINGHAM’S PI THEOREM - For a physical equation involving N variables, if there are R independent dimensions, then there are N-R independent dimensionless groups, denoted Π", …, Π%&'. -
Guide for the Use of the International System of Units (SI)
Guide for the Use of the International System of Units (SI) m kg s cd SI mol K A NIST Special Publication 811 2008 Edition Ambler Thompson and Barry N. Taylor NIST Special Publication 811 2008 Edition Guide for the Use of the International System of Units (SI) Ambler Thompson Technology Services and Barry N. Taylor Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20899 (Supersedes NIST Special Publication 811, 1995 Edition, April 1995) March 2008 U.S. Department of Commerce Carlos M. Gutierrez, Secretary National Institute of Standards and Technology James M. Turner, Acting Director National Institute of Standards and Technology Special Publication 811, 2008 Edition (Supersedes NIST Special Publication 811, April 1995 Edition) Natl. Inst. Stand. Technol. Spec. Publ. 811, 2008 Ed., 85 pages (March 2008; 2nd printing November 2008) CODEN: NSPUE3 Note on 2nd printing: This 2nd printing dated November 2008 of NIST SP811 corrects a number of minor typographical errors present in the 1st printing dated March 2008. Guide for the Use of the International System of Units (SI) Preface The International System of Units, universally abbreviated SI (from the French Le Système International d’Unités), is the modern metric system of measurement. Long the dominant measurement system used in science, the SI is becoming the dominant measurement system used in international commerce. The Omnibus Trade and Competitiveness Act of August 1988 [Public Law (PL) 100-418] changed the name of the National Bureau of Standards (NBS) to the National Institute of Standards and Technology (NIST) and gave to NIST the added task of helping U.S. -
Mercury Barometers and Manometers
NBS MONOGRAPH 8 Mercuiy Barometers and Manometers U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS THE NATIONAL BUREAU OF STANDARDS Functions and Activities The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the national standards of measurement and the provision of means and methods for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials, devices, and structures; advisory services to government agencies on scientific and technical problems; in- vention and development of devices to serve special needs of the Government; and the development of standard practices, codes, and specifications. The work includes basic and applied research, development, engineering, instrumentation, testing, evaluation, calibration services, and various consultation and information services. Research projects are also performed for other government agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's unique competence is required. The scope of activities is suggested by the listing of divisions and sections on the inside of the back cover. Publications The results of the Bureau's work take the form of either actual equipment and devices or pub- lished papers. These papers appear either in the Bureau's own series of publications or in the journals of professional and scientific societies. The Bureau itself publishes three periodicals available from the Government Printing Office: The Journal of Research, published in four separate sections, presents complete scientific and technical papers; the Technical News Bulletin presents summary and pre- liminary reports on work in progress; and Basic Radio Propagation Predictions provides data for determining the best frequencies to use for radio communications throughout the world. -
SI and CGS Units in Electromagnetism
SI and CGS Units in Electromagnetism Jim Napolitano January 7, 2010 These notes are meant to accompany the course Electromagnetic Theory for the Spring 2010 term at RPI. The course will use CGS units, as does our textbook Classical Electro- dynamics, 2nd Ed. by Hans Ohanian. Up to this point, however, most students have used the International System of Units (SI, also known as MKSA) for mechanics, electricity and magnetism. (I believe it is easy to argue that CGS is more appropriate for teaching elec- tromagnetism to physics students.) These notes are meant to smooth the transition, and to augment the discussion in Appendix 2 of your textbook. The base units1 for mechanics in SI are the meter, kilogram, and second (i.e. \MKS") whereas in CGS they are the centimeter, gram, and second. Conversion between these base units and all the derived units are quite simply given by an appropriate power of 10. For electromagnetism, SI adds a new base unit, the Ampere (\A"). This leads to a world of complications when converting between SI and CGS. Many of these complications are philosophical, but this note does not discuss such issues. For a good, if a bit flippant, on- line discussion see http://info.ee.surrey.ac.uk/Workshop/advice/coils/unit systems/; for a more scholarly article, see \On Electric and Magnetic Units and Dimensions", by R. T. Birge, The American Physics Teacher, 2(1934)41. Electromagnetism: A Preview Electricity and magnetism are not separate phenomena. They are different manifestations of the same phenomenon, called electromagnetism. One requires the application of special relativity to see how electricity and magnetism are united. -
