What is the relationship between "centre of gravity" and "centre of buoyancy" in a ship or boat.
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Center of gravity of the displaced liquid is the center of bouyancy. The (resultant) weight of the vessel acts at the center of gravity(downwards) and the (resultant) bouyant force acts at the center of bouyancy upwards.\n\nIt is better to have the center of gravity lower than the center of boyancy. for stabality. The lower it is the more stable.\n\nThis is because, if the vessel is tilted, the weight and the bouyant force make a couple. This can be against the tilt or with the tilt. If center of bouyancy is lower than center of gravity, it will tilt more. And vice versa.\n\n YOu can find this out by drawing small diagram of the forces.\n\nAlso you can try this. \nTake a pencil. \nhold it vertical but little tilted. \nnow assume, the bottom end is center of bouyancy and top end is center of gravity.\n\nso, push up form the bottom and push down form the top. You will see that the pencil becomes horizontal. i.e you ship sinks.\n\nIf you assume the opposite - take the top to be the center of bouyancy. Pull the top up and the bottom down. The pencil straightens. YOur ship stabalises.
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Up or away from the center of gravity.
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gravity and air resistance.
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Principle of all boats is that of buoyancy. Objects will float (will have buoyancy) when the volume of the liquid that they displace is equal in mass to the mass of the object. In a way, you can imagine a 1-to-1 tradeoff. When you place a boat of X volume in water, it displaces (pushes aside) X volume of water. That X volume of water, if you can take it out and weigh it, will equal the weight of your boat. So you can do some calculations for "displacement" (the volume that your boat takes up in water) and then calculate the mass of the water it displaces. If the mass of the water you displace is greater than the mass of your ship, it will float.\n\nNo matter what, make sure the boat is waterproof. In olden days wooden boats were sealed with tar and wax. Any waterproof substance (usually an oil-based resin) should help seal the boat.\n\nYour boat moves faster if it displaces less water. But wait..there's clearly another trade-off here: if you have a lot of displacement, you float better, but that also means your boat takes upa lot of volume, and that will increase water resistance and make your boat slower. So your task here is to find a volume of displacement that allows your boat to float while it doesn't take up so much volume that it will slow the boat down. One solution is to make the hull (underside that is beneath water) more hydrodynamic (more flowy). You can experiment with  different designs (if the materials permit) such as a standard hull or a catamaran. The principles of hyrdodynamics are similar to aerodynamics: sharper contours are less resistant than square shapes. Think of an arrow going through air versus a square brick.
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So Archimedes was lying in one of those Greek bathhouses when he suddenly realized that (besides the rise in water level) he was FLOATING.\n\nThen he came up with his principle in buoyancy, that the weight of water displaced equals the weight of the buoyant object.  This has many uses in the calculations of forces and whether or not an object would float. (You would like to know if your boat can float before getting on, wouldn't you?)
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This is a classic problem from hydrodynamics textbooks. The short answer is, it is approximately simple harmonic motion. You can compute the restoring force caused by the displacement of the liquid if you depress a floating boat (Archimedes principle) and that then, balanced with the weight of the boat, creates the conditions for simple harmonic motion. You can approximate the period and amplitude of motion etc. \n\nHowever it gets more complicated than this of course:\n\na. There are damping forces caused by the motion of the boat through the water and the air\n\nb. The water is not completely incompressible, and the density of the water varies some with depth (a tiny effect)\n\nc. There are surface tension effects and entrainment effects\n\nd. The motion of the boat will be more complicated than simple linear motion in one dimension\n\ne. There will probably be deformation effects on the boat, changing its shape\n\nf. gravity is not constant as the boat is moving up and down a small distance in a gravity gradient\n\nand so on. \n\nHowever, the REASON that sines and cosines are so prevalent everywhere in physics is because simple harmonic motion is such a good approximation for so many things. \n\nWhy is this?\n\nWell consider Newton's Second law: F=ma, where F is force, m is mass and a is acceleration. Newton's second law is not always true, in the quantum world and in relativistic situations, but it is true under many conditions, so it is a good place to start. \n\nIn general, the force F will be some sort of nonlinear function of position x:\n\nF=F(x)\n\nHowever, if x is small, then we can approximate F(x) by a McLaurin series:\n\nF ~ F(0) + x F'(0) + h.o.t. \n\n(h.o.t. is a common acronym for higher order terms).\n\nThis then produces the equation for simple harmonic motion, when substituted into Newton's 2nd law:\n\nF(0) + xF'(0) = m d/dt(d/dt(x))\n\nMany other equations in physics like Schrodinger's equation, or wave equations with forcing, or the heat equation, or the inhomogeneous Laplace's equation include 2nd order derivatives, and can similarly be put in some form where simple harmonic motion is the result. So as strange as it seems when you are just learning about SHM in physics, it really is everywhere in all kinds of unexpected places! \n\n\nOne of my favorites is the waves of heat and cold that are travelling down into the earth from the seasonal forcing produced at the surface. Drilling down, one can observe these waves of hot and cold (with some diffusion) going back many years.
