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Universal Gravitation

Universal Gravitation. Conceptual Physics – Chapter 12. Gravity is so not new!. I discovered it a LONG time ago!. Galileo- 1564-1642 Inertia (Newton made it a law later) Mass does not effect acceleration of gravity Sun and not the earth was the center of our solar system.

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Universal Gravitation

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  1. Universal Gravitation

    Conceptual Physics – Chapter 12
  2. Gravity is so not new! I discovered it a LONG time ago! Galileo- 1564-1642 Inertia (Newton made it a law later) Mass does not effect acceleration of gravity Sun and not the earth was the center of our solar system
  3. Gravity keeps our planets (and all satellites) in orbit I built upon Galileo’s awesome ideas! Kepler- 1571-1630 Supplemented Galileo’s view of the solar system Came up with 3 planetary laws
  4. THANK YOU! I AM awesome. Tell that to the courts! Was under house arrest for some of my ideas! Small minded creatures!
  5. And then there was Newton Newton-1642-1727 Famous for apple falling on his head- may or may not be true Made many observations about the world around him Came up with the Universal Gravitation Law- force of gravity is inversely proportional to the distance between them I make this look good!
  6. Newton and the Moon He determined that the moon is simply moving in a straight line. But because of gravity it’s path becomes curved. The moon is simply falling with the curvature of the earth.
  7. The Falling Moon It wasn’t until after Newton invented a new branch of mathematics, calculus, to prove his center-of-gravity hypothesis, that he published the law of universal gravitation. Newton generalized his moon finding to all objects, and stated that all objects in the universe attract each other.
  8. Falling Earth The tangential velocity of Earth about the sun allows it to fall around the sun rather than directly into it. All satellites (yes the planets are considered satellites) work this way Any object without a significant tangential velocity has long ago fallen into the sun.
  9. Newton’s Universal Gravitation Equation m1 ----is the mass of one of the objects. m2 ----is the mass of the other object. r -------is the radius of separation between the center of masses of each object. FG -----is the force of attraction between the two objects.
  10. Universal Gravitation Newton’s law of universal gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object. Newton deduced that the force decreases as the square of the distance between the centers of mass of the objects increases.
  11. The force of gravity between objects depends on the distance between their centers of mass.
  12. Your weight is less at the top of a mountain because you are farther from the center of Earth.
  13. The Inverse Square Law Consider an imaginary “butter gun” for buttering toast. Melted butter is sprayed through a square opening exactly the size of one piece of square toast The gun deposits a layer of butter 1 mm thick. Twice as far from the butter gun, butter would cover twice as much toast vertically and twice as much toast horizontally. Since the butter has been diluted to cover four times as much area, its thickness will be one quarter as much, or 0.25 mm.
  14. Butter spray travels outward from the nozzle in straight lines. Like gravity, the “strength” of the spray obeys an inverse-square law.
  15. Inverse Square Law Twice as far from the gun, the butter is only 1/4 as thick. Three times as far, it will be 1/9 as thick. 1/9 is the inverse square of 3. When a quantity varies as the inverse square of its distance from its source, it follows an inverse-square law.
  16. The Inverse Square Law The greater the distance from Earth’s center, the less an object will weigh. An apple that weighs 1 N at Earth’s surface weighs only 0.25 N when located twice as far from Earth’s center. When it is 3 times as far, it weighs only 1/9 as much. But no matter how great the distance, Earth’s gravity does not drop to zero. The gravitational influence of every object, however small or far, is exerted through all space.
  17. Mass and Distance effect on the force of gravity.
  18. Inverse Square - Gravitational force is plotted versus distance from Earth’s center.
  19. In your journals answer the following questions How does the force of gravity change with distance? If the distance between 2 objects triples what happens to the force of gravity? Suppose that an apple at the top of a tree is pulled by Earth’s gravity with a force of 1 N. If the tree were twice as tall, would the force of gravity on the apple be only 1/4 as strong? Explain your answer.
  20. Check your answers As distance increases the force of gravity decreases. If distances triples, the force of gravity would decrease to 1/9 of its original strength (inverse square law) No, the twice-as-tall apple tree is not twice as far from Earth’s center. The taller tree would have to have a height equal to the radius of Earth (6370 km) before the weight of the apple would reduce to 1/4 N.
  21. Newton Confirmed I’m the ‘G’ who measured G! Cavendish- 1731-1810 Confirmed Newton’s Universal Gravitational Law determined the mass of the earth Determined the value of the gravitational constant- G in Newton’s equation
  22. Cavendish and the original ‘G’ Cavendish’s first measure of G was called the “Weighing the Earth” experiment. Once the value of G was known, the mass of Earth was easily calculated. G=6.67 x 10-11 The force that Earth exerts on a mass of 1 kilogram at its surface is 10 newtons. The distance between the 1-kilogram mass and the center of mass of Earth is Earth’s radius, 6.4 × 106 meters. from which the mass of Earth m1 = 6 × 1024 kilograms.
  23. Mass of the Earth- is a BIG number! It is 6 × 1024 kilograms!!!! What does that look like written out?!?? 6000000000000000000000000 kg WOW! Not something I have time to do!
  24. Universal Gravitational constant is really small!G=6.67 x 10-11 Scientific Notation at it’s best! OR you could write 0 .0000000000667 When dealing with really big or really small numbers which would you prefer? http://www.youtube.com/watch?v=17jymDn0W6U
  25. Scientific Notation 1st-Move the decimal between the first 2 significant digits. So 12,067,800,000 becomes 1.20678- you can’t omit the significant digits. 2nd- Determine which way and how many place values you moved the decimal. 12,067,800,000. became 1.20678 when we moved the decimal to the left 10 place values. 3rd It is the number times ten to the number of places you moved the decimal. So it will be 12.0678 x 10 10.
  26. Scientific Notation Move the decimal left it is positive exponent (making a big number manageable) move it to the right (making a small number manageable) give you a negative exponent. 0.0000000000345000 3.45 x 10-11 54567500000 5.45675 x 1010 30000670000000000 v 3.000067 x 1016 .000000500657300 5.006573 x 10-7
  27. You Try! Answer in your journals 1. 5,000,089,700,000 2. 00.00000000450070 3. .00067006700 4. 4,500 5. 0.0056 6. 505,400,000
  28. Scientific Notation in Use Must use it to solve for the force of gravity using Newton’s Universal Gravitation Equation
  29. Universal Gravitation Practice 1. Two basketball players are 30 meters apart during their game. Player one’s mass is 83kg, player two’s mass is 90kg. What is the force of gravity between the two? 2. What would happen to the force if they were half the distance apart?
  30. Two basketball players are 30 meters apart during their game. Player one’s mass is 83kg, player two’s mass is 90kg. What is the force of gravity between the two? = 6.67x10-11(83 x90) 302 = 5.54 x 10 -10 Not much force between the two as we would expect!
  31. 2. What would happen to the force if they were half the distance apart? According to the inverse square law, at half the distance the force should increase by 4 times If you do the math it works! At 30 meters f=5.54 x 10-10 At 15 meters f=2.22 x 10-9 5.54 x 10-10 x 4 = 2.22 x 10-9 So half the distance 4 times the amount of force!!
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