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The story of leverage
The story of leverage

Archimedes locked himself in a small room and studied "floating bodies" day and night. On this day, a man suddenly broke into the room and shouted as soon as he entered the door: "Oh, dear! Your father used to hide here. The king is mobilizing a large number of troops to look for you all over the city. " Archimedes recognized him as a court minister and thought, something must have happened outside. He immediately picked up the sheepskin manuscript, reached for a small round shell hat, went out with the minister and went straight to the palace.

When they came to the front steps of the palace, they saw all kinds of carriages stopped, and the guards stood in two rows with silver guns and iron helmets. The hall was crowded with civil and military personnel and was silent. The king paced back and forth anxiously on the carpet. Because of the darkness in the temple, the candlestick was lit before dark. There are maps of coastal defense and land warfare on the long table under the lamp. Archimedes looked at all this and knew that the war he was most worried about finally broke out.

It turns out that after the decline of the Mediterranean coast of ancient Greece, the Macedonian dynasty first rose, and then the Roman dynasty rose. After the Romans unified Italy, they expanded westward and met another powerful country, Carthage. From 264 BC to 22/kloc-0 BC, the two countries fought for 23 years, which was the famous "First Punic War" in history, and the Romans won. In 2 18 BC, it was fought for another four years, that is, the "Second Punic War". This time, Carthage captured five Vandoro centaurs by using Hannibal, a strategist from slavery. In this way, the two great powers along the Mediterranean coast fought for several years, and both sides won and lost. On the other hand, Syracuse is a small city-state sandwiched between Bulgaria and Romania. In this long-term war situation, it is often erratic to abandon the weak and attach strength to the two powerful countries by winning or losing. Archimedes was very uneasy about this diplomatic strategy. He warned the king many times not to get into trouble. But now the king is no longer the good friend of Archimedes, Heinino. He is young and ignorant, but he is headstrong. When the Second Punic War broke out, in 2 16 BC, seeing that the Carthaginians were going to defeat the Romans, the king quickly broke with the Romans and made an alliance with the Carthaginians. The Romans were very angry at this move. Now the Romans won the battle again, so they took revenge and attacked the small city-state from land and sea. The king was afraid of losing his mind. When he saw Archimedes coming in from the outside, he rushed forward and couldn't wait to kneel down to him at once, saying, "Oh, dear Archimedes, you are the smartest person. My late king said when he was alive that you can push the earth! "

Archimedes' idea of promoting the earth was when he was studying in Alexandria. At that time, he was inspired by the boom used by Egyptian farmers to carry water and the crowbar used by slaves to pry stones. He found that the lever can be used to achieve the purpose of saving labor, and found that the longer the distance between the place he holds and the fulcrum, the more labor he saves. From this, he put forward the theorem that the arm of force is inversely proportional to the force (weight). This is the principle of leverage. Using our present expression is: gravity × gravity arm = force × force arm. To this end, he wrote to the then king Heinero: "I can move anything with any weight without blowing off the dust;" Just give me a fulcrum and lever long enough, and I can even push the earth. "But now the little king doesn't know what science is. He only knows how to save his driver with the help of Archimedes' divine power when disaster strikes.

But the Roman army was too strong. When they fight, they form a square. The soldiers in front and on both sides protect their bodies with shields, and the soldiers in the middle put the shields on their heads. As soon as the drums ring, these square teams, like modern tanks, advance step by step to the enemy camp. You can shoot arrows at will without any damage. The Roman army also had particularly strict military discipline. They were found to be running away from the battle, executed immediately, and the soldiers were promoted by meritorious service. When the commander-in-chief returns to Rome successfully, there will be a grand victory ceremony. This army dominates the Mediterranean and is invincible. How can a little Syracuse be ignored? Besides, I've long wanted to settle it completely.