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Buoyancy is a force.  Density is the ratio of an objects mass to volume (D=m/v).\n\nThe buoyancy force exerted on an object is dependent on the amount of (for lack of a better work) "stuff" it displaces.\nFor example, a ship floating in the water floats because the weight of the water it displaces is greater than its own weight.  Likewise, a balloon filled with Helium will float because the weight of the air it displaces it more than its own weight.
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Gravity is the force of attraction between massive particles. Weight is determined by the mass of an object and its location in a gravitational field. While a great deal is known about the properties of gravity, the ultimate cause of the gravitational force remains an open question. General relativity is the most successful theory of gravitation to date. It postulates that mass and energy curve space-time, resulting in the phenomenon known as gravity.\n\nGravity is acceleration.  means that (if the mass is unvarying) there must be a force that causes a mass to accelerate. For a rocket ship, that is the rocket engine. For the earth, it is the compression of the mass between something on the surface of the earth and the earth's center of mass. The acceleration is in relation to spacetime in that the weight one feels is one's resistance to deviating from one's path in spacetime. The same holds true in the rocket ship except that a rocket engine supplies the force to accelerate an occupant from his spacetime path. There is no difference between the weight he feels because of gravity or the rocket.
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Center of gravity\nTo study bases of mechanics, we recommend you to choose one of the following web sites.\nIf you need to explain some mechanical variable, you can use this dictionary. \n\n\nGO TO THIS SITE IT WILL HELP YOU OUT http://guardian.curtin.edu.au/cga/teach-in/kinematics.html\nIf you want to define total centre of gravity of a person, you must know:\n\nthe mass of each body segments \nthe x,  y and z coordinate  of centre of gravity of each body segment (3D motion) \nThe equation for x and y coordinates of total centre of gravity is following:\n\n\n  ,  ,  , ,\nwhere  xT, resp. yT, resp. zT is coordinate of  human body\nmi are masses of particular segments\nxi, resp. yi, resp. zi are coordinates of centres of gravity of particular segments.\n\nTry a nice applet dealing with centre of gravity  - or another one (centre of gravity, stability and lability of the system)\n\nThe centre of gravity of human body varies (for example according to sex - females = larger pelvis => c.g. lays lower then males, baby has greater head with comparison of other parts of body =>c.g. lays upper), see picture\n\nChapters:\nCentre of gravity - calculation
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My understanding is that air has mass - more pressure in a chamber would mean more air - therefore, moving mass (or pressure) from one portion of the sealed vessel to another would shift the mass, be it ever so slightly. This would not affect the bouancy of the vessel, but may change its orientation ever so slightly. Anogulous to being in a boat and moving from the front to the back - the back would drop slightly, and front would raise slightly. \n\nHowever, as stated, the buoyancy of the "entire" vessel would not be affected.
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Hello,\nDensity is mass per unit volume.  The density of fresh water is one gram of mass per cubic centimeter.  Since, the ocean water has salt in it, there is more mass per cubic centimeter of salt water.  If you think about a glass full of fresh water and a glass full of salt water, you can easily see that the glass full of salt water has a lot more material(mass) per cubic centimeter than the fresh water does.  So the glass full of salt water (or the ocean)is more dense than the glass full of fresh water.\nAnd that affects a boat by making it float higher.  When an object is placed in water, it displaces as much mass of water as is contained in the object.  Again you can think of a glass of water.  If the glass is filled to the top and you place an object of mass M-grams in the glass, then the amount of water that spills out is M-grams.  The object displaces the mass of the water by sinking into the glass.  Once it has displaced M-grams of mass, it can't displace any more, therefore it will stop sinking as soon as it displaces M-grams.  So since each cubic centimeter of salt water is made up of more mass than fresh water, the object will displace less cubic centimeters of salt water than of fresh water, so it will float higher.
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p=F/A \n\nSo, you have the pressure of the atmosphere pluss the weight of the water above you.  Which is usually figured as a cylinder.  Hope that helps.
