Chapter 12 - Universal Gravitation

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Summary

The moon and other objects in orbit around the earth are actually falling toward the earth but have great enough tangential velocity to avoid hitting earth.

According to Newton's law of universal gravitation, evrything pulls on everything else with a force that depends upon the masses of the objects and the distances between their centers of mass.

The greater the masses, the greater is the force.

The greater the distance, the smaller is the force.

Gravitation decreases according to the inverse-square law. The force of gravity weakens as the distance is squared.

Sample Test Questions and Problems

The following are questions or problems that are considered testable material in our physics curriculum. When you have chosen an answer for a question, check your answers with the solutions found at the bottom of the page.

1. Why did Newton think there was a force acting on the moon?
a. Because the moon always keeps one side toward the earth
b. Because the moon moves in a curved path
c. Because there is no air on the moon
d. Because the moon is moving
e. all of the above

2. Newton reasoned that the gravitational attraction between the earth and the moon must be
a. directly proportional to distance.
b. reduced by distance.
c. the same at all distances.
d. independent of distance.
e. all of the above

3. Since the earth is attracted to the sun, why doesn't it fall into the sun?
a. Because it has a large tangential velocity
b. Because there is an equal force holding it away from the sun
c. Because it has too much mass to move toward the sun
d. Because it has too much intertia to move toward the sun
e. all of the above

4. The gravitational between two masses
a. is always an attraction.
b. depends on how large the masses are.
c. depends inversely on the square of the distances between the masses.
d. depends on a universal gravitational constant.
e. all of the above

5. A very massive object A and a less massive object B move toward each other under the
influence of mutual gravitation. Which force, if either, is greater?
a. The force on A
b. The force on B
c. Both forces are the same

6. Suppose the gravitational force between two massive spheres is 10 N. If the distance between
the spheres is doubled, what is the force between the masses?
a. 40 N
b. 20 N
c. 10 N
d. 5 N
e. 2.5 N

7. Suppose the gravitational force between two massive spheres is 10 N. If the magnitude of
each mass doubles, what is the force between the masses?
a. 40 N
b. 20 N
c. 10 N
d. 5 N
e. 2.5 N

8. The force of gravity acting on you will increase if you
a. burrow deep inside the planet
b. stand on a planet with a radius that is shrinking.
c. both a and b
d. none of the above

9. A lunar month is about 28 days. If the moon were closer to the earth than it is now, the lunar
month would be
a. less than 28 days.
b. more than 28 days.
c. unchanged at 28 days.

10. A supplier wants to make a profit by buying metal by weight at one altitude and selling it at
the same price per pound at another altitude. The supplier should
a. buy at a high altitude and sell at a low altitude.
b. buy at a low altitude and sell at a high altitude.
c. disregard altitude because it makes no difference.

11. Compare the gravitational force between Earth and Mars, and the gravitional force between
a new-born baby and the doctor who holds it. The greater force is between
a. Earth and Mars
b. the baby and the doctor.
c. cannot be determined

12. Consider the gravitational force between the earth and a meteor in outer space. If the meteor
moves so its distance from the earth's center doubles, the gravitational force on the meteor will be
a. one quarter.
b. half.
c. double.
d. four times greater.
e. eight times greater.

13. The force of attraction between between two masses depends inversely on the square of the
distance between the masses. Any law that has this kind of dependence on distance is called an
inverse distance law.
True
False

14. Because the earth and moon are gravitationally attracted towards each other, they will soon
collide.
True
False

15. If the earth were its present size but twice as massive, we would weigh less.
True
False

Solutions

1. b. Because the moon moves in a curved path

2. b. reduced by distance.

3. a. Because it has a large tangential velocity

4. e. all of the above

5. c. Both forces are the same.

6. a. 40 N

7. a. 40 N

8. b. stand on a planet with a radius that is shrinking.

9. a. less than 28 days.

10. a. buy at a high altitude and sell at a low altitude.

11. b. the baby and the doctor.

12. d. four times greater.

13. False

14. False

15. False

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