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notes-week1 - Spring Quarter 2010 Professor Walter Gekelman...

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Spring Quarter 2010 Physics 1B Class Notes CR Professor Walter Gekelman OFFICE PAB 4-907 Democritus 5 th century BC All matter is made of atoms Aristotle 384-322 BC 4 elements, Earth is a sphere Archimedes 287-212 BC Buoyancy, solid geometry (pre calculus) William of Ockham 1300-1349 No unnecessary assumptions Nicholas Coperni- cus 1473-1543 Earth moves around sun Tycho Brahe 1546-1601 Best data on planets until then Johannes Kepler 1571-1660 Analyzed Brahe data, Kep- lers laws Issac Newton 1642-1727 3 Force laws, calculus, optics Charles Coulomb 1736-1806 Force Law of Electricity Hans Oersted 1777-1851 Electricity and Magnetism are related Andre Ampere 1775-1836 Electric Current and Magnetic Fields Michael Faraday 1791-1867 Concept of Field, Faraday’s Law Boltzman 1844-1906 Statistical mechanics, ther- modynamics 1
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James Clerk Max- well 1831-1879 Displacement current, Max- wells equations Michelson 1852-1931 Perfected interferometer, dis- proved aether Albert Einstein 1879-1955 Relativity, quantum mechan- ics, Brownian motion, photoe- lectric effect, etc THE most general equation of motion is a differential equation and may be written as: (1) m 2 y t 2 + b y t + ky = F ( y , t ) The first term is mass times acceleration. The second term is velocity dependent and is a frictional drag term. The third term is a restoring force which will study when we dis- cuss springs and the term on the left hand side a forcing or driving term. This would be present if you consider a child on a swing and once a period you give her a push. (a) Where does equation (1) come from and what do the terms in it mean? (b) What are the solutions to (1) (c) What are problems in the real world that the equation addresses? The answer to (c) is :Planetary motion, motion of satellites about the earth, pendulums, motion of springs, electrical circuits, vibrations of molecules, motion of cannonballs and projectiles, …… Suppose F(y,t) is a constant and b and k = 0 Then we have what you studies in 1A (1a) m 2 y t 2 = F = m g with solution y y 0 = v 0 t 1 2 gt 2 . We wont go over this you did it already. Suppose k = 0 and F = m g (1b) since gravity points down The solution to this equation is: 2
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v= dy dt - ˆ j ( ) ; v= mg b 1 e bt m ˆ j ( ) This is the equation of an object with a limiting velocity. A graph of v is shown below The abscissa is time and the ordinate is velocity. The velocity does not continually in- crease as it would if the b term (or drag term was missing) but reaches a limit. For ex- ample if you jumped out of a plane 5 miles up you would not hit the ground at superson- ics speeds, you limiting velocity would be about 100 MPH. You could do just as well driving into a wall at that speed. Suppose that F=0 and b = 0 then we get : (1c) m 2 y t 2 + ky = 0 This is the equation of a mass on a spring on a track 3
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The surface that the mass is on is frictionless, and k is the spring constant. This is dis-
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