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A simple model (Fig. 10-56) considers a continent as a

ISBN: 9780130606204 3

Solution for problem 72GP Chapter 10

Physics: Principles with Applications | 6th Edition

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Problem 72GP

A simple model (Fig. 10-56) considers a continent as a block (density = 2SOOkg/m3) floating in the mantle rock around it (density ~ 3300 kg/m'). Assuming the continent is 35 km thick (the average thickness of the Earth's continental crust), estimate the height of the continent above the surrounding mantle rock.

Step-by-Step Solution:

Solution 72GP:

Continent is able to float on the mantle rock because its weight is balanced by the buoyancy force. As the continent is floating on the mantle rock, we have to determine the height of the continent above the mantle rock layer.

Step 1 of 5</p>

Concept:

Density of the body is defined as the ratio of the mass of the body to its volume. Mathematically,

…(1)

…(2)

Archimedes Principle: Buoyancy force acting on an object whose volume is immersed inside the liquid of density is given as,

…(3)

Flotation Law: When the first body floats on the surface of the second body, the buoyancy force by second body balance the weight of the first body.

…(4)

Step 2 of 5</p>

Figure below shows the free body diagram of the continent, floating on the mantle layer.

Thickness of the continent

Density of the continent

Density of mantle rock

Let be the bottom area of the continent. Assuming the continent to be rectangular parallelepiped in shape..

Let be the height of the continent above the surrounding mantle rock.

From the above figure, the height of the displaced mantle rock is .

Step 3 of 5</p>

In accordance to the Archimedes Principle, from equation (3), the buoyancy force acting on the continent is,

…(5)

Weight of the continent                …[From (2)]

…(6)

Step 4 of 5

Step 5 of 5

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