Questions and Answers
What is Newton's Law of Gravity?
F = Gm1 m2/R2
What is the value of the universal gravitational constant (G)?
6.67 x 10^-11 N m^2 kg^-2
What is the approximate acceleration due to gravity (g) near the Earth's surface?
9.8 m/s^2
What is the formula for calculating the average density (p) of the Earth?
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The gravitational force on a mass (m0) falling towards the Earth is given by F = ____.
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The gravitational force experienced by a mass at the equator is greater than at the poles.
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Which of the following equations represents the relationship between gravity (g), mass of the Earth (M), and distance (R)?
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What factor indicates that the Earth's density increases towards its center?
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What does magnetic surveying investigate?
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Who used variations in the Earth’s field to locate deposits of magnetic ore?
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Most rock-forming minerals are non-magnetic.
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What is the phenomenon called when a material acquires magnetization in a magnetic field?
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The points within a magnet where the magnetic flux converges are called the ______.
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What defines the intensity of induced magnetization?
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What type of magnetic material has a low and negative susceptibility?
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Which statement about ferromagnetic materials is true?
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Materials with high and positive susceptibility are termed ______.
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What is the term for materials with incomplete electron shells that become magnetized in the same direction as the applied field?
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Study Notes
Theory of Gravitation
- Newton's Law of Gravity describes the mutual attraction between two masses, represented by the equation ( F = \frac{G m_1 m_2}{R^2} ).
- The universal gravitational constant ( G ) is valued at ( 6.67 \times 10^{-11} , \text{N m}^2 \text{kg}^{-2} ).
- The acceleration due to Earth's gravity ( g ) is approximately ( 9.8 , \text{m/s}^2 ) and is directed toward the Earth's center.
Gravitational Force and Mass
- The gravitational force on an object ( m_0 ) falling towards Earth can be expressed as ( F = mg ).
- Combining ( F = mg ) with Newton's Law gives ( g = \frac{GM}{R^2} ), where ( R ) is Earth's radius and ( M ) is Earth's mass.
Density of Earth
- The average density ( P ) can be calculated as ( P = \frac{3M}{4\pi R^3} ).
- From gravity measurements, the equation ( P = \frac{3g}{4\pi R G} ) allows for the determination of Earth's average density.
- Current measurements show Earth's average density ( \rho ) is ( 5520 , \text{kg/m}^3 ), which is significantly higher than the density of common rocks (2500-3000 kg/m³).
Variations in Gravity
- The value of ( g = 9.8 , \text{m/s}^2 ) is an average; local gravitational anomalies occur due to variations in Earth's density.
- Equation ( g = \frac{4 \pi R G}{3} ) illustrates that gravity depends on both radius and density.
- Local variations in density affect gravity readings, providing insights into subsurface rock structures.
Earth's Shape and Gravity
- The Earth is an ellipsoid, being slightly flattened at the poles, with the equatorial radius approximately ( 21.5 , \text{km} ) longer than the polar radius (6378 km).
- Due to this shape, gravity is slightly stronger at the poles than at the equator since ( g ) is inversely proportional to the square of the radius ( R ).
- The centrifugal force caused by Earth's rotation reduces the effective gravitational force, peaking at the equator and affecting gravity measurements across the surface.
Implication for Geophysical Studies
- Measurement variations in gravity can reveal changes in subsurface rock density, facilitating the understanding of Earth's internal structure.
- The interplay between gravitational pull and centrifugal forces shapes the interpretation of gravity data in geophysical research.
Magnetic Methods
- Magnetic surveying analyzes subsurface geology by identifying magnetic anomalies from the Earth's magnetic field caused by magnetic minerals in rocks.
- Most minerals are non-magnetic; notable exceptions include certain rock types that can create detectable anomalies due to their magnetic properties.
- Rock magnetism includes both magnitude and direction, influenced by the rock’s orientation relative to Earth's magnetic poles.
- Von Wrede pioneered magnetic prospecting in 1843 by using variations in Earth's magnetic field to locate magnetic ores.
- Sir Gilbert's 16th-century research revealed Earth's behavior as a North-South permanent bar magnet.
Principles of Magnetism
- A bar magnet creates a magnetic flux, identifiable by compass needle alignment, with converging poles indicating the magnet's ends.
- Common magnets are dipoles, containing both north-seeking (positive) and south-seeking (negative) poles.
- All materials exhibit magnetic properties at the atomic level; induced magnetization occurs when materials gain magnetic alignment in an external field but lose it when the field is removed.
- Induced magnetization, represented as Ι, correlates to external magnetic field strength (H) with the equation Ι = χH, where χ is the material's susceptibility.
Magnetic Susceptibility
- Susceptibility varies among rock types; it measures how well a material can be magnetized.
- Common rock types exhibit low susceptibility (e.g., sedimentary rocks) to very high susceptibility (e.g., Peridotite).
Classification of Magnetic Materials
-
Diamagnetic materials:
- Full electron shells, no unpaired electrons
- Produce an opposing magnetic field when exposed to an external field
- Weakly negative susceptibility
-
Paramagnetic materials:
- Incomplete electron shells
- Unpaired electrons align with the external field, resulting in positive susceptibility
-
Ferromagnetic materials:
- Metallic elements (e.g., Ni, Co, Fe) allow electron exchange between atoms
- Strong magnetic behavior and spontaneous magnetization in the presence of a field
Summary of Rock Susceptibility
- Datasets show various ranges of susceptibility for different rock types, indicating variable magnetic properties based on mineral content.
- Rocks like basalt and gabbro can exhibit susceptibility values in the thousands, while sedimentary rocks like limestone remain very low (<1).
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Description
Explore the core principles of gravitation through Newton's Law of Gravity. This quiz covers key equations and concepts that define gravitational interactions between masses. Test your understanding of how these laws apply to real-world scenarios.