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An object will float in water if its density is less than the density of water.  Solid steel is more dense than water so it sinks.\nA steel boat is hollow and filled with air.  Its average density is less than a solid piece of steel.  If this average density is less than water the boat will float.  Of course if the boat becomes swamped  (filled with water) then the average density increases and the boat sinks.
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Centrifugal force and gravity.
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Here you go ...\n\na)  The idea of buoyancy was summed up by Archimedes, a Greek mathematician, in what is known as Archimedes Principle: Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. \n\nb)  DENSITY is a physical property of matter, as each element and compound has a unique density associated with it. Density defined in a qualitative manner as the measure of the relative "heaviness" of objects with a constant volume.\n\nFor example: A rock is obviously more dense than a crumpled piece of paper of the same size. \nA styrofoam cup is less dense than a ceramic cup.\n\nDensity may also refer to how closely "packed" or "crowded" the material appears to be - again refer to the styrofoam vs. ceramic cup. \n\nc)  Low pressure areas have less atmospheric mass above their location, whereas high pressure areas have more atmospheric mass above their location. Similarly, as elevation increases there is less overlying atmospheric mass, so that pressure decreases with increasing elevation.  As elevation increases, the number of molecules decreases and the weight of air therefore is less, meaning a decrease in air pressure. In fact, while the atmosphere extends more than 15 miles (24 km).\n\nI hope this helps.
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The standard definition of floating was first recorded by Archimedes and goes something like this: An object in a fluid experiences an upward force equal to the weight of the fluid displaced by the object. So if a boat weighs 1,000 pounds (or kilograms), it will sink into the water until it has displaced 1,000 pounds (or kilograms) of water. Provided that the boat displaces 1,000 pounds of water before the whole thing is submerged, the boat floats.\n\nIt is not very hard to shape a boat in such a way that the weight of the boat has been displaced before the boat is completely underwater. The reason it is so easy is that a good portion of the interior of any boat is air (unlike a cube of steel, which is solid steel throughout). The average density of a boat -- the combination of the steel and the air -- is very light compared to the average density of water. So very little of the boat actually has to submerge into the water before it has displaced the weight of the boat.\n\nThe next question to ask involves floating itself. How do the water molecules know when 1,000 pounds of them have gotten out of the way? It turns out that the actual act of floating has to do with pressure rather than weight. If you take a column of water 1 inch square and 1 foot tall, it weighs about 0.44 pounds depending on the temperature of the water (if you take a column of water 1 cm square by 1 meter tall, it weights about 100 grams). That means that a 1-foot-high column of water exerts 0.44 pounds per square inch (psi). Similarly, a 1-meter-high column of water exerts 9,800 pascals (Pa).\n\nIf you were to submerge a box with a pressure gauge attached (as shown in this picture) into water, then the pressure gauge would measure the pressure of the water at the submerged depth:\n\n\nIf you were to submerge the box 1 foot into the water, the gauge would read 0.44 psi (if you submerged it 1 meter, it would read 9,800 Pa). What this means is that the bottom of the box has an upward force being applied to it by that pressure. So if the box is 1 foot square and it is submerged 1 foot, the bottom of the box is being pushed up by a water pressure of (12 inches * 12 inches * 0.44 psi) 62 pounds (if the box is 1 meter square and submerged 1 meter deep, the upward force is 9,800 newtons). This just happens to exactly equal the weight of the cubic foot or cubic meter of water that is displaced!\n\nIt is this upward water pressure pushing on the bottom of the boat that is causing the boat to float. Each square inch (or square centimeter) of the boat that is underwater has water pressure pushing it upward, and this combined pressure floats the boat.
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According to Archimedes Principle, the upthrust force on a body totally or partially immersed in a fluid is equal to the weight of the fluid displaced by the body. \n\nImagine a ship that has a weight of 2,000,000 N.  A large crane is lowering it into the water.  When a part of the keel is submerged, it displaces, say 500,000 N of water.  There is still a net downwards force of 1,500,000 N.  If lowered further, more water is displaced, and therefore the upward force increases, while the net downward force decreases.  There comes a time when the ship, as it continues to be lowered, has displaced 2,000,000 N of water.  What then?  The upward force just balances the weight of the ship, and it sinks on further into the water.\n\nIncidentally, a needle does not always sink in water.  Smear it with oil and gently lower it in a bowl of water.  It floats!!!  Of course, this has nothing to do with Archimedes Principle but rather with the surface tension of the water molecules.