Loading...

PPT – Chapter 13 Universal Gravitation Examples PowerPoint presentation | free to download - id: 7cb179-MDViZ

The Adobe Flash plugin is needed to view this content

Chapter 13Universal Gravitation

Examples

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

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 ?

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

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

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

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

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