What Are the Different Types of Levers in the Human Body?

The ancient Greek scientist Archimedes has a well-known saying: "If you give me a fulcrum, I can move the earth!" This sentence has strict scientific basis.

Leverage theorem

The principle of leverage is also known as the "lever balance condition". To balance the lever, the two forces (power point, fulcrum point and resistance point) acting on the lever are inversely proportional to their force arms. Power × power arm = resistance × resistance arm, expressed by algebraic formula as F1 · L1 = F2 · L2. In the formula, F1 represents power, L1 represents power arm, F2 represents resistance, and L2 represents resistance arm. As can be seen from the above formula, in order to balance the lever, the power arm is several times the resistance arm, and the power is a fraction of the resistance.

The ancient Greek scientist Archimedes has a well-known saying: "If you give me a fulcrum, I can move the earth!" This sentence has strict scientific basis.

Archimedes first proposed the principle of leverage in his book "On the Balance of Planar Graphics". He first took some of the empirical knowledge in the practical application of leverage as "self-evident axioms", then proceeded from these axioms, and used geometrical theory to rigorously logically demonstrate the principle of leverage. These axioms are: (1) hanging equal weights at equal distances from the fulcrum at both ends of the weightless rod, and they will balance; (2) hanging at equal distances from the fulcrum at both ends of the weightless rod Unequal weight, the heavy end will tilt downwards; (3) Equal weight will be hung at the unequal distance between the two ends of the rod without weight, and the far end will tilt downward; (4) the role of a heavy object It can be replaced by several uniformly distributed weights, as long as the position of the center of gravity remains the same. Instead, several evenly distributed weights can be replaced by a weight suspended from their center of gravity (5) The centers of gravity of similar figures are distributed in a similar way ...

It is from these axioms that based on the "center of gravity" theory, Archimedes discovered the principle of leverage, that is, "the distance between the fulcrum and the weight is inversely proportional to the weight when the dual objects are balanced. The research is not only on the theoretical side, but also a series of inventions based on this principle. It is said that he used the levers and pulleys to make the mast parked on the beach smoothly launch into the water, and defended Suragu from the Roman navy. During the attack, Archimedes used the principle of leverage to create long-range and short-range trebuchets, and used it to launch various missiles and boulders to attack the enemy. He had blocked the Romans outside the ancient city of Syrah for three years.

When using a lever, in order to save effort, you should use a lever with a power arm longer than the resistance arm; if you want to save distance, you should use a lever with a power arm shorter than the resistance arm. Therefore, the use of leverage can save effort and distance. However, if you want to save effort, you must move more distance; if you want to move less, you must work harder. It is impossible to save effort and move distance. It is from these axioms that based on the "center of gravity" theory, Archimedes discovered the principle of leverage, that is, "the distance between the fulcrum and the weight is inversely proportional to the weight when the dual objects are balanced."

The fulcrum of the lever does not have to be in the middle. A system that meets the following three points is basically a lever: a fulcrum, a force point, and a force point.

The formula is written as follows: distance from fulcrum to force point (moment) * force = distance from fulcrum to force point (arm arm) * force, this is a lever.

There are also labor-saving levers and labor-intensive levers, both of which have different functions. For example, there is a pump with a foot or a juicer pressed by hand, which is a labor-saving lever (force arm> torque); but we have to push down a large distance, and there is only a small movement at the end of the force. There is also a laborious lever. For example, a roadside crane, the hook for fishing is at the tip of the entire rod, the fulcrum is the fulcrum, and the hydraulic machine is in the middle (torque> force arm). This is a laborious lever. Distance, the tip hook will move a considerable distance.

Both types of levers are useful, except where they are used to assess whether it is labor-saving or range of motion. There is another kind of thing called wheel axle, which can also be regarded as a kind of lever application, but the performance may sometimes need to be added to the calculation of rotation.

The ancient Greek scientist Archimedes has a famous saying that goes through the ages: "If you give me a fulcrum, I can move the earth!" This sentence is not only an inspiring aphorism, but also has a strict scientific basis.

Leverage can be divided into labor-saving levers, labor-intensive levers, and equal-arm levers. These types of leverage have the following characteristics:

1. Labor-saving lever: L1> L2, F1 <F2, labor-saving and distance-consuming. Such as claw hammers, trowels for pulling nails, bottle cap wrenches, etc.

2. Laborious lever: L1F2, laborious and distance saving, such as fishing rod, tweezers, etc.

3 Equilateral arm levers: L1 = L2, F1 = F2, neither effort nor effort, nor much distance to move, such as balance, fixed pulley, etc.

Leverage is indispensable in almost every machine. Even in the human body, there are many levers at work. Picking up something, bending down, and even tilting your toes are all levers of the human body at work. Understanding the levers of the human body can not only increase physical knowledge, but also learn a lot of physiological knowledge.

