《物理学基捶(哈里德)学习指导 13 Gravitation.pdf

Chapter 13 Gravitation Newton said that any two ma^sses pull on each other with a force of ,-, GMtMz u 12 where G is the universal gravitational constant (G : 6.67 x 10-11 N. ^ IUS\ and r is the distance between the ma^sses. There is a gravitational force between you and this book of about F _ GM\Mz: (6.67 x 10-u ry..r92/kg2)(60 ks)(l ks) _ 4 x10_8 N 12 (0.3 m)2 You pull on the book with a force this big, and the book pulls back on you with the same force. Because this force is so much smaller than the other forces acting on you or the book, we dont bother to include it in our free-body diagrams. Because the force depends on the distance, does the acceleration of gravity change as we move up and down? Yes. When we move up 3 m (about 10 ft) the gravity force becomes weaker by about one millionth, or 0.0001% weaker. The acceleration of gravity is the force of gravity divided by the mass of the object. F GM6^netTrtr \, 1 GMptanet*-a-T a:T At the height at which airplanes fly, gravity is about 0.370 weaker than on the surface of the Earth. We usually ignore this effect because it is small. EXAMPLE The Moon goes around the Earth in a circular path of radius 3.85 x 108 m. The mass of the Earth is 5.98 x I02a kg and the ma,ss of the Moon is 7.35 x 1022 kg. How long does it take for the Moon to orbit the Earth? Student: Couldnt we just look this up in the appendix? T\rtor: We could, but the goal is to understand gravity, not to know one number. What are the forces on the Moon? Student: Gravity from the Earth attracts the Moon. Because the Moon is not at the surface of the Earth, the force is not mg. Tutor: Good. Are there any other forces on the Moon? Student: It is not in contact with anything, so just gravity. r07 108 CHAPTER 73, GRAVITATION T\rtor: Newton says that when you add up all of the forces, all one of them, its equal to the ma^ss times the acceleration. Student: The Moon is going in a circle, so the acceleration is u2 f r inward. GMgu1tr6M14sen - Mrvroo