1. Buoyancy and Archimedes Principle
A little history…
In the first century BC, the Roman architect Vitruvius related a story of how Archimedes, the Greek scientist, discovered that a goldsmith had tried to cheat King Hiero II…
The king had given the goldsmith a particular amount of gold to melt down and make into a crown. When the crown was made and returned to the king, the king was suspicious that the goldsmith had stolen some of the gold and replaced it with an equal weight of silver.
The king turned to Archimedes for help…
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In Vitruvius’s own words:
"Archimedes happened to go to the bath, and on getting into a tub observed that the more his body sank into it the more water ran out over the tub. 
As this pointed out the way to explain the case in question, he jumped out of the tub and rushed home naked, crying with a loud voice that he had found what he was seeking; for he, as he ran, shouted repeatedly in Greek,
‘Eureka, Eureka.’ meaning ‘I have found (it), I have found (it)’.”
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So, what, exactly, had he found?
He realized that if the bath were completely filled in the beginning, the volume of water that would overflow (that was displaced) would have to equal the volume of the person or object placed into the water!!
He now had a way to measure the volume of the irregularly-shaped crown…
He discovered that the crown displaced more water than a chunk of gold of equal weight did. Its volume was greater because it contained some silver, a metal less dense than gold!!
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Imagine a very light, thin-walled sack filled with water that is in equilibrium in a pool.
Clearly, there must be an _______ force exerted on the sack to balance its weight (the pull of gravity down)
upward
This upward force is actually the vector sum of all the forces acting on the object due to the surrounding water, and is called the _________ force.
buoyant
Pressure is greater on bottom of sack!
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7. Archimedes’ Principle
The magnitude of the buoyant force is given by Archimedes’ Principle. It states that… A body fully or partially submerged in a fluid is “buoyed up” by a force that is equal to the _______ of the ___________________.
weight
displaced fluid
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An Example:
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9. How do boats/ships float?
Obviously the density of a metal rowboat or a “concrete canoe” is greater than the density of water, but they float because they contain a large amount of empty space. Because of their _______, they displace enough water to balance their own weight.
shape
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10. How much water is actually needed to float a ship?
Not as much as you’d think!!!...
Imagine that the canal is filled with water, and then the ship is slowly lowered into the canal. If the shape of the canal exactly matches the ship, and if the canal is slightly larger than the ship, then all but a thin layer of water all the way around will be displaced. So…. this thin layer between the ship and the canal is really all that is necessary!!
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11. How do Submarines Dive & Surface?
Does the buoyant force change? ____!
A sub has “ballast tanks” that can be filled with _______ or _____.
To dive, a sub must become heavier, so the tanks allow _______ in while venting ____ out.
To surface, a sub must become lighter. A supply of compressed air on the sub is used to force ______ back out of the ballast tanks. NO
water
air
water
air
water
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13. Water Bridge in Germany
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Six years to build it, 500 million euros later, and 918 meters long.....
This is a channel-bridge over the River Elbe and joins the former East and West Germany, as part of the unification project. It is located in the city of Magdeburg, near Berlin. The photo was taken on the day of inauguration. Did this bridge have to be designed to withstand the additional weight of ship and barge traffic, or just the weight of the water?
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Answer: It only needs to be designed to withstand the weight of the water! 
Why?  
A ship always displaces an amount of water that weighs the same as the ship, regardless of how heavily a ship may be loaded.
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