Name: ________________________________________________ Assignment Due Date: April 20, 2012

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AP Physics: Gravitation

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. The mass of Planet X is one-tenth that of the Earth, and its diameter is one-half that of theEarth. The acceleration due to gravity at the surface of Planet X is most nearlya. 2 m/s2 d. 7 m/s2

b. 4 m/s2 e. 10 m/s2

c. 5 m/s2

____ 2. A newly discovered planet, “Cosmo” has a mass that is 4 times the mass of the Earth. The radius of the Earth is Re. The gravitational field strength at the surface of Cosmo is equal to that at the surface of the Earth if the radius of Cosmo is equal to

a.12

Re d. Re

b. Re e. Re2

c. 2Re

____ 3. If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the Earth, then which of the following is true?a. F1 is much greater than F2. d. F2 is slightly greater than F1.b. F1 is slightly greater than F2. e. F2 is much greater than F1.c. F1 is equal to F2.

____ 4.

A satellite S is in an elliptical orbit around a planet P, as shown above, with r1 and r2 being its closest and farthest distances, respectively, from the center of the planet. If the satellite has a speed v1 at its closest distance, what is its speed at its farthest distance?

a.r1

r2

v1 d.r1 + r2

2v1

b.r2

r1

v1 e.r2 − r1

r1 + r2

v1

c. r2 − r1ÊËÁÁ ˆ

¯˜̃v1

Name: ________________________

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Question 5 refers to a ball that is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the surface of the asteroid.

____ 5. What forces, if any, act on the ball while it is on the way up?a. Only a decreasing gravitational force that

acts downward.d. Both a constant gravitational force that

acts downward and a decreasing force that acts upward.

b. Only an increasing gravitational force that acts downward.

e. No forces act on the ball.

c. Only a constant gravitational force that acts downward.

____ 6.

Two identical stars, a fixed distance D apart, revolve in a circle about their mutual center ofmass, as shown above. Each star has mass M and speed v. G is the universal gravitational constant. Which of the following is a correct relationship among these quantities?

a. v2 = GM / D d. v2 = MGD

b. v2 = GM / 2D e. v2 = 2GM2 / D

c. v2 = GM / D2

Name: ________________________

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____ 7.

The graph above shows the force of gravity on a small mass as a function of its distance R from the center of the Earth of radius Re, if the Earth is assumed to have a uniform density. The work done by the force of gravity when the small mass approaches Earth from far away and is placed into a circular orbit of radius R2 is best represented by the area under the curve betweena. R = 0andR = Re d. R = Re andR = ∞b. R = 0andR = R2 e. R = R2 andR = ∞c. R = Re andR = R2

____ 8. The escape speed for a rocket at Earth's surface is ve. What would be the rocket's escape speed from the surface of a planet with twice Earth's mass and the same radius as Earth?

a. 2v e d.v e

2

b. 2v e e.v e

2c. ve

Name: ________________________

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____ 9.

A comet moves in the Sun's gravitational field, following the path shown above. What happens to its angular momentum as it moves from point X to point Y?a. It increases steadily. d. It increases as it approaches the Sun and

decreases as it moves away from the Sun.b. It remains constant. e. It decreases as it approaches the Sun and

increases as it moves away from the Sun.c. It decreases steadily.

____ 10. Satellite X moves around Earth in a circular orbit of radius R. Satellite Y is also in a circular orbit around Earth, and it completes one orbit for every eight orbits completed by satellite X. What is the orbital radius of satellite Y?

a.14

R d. 4R

b.12

R e. 8R

c. 2R

Name: ________________________

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Problem

An explorer plans a mission to place a satellite into a circular orbit around the planet Jupiter, which has mass MJ = 1.90 x 1027 kg and radius RJ = 7.14 x 107 m.

11. If the radius of the planned orbit is R, use Newton's laws to show each of the following.

i. The orbital speed of the planned satellite is given by v = GM j

R.

ii. The period of the orbit is given by T = 4π 2R3

GM j

.