DIMENSIONS and UNITS to Get the Value of a Quantity in Gaussian Units, Multiply the Value Ex- Pressed in SI Units by the Conversion Factor
DIMENSIONS AND UNITS To get the value of a quantity in Gaussian units, multiply the value ex- pressed in SI units by the conversion factor. Multiples of 3 intheconversion factors result from approximating the speed of light c =2.9979 1010 cm/sec × 3 1010 cm/sec. ≈ × Dimensions Physical Sym- SI Conversion Gaussian Quantity bol SI Gaussian Units Factor Units t2q2 Capacitance C l farad 9 1011 cm ml2 × m1/2l3/2 Charge q q coulomb 3 109 statcoulomb t × q m1/2 Charge ρ coulomb 3 103 statcoulomb 3 3/2 density l l t /m3 × /cm3 tq2 l Conductance siemens 9 1011 cm/sec ml2 t × 2 tq 1 9 1 Conductivity σ siemens 9 10 sec− 3 ml t /m × q m1/2l3/2 Current I,i ampere 3 109 statampere t t2 × q m1/2 Current J, j ampere 3 105 statampere 2 1/2 2 density l t l t /m2 × /cm2 m m 3 3 3 Density ρ kg/m 10− g/cm l3 l3 q m1/2 Displacement D coulomb 12π 105 statcoulomb l2 l1/2t /m2 × /cm2 1/2 ml m 1 4 Electric field E volt/m 10− statvolt/cm t2q l1/2t 3 × 2 1/2 1/2 ml m l 1 2 Electro- , volt 10− statvolt 2 motance EmfE t q t 3 × ml2 ml2 Energy U, W joule 107 erg t2 t2 m m Energy w, ϵ joule/m3 10 erg/cm3 2 2 density lt lt 10 Dimensions Physical Sym- SI Conversion Gaussian Quantity bol SI Gaussian Units Factor Units ml ml Force F newton 105 dyne t2 t2 1 1 Frequency f, ν hertz 1 hertz t t 2 ml t 1 11 Impedance Z ohm 10− sec/cm tq2 l 9 × 2 2 ml t 1 11 2 Inductance L henry 10− sec /cm q2 l 9 × Length l l l meter (m) 102 centimeter (cm) 1/2 q m 3 Magnetic H ampere– 4π 10− oersted 1/2 intensity lt l t turn/m × ml2 m1/2l3/2 Magnetic flux Φ weber 108 maxwell tq t m m1/2 Magnetic -
Alkali Metal Vapor Pressures & Number Densities for Hybrid Spin Exchange Optical Pumping
Alkali Metal Vapor Pressures & Number Densities for Hybrid Spin Exchange Optical Pumping Jaideep Singh, Peter A. M. Dolph, & William A. Tobias University of Virginia Version 1.95 April 23, 2008 Abstract Vapor pressure curves and number density formulas for the alkali metals are listed and compared from the 1995 CRC, Nesmeyanov, and Killian. Formulas to obtain the temperature, the dimer to monomer density ratio, and the pure vapor ratio given an alkali density are derived. Considerations and formulas for making a prescribed hybrid vapor ratio of alkali to Rb at a prescribed alkali density are presented. Contents 1 Vapor Pressure Curves 2 1.1TheClausius-ClapeyronEquation................................. 2 1.2NumberDensityFormulas...................................... 2 1.3Comparisonwithotherstandardformulas............................. 3 1.4AlkaliDimers............................................. 3 2 Creating Hybrid Mixes 11 2.1Predictingthehybridvaporratio.................................. 11 2.2Findingthedesiredmolefraction.................................. 11 2.3GloveboxMethod........................................... 12 2.4ReactionMethod........................................... 14 1 1 Vapor Pressure Curves 1.1 The Clausius-Clapeyron Equation The saturated vapor pressure above a liquid (solid) is described by the Clausius-Clapeyron equation. It is a consequence of the equality between the chemical potentials of the vapor and liquid (solid). The derivation can be found in any undergraduate text on thermodynamics (e.g. Kittel & Kroemer [1]): Δv · ∂P = L · ∂T/T (1) where P is the pressure, T is the temperature, L is the latent heat of vaporization (sublimation) per particle, and Δv is given by: Vv Vl(s) Δv = vv − vl(s) = − (2) Nv Nl(s) where V is the volume occupied by the particles, N is the number of particles, and the subscripts v & l(s) refer to the vapor & liquid (solid) respectively. -
20 Coulomb's Law Of