Most of them are labor-intensive levers, and a small number are equal-arm and labor-saving levers.

Nodding or raising your head is based on the lever (see picture). The fulcrum of the lever is at the top of the spine, there are muscles before and after the fulcrum, and the weight of the skull is resistance. The muscles before and after the fulcrum are matched, and some are contracted and some are elongated to form a bowed head. It can be seen from the figure that lowering the head is more labor-saving than lifting the head.

When the elbow lifts a heavy object, the arm is also a lever (pictured). The elbow is the fulcrum, with muscles to the left and right. This is a labor-intensive lever. Lifting a share of weight requires 6 times more energy for muscles. Although laborious, it can save a certain distance.

When you tilt your toe up, it is the muscles behind the heel that are acting, the toe is the fulcrum, and the weight falls between the two. This is a labor-saving lever (pictured), the muscle pull is less important than the body. And the longer the feet, the less effort.

If you bend down, your muscles will pull about 1200 Newtons. This is because the lever formed between the lumbar muscles and the spine is also a laborious lever (see picture). So when bending over to lift the standing object, the correct posture is to make the weight as close to the body as possible. To avoid strained muscles.

Archimedes first proposed the principle of leverage in his book "On the Balance of Planar Graphics". He first took some of the empirical knowledge in the practical application of leverage as "self-evident axioms", then proceeded from these axioms, and used geometric theory to rigorously demonstrate the logic, and then came to the principle of leverage. These axioms are: (1) hanging equal weights at equal distances from the fulcrum at both ends of the weightless rod, they will balance; (2) hanging at equal distances from the fulcrum at both ends of the weightless rod Unequal weight, the heavy end will tilt downwards; (3) Equal weight will be hung at the unequal distance between the two ends of the rod without weight, and the far end will tilt downward; (4) the role of a heavy object It can be replaced by several uniformly distributed weights, as long as the position of the center of gravity remains the same. On the contrary, several evenly distributed weights can be replaced by a weight suspended from their center of gravity; the center of gravity of the graph-like distribution is similar ... It is from these axioms, based on the "center of gravity" theory Archimedes also discovered the principle of leverage, which is "the distance between the fulcrum and the weight is inversely proportional to the weight when the two weights are balanced."

Archimedes' research on leverage is not only in the theoretical aspect, but also in a series of inventions based on this principle. It is said that he used the lever and pulley block to launch the mast parked on the beach smoothly. In the battle to defend Syracuse from the Roman navy, Archimedes used the principle of leverage to create long-range and short-range slingers, and used it to launch various missiles and boulders to attack the enemy. He once blocked the Romans in Syrah Outside the ancient city for 3 years.

It should also be mentioned by the way that there have been long records of leverage in our history. The Mohists of the Warring States Period once summarized the laws in this respect, and in the "Mo Jing" there are two special records of the principle of leverage. These two are very comprehensive about the balance of leverage. There are equal arms and unequal arms; there are those that change the weight of the two ends to make it deflect, and there are those that change the length of the two arms to make it deflect. Such records are also very valuable in the history of world physics, and

Archimedes locked himself in a hut, and buried his head around the clock to write "Floating Body Theory" day and night. This day suddenly broke into a person, as soon as he entered the door, he shouted: `Oh! Your old gentleman was hiding here. The king is mobilizing a large number of men and horses, looking for you all over the city; 'Archimed recognized him as the court minister and thought, something must have happened outside. He immediately picked up the sheepskin manuscript, reached out and grabbed a round shell cap, went out with the minister, and went straight to the palace.

When they came to the front steps of the palace, they saw a variety of carriages stopped, guards with silver guns and iron helmets, standing in two rows, the hall was full of civil and military, and the crows were silent. The king was pacing anxiously on the carpet. Due to the darkness in the temple, a tall candlestick was lit before it was dark. Under the lights, there is a sea defense map and a land defense map. Archimedes looked at all this and knew that the war he was most worried about finally broke out.

