The Archimedes principle

Wilfredo Feliciano

King Hiero II gave a goldsmith pure gold to build a crown for him, but the king had suspicious that the goldsmith was being dishonest and had mix silver with the gold to keep some of the  gold to himself. The king then asked Archimedes if he could find a way to determine if the crown had some silver without damaging the crown itself. Because the crown was a holly object that was dedicated to the gods. In that time it was a difficult task because if he wanted to compare its density he needed to know the volume of the crown, since density is equal to mass divided by volume. Archimedes needed to figure out a way to determine the volume of the crow itself in order to answer the king’s question but that was a very difficult task because the crown is an irregular object.

The story says that one day Archimedes was taking a bath thinking how to solve this problem. He noticed that once he submerges in the tub some water tip out of the tube. That’s when he had a moment of inspiration and realize that the water being displace had to be equal to the volume of his body submerged. Archimedes jumped out of the tub and was so excited he even forgot to put clothes on and wet running into the streets yelling: ‘eureka!’ which is a Greek word for ‘I found it”. The story is not clear in which method was used by Archimedes to actually compare the water displace by the crown and the gold. Vitruvius, a famous Architect and writer described that Archimedes put the same amount of gold given by the king, and known to be pure in a container, then he would replace the amount of gold with the crown itself, and if the crown contained any silver it would cause the water to overflow the container. This method has been criticized because the Archimedes did not have any tools to accurately measure the water, and the difference could be too small to observe.

A possible method, that is more realistic as the one describe by Vitruvius, is to balance the amount of gold, equal to what the king gave to Archimedes, with the crown itlsef, and the submerged both in water. If the crown and the gold remain balanced, then it the crown was made off of pure gold, but if it tilted to the direction of the gold then the crown would have greater volume and there for less density than the gold. 

The important part was the principle itself that was later called: “The Archimedes principle” which says that an immersed object is buoyed up by a force equal to the weight of the fluid it actually displaces. This shows how just a moment of enlighten could clear the mind to allow for some critical thinking, such that would eventually become a Law of physics just like this example of Archimedes. The story concludes that the crown was not of pure gold and the goldsmith was executed by the king. What we know of this story is told by roman author and architect, Vitruvius. Archimedes didn’t actually relate this story. We think that he applied the principle in his treatise “On floating bodies”. In which he describe what we study this semester, the buoyant force.