Archimedes was an ancient Greek mathematician and inventor. He made mathematical discoveries as he solved everyday problems. He invented machines to move heavy objects, carry water, and fight battles. Archimedes recorded his discoveries so that others could learn from them.
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Archimedes is a fossil that looks like a screw. It is a genus of fenestrate bryozoans, defined by a corkscrew-shaped axial support column and spiraling mesh-like fronds attached to the column. Broken fragments of Archimedes are common in Mississippian rocks of both eastern and western Kentucky. The fossils are named after the Greek scientist and philosopher Archimedes, who designed a corkscrew-shaped irrigation pump.
- Archimedes' principle, physical law of buoyancy, discovered by the ancient Greek mathematician and inventor Archimedes, stating that any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force, the magnitude of which is equal to the weight of the fluid displaced by the body.
- He formulated the Archimedes' principle. One of the most famous contributions of Archimedes is.
Bryozoa are a phylum of marine invertebrate organisms that still live today. They are tiny (less than 1 millimeter long) organisms that construct colonial structures. Different types of prehistoric bryozoa built colonial mounds, branching bushes, crusts, and fan- or frond-like structures. Bryozoan structures look similar to the types of colonial structures built by corals, but they are a distinctly different phylum of organisms. Fenestrates are a type of bryozoan that had fan- and frond-shaped colonies. Fans and fronds were mesh-like—perforated by tiny holes.
Description. The genus name Archimedes is most commonly used to describe a corkscrew-shaped, bryozoan axial support column, although attached fronds are also defined under the genus. Columns are commonly fragmented. Most are a few millimeters wide and two to three centimeters in length, although longer columns are sometimes found. Archimedes structures appear to have been fragile and easily broken; therefore, whole three-dimensional fossils with complete fronds attached to axes are rare In addition to Archimedes frond genera, some species of the frond genera Fenestella and Fenestellina also are found attached to Archimedes support columns (although not all of the species of these genera were coiled and associated with Archimedes).
Species. At least 16 species of Archimedes, several with multiple varieties, have been reported from Kentucky (Butts, 1917; McFarlan, 1942; Conkin and Fuson, 1970; Chesnut and Ettensohn, 1988; Sable and Dever, 1990). Both the coiled axes and fronds may have species names (McFarlan, 1942; Bassler, 1953). Most of the species names assigned to Archimedes axial columns are based on variations in the shape of the convolutions (coils) and spacing of convolutions (McFarlan, 1942; Condra and Elias, 1944). Many species names were defined by Arthur C. McFarlan, a professor in the geology department (now the Department of Earth and Environmental Sciences) at the University of Kentucky, and past state geologist and director of the Kentucky Geological Survey. Some of the specimens he studied are in the Department of Earth and Environmental Sciences' paleontological collection. One species, found in the Mississippian Floyds Knob Bed of the Borden Formation, in Marion and Jefferson Counties, is called Archimedes kentuckiensis. The holotype, No. 164200, and many paratypes (Nos. 164201–164207) are in the U.S. National Museum collection (Conkin and Fuson, 1970).
Range and geographic occurrence. The oldest Archimedes fossils reported in Kentucky are from the Middle Mississippian Borden Formation, and they range through the uppermost Mississippian strata preserved in Kentucky. Archimedes fossils are very common in the Salem-Warsaw, Paint Creek, Golconda, Glen Dean, and Slade Formations, especially in shaly interbeds between limestones. Archimedes fossils are so common in the Warsaw Formation in the Illinois Basin (including western Kentucky) that historically the formation was called the 'Archimedes Limestone' (Willman, 1975).
Life and paleoecology. During the Mississippian Period, sea levels rose and fell many times, and Kentucky was sometimes covered by shallow tropical seas and at other times was a low-lying coastline. Archimedes thrived during the times Kentucky was covered by shallow tropical seas. Where Archimedes are found, their fossils are common to abundant, suggesting they lived in groups, sometimes called 'gardens' or 'thickets' on the sea floor. Archimedes commonly grew with crinoids and brachiopods in these thickets. Breakdown of fragile colonies also causes abundant fossil fragments where these fossils are found. Archimedes appears to have favored muddy seafloors, and perhaps the lee-side of shoals (McKinney, 1979; McKinney and Gault, 1980). Individual bryozoan zooids lined holes in the coiled fans, and filtered seawater through the fans for food (Cowen and Rider, 1972). Colonies were apparently capable of asexual reproduction, budding new fans from the fragments of broken fans (McKinney, 1983), which would have been an ecological advantage in soft bottoms and shallow, stormy seas in which thickets of Archimedes were periodically knocked over and fragmented.
References
- Bassler, R.S., 1953, Part G—Bryozoa, in Moore, R.C., ed., Treatise of invertebrate paleontology: Geological Society of America and University of Kansas Press, p. G120.
- Butts, C., 1918, Description and correlation of the Mississippian formations of western Kentucky: Kentucky Geological Survey, ser. 4, Geological Reports, 1918, 119 p.
- Chesnut, D.R., Jr., and Ettensohn, F.R., 1988, Hombergian (Chesterian) echinoderm paleontology and paleoecology, south-central Kentucky: Bulletins of American Paleontology, v. 95, p. 5–102.
- Condra, G.E., and Elias, M.K., 1944, Study and revision of Archimedes (Hall): Geological Society of America, Special Paper 53, 243 p.
