Lesson11 Gravitational Fields

Lesson 11: Gravitational Fields

Key Points: • Learn that gravity is a field because it exerts a force without being in physical contact with another object. • Understand that gravitational field strength is numerically equal to acceleration due to gravity at that point.

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The Gravitational Field

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The Gravitational Field In the nineteenth century, Michael Faraday invented the concept of the “field” to explain how a magnet attracts objects. Later, the field concept was applied to gravity. Anything that has mass is surrounded by a gravitational field. It is the field that acts on a second body at the location of that body. In general, the field concept makes the idea of a force acting across great distances unnecessary.

Nov 2910:48 AM

The Gravitational Field To find the strength of the gravitational field, place a small body of mass m in the field and measure the force. We define the field strength, g, to be the force divided by a unit mass, F/m. It is measured in newtons per kilogram. The direction of g is in the direction of the force. Thus g = F/m

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The Gravitational Field Note that the field is numerically equal to the acceleration due to gravity at the location of the mass. On Earth’s surface, the strength of the gravitational field is 9.8N/kg. It is independent of the size of the mass. The field can be represented by a vector of length g and pointing toward the object producing the field.

Nov 2910:48 AM

The Gravitational Field We can picture the gravitational field of Earth as a collection of vectors surrounding the earth and pointing toward it as shown at right. The strength of the field varies inversely with the square of the distance from the center of the Earth.

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Review Activities • Do examples 4.5 (p.218), and 4.6 (p. 220) • Read pages 200201, 216222 do all practice problems on 219 and 220. • Do check and Reflect questions 2, 3, 4, 5, 7, 13 on p. 229.

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Jan 2510:53 AM 4 Lesson11 Gravitational Fields

Jan 2612:40 PM

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Jan 2612:42 PM

1. Calculate the gravitational field strength on the surface of mars. Mars has a radius of 3.43x10 6m and a mass of 6.37x1023kg. (3.61N/kg)

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2. At what distance from the Earth’s surface is the gravitational field strength 7.33n/kg? 1.01x106m

3. On the surface of Planet X an object has a weight of 63.5N and a mass of 22.5kg. What is the gravitational field strength on the surface of Planet X? (2.82N/kg)

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4. On the surface of Planet Y, which has a mass of 4.83x10 24kg, an object has a weight of 50.0N and a mass of 30.0kg. What is the radius of this planet? (1.39x107m)

5. What is the gravitational field strength 1.27x10 7m above the earth’s surface? (1.09N/kg)

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6. Planet B has a mass of 4.00x10 22kg and a radius of 6.0x10 5m. What is the gravitational field strength on the surface of planet B? (7.4N/kg)

7. Our solar system is in the Milky Way Galaxy. The nearest galaxy is Andromeda, a distance of 2 x10 22m away. The masses of the Milky Way and Andromeda Galaxies are respectively, 7 x10 41kg and 6 x1041kg. Treat the galaxies like particles and calculate the magnitude of the gravitational force between them. 7x1028N.

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8. Three objects are positioned along a straight line. From left to right their masses are 181, 70.0 and 405 kg. The 70kg mass is 0.310m from the 181kg object, and 0.460m from the 405kg object. What is the net gravitational force acting on the 181kg object? 1.70 x 10 5N

9. The drawing at right (not to scale) shows one alignment of the sun, earth and moon. The gravitational force F SM that the sun exerts on the moon is perpendicular to the force F EM that the earth exerts on the moon. The masses are: mass of the 30 24 22 sun = 1.99x10 kg, mass of earth = 5.98x10 kg, mass of moon = 7.35x10 kg. The distances shown are: r SM = 11 8 20 1.50x10 m and rEM = 3.85x10 m. Determine the magnitude of the net gravitational force on the moon. 4.78x10 N

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10. The drawing at right (not to scale) shows one alignment of the sun, earth and moon. The gravitational force F SM that the sun exerts on the moon is perpendicular to the force F EM that the earth exerts on the moon. The masses are: mass of 30 24 22 the sun = 1.99x10 kg, mass of earth = 5.98x10 kg, mass of moon = 7.35x10 kg. The distances shown are: r SM = 11 8 1.50x10 m and rEM = 3.85x10 m. Determine the magnitude of the net gravitational force on the moon.

moon

sun earth