General Physics – Ph 201



General Physics – Ph 211 Name: ___________

Practice Exam Questions – Universal Law of Gravitation and Kepler’s Laws

February 17, 2006

Part I – True or False (2 points each): For questions 5 – 12, state whether each statement is true or false. On the scantron sheet use A) True and B) False

1. A disk and a ring, both solid and uniform and having the same mass and diameter, roll without slipping down the same ramp starting from rest. Both of them will reach the ground at the same time.

2. An ordinary car would not be able to go around an unbanked curve of a perfectly smooth road, no matter how the driver turned the wheels.

3. If Earth had twice as much mass as it now does but were also twice its present diameter, the acceleration due to gravity at its surface would be the same as it is now.

4. For satellites in orbit, their kinetic energy is equal to their gravitational potential energy.

5. The planet closest to the sun, on the average has the shortest orbital period.

PART – II – Multiple Choice Questions (2 points each): It is not necessary to show your work for the multiple choice questions.

Choose the one correct choice for each of the following questions that best answers or completes the question. Fill in the appropriate circle on the scantron sheet.

6. If the distance between two point masses is doubled then the gravitational force between them

a. remains the same c. decreases by a factor of 2

b. increases by a factor of 2 d. decreases by a factor of 4

7. Satellite #1 has three times the mass of satellite #2. Both are in circular orbits of the same radius about Earth. The ratio of the speed of satellite #1 to the speed of satellite #2 is

a. 3:1 b. 1:3 c. 2:1 d. 1:1

8. How far June must travel to get away from the earth’s gravitational field?

A) To a region above the earth atmosphere.

B) To a region well beyond the moon.

C) To a region beyond the solar system.

D) To a region beyond Milky Way (about 80,000 light years away).

E) …forget it body, you can’t travel far enough.

9. Consider a spherical asteroid with a mass of 3.5 × 1016 kg and a radius of 8.8 km. What is the escape speed from the asteroid?

A) 730 m/s B) 520 m/s C) 16 m/s D) 23 m/s

10. If the sun suddenly collapsed to become a black hole, the earth would

a) leave the solar system in a straight line path.

b) spiral into the black hole.

c) undergo a major increase in tidal forces.

d) continue to circle in its usual orbit

Questions and Problems – Show your work or explain your reasoning for each problem.

1. Star B is half as massive as star A.

a) Draw to gravitational force vectors acting on each star; draw the vector lengths with proper scaling.

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mB mA

b) Is the acceleration of star B smaller than, larger than, or equal to acceleration of A? Explain.

2. Two Planets A and B are orbiting a common star. Planet A is twice as massive as planet B and orbits at twice distance from the star. Let FB be the gravitational force on star B. What is the ratio of FA/FB? Assume same average density for both planets.

3. If the acceleration of gravity at the surface of Planet A in problem 2 is 14.7 m/s2, what is g on planet B?

4. In problem 2, Planet A orbits the star with a ‘year’ that is 240 day long, How long is a year on planet B?

5. Satellite a orbits a planet with a speed of 12000 m/s. Satellite b is 3 times more massive than satellite a but orbits only half as far away from the center of the planet as a does. What is the speed of satellite b?

6. A particle is projected from the surface of the earth with speed twice the escape speed. When it is very far from the earth, what is its speed?

7. Consider two satellites in orbit about a star (like our sun). If one satellite is twice as far from star as the other, but both satellites are attracted to the star with the same gravitational force, how do the masses of satellites compare?

8. A satellite of mass m is in a circular orbit of radius R2 around a spherical planet of radius R1 made of a material with density ρ. ( R2 is measured from the center of the planet, not its surface.) Use G for the universal gravitational constant.

A) Find the kinetic energy of this satellite, KE. Express the satellite's kinetic energy in terms of G, m, π, R1, R2, and ρ.

B) Find U, the gravitational potential energy of the satellite. Take the gravitational potential energy to be zero for an object infinitely far away from the planet. Express the satellite's gravitational potential energy in terms of G, m, π, R1, R2, and ρ.

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B

A

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