Lesson Plans

Physics: Principles with Applications 5th Revised Edition ©2002

by Douglas Giancoli

Week 6

Chapter 5: Circular Motion; Gravitation

College Board Performance Objectives:

• Use Newton's Universal Law of Gravitation to derive the acceleration due to gravity for the surface of the earth and for the surfaces of other planets when the radii and the masses of the planets are given.
• Use Newton's Universal Law and Newton's Second Law of Motion to express weight for any location in the universe.
• Determine mass from weight or weight from mass where a value for the acceleration due to gravity is known.
• Describe an experiment that would measure the Universal Gravitational Constant.
• Determine the acceleration due to gravity for various positions on the surface and above the surface of the earth.
• Apply centripetal force and gravitation to satellite motion.
• State Kepler's Three Laws of Planetary Motion.
• Use Kepler's Third Law to relate the radius of an orbit to its period.

College Board Lab Objectives:

• Design a laboratory experiment to measure the mass of an unknown object moving in a horizontal circle of radius R.
• Be able to plot and analyze a Force vs. Period and a Force vs. Period Squared graph for a body moving in a horizontal circle.

Suggested Labs:

• Centripetal Force

Resources:

• Chapter 5: Circular Motion; Gravitation — pp. 124–138
• Student Study Guide — pp. 5-1–5-16
• Instructor's Solution Manual — pp. 61–76
• Test Items File — pp. 75–92

Pacing Guide:

• Newton's Law of Universal Gravitation—days 1 and 2
• Gravity near the Earth's Surface—days 2 and 3
• Satellites and Weightlessness—days 2 and 3
• Kepler's Laws—days 3 and 4
• Types of Forces in Nature—day 4
• Lab—day 5
• Block Scheduling
  Newton's law of gravitation, gravity near the surface of the earth, satellites, and weightlessness require two blocks of time. Satellite motion, Kepler's laws of planetary motion, and the types of forces in nature require a single block.

Key Words:

Critical Thinking Questions:

1. Determine the fractional difference in your apparent weight if you are riding in a car on a Ferris wheel that has a radius of 5 m and is rotating at 10 rpm. What is the period of rotation if your apparent weight at the top of the Ferris wheel is zero?
2. Determine the net gravitational force on the moon due to the sun and earth during a solar eclipse. What is the net gravitational force on the earth due to the sun and the moon?
3. Calculate the mass of the sun from approximating the period of revolution of the earth as 365 days. Use a circular orbit of 1.5x10⁸ km.
4. Planet Kyle I has half the radius and half the mass of the earth. Show that the acceleration due to gravity on the surface of Kyle I is 2g.
5. Centripetal force acts on all bodies undergoing circular motion. Is work being done on a body by centripetal force? Explain.
6. Calculate the acceleration due to gravity on the surface of Mars.
7. Three spheres of mass 10 kg are located at the vertices of an equilateral triangle 0.5 m on a side. What is the gravitational force on any one mass due to the other two?

Troubleshooting Tips/Error Traps:

• The equations of circular motion can be confusing. Dimensional analysis of the equations in the chapter will help students understand this concept.

End of Chapter Activity:

1. The Universal Law of Gravitation shows that the attractive force between two bodies
   1. is independent on the mass of the bodies
   2. depends on the differences between the masses of the bodies
   3. depends on the sum of the masses of the bodies
   4. depends on the ratio of the masses of the bodies
   5. depends on the product of the masses of the bodies
2. The Universal Law of Gravitation shows that the attractive force between two bodies
   1. is independent of the distance between the two bodies
   2. increases as the distance between the bodies increases
   3. increases as the square of the distance between the bodies
   4. is inversely proportional to the distance between the bodies
   5. is inversely proportional to the square of the distance between the bodies
3. The Universal Gravitational Constant G
   1. is a constant of nature
   2. is an expression of the acceleration due to gravity for a given planet
   3. has a greater value closer to the surface of the earth than at great altitudes
   4. is dependent on the mass of a planet
   5. is dependent on the distance from the center of a planet
4. According to the Universal Law of Gravitation, when the distance between the centers-of-mass of two bodies is doubled the gravitational force between the bodies is multiplied by a factor of:
   1. 1/4
   2. 1/2
   3. 1
   4. 2
   5. 4
5. Kepler's Third Law of Planetary Motion deals with
   1. gravitation
   2. periods and orbits of planets
   3. areas of orbits
   4. shapes of orbits
   5. eccentricity of orbits
6. The relationship expressed in Kepler's Third Law of Planetary Motion is
   1. 
   2. 
   3. 
   4. 
   5. 
7. If the mass of the planet Mercury is 3.18x10²³ kg and its radius is 2.43x10⁶ m, the acceleration due to gravity at the surface of the planet is:
   1. 1.87 m/s²
   2. 2.42 m/s²
   3. 3.02 m/s²
   4. 3.59 m/s²
   5. 3.98 m/s²
8. A communications satellite is in an elliptical orbit about the earth. It has its greatest speed when it
   1. is nearest the earth
   2. farthest from the earth
   3. moving toward the earth
   4. moving away from the earth
   5. between the earth and the sun
9. A body orbits the earth at an altitude of 3.0 earth radii as measured from the center of the earth. If the body experiences a weight of 1.00 N, its mass is
   1. 0.092 kg
   2. 0.102 kg
   3. 0.333 kg
   4. 0.918 kg
   5. 1.00 kg
10. There is a point between the earth and the moon where the gravitational attraction of the earth is "canceled" by the gravitational attraction of the moon. If the mass of the earth is 81 times greater than the mass of the moon, how far from the center-of-mass of the earth is this point?
    1. 1/9 of the way to the moon
    2. 8/9 of the way to the moon
    3. 9/81 of the way to the moon
    4. 19/81 of the way to the moon
    5. 9/10 of the way to the moon
    
    

answers: 1 (e), 2 (e), 3 (a), 4 (a), 5 (b), 6 (c), 7 (d), 8 (a), 9 (d), 10 (e)

Suggested Problem Assignments: