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Locate the centroid (x, y) of the shaded area. y 6 in. 3

Engineering Mechanics: Statics | 14th Edition | ISBN: 9780133918922 | Authors: Russell C. Hibbeler ISBN: 9780133918922 126

Solution for problem 9-62 Chapter 9

Engineering Mechanics: Statics | 14th Edition

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Engineering Mechanics: Statics | 14th Edition | ISBN: 9780133918922 | Authors: Russell C. Hibbeler

Engineering Mechanics: Statics | 14th Edition

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Problem 9-62

Locate the centroid (x, y) of the shaded area. y 6 in. 3 in. 6 in. 6 in. x Prob. 962

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Week 9 Notes Astr 100, Bob Berrington The Nature of Light Continued  Constructive and deconstructive nature of light  Longitudinal Waves o Compression wave  Sound  Alternating regions of high and low densities  Displacement of air molecules in direction of travel  Slinky example: Compress a part of the slinky that is stretched out. When you let go, the motion moves back and forth o Transverse Waves  Sea waves  Displacement perpendicular to motion of travel  Light Waves  Transverse waves of electric and magnetic fields  Move the slinky up and down, that demonstrates a transverse waves  Wavelength (λ) o Distance over which the wave repeats itself o Or, distance between 2 crests (highest point of each wave)  Frequency (v) o Number of crests that passes a point in one second  Period of wave = 1/v  Frequency is the number of waves (cycles passing any point each second  Relationship between frequency and wavelength o λv = (speed of wave) => for light this becomes λv = c  Units o Visible light λ is often given in nanometer (nm) -9 o 1 nm = 1 x 10 meters  Example o Calculate the frequency of yellow light  Yellow light has λ = 500 nm = 5 x 10 meters  V = c/λ, or v = 3 x 10 (m/z) / 5 x 10 m = 6 x 10 / s 14  6 x 10 / s cycles per second (also called a hertz)  Notice units  Units in cycles  Spectrum o Intensity of Light versus Wavelength/Frequency  Optical light goes from Violet (short λ, high v) to Red (long λ, low v)  ROY G BIV (Red, Orange< Yellow, Green, Blue, Indigo, Violet)  Electromagnetic Spectrum o Optical Spectrum is only a small part of the electromagnetic (EM) Spectrum o Radio at the low v/long λ end o Gamma (y) rays at the high v/short λ o Order from low v to high V: radio, microwaves, infrared, optical ultraviolet, X rays, y rays o Not all EM spectrum makes it through the atmosphere  Light as a particle o Packets of energy  Energy is related to frequency E= hv = hc/ λ  h = Planc’s constant (in back of book)  Higher frequency photons have greater energy  X rays penetrate skin and bone  Ultraviolet light causes sunburns  Infrared is felt as heat Wednesday ASTR 100 Notes  Packets of energy o Energy is related to frequency E= hv = hc/ λ o h = Planc’s constant (in back of book) o Higher frequency photons have greater energy  X rays penetrate skin and bone  Ultraviolet light causes sunburns  Infrared is felt as heat  Electromagnetic Spectrum o Red has the lowest energy (frequency); and violet has the highest frequency in the visible spectrum o Radio has the longest wavelength and the lowest energy while Gamma rays have the shortest wavelength and highest energy  Angstrom o Written as: -10 o 1 angstrom = 10 m  Expresses wavelength of optical ight  1 nm = 10 angstroms  Typical size of an atom  Optical light is 4000 – 7000 angstroms  It’s an older unit that is losing popularity but still very much in use  Atomic structure o Atoms are made of proton, electrons, and neutrons o Most of us probably learned the Bohr Model in high school  One part of that model is incorrect  The electrons do not circle the nucleus in orbits, but swarm around it in a “cloud” o Protons (positive charge) and neutrons (no charge) are found in the nucleus o Electrons (negative charge) swarm the nucleus in a cloud (they do orbit, just not in a predictable manner)  Opposite charges attract  Like charges repel o The nucleus is about 100,000 times smaller than the atom itself  Atomic structure continued o It takes energy to remove an electron or increase its energy  Provided by photons  Energy = conserved o Quantum mechanics allows only specific energies for an electron  Specific energies are emitted or absorbed by an electron bound to an atom  Gives rise to atomic spectra o Ionization levels   Each “level” of the electron cloud has different amounts of energy expressed in n=1, n=2, etc.  When an atom is ionized, that means an electron has achieved a higher level of energy, or has gone down a level.  When the level goes down= emission  When the level goes up = absorption  Nuclear Energy o Protons and neutrons are bound to each other in the nucleus o Heavy atoms give up energy when they break up into constituent parts (fission)  The mass of the parts is less than the mass of the initial nucleus  Called nuclear fission 2  Stays true to Einstein’s E = mc  Atomic bombs are powered by nuclear fission o The sun is powered by nuclear energy (fusion)  The energy is released as a photon when the light atom is formed by combining two lighter atoms (fusion)  Mass of constituents is greater than the final nucleus  4 Hydrogen atoms = 1 Helium  Energy Units o MKS system  We won’t use this one very often  Just know that a Joule is a measurement of energy 2 2  1 J = Nm=kgm /s o CGS system  Ergs (measurement of energy) = dyres cm = g=cm /s 2 2  Atomic scales are smaller (we use electron volts abbreviated as ev)  1 ev = 1.602 x 10-12erg  1 J = 1 x 10 erg  Atomic Spectra o The difference of possible energy levels the electron can orbit in  If an electron is knocked out of an atom it is ionized  Photons with energy greater than the ionization energy will be absorbed o (The equation works the same way as the universal law of gravity, just different symbols/letters to represent values) o Electron orbits and energies are unique to the element  Each element given by the periodic table has unique energy levels  Each spectrum is therefore unique  Atomic Designations o Each element on the periodic table is represented by a 1 or 2 letter code  The following superscript gives the atomic weight  Atomic weight = number of protons and neutrons in the nucleus  Atomic number  Can precede the letter designation (usually written as a subscript)  Number of protons and neutrons in the nucleus 56  Example F26or 56 on the other side of Fe (iron)  Atomic spectra o Spectra of each element is unique  Each element has a “fingerprint”  We can figure out the composition of something by looking at its spectra  Spectra of Orion nebula shows superposition of hydrogen, helium, oxygen, neon, etc.

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Chapter 9, Problem 9-62 is Solved
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Textbook: Engineering Mechanics: Statics
Edition: 14
Author: Russell C. Hibbeler
ISBN: 9780133918922

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Locate the centroid (x, y) of the shaded area. y 6 in. 3