It turned out that after the decline of ancient Greece along the Mediterranean coast, the rise of the Macedonian dynasty first, the decline of the Macedonian dynasty, and then the rise of the Roman dynasty. After the Romans unified Italy, they expanded westward and met another powerful country, Carthage. From 264 BC to 221 BC, the two countries fought for 23 years. This was the famous 'First Punic War' in history. The Romans won. After another four years in 218 BC, this is the 'Second Punic War'. This time Carthage started Hannibal, a military man who was a slave, and captured more than 50,000 Romans in one fell swoop. The two great powers along the Mediterranean coast have been fighting for years, and both sides have won and lost. Syracuse, on the other hand, is a small city-state between the two great powers, Jia and Luo. In this kind of long-term war, the weak and powerful are often abandoned with the victory and defeat of the two powerful powers. Archimedes was very uneasy about this diplomatic strategy, and has repeatedly warned the king not to cause trouble. But the current king is no longer Archimedes's friend Heinlow. He was ignorant when he was young, but he was just used for his own purposes. When the Second Punic War broke out, in 216 BC, seeing that the Carthages were about to defeat the Romans, the king soon broke with the Romans, forming an alliance with the Carthages, and the Romans opposed This is annoying. Now that the Romans had won the battle again, they took revenge and attacked this small city-state from both the sea and the land. The king was frightened. When he saw Archimedes coming in from the outside, he rushed forward, and wished to kneel immediately to him, and said: `Ah, dear Archimedes, you are the smartest man, and said before the king was alive You can push the earth. '

The claim that Archimedes pushed the earth was still something he had done while studying in Alexandria. At that time, he was inspired by the lifting rods used by Egyptian farmers to lift water and the crowbars used by slaves to pry stones, and found that a lever could be used to achieve labor-saving purposes. , The more effort you save. Therefore he proposed such a theorem: the relationship between the arm and the force (weight) is inversely proportional. This is the principle of leverage. Expressed in our current expression: weight × heavy arm = force × force arm. To this end, he wrote to the then king Heinlow: "I can move anything of any weight without any effort; just give me a fulcrum and give me a lever that is long enough. I even have the earth Can be promoted. 'But now this little king doesn't know what science is, he only knows that when the calamity is approaching, he will use the power of Archimedes to save him.

But the Roman army was too powerful. When they battled, they formed a squadron. The soldiers on the front and sides guarded their shields. The soldiers in the middle held their shields on their heads. When the drums rang, each team was like a modern tank, marching toward the enemy camp. Push forward step by step, even if you shoot arrows indiscriminately; The Roman army also had a particularly strict military discipline. When it was found that it was fleeing, it was immediately executed. The soldiers were promoted. When the commander returned to Rome to win a grand triumphal ceremony. This army dominates the Mediterranean, and it is invincible. Where is a little Syracuse? Moreover, the old hate the new hatred, long ago wanted to conduct a complete liquidation. At this time, the four army regiments commanded by Roman consul Marcelas had advanced to the northwest of the ancient city of Syrah. Now the drums are ringing outside the city. At this critical juncture, although Archimedes was very dissatisfied with the calamity caused by the shortsightedness of the king, but the wood was a boat and the country was the most important thing. Military strength, we are by no means the opponents of the Romans. Now if we can create a new type of weapon, we might still be able to defend the city and wait for reinforcements. 'When the king heard this, he immediately turned his sorrow into joy and said: `The king first said it when he was alive. Everyone you say must believe it. You are in charge of this guard battle. '

Two days later, just after dawn, Roman captain Marcelas directed his tightly-formed square array towards the moat. Today, both sides of the Phalanx also prepared iron cavalry, and the strong soldiers in the Phalanx carried shoulder ladders. Before leaving, Marcelas yelled: `Break through Syracuse and have lunch in the city. 'In the shout, the matrix slowly moved forward. As usual, it's time to throw an arrow over the city. But today the city wall was quietly missing a person. Perhaps the fierce battles in the past few days have exhausted the Syrians. The Romans were wondering. There was a squeaking noise in the city, and then large and small stones flew over the city. At the beginning, the size was like a bowl, and it grew bigger and bigger, just like a pot. , Pouring down like a torrent. The stones fell in the enemy's formation, and the soldiers quickly raised their shields. Who knew that the stones were heavy and the speed was swift. All of a sudden the shield and people were smashed into a ball of meat. The Romans were gradually unable to support them, and they crawled to escape. At this time, the city of Syracuse fired another dense arrow, and the Romans did not have shields and iron armor behind it. The arrow went straight through the back of the thigh, crying and crying, it was miserable.

What secret weapon did Archimedes create that made the Romans defeat? It turned out that he had made some very large crossbow bows-stone machines. With such a large bow, a person cannot pull at all, and he uses the principle of leverage. As long as the handle of the shaft on the crossbow is pulled strongly, the beef tendon connected to the handle tightens the thick bow string composed of many beef tendons. When it is pulled to the tightest, it is suddenly released, and the bow string will drive the stone-loading device. Throw the stone high outside the city, and it can fall more than 1,000 meters away. It turns out that the principle of leverage is not simply to use a straight stick to pry things. For example, on a water well, its fulcrum is the axis of , the heavy arm is the radius of , and its power arm is the handle. The handle must be longer than the radius of . It is very labor-saving to lift water. Archimedes's stone machine also applies this principle. Where did the Romans know that there were many new games in the ancient city of Syria?

