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Ch12-1 Newton’s Law of Universal Gravitation

Chapter 12: Gravity. Ch12-1 Newton’s Law of Universal Gravitation. F g = Gm 1 m 2 /r 2 G = 6.67 x 10 -11 Nm 2 /kg 2. Figure 12-2 Dependence of the Gravitational Force on Separation Distance, r.

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Ch12-1 Newton’s Law of Universal Gravitation

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  1. Chapter 12: Gravity Ch12-1 Newton’s Law of Universal Gravitation Fg = Gm1m2/r2 G = 6.67 x 10-11 Nm2/kg2

  2. Figure 12-2Dependence of the Gravitational Force on Separation Distance, r

  3. CT1: Suppose Earth had no atmosphere and a ball were fired from the top of Mt. Everest in a direction tangent to the ground. If the initial speed were high enough to cause the ball to travel in a circular trajectory around Earth, the ball’s acceleration would • be much less than g (because the ball doesn’t fall to the ground). • be approximately g. • depend on the ball’s speed.

  4. Not to scale! P12.8 (p.389) FSM 1.5 x 1011 m  3.84 x 108 m F FEM 1.5 x 1011 m

  5. CT2: It is best to say that the Moon orbits the • Earth. • Sun.

  6. Chapter 12: Gravity Ch12-2 Gravitational Attraction of Spherical Bodies

  7. CT3: Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of the centripetal force acting on B to that acting on A? (FB/FA) • 2 • 1/4 • 1/2 • 1/2 • 4

  8. CT4: In addition to using kinematics, the big picture principle in P12.20 (p.390) will be • Newton’s laws. • conservation of energy. • conservation of momentum. • the work-kinetic energy theorem.

  9. Chapter 12: Gravity Ch12-3 Kepler’s Laws

  10. Kepler’s First Law: The planets orbit the Sun in ellipses with the Sun at one of the foci.Semi-major axis = a. 2a 2a 2a = 2r

  11. Kepler’s Second Law: The orbits sweep out equal areas in equal times.

  12. greater v smaller v L = mvr is constant. Angular momentum is conserved because the central force of the Sun produces net = 0.

  13. Kepler’s Third Law: T  a3/2, where a is the semi-major axis of the ellipse. For a circle, a = r.

  14. CT5: In addition to using kinematics, the big picture principle in P12.28 (p.390) will be • Newton’s laws. • conservation of energy. • conservation of momentum. • the work-kinetic energy theorem.

  15. CT6: For P12.31 (p.390), the period depends on • the mass of the Earth. • the mass of the satellite. • both the mass of the Earth and the satellite. • neither the mass of the Earth nor the mass of the satellite.

  16. Chapter 12: Gravity Ch12-4 and 5 Potential Energy and Energy Conservation Ug = -GMm/r for two masses M and m separated by r E = K + Ug is conserved when only the gravitational force is acting because the universal gravitational force is a conservative force

  17. CT7: In addition to using kinematics, the big picture principle in P12.41 (p.391) will be • Newton’s laws. • conservation of energy. • conservation of momentum. • the work-kinetic energy theorem.

  18. P12.66 (p.392)

  19. CT8: In addition to using kinematics, the big picture principle in P12.67 (p.392) will be • Newton’s laws. • conservation of energy. • conservation of momentum. • the work-kinetic energy theorem.

  20. CT9: • System A has masses m and m separated by r; • system B has masses m and 2m separated by 2r; • system C has masses 2m and 3m separated by 2r; • and system D has masses 4m and 5m separated by 3r. • Which system has the smallest attraction between the two masses? • A • B • C • D

  21. CT10: • System A has masses m and m separated by r; • system B has masses m and 2m separated by 2r; • system C has masses 2m and 3m separated by 2r; • and system D has masses 4m and 5m separated by 3r. • Which system has the next smallest attraction between the two masses? • A • B • C • D

  22. CT11: • System A has masses m and m separated by r; • system B has masses m and 2m separated by 2r; • system C has masses 2m and 3m separated by 2r; • and system D has masses 4m and 5m separated by 3r. • Which system has the greatest attraction between the two masses? • A • B • C • D

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