Isostacy and Buoyancy Extra Credit Activity

.xlsx

School

University of Minnesota-Twin Cities *

*We aren’t endorsed by this school

Course

2550

Subject

Geology

Date

Apr 3, 2024

Type

xlsx

Pages

Uploaded by MajorSnake2064

NAME: Beckee Beulke Isostacy and Buoyancy Introduction Archimedes’ Principle You must enter your name above credit for your lab assignmen The term ‘isostacy’ comes from the Greek words ‘ísos’ which means equal and ‘stásis’ wh standstill. It refers to a state of gravitational equilibrium between the Earth’s lithosphere underlying asthenosphere that results in the Earth’s surface having different elevations d on changes in the lithosphere’s thickness and density. To some extent, you can imagine the basic difference between isostacy and buoyancy as isostacy is the concept of ‘buoyancy’ applied to the physical Earth. It is an application of Archimedes’ principle which states that the upward buoyant force exerted on a body imm fluid is equal to the weight of the fluid that the body displaces. However, in terms of the Earth it is important to keep in mind that isostacy does not invo response of a fluid mantle but rather a solid rock mantle capable of flow because of its he pressure. This is similar to ice at the bottom of a glacier that, despite remaining solid, can flow under the pressure of overlying snow and ice. We will start this lab with a simply exploration of traditional buoyancy using fluids, then m isostacy models that cover different Earth settings, before returning to classical buoyancy explore various ways that organisms have adapted to life in a marine setting. Archimedes’ principle states that when you place a buoyant material (such as blocks of w Styrofoam) in water, that material will sink down until it displaces a mass of water equal t mass of the buoyant material (Figure 1).

Question 1 Roughly what percent of the ice cube stays above the water surface? - less than 2% X - from 5% to 10% - from 20% to 40% - more than 40% Figure 1. A is a partially filled water container. B is the same container with a buoyant block o material floating in the water. No water was added to the container, but the darker blue indica water displaced by the buoyant material. The mass of the displaced water is equal to the total the buoyant material (not just the part below the water level). Water is a remarkable substance that we still do not fully understand, despite its prevalen world and ourselves. Despite its simple composition (H 2 O) water’s hydrogen bonds provid structure that we still have not completely figured out. One of its many peculiarities, com most fluids, is that water is one of the few substances that is denser in its liquid form tha solid form (ice). This is because as it cools and crystallizes, the solid phase (ice) forms a m ordered structure that takes up more space than the same mass of liquid water does. Wa the only substance that does this. Silicon, gallium, germanium, bismuth, and plutonium a well as acetic acid. (However, for most people, water is rather anomalous to most substa deal with.) Fresh water has a density of 1000 kg/m 3 (or 1 gm/cm 3 ). In contrast, the density of ice is o 920 kg/m 3 (or 0.92 gm/cm 3 ) which is why ice will float in water. Since this is can be easily demonstrated, place an ice cube in a transparent glass of water. (if you do not have acce cubes, you can search for images online). Examine the ice and then answer the following Most ice cubes have one longer dimension. When left to its own devices, the ice cube wil float with its long dimension parallel to the water’s surface, just as a broken piece of wint or a polar ice sheet will. Next, loosely trap the ice cube against the side of the glass using your fingers or an im so that it still floats freely but its long axis is vertical. What is the maximum height of cube above the water level now compared to what it was before? If you do not have a to play with, you should still be able to figure this out using Archimedes’ principle.

X - higher - lower - remains the sa Question 2 X - the water level would stay the same as the ice cube melted - the water level would overflow the edge of the glass as the ice cube melted - the water level would drop just below the edge of the glass as the ice cube m Question 3 - a greater proportion of the iceberg would be above the water surface X - a smaller proportion of the iceberg would be above the water surface - the same proportion of the iceberg would be above the water surface Note that we could have asked a similar question about the maximum depth of the ice cu the water surface. When we return to isostacy, it is important to remember that, like ice c different rock masses can extend down to different depths. If you filled your glass with its floating iceberg to the very top of the glass, what woul to the water level in the glass as the ice melted. Again, you should be able to figure t without taking the time to wait for your ice cube to melt. Unlike fresh water, ocean water is saline so its density varies depending on its salt conten temperature. However, for the polar waters where most icebergs lurk, the average densit water at 0°C is 1027.3 kg/m 3 (1.0273 gm/cm 3 ). As a result, for an iceberg floating in a polar sea, how would the relative proportion of volume floating above the water compare to your ice cube floating in fresh water? In all of these scenarios, at a depth below the ice, the pressure will remain the same. Hen mass of the floating ice and underlying water must equal the mass of a similar column of the side. Hence, the elevation of the less dense material is higher (Figure 2). Figure 2. When materials are in buoyant e the pressure at the depth of the dashed ye constant. The mass of the water overlying t point A is equal to the mass of the water an

