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Chapter 12- Universal Gravitation

Chapter 12- Universal Gravitation. Do question 180, 1-4 and 7-10 after test. It was fairly apparent to people for centuries that the earth, attracted objects on earth to it. Newton knew that since the apple changed speed Gravity must be a force.

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Chapter 12- Universal Gravitation

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  1. Chapter 12- Universal Gravitation

  2. Do question 180, 1-4 and 7-10 after test.

  3. It was fairly apparent to people for centuries that the earth, attracted objects on earth to it.

  4. Newton knew that since the apple changed speed Gravity must be a force

  5. Newton knew that the moon’s velocity changed constantly and therefore there must be a force on it.

  6. Might the earth pull on the moon just like the apple?

  7. Can Earth’s gravity reach all the way to the moon? Where does it stop????

  8. If the moon is falling to the earth like the apple, then WHY doesn’t it fall

  9. Newton realized that the moon and the apple are both falling like projectiles.

  10. Cannonballs are shot with increasing speed They are all falling towards the earth gravity free path

  11. v Fg Gravity pulls the moon towards the center of the earth providing the ___________ Force to keep it moving in a circle CENTRIPETAL

  12. v The velocity is always perpendicular to the force of gravity Fg The tangential velocity is sufficient to keep it from falling into the earth

  13. In order to “prove” his theory he wanted to predict the acceleration of the moon and see if it matched observation. He knew an apple on earth accelerates at 9.8 m/s2. But what about the moon out in space?

  14. If both the moon and the apple were just above the surface of the earth. Which would hit the ground first: The massive moon or the tiny apple?

  15. Heavy and light objects fall at the same rate on earth, he figured the mass of the moon wouldn’t affect its acceleration

  16. But the apple is much closer to the earth than the moon. The apple is a distance 1 earth radius for the center of mass of the earth

  17. The moon is 60 earth radii away. The apple is only 1. Note: apple not to scale

  18. Newton reasoned that gravity would get weaker the farther away two objects are. Think of 2 magnets

  19. For reasons we will see later, He calculated that at a distance 60 times From the center of the earth. 9.8 m/s2 amoon = 602 amoon = .0027 m/s2

  20. After falling for 1 second on earth’s surface an apple would have fallen 4.9 m from a gravity free path 4.9 m

  21. Without gravity after 1 second the moon would be here it falls 1.4 mm each second His answer matched what we know today But he wasn’t sure if the distance used should be between the centers of the objects and didn’t publish for another 20 years

  22. It would fall to the earth. The fall would take about 3.5 hours What would happen if the moon suddenly stopped

  23. The earth is constantly falling toward the sun Sun If the earth lost some of its tangential velocity?

  24. The objects in our solar system have just the right speed to stay in their orbit. If an object is moving too slow, it falls closer to the sun. As it does it speeds up.

  25. What makes the earth and the sun so special that they attract objects to them with an invisible force of gravity? They have MASS What else has mass?

  26. Are you attracted to the person sitting next to you? YES!! Its called GRAVITY

  27. Newton didn’t discover gravity, He discovered that anything that has mass attracts anything else that has mass. If there was no friction on the table you could pull your pencil to you not by magic but by gravity

  28. NEWTON’s Universal Law of Gravitation m1 m2 d Distance between center of masses m1 m2 Fg ~ d2 Proportional to – not equal to

  29. This is the force of gravity on EACH Object m1 m2 r Remember Newton 3rd law: When m1 exerts a force on m2 then….. m1 m2 Fg ~ r2

  30. Which feels a greater FORCE from the other The exert EQUAL but opposite forces on each other

  31. If the mass of 1 object is doubled, Then Fg ________ doubles m1 m2 r m1 m2 Fg ~ r2

  32. Compare the force of gravity between the earth & 1kg object to earth & 2kg object m1 m2 Fg ~ r2

  33. If the mass of both object is doubled, Then Fg ________ quadruples m1 m2 r m1 m2 Fg ~ r2

  34. If the distance between them doubles, Then Fg ________ is 1/4 m1 m2 r m1 m2 Fg ~ r2

  35. If everything attracts everything else, Why isn’t it more obvious? The mass of the earth is HUGE!!!!! The force between earth and a 1 kg object is only 10 N How big will the attraction be between two 1 kg objects?

  36. m1 m2 Fg ~ r2 In order to make this an equation we need a fudge factor. m1 m2 G Fg = r2 If we knew G we could calculate the force between any two objects

  37. In order to find G, both masses would need to be known. As well as the force and distance between them. What is so hard about this? The force of gravity between normal objects that can be weighed is VERY weak. How to measure? m1 m2 G Fg = r2

  38. Henry Cavendish English chemist and physicist who was shy and absent-minded. He was terrified of women, and communicated with his female servants by notes.

  39. G = 6.67 10-11 Nm2/kg2 G = .0000000000667 A very small number because gravity is a relatively weak force m1 m2 G Fg = r2

  40. A 1 kg object on the surface of the earth has a force of gravity of 9.8 N between it and the earth. The radius of the earth is 6,380,000 m. With G known, they could find the mass of the earth G 1kgmearth 9.8 N= (6,380,000 m)2

  41. Cavendish’s experiment is often said to have weighed the earth in his experiment 5.98 1024 mearth = 5.98 1024 kg

  42. Phillip von Jolly Around 1850 later used a simpler apparatus and got more accurate results

  43. What is the force of gravity between a 65 kg student sitting .50 m away from a 75 kg student? G = 6.67 x 10 -11

  44. What is the force of gravity between the earth and the planet mars at their closest approach (which is 1.01x1011 m between centers of mass) mearth = 5.98 1024 kg mmars = 6.41 x 1023 kg Closest approach 101.1 million kilometers 2.51 x 1016 N

  45. What is the force of gravity between the earth and 5.0 kg object which 12,760,000 m (2 earth radii) above the surface of the earth? mearth = 5.98 1024 kg rearth = 6,380,000 m

  46. Add to questions page 180 11, 15, 16, 17, 19, 20, 21, 22

  47. If you increase the separation of two objects by 3 times, why doesn’t Fg decrease by 3 instead of decreasing by________ 9 How much more pizza do you get when you go from a pizza which is 1 m in radius to one that is 2 m Area = pr2

  48. When a light shines it spreads out as a sphere getting dimmer as you go further

  49. Picture a hollow sphere with the light bulb in the middle.

  50. If the sphere was doubled in radius, the same amount of light is spread out over 4 times the area. So it is 4 times dimmer Area of a sphere = 4 p r2

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