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# Archimedes' Law

## The force exerted by a fluid on a floating or submerged object is equal to the weight of the water displaced.

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USS Iowa

### USS Iowa

Credit: Expert Infantry
Source: http://www.flickr.com/photos/58297778@N04/5417958112

Above is the USS Iowa firing 50-caliber guns during a 1984 demonstration. It was the only ship of its class to have served in the Atlantic Ocean during WWII. The USS Iowa has a total length of 270 meters and a displacement of 45,000 tons. Between 1942 and 1990, the USS Iowa received nine battle stars for its service in WWII and the Korean War.

#### Amazing But True

• According to the Archimedes' principle, an object placed in a fluid will experience and upward force that is equal to the weight of the fluid that is displaced by the object. For a ship that weighs 45,000 tons to float, it will need to displace 45,000 tons of water. Since the majority of a boat's interior is mostly air, boats are very light considering the average density of water. The actual act of floating has more to do with pressure than weight, which explains why heavy objects that float in water have very large surface areas in contact with the water.
• Credit: Hannes Grobe
Source: http://commons.wikimedia.org/wiki/File:Plimsoll-mark_hg.jpg

Plimsoll marks determine how much cargo a ship can hold [Figure2]

• To help determine whether a loaded boat will float, most commercial ships also have markings called Plimsoll marks to help determine how much cargo the ship can handle. These marks represent where the waterline should be for either fresh water or salt water voyages and allow for proper loading of the ships to ensure that the ship does not float at a dangerously low level.

#### Show What You Learned

Using the information provided above, answer the following questions.

1. An orange is completely submerged in a body of water. If the orange is moved to a point that is 10 m below the point it was initially submerged, how much extra force is needed to hold it in this new position?
2. The pressure at the bottom of a glass of unknown liquid of density 1000 kg/m3 is given as \begin{align*}P_o\end{align*}. If all the liquid is removed and replaced with the same total amount of a different liquid that has half the density, what would you expect of the pressure at the bottom of the glass?
3. Which of the two exerts a great pressure: a 100 lb woman standing on high heeled shoes of diameter 0.5 in or a 1000 lb elephant with a foot diameter of approximately 17.7 in?

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