At this time, the Roman consul marcellus's four legions had advanced to the northwest of Syracuse. Now the drums are ringing outside the city, and the sound of killing is deafening. At this critical moment, Archimedes was very dissatisfied with the disaster caused by the king's shortsightedness, but what he did was the most important thing for the country. He glanced at the dull hall, twisted his silver beard and said, "If we rely solely on military power, we will never be the opponents of the Romans. If we can build a new weapon now, we may be able to hold the city for reinforcements. " Hearing this, the king immediately turned grief into joy and said, "My late king said a long time ago when he was alive that everyone should believe everything you said. This guard battle is under your full command. "

Two days later, at dawn, Roman commander marcellus commanded his tight and neat phalanx to attack the moat. Today, armored cavalry are also prepared on both sides of the phalanx, and the strong men in the phalanx carry ladders on their shoulders. Before leaving, Marcellus said, "Break through Syracuse and have lunch in the city." In the shouting and killing, the phalanx slowly moved forward. As a rule, an arrow should be placed on the head of the city. But no one on the wall quietly today. Perhaps the fierce fighting in the past few days has exhausted the ancient Syracuse. The Romans were wondering, there was a faint creak in the city, and then large and small stones flew out of the city. At first, it was as big as a bowl and a fist, and then it became bigger and bigger, like pots and pans, pouring down like a mountain torrent. The stone fell into the enemy's array, and the soldiers quickly raised their shields to protect themselves. Unexpectedly, the stone was so heavy and fast that even the shield and people were smashed into a paste at once. The Romans gradually lost their support and fled for their lives. At this time, the head of the ancient city of Syracuse shot intensive sharp arrows, and the Romans had no shield or armor behind them. Sharp arrows went straight through their backs, crying and crying, very sad.

What secret weapon did Archimedes create to defeat the Romans? It turned out that he made some extra-large crossbows-stone machines. Man couldn't pull such a big bow at all, so he used the lever principle. As long as the crank of the rotating shaft on the crossbow is pulled hard, the tendons connected with the crank tighten the thick bowstring composed of many tendons, and when it is pulled to the tightest, it suddenly loosens, and the bowstring drives the stone transport device to throw the stone high out of the city, which can fall far away. It turns out that this lever principle is not simply to pry things with a straight stick. For example, the shaft of the windlass is its fulcrum, its gravity arm is the radius of the windlass, and its moment arm is the crank, which must be longer than the radius of the windlass, so pumping water will be labor-saving. Archimedes' stone chipper also used this principle. Where did the Romans know that there were so many new things in the ancient city of Silas?

Shortly after Marseille's defeat, the commander-in-chief of the navy, Guludius, also sent a battle report. It turned out that while the army attacked the city from the northwest, the Roman navy also launched an attack from the southeast sea. The Roman navy was not very powerful at first, but later invented a side hook to be installed on the ship. When they meet enemy ships, they hook each other, and soldiers jump on them again, turning naval battles into land battles, which has a certain advantage. Today, in order to deal with Syracuse, Claudius specially wrapped the warship with a layer of armor and prepared a ladder, and ordered the soldiers to move forward only, not backward. Strangely, on this day, the city head of Syracuse was particularly quiet. There is not a single soldier behind the wall, but several wooden shelves stand far away from the city head. When the Roman warships drove to the city gate, the soldiers were preparing to climb the wall by ladder. Suddenly, a chain hung from the wooden frame, and there were iron hooks and claws on the chain head, which hooked the Roman naval warships. No matter how hard the sailors try to paddle, it is in vain. The battleship can't move a step. They cut it with a knife and burned it, and the big chain was intact. Just when the ship was in a panic. I saw the wooden wheel on the big wooden frame "quack" again, and then the chain was pulled tighter and tighter, and the ship was gradually hoisted out of the water. As the hull tilted, the soldiers fell into the sea and the mast was broken. After the hull is hoisted into the air, the big wooden frame will turn left and right, so the warship will swing in the air like a swing, and then some will be thrown onto the wall or rock and become piles of fragments; Some of them hung on the city walls and became trophies of ancient Syracuse. At this time, Syracuse is still very quiet. No one was shooting arrows or shouting. This seems to be an empty city. Only a few monster-like wooden frames stretched out from time to time to hook away the battleship. The Romans looked at the creaking monster, trembling with fear, and their hands and feet were weak. All they heard was a cry on the sea and a cry for help after falling into the water and hitting a stone. Claudius said in the battle report: "We can't see the enemy at all, just like hitting a bucket." These "monsters" of Archimedes originally used the principle of lever and pulley.

After this great war, the Romans lost many weapons and warships in vain, but they didn't even see Archimedes' face.