Geology 1203 Earth history Assignment - Isostasy Preamble: The concept of isostasy has its beginnings with Archimedes, a Greek inventor who lived during the third century BC. The story goes that the King of Syracuse suspected that a goldsmith had cheated him by substituting cheaper silver for gold when creating his crown. Archimedes was asked to solve the problem of the goldsmith’s honesty. Supposedly while getting into his bathtub Archimedes realized that the volume of water he displaced weighed the same amount as he did, (obviously some problems with this story) and this led him to the idea of buoyancy. So the submerged crown would displace an amount of water equal to its own volume. And by dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. Archimedes knew that the density (the ratio of an objects mass to its volume) of silver was less than that of gold. The density of the crown would be lower than that of pure gold if silver added. Archimedes demonstrated that the goldsmith had indeed substituted silver for some of the gold. His theory on floating objects and buoyancy is known as Archimedes Principle - an object floating in water will displace a weight of water equal to the weight of that object. You can float in water because your body is slightly less dense than water. 10% For the same reason an iceberg with a mass of 1000 kg does not sink because it displaces exactly 1000 kg of water. Ice is nine-tenths as dense as water so 90% of the ice is below the surface and 10% is above. 90% 0.9g/cm3 1g/cm3 To a fish that swims beneath the ice the pressure does not change because the weight of the open water above him is the same as the weight of the water plus the weight of the ice. Archimedes' Principle tells us that as the weight of the ice increases it will displace a volume of water that is exactly equal to its own weight. Understanding how isostatic forces work will help you better understand tectonic features from the shape of the ocean basins to the rise and erosion of mountains. 50 100 Continental crust Oceanic crust Lithospheric mantle Oceanic lithosphere 0 km Continental lithosphere This concept can be applied to the way the Earth's lithospheric plates work. The lithosphere floats on top of the slightly denser asthenosphere. This is the what we mean by isostasy. It is calculated that 200 kilometers below the Earth's surface the pressure in the asthenosphere is constant whether it is below continents or oceans. 150 Asthenosphere 200 What do I have to do? Archimedes' Principle states that a floating body will displace its own weight of liquid. It is possible to use this principle to determine the equilibrium position of a floating object based on the differences in density between the object and the liquid in which it is floating. In this assignment you will test this idea by comparing floating blocks of wood. Study the figures on the following pages and answer the related questions. Remember that we are looking at density - the mass per unit volume; we will ignore the effects of changes in surface area for these exercises. NAME: STUDENT # Questions Print the following pages, answer the questions and annotate the figures as instructed. Model One Two blocks of wood of different densities are floating in water. air Block A Block B water Question 1: Which of the blocks is denser? a) Block A b) Block B Question 2: Briefly explain what led you to believe it is denser? Model Two Suppose a Block that is floating exactly half submerged was stretched so that the area was doubled but the volume remained the same. air 50% water air ? water Question 3: How will the block float compared to its previous position? Draw this on the figure at right. Make sure you indicate the proportions that are above and below the surface (in case you are a bad artist) Question 4: Briefly explain the reasoning for your answer. NAME: STUDENT # Model Three Two blocks of wood are floating in water. They are the same type of wood with the same density and are the same size and shape.(left diagram) Both blocks are exactly half submerged. Suppose the top half of Block A is removed and added to Block B. (right diagram) air air Block B Block A Block A water Block B water Question 5: What is the density of the blocks? a) 0.25 g/cm3 c) 0.75 g/cm3 b) 0.50 g/cm3 d) 1.00 g/cm3 Question 6: What will happen to modified blocks in the diagram at the right? Block A - a) will rise b) will sink c) will remain in the same position it is in the diagram Block B - a) will rise b) will sink c) will remain in the same position it is in the diagram Question 7: How much of block A will now be exposed above the water? a) 0% c) 35% b) 25% d) 50% Question 8: How much of block B will now be exposed above the water? a) 0% c) 35% b) 25% d) 50% Question 9: Briefly explain the reasoning for your answers to questions 7 and 8. NAME: STUDENT # Model Four Question 10: Draw a block with a density of 0.25 g/cm3 floating in water. (on figure below) Make sure you indicate the proportions that are above and below the surface (in case you are a bad artist) ? air water Model Five Question 11: Draw a block with a density of 1.00 g/cm3 floating in water. (on figure below) Make sure you indicate the proportions that are above and below the surface (in case you are a bad artist) ? air water Model Six Suppose you have a block with a density of 0.50 g/cm3 floating in water. (figure to left below) And you add a block of the same volume and shape but with a density of 1.00 g/cm3 on top of it. Question 12: What proportion of this combined block will be above water? Question 13: Draw the block on the figure to the right. Make sure you indicate the proportions that are above and below the surface (in case you are a bad artist) 1.00 g/cm3 air ? 0.50 g/cm3 water water air NAME: STUDENT # Model Seven Two blocks of wood with different densities are floating in water. air Block A Block B water Question 14: Which of the blocks is denser? a) Block A b) Block B Question 15: Briefly explain your choice. Question 16: How are blocks A and B analogous to oceanic and continental crust? (think density) a) Block A represents oceanic crust and Block B represents continental crust. b) Block A represents continental crust and Block B represents oceanic crust. Question 17: Why doesn’t the crust of the Earth (continental or oceanic) sink into the underlying mantle?
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