Coulomb’s Law of 20 Electrostatic Forces Charge Interactions Are Described by Coulomb’s Law Electrical interactions between charges govern much of physics, chemistry, and biology. They are the basis for chemical bonding, weak and strong. Salts dis- solve in water to form the solutions of charged ions that cover three-quarters of the Earth’s surface. Salt water forms the working fluid of living cells. pH and salts regulate the associations of proteins, DNA, cells, and colloids, and the conformations of biopolymers. Nervous systems would not function without ion fluxes. Electrostatic interactions are also important in batteries, corrosion, and electroplating. Charge interactions obey Coulomb’s law. When more than two charged par- ticles interact, the energies are sums of Coulombic interactions. To calculate such sums, we introduce the concepts of the electric field, Gauss’s law, and the electrostatic potential. With these tools, you can determine the electrostatic force exerted by one charged object on another, as when an ion interacts with a protein, DNA molecule, or membrane, or when a charged polymer changes conformation. Coulomb’s law was discovered in careful experiments by H Cavendish (1731–1810), J Priestley (1733–1804), and CA Coulomb (1736–1806) on macro- scopic objects such as magnets, glass rods, charged spheres, and silk cloths. Coulomb’s law applies to a wide range of size scales, including atoms, molecules, and biological cells. It states that the interaction energy u(r ) 385 between two charges in a vacuum is Cq q u(r ) = 1 2 , (20.1) r where q1 and q2 are the magnitudes of the two charges, r is the distance sep- arating them, and C = 1/4πε0 is a proportionality constant (see box below). -
Creating Programs on a Computer Using Local Variables
Save the edited version of SPH in the variable. Then, to verify that the changes were saved, view SPH in the command line. `J!%SPH% @%SPH% ˜ Press − to stop viewing. Creating Programs on a Computer It is convenient to create programs and other objects on a computer and then load them into the calculator. If you are creating programs on a computer, you can include “comments” in the computer version of the program. To include a comment in a program: Enclose the comment text between two @ characters. or Enclose the comment text between one @ character and the end of the line. Whenever the calculator processes text entered in the command line — either from keyboard entry or transferred from a computer — it strips away the @ characters and the text they surround. However, @ characters are not affected if they’re inside a string. Using Local Variables The program SPH in the previous example uses global variables for data storage and recall. There are disadvantages to using global variables in programs: After program execution, global variables that you no longer need to use must be purged if you want to clear the VAR menu and free user memory. You must explicitly store data in global variables prior to program execution, or have the program execute STO. Local variables address the disadvantages of global variables in programs. Local variables are temporary variables created by a program . They exist only while the program is being executed and cannot be used outside the program. They never appear in the VAR menu. In addition, local variables are accessed faster than global variables. -
3.1 Dimensional Analysis
3.1 DIMENSIONAL ANALYSIS Introduction (For the Teacher).............................................................................................1 Answers to Activities 3.1.1-3.1.7........................................................................................8 3.1.1 Using appropriate unit measures..................................................................................9 3.1.2 Understanding Fundamental Quantities....................................................................14 3.1.3 Understanding unit definitions (SI vs Non-sI Units)................................................17 3.1.4 Discovering Key Relationships Using Fundamental Units (Equations)...................20 3.1.5 Using Dimensional Analysis for Standardizing Units...............................................24 3.1.6 Simplifying Calculations: The Line Method.............................................................26 3.1.7 Solving Problems with Dimensional Analysis ..........................................................29 INTRODUCTION (FOR THE TEACHER) Many teachers tell their students to solve “word problems” by “thinking logically” and checking their answers to see if they “look reasonable”. Although such advice sounds good, it doesn’t translate into good problem solving. What does it mean to “think logically?” How many people ever get an intuitive feel for a coluomb , joule, volt or ampere? How can any student confidently solve problems and evaluate solutions intuitively when the problems involve abstract concepts such as moles, calories, -
Introduction to Electrostatics
