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Lecture 2 - Universal Gravity Ch 12:1-3 Review of Statics...

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April 3, 2008 Physics 40B Lecture 2 1 Universal Gravity Ch. 12:1-3 Review of Statics Rigid bodies in stable static equilibrium 1. Translational: F x = F y = 0 (external forces) 2. Rotationl: τ = 0 (any axis) Center of Gravity: force of gravity acts at cg Stress & Strain 1. Tensile, compression, Young’s Modulus (Y) in Pa 2. Bulk, change in volume, F , Bulk Modulus, B in Pa 3. Shear Modulus, S in Pa Shear Stress & Strain Shear Stress = F Area (Pa or psi) Shear Strain = x h (dimensionless) S (Shear Modulus) = F A x h (Pa or psi)
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April 3, 2008 Physics 40B Lecture 2 2 Statics Example Find maximum force F with no “slipping” of post on ground. Use f S = μ S N F T w N f s μ S θ h h/2 F x " = 0 F # f S # T sin $ = 0 % F = μ S N + T sin $ F y " = 0 N # T cos $ # w = 0 % N = w + T cos $ & = 0 " # F h 2 + Th sin $ = 0 % F = 2 T sin $ Unknowns are F, N and T. Eliminate N, T T = F 2sin $ % N = w + F 2sin $ cos $ = w + F 2tan $ F = μ S w + F 2tan $ ( ) * + , - + F 2sin $ ( ) * + , - sin $ = μ S w + F 2tan $ ( ) * + , - + F 2 ( ) * + , - F 1 2 # μ S 2tan $ ( ) * + , - = μ S w % F max = 2 μ S w 1 # μ S tan $ ( ) * + , -
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April 3, 2008 Physics 40B Lecture 2 3 Stonehenge-Salisbury Plain in England • About 2800 BC to 1100 BC • Stone Age and Bronze Age • Druids • Astronomical Observatory Sun at sunrise on “Summer Solstice”
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April 3, 2008 Physics 40B Lecture 2 4 Stonehenge
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April 3, 2008 Physics 40B Lecture 2 5 Observatories in the Americas Big Horn Medicine Wheel in Wyoming-built by Plains Indians. Originally thought that spokes aligned with risings and settings of Sun and other stars. Further investigation showed this not true. Sun Dagger in New Mexico-Rocks shape Sun’s light into dagger with a spiral carved on the rock. Dagger pierces spiral each year at noon on summer solstice. Caracol Mayan temple (1000 AD) in Mexico- many windows aligned with astronomical events.
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April 3, 2008 Physics 40B Lecture 2 6 China: Earliest known records of supernova explosions (1400 B.C.) Bone or tortoise shell inscription from the 14th century BC. "On the Xinwei day the new star dwindled." "On the Jisi day, the 7th day of the month, a big new star appeared in the company of the Ho star." Remnant of Supernova Explosion seen in 1054 AD by Chinese Astronomers Medieval Arab Manuscript of Astronomers at work. Much of the scientific information was preserved and enhanced by Arab astronomers during the Dark Ages.
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April 3, 2008 Physics 40B Lecture 2 7 Greek Astronomers Homer: named constellations around the North Celestial Pole Pythagoras: earth was round, by observing shadow of earth during lunar eclipse, celestial objects moved in circles Eudoxus (400 BC): Earth-centered Geocentric model with 8 co-rotating. Spheres were all aligned differently to give approximate synodic motions. Needed two extra spheres for Moon and Sun and three extra spheres for each planet for retrograde motion. Total of 27 spheres.
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