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Universal Gravitation and Kepler’s Laws

Universal Gravitation and Kepler’s Laws. Newton’s Apple. Does the apple falling relate to planetary behavior? Newton believed laws of motion on Earth would apply anywhere in the universe. Law of Universal Gravitation. Force of attraction between all objects in the universe

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Universal Gravitation and Kepler’s Laws

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  1. Universal Gravitation and Kepler’s Laws

  2. Newton’s Apple • Does the apple falling relate to planetary behavior? • Newton believed laws of motion on Earth would apply anywhere in the universe

  3. Law of Universal Gravitation • Force of attraction between all objects in the universe • Proportional to masses and distance • G • Equation

  4. Tom has a mass of 70.0 kg and Sally has a mass of 50.0 kg. Tom and Sally are standing 20.0 m apart on the dance floor. Sally looks up and sees Tom. She feels an attraction. If the attraction is gravitational, find its size. (G = 6.67 x 10-11)

  5. Lab – “The Orbit”

  6. Day 2

  7. Kepler’s Laws

  8. Johannes Kepler (1571-1630)

  9. Kepler’s 1st Law The planets move in elliptical orbits with the sun at a focus.

  10. Kepler • Ellipses • Equal areas in equal times • Period, orbital radius of satellites

  11. Kepler’s 3rd Law • T2 / r3 ratio is the same for all satellites of an object

  12. Astronomical Unit • Average orbital radius from Earth to sun is 1 AU

  13. Practice Problems

  14. Day 3

  15. If the sun suddenly collapsed to become a black hole, the earth would: • Leave the solar system in a straight-line path • Spiral into the black hole • Undergo a major increase in tidal forces • Continue to circle in its usual orbit

  16. If you wanted to make a profit buying gold by weight at one altitude and selling it at another altitude for the same price per weight, should you buy or sell at the higher altitude location?

  17. What is the direction of the force that acts on clothes in the spin cycle of a washing machine?A. outwardb. inwardc. upd. down

  18. If you whirl a tin can on the end of a string and the string suddenly breaks, the can will • A. fly directly away from you • B. fly directly towards you • C. fly off, tangent to its circular path • D. spiral away from your hand • E. spiral in toward your hand

  19. A car travels in a circle with constant speed. The net force on the car • A. is directed forward, in the direction of travel • B. is directed toward the center of the curve • C. is zero because the car is not accelerating • D. none of the above

  20. Which has the greatest linear speed, a horse near the outside rail of a merry-go-round or a horse near the inside rail? • A. the outside horse • B. the inside horse • C. neither, they have the same linear speed

  21. A 3.0 kg mass is traveling in a circle of 0.20 m radius with a speed of 2.0 meters per second. What is its centripetal acceleration? • A. 20. m/s2 • B. 10. m/s2 • C. 60. m/s2 • D. 6.0 m/s2

  22. A car going around a curve is acted upon by a centripetal force, F. If the speed of the car were twice as great, the centripetal force necessary to keep it moving in the same path would be • A. 4F • B. F • C. 2F • D. ½ F

  23. A motorcycle of mass 100 kg travels around a flat, circular track of radius 10 meters with a constant speed of 20 m/s. What force is required to keep the motorcycle moving in a circular path at this speed? • A. 4000 N • B. 200 N • C. 400 N • D. 2000 N

  24. The shape of the path of the Earth about the Sun is • A. an ellipse with the sun at one focus • B. a circle with the sun at the center • C. an ellipse with the moon at one focus • D. an ellipse with nothing at either focus

  25. For planets orbiting the sun, the ratio of the mean radius of the orbit cubed to the orbital period of motion squared is • A. the same for all planets • B. greatest for the most massive planets • C. greatest for the least massive planets • D. constantly changing as a planet rotates

  26. As the distance between the Moon and Earth increases, the Moon’s orbital speed • A. decreases • B. increases • C. remains the same

  27. What is the gravitational force between two trucks, each with a mass of 2.0 x 104 kg, that are 2.0 m apart? • a. 5.7 x 10–2 N • b. 6.7 x 10–3 N • c. 1.3 x 10–2 N • d. 1.2 x 10–7 N

  28. Which of the following statements is correct?a. The farther the force is from the axis of rotation, the more torque is produced. b. The closer the force is to the axis of rotation, the more torque is produced. c. The closer the force is to the axis of rotation, the easier it is to rotate the object. d. The farther the force is from the axis of rotation, the less torque is produced.

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