Question 4 - the top of the ice cube would be ever so slightly above the waterline X - the top of the ice cube would be ever so slightly just below the waterline - the ice cube would sink straight down to the bottom of the glass Question 5 In ‘B’ which wooden block has the greater density? - pine X - oak point A is equal to the mass of the water an material overlying point B. What would happen if ice had a different density, one just ever so slightly above that say 1000.5 kg/m 3 (1.0005 gm/cm 3 )? What would happen then if you placed an ice cub glass of fresh water? Well let’s expand our exploration of buoyancy to consider objects of different thickness o of different density. If we placed different thicknesses of pine blocks in water, the proportions of each block th above the water would remain the same since the blocks all had the same density. Conse the pine blocks would float at different heights and sink to different depths (Figure 3 A). H two same-sized blocks of different density were placed in water, the proportions of the bl rose above the water would vary with density (Figure 3 B). Figure 3. ‘A’ show as number of wooden pine blocks of similar density floating in water. Since has the same relative proportions above and below the water surface, the heights of the block depths) will vary with thickness. In ‘B’, a pine block and oak block of similar thickness are show in water. Since the two differ in density, the relative proportions of the blocks above and below surface also differ.

- pressure would be higher at point ‘Y’ - pressure would be higher at point ‘X’ X - pressure would be the same at both points - the answer cannot be determined without additional information Question 6 X - stack A - stack B - both would sink to the same level - the answer cannot be determined without additional information Question 7 - at least 5% - at least 15% - at least 25% - at least 45% If the blocks are floating freely, how would the total pressure at points ‘X’ and ‘Y’ com one another? What if you stacked two blocks atop one another and then placed them in water? Which of the two stacks (A or B) would sink lower into the water? Almost any rock that you toss into water will sink (although if it is the right shape and you good spin on it, you may be able to get it to skip across the water a few times before it do Even volcanic ash and glass are denser than water. Yet some pieces of pumice, which is a froth of volcanic glass, can float (Figure 4). Pure volcanic glass has a density of roughly 2400 k However, much of a pumice sample’s volume cons small air-filled pores. At sea level, air has a density kg/m 3 , which is low enough that we can basically t being 0 for our purposes here. In order for a specimen of pumice to float in fresh what percent of its volume must consist of trapped

X - at least 60% - at least 75% Isostacy Figure 4. Pumice floating in water. However, when we move on to the Earth we have to adapt our concept of buoyancy to de heat-softened asthenosphere that is capable of flow, rather than a fluid. Although that asthenosphere can flow, it does so much more slowly than a fluid would so it may take tim isostatic equilibrium to be re-established after a change occurs. There are a number of isostatic models used to explain different areas of the Earth. We w two of them. The Airy model (named after George Biddell Airy, British astronomer and mathematician who also was responsible for establishing Greenwich, England as the prim meridian) attempts to explain differences in elevation through variations in crustal thickn contrast, the Pratt model (named after another British astronomer and mathematician na Henry Pratt who worked in India on geographic surveys) seeks to explain differences in e through lateral differences in rock density. The difference between the two models is sho Figure 5. But why are there separate models? Well, blame plate tectonics or at least a heterogeneo The two models work better in different settings. In some plate tectonic settings, it really thickness of the lithosphere that matters as all of the lithosphere present is capped by th type of crust, oceanic or continental. But in other areas, the crust that comprises the upp part of the lithosphere varies laterally from rock of one density to rock of another. And in settings, things can get even more complicated and neither of these two models is a goo so we have to use elements of both or abandon them entirely in favor of yet another isos model. Figure 5. Two models of isostacy. In A, the Airy model, differences in elevation are due to late differences in the thickness of the lithosphere overlying a dense heat-softened asthenosphere can flow. In B, the Pratt model, differences in elevation are due to lateral differences in the den

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help