Shortly after Marcelas was defeated, the commander of the Navy, Glaudius, sent a report. It turned out that when the Army attacked the city from the northwest, the Roman Navy launched an offensive from the southeast. The Roman Navy was not very powerful at first. Later, it invented a side hook to be mounted on the ship. When it met an enemy ship, it hooked each other. The soldiers then jumped on the enemy ship and turned the sea battle into a land battle, which had a certain advantage. Today Claudius deliberately wrapped the warship with a layer of iron armor in order to deal with Syracuse, prepared a ladder, and ordered the soldiers to move forward but not back. Strangely, the ancient city of Syracuse was extremely quiet on this day. There were no soldiers or soldiers behind the wall, but only a few wooden stands standing in the distance. When the Roman warship was driving down the city, and the soldiers were holding the ladder to the wall, suddenly a wooden chain hung from the wooden frames, with iron hooks and iron claws on the chain ends, which caught the Roman navy. Warship. No matter how hard the sailors paddled, the warship could no longer move half a step. They chopped it with a knife and burned it with fire; Just when the ship was in panic. I saw the wooden wheel on the big wooden frame turning again, and then the chain became more and more tight, and the ship was gradually lifted out of the water. As the hull tilted, the soldiers fell into the sea and their masts were broken. After the hull is suspended in midair, the large wooden frame will still turn left and right, so the battleship swayed in the air like a swing, and then some were dropped on the wall or reef and became piles of debris; some Suspended over the city wall, it became a trophy of the Syracuses. At this time, the city of Syracuse was still quiet, no one was shooting arrows, and no one was shouting. It seemed like an empty city. There were only a few wooden frames like monsters. From time to time, they went down one by one and went away. Warship. The Romans looked at the rattling monster, and they were frightened, their hands and legs were weak, and they only heard a cry on the sea and a cry for help after falling into the water. Claudius said in the battle report: `We don't see the enemy at all, it's like fighting a wooden barrel. These 'monsters of Archimedes' also used the principle of leverage and added pulleys.

After this war, the Romans lost their soldiers and defeated their soldiers, and lost many weapons and warships in vain, but they did not even see Archimedes.

There are basically three types of lever principles. Examples of the first type of levers are balances, scissors, pliers, etc. Examples of the second type of levers are bottle openers, nutcrackers, and third types of levers such as hammers and tweezers.

There are three types of leverage. The first is a labor-saving lever, such as a bottle opener. The second is a laborious lever, such as tweezers. The third is leverage that is neither laborious nor laborious, such as balances and fishing rods.

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Can Archimedes lift the earth?

"Give me a fulcrum and I can lift the earth," according to legend, Archimedes, who discovered the principle of leverage in ancient times, said.

Archimedes knew that if he used a lever, he could use a minimum force to lift any heavy thing. Just put this force on the long arm of the lever and let the short arm work on the heavy object. Therefore, his hand can lift a weight equal to the weight of the earth.

However, if this great ancient scientist knew how massive the earth was, he might not have boasted that way. Let's imagine that Archimedes really found another earth as a fulcrum; imagine that he also made a long enough lever. Do you know how long it will take him to lift a weight equal to the earth, even if it only lifts 1cm? At least 30 trillion years!

Astronomers know the quality of the earth. An object of this mass, if it is weighed on the earth, its weight is about 6 000 000 000 000 000 000 t.

If a person can only lift a heavy weight of 60kg directly, then if he "lifts the earth", he must put his hand on such a long lever. His long arm should be equal to 100 000 000 000 000 000 000 times!

After a simple calculation, you can know that if you raise the end of the short arm by 1cm, you must draw a large arc in the space of the long arm. The length of the arc is approximately: 1 000 000 000 000 000 km.

That is to say, if Archimedes wants to lift the earth 1cm, his hand holding the lever must move to such an unimaginable distance! So how long will it take him to finish it? If we think Archimedes can lift a 60kg weight by one meter in one second (this working capacity is almost equal to one horsepower!), Then he needs to use 100 to lift the earth by 1cm 000 000 000 000 000 000S, or thirty trillion years! It can be seen that Archimedes was unable to complete this task.

The above is the theoretical basis. In fact, human understanding of space (the phenomenon of weightlessness) cannot complete the prying of the earth at all.

A thick and thin wooden rod with a length of 4 meters is supported at a distance of 1 meter from the thick end. If it is supported at a distance of 2 meters from the thick end and a 20N weight is hung on the other end, the lever Still balanceable, so how much does this stick weigh?

Supporting it at 1 meter from the thick end can balance his center of gravity at 1 meter from the thick end.

If it is supported at a distance of 2 meters from the thick end and a 20N weight is hung on the other end, the leverage can still be balanced. F1 * L1 = F2 * L2 is:

G * 1m = 20N * 2m

Solve: G = 40N

So this stick weighs 40N.