Bouyancy

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Bouyancy is a principle that is often overcomplicated by the student. I remember as a student I over thought the principle of buoyancy all the time. The best example to illustrate this principle are ones that involve objects floating in or on top of water. Water is a substance that will appear time and time again and it is worth while to not that it has a density of  !! 1000kg/cm^3 or 1kg / L !!

When an object is resting in or on top of water it will have two forces acting on it: gravity and buoyancy. The gravitational force is the mass of the object times the gravitational constant. The bouyant force is the volume of the body that is below the surface of the water (the water displaced). This is clear in the image above, take a moment to wrap your head around the idea of displaced water. As you can see if the object is place on the surface of the water and released it will sink into the water until the volume of water it dispaces has an equivalent mass to the mass of the object. It can also be helpful to think of why there is a buoyant force. Water at the top of the container is pushed on by the column of air above it, while water at the bottom of a glass must be exert an upwards force to support the weight of both the column of air and the water above it. When applying this to an object submerged in water (either partially or completely) the pressure in the water is different from the most submerged part compared to the least submerged part. As such, the net pressure difference pushes up on the object at the more submerged point(s) thereby supporting the weight of the object. As such, objects appear to have less weight in water than air. The buoyant force can also be thought of as derived from Newton's third law (i.e. equal/opposite forces). The force of gravity of a mass pushes down, displacing a volume of water equal to the volume of your mass. However, the displaced water (or other substance) will exert an EQUAL and OPPOSITE force, thereby pushing the object up. Even objects which sink to the bottom of a container will appear "lighter" when weighed on a scale (eg. often measured by the tension of a string it is suspended on) since the object still displaces a certain volume of water.

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As seen in the photo above, water and ice have nearly the same density but ice is slightly less dense. The result is that a volume of water almost equal but slightly less than the volume of the ice cube needs to be displaced in order for the bouyant force to equal the gravitational force on the ice cube.