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can be written as where ● Diagram not drawn to scale ● 1800 miles thick 1400 miles Thick ● 800 miles thick Scale everything in terms of the radius of the Earth R (4000 miles here for simplicity), so that in terms of the variable y = r/R, 0 ≤ y ≤ 1, the integral for the average density p = 3 R³ Mantle (Flows with the consistancy of asphalt) Continental Plate Outer Core (Iron and nickel in the liquid state) Inner Core (Iron and nickel in the solid state) 5₁² r²p(r)dr 0 p = 3₁ y²p(y)dy, = P3, y2 ≤ y ≤ 3, = P4, Y3 ≤ y ≤ 1. INNER CORE (0 ≤ y ≤ y₁): Earth's inner core has the highest density P₁ 13 g/cm³. OUTER CORE (1 ≤y ≤ y2): Next, the outer core has a density P2 11 g/cm³. LOWER MANTLE (y2 ≤y ≤ y3): The lower mantle has a significantly lower density P35 g/cm³. This is about 1400 miles thick. p(v) = P₁, 0 ≤ y ≤ yı, = P2, y1 ≤y ≤ y2,

can be written as where ● Diagram not drawn to scale ● 1800 miles thick 1400 miles Thick ● 800 miles thick Scale everything in terms of the radius of the Earth R (4000 miles here for simplicity), so that in terms of the variable y = r/R, 0 ≤ y ≤ 1, the integral for the average density p = 3 R³ Mantle (Flows with the consistancy of asphalt) Continental Plate Outer Core (Iron and nickel in the liquid state) Inner Core (Iron and nickel in the solid state) 5₁² r²p(r)dr 0 p = 3₁ y²p(y)dy, = P3, y2 ≤ y ≤ 3, = P4, Y3 ≤ y ≤ 1. INNER CORE (0 ≤ y ≤ y₁): Earth's inner core has the highest density P₁ 13 g/cm³. OUTER CORE (1 ≤y ≤ y2): Next, the outer core has a density P2 11 g/cm³. LOWER MANTLE (y2 ≤y ≤ y3): The lower mantle has a significantly lower density P35 g/cm³. This is about 1400 miles thick. p(v) = P₁, 0 ≤ y ≤ yı, = P2, y1 ≤y ≤ y2,

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(i) Using the integral definition below, find the average density of the Earth given the following information: Oceanic Plate where can be written as 3-5 miles thick ● Diagram not drawn to scale 1400 miles Thick 1800 miles thick 5-25 miles thick 800 miles thick Continental Plate Mantle (Flows with the consistancy of asphalt) Scale everything in terms of the radius of the Earth R ( 4000 miles here for simplicity), so that in terms of the variable y r/R, 0 ≤ y ≤ 1, the integral for the average density p=2³3r²p(r)dr Outer Core (Iron and nickel in the liquid state) Inner Core (Iron and nickel in the solid state} p=3√ 1²p(v)dy, p(y) = P₁, 0≤ y ≤yi, = P2, y1 ≤y ≤y2, = P3, y2 ≤y ≤ y3, = P4, Y3 ≤ y ≤ 1. INNER CORE (0 ≤ y ≤ yı): Earth's inner core has the highest density p₁ 13 g/cm³. OUTER CORE (1 ≤ y ≤ y2): Next, the outer core has a density P2 11 g/cm³. LOWER MANTLE (y2 ≤ y ≤y3): The lower mantle has a significantly lower density P35 g/cm³. This is about 1400 miles thick.
Transcribed Image Text:(i) Using the integral definition below, find the average density of the Earth given the following information: Oceanic Plate where can be written as 3-5 miles thick ● Diagram not drawn to scale 1400 miles Thick 1800 miles thick 5-25 miles thick 800 miles thick Continental Plate Mantle (Flows with the consistancy of asphalt) Scale everything in terms of the radius of the Earth R ( 4000 miles here for simplicity), so that in terms of the variable y r/R, 0 ≤ y ≤ 1, the integral for the average density p=2³3r²p(r)dr Outer Core (Iron and nickel in the liquid state) Inner Core (Iron and nickel in the solid state} p=3√ 1²p(v)dy, p(y) = P₁, 0≤ y ≤yi, = P2, y1 ≤y ≤y2, = P3, y2 ≤y ≤ y3, = P4, Y3 ≤ y ≤ 1. INNER CORE (0 ≤ y ≤ yı): Earth's inner core has the highest density p₁ 13 g/cm³. OUTER CORE (1 ≤ y ≤ y2): Next, the outer core has a density P2 11 g/cm³. LOWER MANTLE (y2 ≤ y ≤y3): The lower mantle has a significantly lower density P35 g/cm³. This is about 1400 miles thick.
UPPER MANTLE (3 ≤ y ≤ 1): The upper mantle has a density P44 g/cm³. This is about 400 miles thick. You can neglect the crust since it is so thin compared with the other layers. ● ● (ii) Compare your result from part (i) by calculating p from the mass of the Earth and its radius: Mass of the Earth = 6x1024 kg = 6×1027 g; Radius = 6400 km = 6.4×108 cm.
Transcribed Image Text:UPPER MANTLE (3 ≤ y ≤ 1): The upper mantle has a density P44 g/cm³. This is about 400 miles thick. You can neglect the crust since it is so thin compared with the other layers. ● ● (ii) Compare your result from part (i) by calculating p from the mass of the Earth and its radius: Mass of the Earth = 6x1024 kg = 6×1027 g; Radius = 6400 km = 6.4×108 cm.
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