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Five Equations That Changed the World

Five Equations That Changed the World. FBE6668 - Philosophy of Science and Ethics - Prof.Dr . Erol KAYA Yaşar DERELİ. Five Equations That Changed the World. Five Equations That Changed the World: The Power and Poetry of Mathematics  is a book by  Michael Guillen , published in 1995

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Five Equations That Changed the World

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  1. FiveEquationsThatChangedthe World FBE6668 - Philosophy of Science and Ethics - Prof.Dr. Erol KAYA Yaşar DERELİ

  2. Five Equations That Changed the World • Five Equations That Changed the World: The Power and Poetry of Mathematics is a book by Michael Guillen, published in 1995 •  It is divided into five chapters that talk about five different equations in physics and the people who have developed them. The scientists and their equations are: • Isaac Newton (Universal Law of Gravity) • Daniel Bernoulli (Law of HydrodynamicPressure) • Michael Faraday (Law of ElectromagneticInduction) • RudolfClausius (Second Law of Thermodynamics) • Albert Einstein (Theory of Special Relativity) https://en.wikipedia.org/wiki/Five_Equations_That_Changed_the_World

  3. Isaac Newton & Universal Law of Gravity • This drawing by Isaac Newton shows that a cannonball fired fast enough from a tall mountain could fall all the way around Earth without touching its surface. • The surface of Earth curves a vertical distance of 5 m for each 8,000 m tangent • Imagine an ideal super cannon that fires a projectile horizontally across a desert floor. Can you see that it would strike the ground at any speed less than 8,000 m/second? And can you see that if fired at 8,000 m/second, at the end of its first second it would fall 5 m beneath a straight-line path without getting closer to the ground. http://nstacommunities.org/blog/2016/11/15/focus-on-physics-the-moon-is-falling/

  4. Moon is falling • The Moon is approximately 384,000 km from Earth, but even at that vast distance, Earth’s gravity is about 0.03% of that at Earth’s surface—just enough to pull the Moon into an almost circular state of free fall. • The Moon has been falling around Earth for billions of years and is expected to continue doing so for billions more.

  5. Universal Law of Gravity • Every object with mass attracts every other object with mass. • Newton realized that the force of attraction between two massive objects: • Increases as the mass of the objects increases. • Decreases as the distance between the objects increases. • G = Gravitational Constant • G = 6.67x10-11 N*m2/kg2 • M1 and M2 = the mass of two bodies • r = the distance between them Rule is universal : applies to all objects!!! https://upload.wikimedia.org/wikipedia/commons/0/0e/NewtonsLawOfUniversalGravitation.svg

  6. Universal Law of Gravity • Newton’sUniversal Law of Gravityan inverse-square law: • If the distance doubles, the force drops to 1/4. • If the distance triples, the force drops to 1/9. • Distance x 10 =>FG / 100. https://www.patana.ac.th/secondary/science/anrophysics/ntopic6/commentary.htm

  7. Distances • The moon is 60x further fromthe Earth’s center than objectson (near) the Earth’s surface • The strength of Earth’s gravitynear the Moon is(1/60)2 t=1/3600 times weaker r=3.84x108m = 60 x 6.4x106 m = 60 x RE 1 60 1 3600 ( )2= RE = 6.4x106m https://kaiserscience.files.wordpress.com/2015/08/how-newton-discovered-the-law-of-gravity-by-olson.ppt

  8. Daniel Bernoulli & Law of HydrodynamicPressure • Have you ever thought about the forces behind the takeoff of planes? • Well, how is the smoke in the house or stove coming out of the chimney? • Here is the Bernoulli principle behind all this. https://www.kozmikanafor.com/bernoulli-prensibi/ http://pngimg.com/download/5253

  9. Daniel Bernoulli& Lawof HydrodynamicPressure • In 1738, Bernoulli published“Hydrodynamica”, hisstudy in fluid dynamics,or the study of howfluids behave whenthey’re in motion. • Whatis Bernoulli'sprinciple? • Bernoulli's principle: Within a horizontal flow of fluid, points of higher fluid speed will have less pressure than points of slower fluid speed. https://www.khanacademy.org/science/physics/fluids/fluid-dynamics/a/what-is-bernoullis-equation

  10. The pressure in a moving fluid depends on the velocity of the fluid. • Bernoulli’s principle states that pressure is inversely proportional to the velocity of a flowing fluid. • In a steady flow of fluid, the pressure in the liquid is low when velocity of the liquid is high. • The pressure in the liquid is high when the velocity of the liquid is low. https://anjungsainssmkss.wordpress.com/2011/09/20/bernoullis-principle-and-its-application-in-air-flight/