12. The explorer wants the satellite's orbit to be synchronized with Jupiter's rotation. This requires an equatorial orbit whose period equals Jupiter's rotation period of 9 hr 51 min = 3.55 x 104 s. Determine the required orbital radius in meters.

Name: ________________________

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13. Suppose that the injection of the satellite into orbit is less than perfect. For an injection velocity that differs from the desired value in each of the following ways, sketch the resulting orbit on the figure. (J is the center of Jupiter, the dashed circle is the desired orbit, and P is the injection point.) Also, describe the resulting orbit qualitatively but specifically.

i. When the satellite is at the desired altitude over the equator, its velocity vector has the correct direction, but the speed is slightly faster than the correct speed for a circular orbit of that radius.

ii. When the satellite is at the desired altitude over the equator, its velocity vector has the correct direction, but the speed is slightly slower than the correct speed for a circular orbit of that radius.

Name: ________________________

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A student is given the set of orbital data for some of the moons of Saturn shown below and is asked to use the data to determine the mass Ms of Saturn. Assume the orbits of these moons are circular.

14. Write an algebraic expression for the gravitational force between Saturn and one of its moons.

15. Use your expression from part (a) and the assumption of circular orbits to derive an equation for the orbital period T of a moon as a function of its orbital radius R.

16. Which quantities should be graphed to yield a straight line whose slope could be used to determine Saturn's mass?

Name: ________________________

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17. Complete the data table by calculating the two quantities to be graphed. Label the top of each column, including units.

18. Plot the graph on the axes below. Label the axes with the variables used and appropriate numbers to indicate the scale.

19. Using the graph, calculate a value for the mass of Saturn.

ID: A

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AP Physics: GravitationAnswer Section

MULTIPLE CHOICE

1. ANS: B REF: 1984 AP Physics Mult Choice Final (Mechanics C )#20KEY: universal gravitation|acceleration due to gravity

2. ANS: C REF: 1988 AP Physics Mult Choice Final (Mechanics C )#21KEY: Universal gravitation

3. ANS: C REF: 1993 AP Physics Mult Choice Final (Mechanics C )#5KEY: Newton's 3rd law

4. ANS: A REF: 1993 AP Physics Mult Choice Final (Mechanics C )#32KEY: angular mometum|conservation of angular momentum

5. ANS: A REF: 1998 AP Physics Mult Choice Final (Mechanics C )#7KEY: force|distance|universal gravitation

6. ANS: B REF: 1998 AP Physics Mult Choice Final (Mechanics C )#20KEY: center of mass|velocity|orbit

7. ANS: E REF: 2004 AP Physics Mult Choice Final (Mechanics C )#27KEY: Force|graphical analysis|work|energy|integration

8. ANS: B REF: 2004 AP Physics Mult Choice Final (Mechanics C )#35KEY: escape velocity|varying mass

9. ANS: B REF: 2008 AP Physics Mult Choice Prac Exam (Mechanics C )#13KEY: angular momentum|planet|orbit

10. ANS: D REF: 2008 AP Physics Mult Choice Prac Exam (Mechanics C )#14KEY: planet|orbit|angular momentum

ID: A

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PROBLEM

11. ANS:

ID: A

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REF: Free Resp Ques 2001 Mech #2a

ID: A

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12. ANS:

REF: Free Resp Ques 2001 Mech #2b

ID: A

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13. ANS:

REF: Free Resp Ques 2001 Mech #2c

ID: A

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14. ANS:

REF: Free Resp Ques 2005 Mech #2a 15. ANS:

REF: Free Resp Ques 2005 Mech #2b 16. ANS:

REF: Free Resp Ques 2005 Mech #2c

ID: A

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17. ANS:

REF: Free Resp Ques 2005 Mech #2d

ID: A

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18. ANS:

REF: Free Resp Ques 2005 Mech #2e

ID: A

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19. ANS:

REF: Free Resp Ques 2005 Mech #2f