Introduction to Electrostatics Charles Augustin de Coulomb (1736 - 1806) December 23, 2000 Contents 1 Coulomb's Law 2 2 Electric Field 4 3 Gauss's Law 7 4 Di®erential Form of Gauss's Law 9 5 An Equation for E; the Scalar Potential 10 r £ 5.1 Conservative Potentials . 11 6 Poisson's and Laplace's Equations 13 7 Energy in the Electric Field; Capacitance; Forces 15 7.1 Conductors . 20 7.2 Forces on Charged Conductors . 22 1 8 Green's Theorem 27 8.1 Green's Theorem . 29 8.2 Applying Green's Theorem 1 . 30 8.3 Applying Green's Theorem 2 . 31 8.3.1 Greens Theorem with Dirichlet B.C. 34 8.3.2 Greens Theorem with Neumann B.C. 36 2 We shall follow the approach of Jackson, which is more or less his- torical. Thus we start with classical electrostatics, pass on to magneto- statics, add time dependence, and wind up with Maxwell's equations. These are then expressed within the framework of special relativity. The remainder of the course is devoted to a broad range of interesting and important applications. This development may be contrasted with the more formal and el- egant approach which starts from the Maxwell equations plus special relativity and then proceeds to work out electrostatics and magneto- statics - as well as everything else - as special cases. This is the method of e.g., Landau and Lifshitz, The Classical Theory of Fields. The ¯rst third of the course, i.e., Physics 707, deals with physics which should be familiar to everyone; what will perhaps not be familiar are the mathematical techniques and functions that will be introduced in order to solve certain kinds of problems. -
DIMENSIONS and UNITS to Get the Value of a Quantity in Gaussian Units, Multiply the Value Ex- Pressed in SI Units by the Conversion Factor
DIMENSIONS AND UNITS To get the value of a quantity in Gaussian units, multiply the value ex- pressed in SI units by the conversion factor. Multiples of 3 in the conversion factors result from approximating the speed of light c = 2.9979 1010 cm/sec × 3 1010 cm/sec. ≈ × Dimensions Physical Sym- SI Conversion Gaussian Quantity bol SI Gaussian Units Factor Units t2q2 Capacitance C l farad 9 1011 cm ml2 × m1/2l3/2 Charge q q coulomb 3 109 statcoulomb t × q m1/2 Charge ρ coulomb 3 103 statcoulomb 3 3/2 density l l t /m3 × /cm3 tq2 l Conductance siemens 9 1011 cm/sec ml2 t × 2 tq 1 9 1 Conductivity σ siemens 9 10 sec− 3 ml t /m × q m1/2l3/2 Current I,i ampere 3 109 statampere t t2 × q m1/2 Current J, j ampere 3 105 statampere 2 1/2 2 density l t l t /m2 × /cm2 m m 3 3 3 Density ρ kg/m 10− g/cm l3 l3 q m1/2 Displacement D coulomb 12π 105 statcoulomb l2 l1/2t /m2 × /cm2 1/2 ml m 1 4 Electric field E volt/m 10− statvolt/cm t2q l1/2t 3 × 2 1/2 1/2 ml m l 1 2 Electro- , volt 10− statvolt 2 motance EmfE t q t 3 × ml2 ml2 Energy U, W joule 107 erg t2 t2 m m Energy w,ǫ joule/m3 10 erg/cm3 2 2 density lt lt 11 Dimensions Physical Sym- SI Conversion Gaussian Quantity bol SI Gaussian Units Factor Units ml ml Force F newton 105 dyne t2 t2 1 1 Frequency f,ν hertz 1 hertz t t 2 ml t 1 11 Impedance Z ohm 10− sec/cm tq2 l 9 × 2 2 ml t 1 11 2 Inductance L henry 10− sec /cm q2 l 9 × Length l l l meter (m) 102 centimeter (cm) 1/2 q m 3 Magnetic H ampere– 4π 10− oersted 1/2 intensity lt l t turn/m × ml2 m1/2l3/2 Magnetic flux Φ weber 108 maxwell tq t m m1/2 Magnetic -
CONVERSION ANYTHING – Readme
CONVERSION ANYTHING – Readme 1. Package Overview This package performs the following: ・ Converting Measurement Unit - After receiving value and type of Unit, ConversionAnything will calculate and provide values of equivalent units in the same category within a short time. - Recently, this package is able to provide 10 different categories of measurement ・Converting Currencies - After receiving base currency, ConversionAnything will access European Central Bank’s server and return the lastest exchange rates of all currencies that are available. - In case Bot requires ConversionAnything to provides exchange rates in a specific date, ConversionAnything will follow the requirement and return the exact historical rates that are - At the moment, this package can exchange among 30 strongest currencies in the world. 2. Activities List No Activities Description 1 Convert Length Converting between different length unit. 2 Convert Speed Converting between different speed unit. 3 Convert Mass Converting between different mass unit. 4 Convert Temperature Converting between different temperature unit. 5 Convert Angle Converting between different angle unit. 6 Convert Area Converting between different area unit. 7 Convert Time Converting between different time unit. 8 Convert DataStorage Converting between different data unit. 9 Convert Pressure Converting between different pressure unit. 10 Convert Volume Converting between different length unit. 11 Convert DataTransferRate Converting between different data transfer rate unit. 12 Convert Currencies Converting between different currencies. 13 Convert Currencies By Date Converting between different currencies by date. 3. Activities Detail 3.1 Convert Length ・Input description Input Description From Unit Current unit of length. From Value Value to convert. To Unit Unit want to convert. Round The number of fractional digits in the return value.