  11. http://hyperphysics.phy-astr.gsu.edu/hbase/pber.html

  12. Air as a fluid • Air,like water, is a fluid;however, unlike water,which is a liquid, air is agaseous substance. • Air is considered a fluid because it flows and can take on different shapes. Bernoulli assertedin “Hydrodynamica” that as a fluid moves faster, it produces less pressure, and conversely, slower moving fluidsproduce greater pressure • Bernoulli principle, as part of the fluid dynamics, explains why the pressure decreases as the fluid velocity increases in the horizontal plane. https://flight.nasa.gov/pdf/bernoulli_principle_5_8.pdf

  13. How do aircraftsflight? • Due to the aerodynamic design, the aircraft blades are designed with straight bottomand a curved top. This is a small aerodynamic meaning. This wing structure enables the Bernoulli principle to be applied to the aircraft. • When an airplane accelerates for take off, the air passing over the wing is faster than the air passing under it, because the top of the wing is inclined. • Because the air passing through the wing is fast, the wing is pressurized; a stronger pressure area under the wing. To accelerate the aircraft departure limit.

  14. Bernoulli & thestove • Let's say you live in a stove house. You came home and burned the stove. As soon as you burned the stove, the smoke turned towards the chimney. Because the air flows in the mouth of the chimney. Therefore, it reduces the pressure on the chimney. • Stoves are more efficient especially when the outside is windy. Because the wind greatly reduces the pressure on the chimney and the smoke quickly leaves the environment without strangling the stove. https://www.kozmikanafor.com/bernoulli-prensibi/

  15. Michael Faraday& Lawof ElectromagneticInduction • Before Faraday made it on the scene, scientists were aware of electricity, though they had done little to harness it for practical use.  • Faraday changed all that when he discovered electromagneticinduction in 1831. • He found that by placing a conductor in a changing magnetic field, it would produce voltage across the conductor. • In simpler terms,he found a way to cause an electric current, and that discovery was later applied to many devices we use today. https://flatironschool.com/blog/3-ways-michael-faraday-revolutionized-the-world/

  16. Faraday’s Laws of Electromagnetic Induction • Whenever electric current flows through a conductor, a magnetic field will set up in the space surrounding the conductor. • So, we can say that when the electron is in motion, they produce a magnetic field. • Alternatively, when a magnetic field cuts a conductor, it produces a flow of electrons in the conductor. http://www.electricalunits.com/faradays-laws-of-electromagnetic-induction/

  17. Induction Experiment • Faraday's experiment showing induction between coils of wire: • The liquid battery (right) provides a current which flows through the small coil (A), creating a magnetic field. • When the coils are stationary, no current is induced. • But when the small coil is moved in or out of the large coil (B), the magnetic flux through the large coil changes, inducing a current which is detected by the galvanometer (G). https://en.wikipedia.org/wiki/Faraday%27s_law_of_induction

  18. FaradaysLaw • 1) First Law:Whenever a conductor cuts magnetic flux , an e.m.f is induced in that conductor. • 2) Second Law: The magnitude of the induced e.m.f is equal to the rate of change of flux linkages. http://www.iitk.ac.in/eakshar/virtualteacher/lenz%27slaw.htm http://www.electricalunits.com/faradays-laws-of-electromagnetic-induction/

  19. Michael Faraday& Lawof ElectromagneticInduction • By age 40, Faraday invented the electric motor, transformer, and generator. • Without the discovery of electromagnetic induction, we wouldn’t have • Transformers---> no power distribution • heavyduty cranes/ Industrial machines .. • maglevtrains • MRIs/X-ray machine/Particle accelerators... • Monitors/speakers/Microphones/hard drives... • The list can be endless!! https://flatironschool.com/blog/3-ways-michael-faraday-revolutionized-the-world/ https://www.quora.com/How-different-would-the-world-be-without-advancement-in-electromagnetism

  20. Rudolf Clausius& Second Law of Thermodynamics • The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. • The total entropy can remain constant in ideal cases where the system is in a steady state (equilibrium), or is undergoing a reversible process. • In all spontaneous processes, the total entropy increases and the process is irreversible. https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

  21. FirstLaw of Thermodynamics • Problemswiththefirstlaw: • Spontaneousheat from hot to cold - reverse is NOTtrue.Why? • 100% mechanical energy to heatreverse is NOTtrue. Why? http://www.physics.usyd.edu.au/teach_res/jp/thermal/ptF_entropy.ppt

