The first time I came across the word eureka was in my secondary school days during one of our weekly physics classes. Physics happened to be one of the subjects I loathed the most back then. But as a science student, I had no option but to trudge along in trying to understand, if only just enough to pass it. However, this particular class was perhaps the most interesting class I have ever had in physics.
Good morning class! The physics teacher entered and greeted us as usual.
Good morning sir! The class chorused.
The tone of the greeting by the teacher gave off an indication that the class for the day would be different. While I was still wondering what trick the teacher might have up his sleeve this time, he truncated my thought:
Today, we are going to talk less about physics and more of a story.
Did I just hear a story? Please bring it on! I readjusted my seat to pay proper attention. As a 14-year-old teenager, reading or listening to stories was one of my best hobbies. I could finish a 500-page novel within 24 hours and can do so without batting an eyelid throughout the night.
There was once a powerful king in the old Greek empire who decided to make a crown for himself. He took out a good quantity of gold and gave it to one of the most famous blacksmiths in the empire to make him a crown like no other. The goldsmith accepted the offer and brought the final product within a few days.
The king assessed the final product and felt some tinges of discontentment. Something seemed amiss to him but he could not just pick it. He thanked the goldsmith, paid him his due but kept the discontentment thought to himself so as not to sound ungrateful.
After a few days of deep thought and a strong feeling of being cheated, the king decided to give the assignment of finding out what is wrong with the crown to Archimedes who happened to be one of the greatest scientists around back then. The king felt that the crown is substandard when compared to the amount of gold he gave to the goldsmith. Archimedes accepted the challenge, even though he was not certain how to go about it.
Archimedes pondered on how to go about the task for days without arriving at any obvious solution. Then an inspiration came to him while trying to get into the bathtub in his house one afternoon. The tub was filled to the brim with water which kept on splashing to the floor the more he tried to inundate his body in the water. All of a sudden, he ran out of his house and into the street shouting Eureka! Eureka! I have found it!!
Onlookers initially thought Archimedes was running amok until he found his way to the palace of the king and explained himself. Here is where the physics comes in -
The entire class groaned in discontentment. We were all deeply immersed in the story we forgot that there would be a physics part to it as stated earlier. We all wanted to know where the story would end.
The teacher continued.
Archimedes discovered that the more he inserted his body into a tub filled with water, the more the water that was displaced. He reasoned that if he can measure the volume of water displaced from the tub by his full body, it should equate to the volume of his body - a thought that is technically and scientifically true.
Archimedes also knew that people or objects of the same weight can have different volumes. For example, 1 g of stone and 1 g of cotton wool would displace different volumes of water from a vessel filled to the brim with water. This is also a truism.
Following these thoughts, Archimedes knew that if he knows the weight of the original gold given to the goldsmith, he can take the same quantity of gold, determine the amount of water it will displace from a filled vessel, and then compare it to the amount of water that would be displaced from the same filled vessel by the newly-designed crown.
At this junction, the entire class gave a round of applause. Everyone now understands why Archimedes was so excited that he had to run around like a mad man. The manner with which he was able to solve what seemed like a complex case deserves to be celebrated.
What Archimedes worked with to solve the case was the density of objects. The density of objects is given as:
Density = mass/volume .............. (1)
Of course, the mass of an object is directly proportional to its weight. From the equation (1) above:
the volume of an object = mass/density ............(2)
From equation (2), it means that the more the density of an object, the lesser the volume. In other words, the volume of an object is inversely proportional to its density. This means that an object of 1 kg with a density of 0.5 will have more volume than another object of the same weight but with a density of 1.
Ok. So the king was suspicious that the crown he was presented has been adulterated. Archimedes took the same amount of gold given to the goldsmith and determined the volume of water it displaced. He then determined the volume of water displaced by the crown itself and found out that it displaced more water than the gold. Upon further investigation, including the quizzing of the goldsmith, they found out that the gold was adulterated with silver during the preparation of the crown.
This is as simple as physics can get, I thought deeply. If only every topic would be explained by storytelling. I was reveling in the spur of the moment when the physics teacher's voice jostled me back to life.
Any question on density?
I have never asked a question in physics class because I have never been interested enough. I decided to ask one this time:
Sir, what eventually happened to the goldsmith?
Go and find out as your assignment. The teacher responded.
Not really the answer I wanted to hear but it did not matter. I more than satisfied with the class and I grinned all day.
It was my own Eureka moment.