Chapter 7 Problems: Gravitation
1. Two 10,000 kg asteroids in deep space are 150. m apart. Determine the force of gravitational attraction between them.
2. Two automobiles of 2500 kg each are standing with their centers of mass 3.00 m apart. Calculate the gravitational force of attraction between them.
3. Two large steel spheres, each with a mass of 2.00 x 105 kg, are located2.00 m apart. Find the gravitational force between them. ( Ans: 0.667 N)
4. Two 4.00 kg bowling balls used in a tournament lie on a shelf with their
centers 30.0 cm apart. Calculate the force of attraction between them.
5. A 25,000 kg object is 2.55 x 107 m above the surface of the earth. A) Determine the weight of the object at that position. (i.e. the gravitational force of attraction.) B) Determine the acceleration of the object caused by gravity at that position. C) Determine the gravitational field strength at that position.
6. A 1.00 kg mass on the surface of a planet has a weight of 27 N. The radius of the planet is 6.5 x 107 m. Find the mass of the planet.
7. The mass of the moon is 7.35 x 1022 kg and the radius of the moon is 1.74 x 106 m. Use Newton’s Law of Universal Gravitation to compute the acceleration due to gravity for an object on the surface of the moon. Determine the gravitational field strength for the surface of the moon.
8. A planet of mass 3.60 x 1024 has a radius of 2.00 x 106m. What is the value of surface gravity on this planet?
9. A 5.00 kg mass on the surface of a planet has a weight of 270 N. If the radius of the planet is 7.00 x 104 km, find the mass of the planet.
10. A) Compute your mass in kg (weight in pounds/ 2.2 pounds/kg). B) Use Newton’s Law of Universal Gravitation to calculate the gravitational force between you and the earth. C) Calculate your weight in Newton’s by using Fg = mg. How do the answers to B and C compare?
11. Two masses, m1 and m2, are separated by a distance, r. The force of attraction between the two masses if F. Determine the force of attraction in terms of F for each of the following:
a) double m1e) double m1 and triple m2
b) double rf) triple r
c) double both m1 and m2g) double m1, triple m2 and
d) double both masses, and change the distance to r/2 change the distance to r/3
12. A geosynchronous satellite (T =1day) orbits the earth at an orbital radius
of 4.3 x 107 m. On February 20, 1962, John Glenn became the first American to orbit the earth reaching an altitude of 260 km above the earth’s surface. What was John Glenn’s orbital period?
13. A 36 kg object is placed in a position where it weighs 48 N. What is the gravitational field strength at that position?
14. A 12 kg object is located where the gravitational field strength has a value
of 0.6 N/kg. How much does the object weigh at this location?
Matching. Place the initials in parenthesis in the blank
(A) Aristotle, (P) Ptolemy, (C) Copernicus, (G) Galileo,
(TB) Tycho Brahe, (K) Kepler, (N) Newton
15. _____ Proposed the heliocentric model of the solar system
16. _____ Believed that the circle and sphere were the perfect form of the universe
17. _____ Tried to explain retrograde motion by proposing that planets orbited on
smaller circles attached to larger circles
18. _____ Formulated the law of gravity
19. _____ Used a telescope to discover the moon’s of Jupiter
20. _____ Showed that a comet was further away than the moon
21. _____ Stole planetary data, worked on them for ten years and discovered
three laws of planetary motion
22. An object weighs 24,000 N on the surface of the earth. Fill in the following chart for each of the positions shown.
Position / Weight / Mass / “g” / Field Strength2 earth radii from surface
3 earth radii from surface
4 earth radii from surface
Double distance
Triple distance
6.38 x 106 m from surface
1.276 x 104 km from surface
Orbital radius of 1.276 x107 m