  22. https://slideplayer.com/slide/5704685/

  23. Second Law: HeatEngines • Second Law of Thermodynamics: It is impossible to extract an amount of heat QH from a hot reservoir and use it all to do work W. • Some amount of heat QC must be exhausted to a cold reservoir. This precludes a perfect heat engine. • This is sometimes called the "first form" of the second law, and is referred to as the Kelvin-Planck statement of the second law. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/seclaw.html

  24. Second Law: Refrigerator • It is not possible for heat to flow from a colder body to a warmer body without any work having been done to accomplish this flow. • Energy will not flow spontaneously from a low temperature object to a higher temperature object. This precludes a perfect refrigerator.  • Work is required to transfer net energy to the hot object. http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/seclaw.html

  25. Entropy :quantitative measure of disorder In any cyclic process the entropy will either increase or remain the same. http://www.physics.usyd.edu.au/teach_res/jp/thermal/ptF_entropy.ppt

  26. When a system changes state, there can be a change in the entropy State 1 State 2 http://www.physics.usyd.edu.au/teach_res/jp/thermal/ptF_entropy.ppt

  27. Rudolf Clausius& Second Law of Thermodynamics • HeatPumps • Refrigerators • Airconditioners • PowerPlants • Second law of TD is applicable everywhere. No machine or system converts 100% of its energy into work. Always there are losses, most of which being thermal losses. http://wikieducator.org/Thermodynamics/Consequences https://www.quora.com/What-are-the-applications-of-the-second-law-of-thermodynamics

  28. Einstein's Theory of Special Relativity • The theory of special relativity explains how space and time are linked for objects that are moving at a consistent speed in a straight line. • As an object approaches the speed of light, its mass becomes infinite and it is unable to go any faster than light travels. • The theory of special relativity was developed by Albert Einstein in 1905, and it forms part of the basis of modern physics. After finishing his work in special relativity, Einstein spent a decade pondering what would happen if one introduced acceleration. This formed the basis of his general relativity, published in 1915. https://www.space.com/36273-theory-special-relativity.html

  29. Space-Time • Einstein reasoned that space and time are two parts of one whole called space-time • From the viewpoint of special relativity, we travel through a combination space and time • When we stand still, we are only traveling through the time portion of space-time • When we move a bit, we travel through both aspects of space-time https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  30. Space-Time • If we could somehow travel through space at the speed of light, no time would elapse in our own perspective • Whenever we move through space, we alter our rate of moving through time • Time Dilation: The stretching of time an object experiences as it approaches the speed of light https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  31. Motion is Relative • Whenever we discuss motion, we must pick a reference point • Usually we refer to motion relative to the surface of the earth • Example: On a bus, you may travel 0 mi/h relative to the seat, but 60 mi/h relative to the road outside • Speed is a relative quantity, meaning its value changes based on location, or frame of reference https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  32. The speed of an object coming from a moving reference frame: • vball= 40 mph (relative to the ground) • vtruck = -20 mph (opposite direction of ball) • Catcher catches ball at 20 mph https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  33. The Speed of Light is Constant • Light does not behave like the baseball thrown from the truck • No matter what the speed of the source of the light, light will always travel toward an observer at the same speed • If light is a constant, then space and time must be a single unit • Altering the rate of one will alter the rate of the other https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  34. The Twin Trip • Consider identical twins: • One twin takes a high speed round-trip journey • The other twin stays on Earth • When he returns, the traveling twin will be younger than his stay-at-home twin • i.e.) Traveling at 50% c, 1.15 years will elapse on earth • i.e.) Traveling at 99.5% c, 10 years will elapse on earth https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  35. The Twin Trip • If motion is relative, why wouldn’t the traveling twin come home to find the Earth twin younger than himself? https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  36. The Twin Trip The light flashes have less distance to travel as the ship gets closer to the receiver https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  37. The Twin Trip The light flashes have more distance to travel as the ship gets farther from the receiver https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  38. The Twin Trip https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  39. The Twin Trip https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  40. The Twin Trip https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  41. The Twin Trip https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  42. The Twin Trip • Therefore, both twins agree on the same results: • The Earth twin has aged more than the traveling twin • The traveling twin experiences two frames of reference: One on the way out and one on the way back • The Earth twin experienced a single, different reference frame • They meet again at the same point in space, but never the same point in time https://www.esasd.net/site/handlers/filedownload.ashx?moduleinstanceid=5386&dataid=3536&FileName=special%20relativity%20notes.ppt

  43. Thankyouforlistening. Questions? • Isaac Newton (Universal Law of Gravity) • Daniel Bernoulli (Law of HydrodynamicPressure) • Michael Faraday (Law of ElectromagneticInduction) • RudolfClausius (Second Law of Thermodynamics) • Albert Einstein (Theory of Special Relativity)

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