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Chapter 13 Universal Gravitation Examples

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Example 13.2 The Density of the Earth (Example 13.3 Text Book) Using the last result, find the . average density. of the Earth: From Example 13.1. mg = – PowerPoint PPT presentation

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Title: Chapter 13 Universal Gravitation Examples


1
Chapter 13Universal Gravitation
Examples
2
Example 13.1 Weighing Earth
  • Weighing Earth! Determining mass of Earth.
  • ME mass of Earth (unknown)
    RE 6,370 km 6.37 x
    106 m
  • Assume the Earth is a uniform, perfect sphere.
  • m mass of object on the surface of Earth
    (known)
  • The weight of m is Fg mg
  • The gravitational force on m is Fg
    G(MEm)/RE2
  • But these two are the same!!!
  • mg G (mME)/RE2 ?
  • g G ME/RE2 ?
  • Solving for ME
  • ME g RE2/G 5.98 ? 1024kg

m
RE
ME
3
Example 13.2 The Density of the Earth (Example
13.3 Text Book)
  • Using the last result, find the average density
    of the Earth
  • From Example 13.1
  • mg G (mME)/RE2 g G ME/RE2 ?
  • ME g RE2/G
  • Since ?E ME /VE VE (4/3)? RE3 ?

4
Example 13.3 Spacecraft at 2RE
  • Find Fg acting on a 2000 kg spacecraft at 2RE
  • RE 6,380 km ME 5.98 ? 1024 kg
  • FG G(mME/r2)
  • At surface (r RE)
  • FG mg G(mME/RE2)
  • At r 2RE
  • FG G(mME)/(2RE)2 ?
  • FG G(mME)/4RE2 ?
  • FG ¼ G(mME/RE2) ?
  • FG ¼mg 4900 N

5
Example 13.4 Geosynchronous Satellite
  • A Geosynchronous Satellite appears to remain over
    the same point on the Earth
  • The gravitational force supplies a centripetal
    force
  • A satellite of mass m is moving in a circular
    orbit around the Earth at a constant speed v and
    at an altitude h above the Earths surface. Find
    the speed (v) of the satellite in terms of G, h,
    RE and ME

6
Example 13.4 Geosynchronous Satellite, final
  • Assume m is moving around the Earth in a circular
    orbit. Applying Newtons 2nd Law
  • Taking (1) (2)
  • Since r RE h

7
Example 13.5The Change in Potential
Energy(Example 13.6 Text Book)
  • A particle of mass m is displaced through a small
    vertical displacement ?y near the Earths
    surface. Show that the general expression for the
    change in gravitational potential energy
    (Equation 13.12) reduces to the familiar
    relationship ?U mg?y
  • From Equation 13.12
  • Since ri and rf are to close to the Earths
    surface, then
  • rf ri ?y and rfri RE2
  • Remember r is measured from center of the Earth
  • ?U mg?y

8
Material for the Final Exam
  • Examples to Read!!!
  • Example 13.1 (page 376)
  • Material from the book to Study!!!
  • Objective Questions 2-4-9
  • Conceptual Questions 1-6-7
  • Problems 3-6-12-25-27-29
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