- Conkin, J.E., and Fuson, M.L., 1970, Archimedes kentuckiensis, a new fenestrate bryozoan from the Floyds Knob Formation (Upper Osagean) of Kentucky: Journal of Paleontology, v. 44, p. 669–672.
- Cowen, R., and Rider, J., 1972, Functional analysis of fenestellid bryozoan colonies: Lethaia, v. 5, no. 2, p. 147–164.
- McFarlan, A.C., 1942, Chester bryozoa of Illinois and western Kentucky: Journal of Paleontology, v. 16, p. 437–458.
- McKinney, F.K., 1979, Some paleoenvironments of the coiled fenestrate bryozoan Archimedes, in Larwood, G.P., and Abbott, M.B., eds., Advances in bryozoology: London, Academic Press, p. 321–355.
- McKinney, F.K., 1983, Asexual colony multiplication by fragmentation: An important mode of genet longevity in the Carboniferous bryozoan Archimedes: Paleobiology, v. 9, no. 1, p. 35–43.
- McKinney, F.K., and Gault, H.W., 1980, Paleoenvironment of Late Mississippian fenestrate bryozoans, eastern United States: Lethaia, v. 13, p. 127–146.
- Sable, E.G., and Dever, G.R., Jr., 1990, Mississippian rocks in Kentucky: U.S. Geological Survey Professional Paper 1503, 125 p.
- Willman, H.B., 1975, Handbook of Illinois stratigraphy: Illinois State Geological Survey, Bulletin 95, 261 p.
Definition: What is Archimedes' Principle?
Archimedes' principle is a law of physics fundamental to fluid dynamics. It states that the upward buoyant force exerted on a body immersed in a fluid, whether wholly or partially submerged, is equal to the weight of the fluid that the body displaces. If the weight of the fluid displaced is less than the weight of the object, the object will sink. The object will float if the weight of the fluid displaced is equal to the weight of the object. This upward force is known as thrust or buoyant force. It is a consequence of the difference in pressure the fluid exerts at different heights. The fluid pressure is exerted in all directions (Pascal's principle) and increases with depth. There is an unbalanced upward force on the bottom of a submerged object.
History of Archimedes' Principle
The history of this principle goes back to 3rd century BC when it was discovered by Archimedes of Syracuse, who was a Greek mathematician, physicist, engineer, inventor, and astronomer. This discovery is often associated with the term 'Eureka moment.'
According to the popular legend, Archimedes was given the job of finding out whether a crown made for a king was either solid gold or fake gold. One day he was taking a bath and noticed how the water level rose as he immersed his body. Realizing that if a gold crown were dropped into a bath, it would displace its volume of water over the side. This idea, effectively, gave him an easy way to measure the crown's volume. By weighing the crown, he could then efficiently work out its density (mass divided by the volume) and compare it with that of gold. If the density was lower than that of gold, the crown was a fake.
Video: Archimedes' Principle Explained
Examples of Archimedes' Principle
Archimedes principle is a commonly occurring phenomenon in real life. Some notable examples are as follows.
Image Courtesy: Satyam Bhuyan
- A ship or a boat can float on water because the weight of the displaced water is equal to the weight of the ship or boat.
- A submarine can dive into the water or can float on it. A submarine consists of ballast tanks that are filled with air or water. The tanks weigh less than an equal volume of water and make the sub float on the surface. If the tanks are partly filled with air, it is possible to make the submarine float at some depth of the water without either rising or sinking.
- Hot air balloons rise into the air because the density of the warmer air inside the balloon is less dense than the colder air outside. The basic principle of hot air balloon is the use of hot air to create buoyancy, which generates lift.
- Water striders can float on the water since its legs expel water, and the weight of the expelled water is equal to the floating force.
Theory of Archimedes' Principle
The thrust provided by the fluid opposes the weight due to gravity. The object inside the fluid only feels the total force acting on it, which is called the apparent weight. Because the fluid's thrust decreases the actual gravitational force, the object feels as though its weight is reduced. The apparent weight is given by,
Archimedes Banya
Apparent weight = Weight of the object in the air – Thrust or buoyant force
Archimedes' Principle Equation
Archimedes' principle tells us that this loss of weight is equal to the weight of the fluid, wholly or partially, displaced by the object. The corresponding equation is given by,
Fb = ρ X g X V
Where,
Fbis the buoyant force (or thrust)
ρ is the density of the fluid in which the object is immersed
V is the volume of the object that is submerged in the fluid
g is the acceleration due to gravity
Archimedes Painting
Derivation Archimedes' Principle Formula: Law of Buoyancy
The mass of the liquid displaced is,
Mass = Density X Volume
M = ρ X V
The weight of the displaced liquid is,
Weight = Mass X Gravity
W = M X g
Or, W = ρ X V X g
According to Archimedes' principle,
Apparent loss of weight = Weight of the displaced liquid
This apparent loss of weight is the thrust or buoyant force (Fb). Therefore,
Fb = ρ X g X V
It is this force that is responsible for objects to float. Thus, this equation is also called the law of buoyancy.
Uses and Applications of Archimedes' Principle
Archimedes Biography
Archimedes' principle is applied to the following situation.
- An essential application of the Archimedes' principle is to measure the volume and density of irregularly shaped objects.
- In a hydrometer, a solid is suspended in a fluid and buoyed by force equal to the weight of the fluid displaced by the submerged part.
- It is used in a large variety of scientific research subjects, including medical, engineering, entomology, engineering, and geology. For example, it is used to determine the densities of bones and teeth.
Article was last reviewed on Tuesday, July 7, 2020
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