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Introduce Density Applet and show how Archimedes’ Principle is used to calculate the volume:
To start our exploration, we will observe a phenomenon of fluid mechanics known as Archimedes’ principle. Its definition is that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. Don't worry; this principle will be simplified in the next few paragraphs.
Archimedes of Syracuse noticed that when he stepped into a bathtub of water, the water rose to a level equal to the actual volume of his submerged feet and ankles. He began to drop other objects of known volume into the tub, and noticed the same thing: the volume of the water displaced was identical to the volume of the object itself. He then proceeded to shout “Eureka!” in revelation.
He decided to put this observation to use. He believed the current king was being bamboozled, and that his crown was not actually made of gold. To test this hypothesis, he borrowed the king’s crown and noted the amount of volume it displaced when submerged in water. Knowing the mass of the crown, he was then able to deduce that the density of the crown was far less than the density of genuine gold.
It turned out that the king’s goldsmith had replaced a lot of the king’s crown with more inexpensive silver. As expected, this was shocking to the king, and he immediately squared up with the goldsmith.
If we know the mass and volume of the displaced fluid, we can determine the density of the associated object. We can identify the object by looking up its density.
By applying Archimedes principle, we can work towards determining the construction content of an unknown sample in much the same way that a person can determine if a suspect piece of gold is truly real or fake.
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