How did Archimedes identify a fake crown?

The story took place on the island of Sicily in southern Italy more than 2,000 years ago. On this island, there was the Kingdom of Syracuse. The king of the Syracuse Kingdom was very proud of himself for ruling such a wealthy country.

One day, the king received a group of visiting foreign businessmen. In front of him, these businessmen naturally said a lot of flattery. However, an old businessman said that he did not even have a pure gold crown, and laughed that his clothes were not commensurate with his status. In this regard, the always strong king was very unconvinced. He said: "Isn't it easy to make a gold crown? Please come back in a month, and you can see me wearing a gold crown. "After the foreign businessman left, the king immediately ordered to summon a skilled goldsmith, gave him gold, and asked him to make a pure gold crown, and gave him a month to deliver the finished crown. Come.

The deadline is up. The king was in high spirits and summoned all the civil and military ministers to prepare for the golden crown. Amidst the sound of drums, the craftsman came to the front of the palace holding a shining, exquisite and beautiful crown in his hands. All the civil and military officials present expressed their admiration for the crown. The king was even more happy, and regardless of his usual dignity, he hurriedly stepped down from the throne, took the crown and put it on.

The king liked this crown very much. He would show off the crown to everyone he met, and sometimes let his close associates take a closer look. These cronies felt a little strange when they took over the crown. I always feel that the crown is not made of pure gold, and I thought: "If it is made of pure gold, why is such a big crown not so heavy?"

"Maybe it is only gold on the surface, but adulterated on the inside. ”

“Yes, the goldsmith must have played a trick.”

However, no one could provide any obvious evidence, so no one dared to question the king. speak. But these discussions spread quietly below. Soon, the king found out about all the gossip behind his back. This was terrible, and the king was furious. If the crown is indeed adulterated, the goldsmith deceived the king; if the crown is pure gold, then those who spread "the crown is fake" will become sinners who undermine the king's dignity.

So the craftsman was arrested. The king immediately scolded: "You thief, how dare you steal from my head. Come on, how dare you adulterate my crown? Where did you steal the gold?" The craftsman argued: "I Lord, how dare I steal your gold? If you don’t believe it, please weigh the crown to make sure its weight is exactly the same as the gold I received.”

The crown was placed on the scale. Weighed it. Sure enough, it weighed exactly the same amount of gold as the king had given him. In this way, those who said "the crown is not made of pure gold, it must be adulterated" will become the sinners who slander the dignity of the king. Therefore, everyone around the king was terrified. "But, Your Majesty, the goldsmith may have replaced some of the gold and made it the same weight as the original." "Oh, that's possible. But how do you know? Have you opened the crown and looked inside?" The king said. After saying this, no one dared to say anything anymore.

In fact, at this time, the king seemed to feel that the crown was not so heavy. So, at the minister's request, the minister was given a few days to come up with evidence to prove whether the crown was real or fake.

When the minister was struggling with no solution, someone gave him an idea: "Let's go find Archimedes. Maybe he will have a good idea." Archimedes was a famous man at the time. A scientist who has made many inventions and creations, everyone respects him very much. The minister felt that only by turning to Archimedes could this problem be solved. So they found Archimedes and told him what happened, asking him to help find out the secret of the crown.

Is the crown made of pure gold? Archimedes found it very interesting. This mystery fascinated him deeply. He worked day and night to find a solution. He thought that if the crown was adulterated, it might be silver or copper. The same weight of silver or copper has a larger volume than the same weight of gold.

Now the weight of the crown is the same as that of pure gold. If it is adulterated, the volume must become larger. Unfortunately, the volume of the crown cannot be calculated! Because the crown is not allowed to be damaged at all. This problem made it difficult for him to eat well and sleep poorly. When the family saw him like this, they ordered their servants to accompany him to the bathhouse to take a bath.

Archimedes never stopped thinking along the way. Finally got to the bathhouse. In front of the full pool of hot water, he was still thinking.

When he stepped into the bathtub, he suddenly noticed that when he sank in the bathtub, some of the water overflowed from the bathtub. The deeper the body enters the water, the more water overflows. When the whole body is in the water, the water stops overflowing. At the same time, he felt that his body seemed lighter. This common phenomenon suddenly enlightened Archimedes, who was in deep contemplation. He immediately jumped out of the bath, and the water in the bath immediately became shallower. At this time, he had completely understood: wasn't the volume of the water that just overflowed from the bathtub exactly the volume of his own body?

He was so happy that he didn't even bother to get dressed and ran out of the bath. He was dripping wet and shouted as he ran home. Get home and start experimenting right away. Two pieces of copper and silver of equal weight were prepared, and two equally large basins were filled with water. Then, he put the copper block and the silver block into two basins respectively, and found that the basin with the copper block overflowed with more water, while the basin with the silver block overflowed with less water. In this way, Archimedes was well prepared for the difficult problem of testing whether the crown was adulterated.

Archimedes found the minister, who took him to the palace to meet the king and said to the king: "Archimedes is an outstanding scientist in our country. He has a way to test whether the crown is adulterated." False." The king asked Archimedes: "Can your method ensure that my crown is not damaged?" Archimedes answered in the affirmative.

In front of the king and ministers, Archimedes immersed gold nuggets and crowns of the same weight into basins filled with water, and then compared the water overflowing from them. It was found that the basin with the crown overflowed with much more water than the basin with the pure gold. After Archimedes took the crown out of the water, he clearly told the king: "The crown is adulterated." The king and ministers did not understand the reason and looked at Archimedes with doubts.

Archimedes asked people to bring two wooden blocks and iron balls of the same weight, and asked the people around him: "Which of them is larger?"

"Of course The wooden block is big. "

"So, which one will discharge more water when they are completely immersed in water?"

"Of course the wooden block will discharge more water."

At this time, everyone suddenly realized. Understand the reason: when an object is immersed in water, part of the water must be discharged. If an object is completely immersed in water, the volume of water displaced by it is equal to the volume of the object. A piece of gold and a piece of adulterated gold of the same weight have different volumes. Therefore, the volumes of water that overflow when they are immersed in water are also different. If the crown were made of pure gold, its volume would be equal to the volume of the same weight of gold, and the volume of water that would escape from it when it was immersed in water would be the same as the volume of water that would escape from the same weight of gold. Since the result of the experiment is that the basin with the crown overflowed with much more water than the basin with the gold nuggets, the conclusion that the crown is not made of pure gold is certain.

The mystery of the crown was finally revealed by Archimedes, and the king praised Archimedes. Needless to say, the craftsman who dared to play tricks on the king was severely punished.

From our perspective today, this problem is very simple: just weigh the crown and divide it by the weight of the same volume of water to find the specific gravity of the crown; In the basin of water, measure or weigh the water that overflows, and you can get the weight of the same volume of water as the crown. This is nothing more than doing an uncomplicated middle school physics experiment. However, at that time, physics could be said to have just seen a glimmer of light. It was not easy to carry out such pioneering work! Archimedes thought day and night and racked his brains in order to measure the proportion of the king's crown. Archimedes considered measuring specific gravity. The known gravity of gold at that time was 19.3.

If the specific gravity of the crown is not 19.3, it proves that the gold is mixed with other things.

After Archimedes solved the mystery of the crown, he continued to study liquids. It was found that after an object is immersed in a liquid, it is acted upon by an upward force, which is the buoyancy force. Through the study of buoyancy, he summarized the famous Archimedes' law.

Knowledge Point Archimedes’ Law

Archimedes’ Law is a basic principle of mechanics. An object immersed in a liquid experiences an upward buoyant force equal to the weight of the liquid displaced by the object. This law applies not only to liquids, but also to gases.