Municipal budgetary educational institution Mikheikovskaya secondary school of Yartsevsky district, Smolensk region Lesson on the topic “Simple mechanisms. Application of the law of equilibrium of the lever to the block "Grade 7 Compiled and conducted by a physics teacher of the highest category Sergey Pavlovich Lavnyuzhenkov 2016 - 2017 academic year Lesson objectives (planned learning outcomes): Personal: the formation of skills to manage their educational activities; the formation of interest in physics in the analysis of physical phenomena; the formation of motivation by setting cognitive tasks; developing the ability to conduct a dialogue on the basis of equal relations and mutual respect; development of independence in acquiring new knowledge and practical skills; development of attention, memory, logical and creative thinking; students' awareness of their knowledge; Metasubject: development of the ability to generate ideas; develop the ability to determine the goals and objectives of the activity; conduct an experimental study according to the proposed plan; formulate a conclusion based on the results of the experiment; develop communication skills when organizing work; independently evaluate and analyze their own activities from the standpoint of the results obtained; use various sources to obtain information. Subject: the formation of an idea of ​​simple mechanisms; the formation of the ability to recognize levers, blocks, inclined planes, gates, wedges; do simple mechanisms give a gain in power; the formation of the ability to plan and conduct an experiment, based on the results of the experiment, formulate a conclusion. Lesson progress No. p. 1 2 3 4 5 6 7 8 9 Activities of the teacher Activities of the student Notes Organizational stage Preparation for the lesson The stage of repetition and verification of the assimilation of the passed material Working with pictures, work in pairs - oral story According to the plan, mutual verification of knowledge Stage of updating knowledge , goal-setting Organizational-activity stage: help and control over the work of students Physical minutes Organizational-activity stage: practical work, actualization and goal-setting The stage of practical consolidation of the knowledge gained: solving problems The stage of consolidating the passed material Introduction of the concept of "simple mechanisms", according to Working with a textbook, drawing up a scheme Self-assessment Physical exercises Collecting the installation Introduction of the concept of "leverage", setting goals Introduction of the concept of "shoulder of force" Experimental confirmation of the rule of equilibrium of the lever Self-assessment Solve problems Mutual examination Answer questions Stage of discussion of homework Writing homework 10 Stage of reflection: suggestion Pupils are trying to highlight new, interesting, difficult things in the lesson Share their impressions in oral and written form Teacher: Today in the lesson we will look into the world of mechanics, we will learn to compare, analyze. But first, let's complete a series of tasks that will help open the mysterious door wider and show all the beauty of such a science as mechanics. There are several pictures on the screen: What are these people doing? (mechanical work) Egyptians build a pyramid (lever); A man raises (with the help of a gate) water from a well; People roll the barrel onto the ship (inclined plane); A person lifts a load (block). Teacher: Make a story according to the plan: 1. What conditions are necessary for performing mechanical work? 2. Mechanical work is ……………. 3. Conventional designation of mechanical work 4. Formula of work ... 5. What is taken as a unit of measure of work? 6. How and after what scientist is it named? 7. When is the work positive, negative or zero? Teacher: Now let's look at these pictures again and pay attention to how these people do the work? (people use a long stick, a gate, an incline device, a block) Teacher: Students: Simple mechanisms Teacher: Correct! Simple mechanisms. What do you think on what topic in the lesson we will be with you. How can you call these devices in one word? talk today? Students: About simple mechanisms. Teacher: Right. The topic of our lesson will be simple mechanisms (writing the topic of the lesson in a notebook, a slide with the topic of the lesson) Let us set the goals of the lesson: Together with the children: to study what simple mechanisms are; consider the types of simple mechanisms; the equilibrium condition of the lever. Teacher: Guys, what do you think the simple mechanisms are used for? Students: They are used to reduce the force we apply, i.e. to transform it. Teacher: There are simple mechanisms in everyday life, and in all complex factory machines, etc. Guys, what household appliances and devices have simple mechanisms. Students: Lever scales, scissors, meat grinder, knife, ax, saw, etc. Teacher: What a simple mechanism a crane has. Students: Lever (arrow), blocks. Teacher: Today we will dwell in more detail on one of the types of simple mechanisms. It is on the table. What is this mechanism? Students: This is a lever. Hang the weights on one of the arms of the lever and, using the other weights, balance the lever. Let's see what happened. We see that the shoulders of the weights are different from each other. Let's swing one of the levers. What do we see? Students: Swinging, the lever returns to the balance position. Teacher: What is called a lever? Students: A lever is a rigid body that can rotate about a stationary axis. Teacher: When is the lever in balance? Students: Option 1: the same number of weights at the same distance from the axis of rotation; Option 2: more load - less distance from the axis of rotation. Teacher: What is the name of this dependence in mathematics? Students: Inversely proportional. Teacher: With what force do weights act on the lever? Students: Body weight due to the gravity of the Earth. P = Ftyazh = F F  1 F 2 l 2 l 1 where F1 is the modulus of the first force; F2 - module of the second force; l1 - shoulder of the first force; l2 - shoulder of the second force. Teacher: This rule was established by Archimedes in the 3rd century BC. Task: With the help of a crowbar, a worker lifts a box weighing 120 kg. What force does he apply to the larger arm of the lever if the length of this arm is 1.2 m, and the smaller reach is 0.3 m. What will be the gain in strength? (Answer: The gain in strength is 4) Problem solving (independently with subsequent mutual check). 1. The first force is 10 N, and the shoulder of this force is 100 cm. What is the second force if its shoulder is 10 cm? (Answer: 100 N) 2. The worker uses a lever to lift a load weighing 1000 N, while he applies a force of 500 N. What is the arm of the greater force if the arm of the lesser force is 100 cm? (Answer: 50 cm) Summing up. What mechanisms are called simple? What kinds of simple mechanisms do you know? What is Leverage? What is a shoulder of strength? What is the rule of balance for a lever? What is the significance of simple mechanisms in human life? D / s 1. Read the paragraph. 2. List the simple mechanisms that you find at home and those that a person uses in everyday life, writing them down in a table: Simple mechanism in everyday life, in technology View of a simple mechanism 3. Additionally. Prepare a message about one simple mechanism used in everyday life, technology. Reflection. Finish the sentences: now I know ……………………………………………………… .. I realized that ……………………………………… ……………………… I can……………………………………………………………………. I can find (compare, analyze, etc.) ……………………. I did it right on my own ……………………………… ... I applied the studied material in a specific life situation …………. I liked (did not like) the lesson …………………………………

Do you know what a block is? This is such a round contraption with a hook, with the help of which loads are lifted to a height at construction sites.

Does it look like a lever? Hardly. However, the block is also a simple mechanism. Moreover, we can talk about the applicability of the law of equilibrium of the lever to the block. How is this possible? Let's figure it out.

Application of the law of equilibrium

The block is a device that consists of a wheel with a groove through which a cable, rope or chain is passed, as well as a clip with a hook attached to the axle of the wheel. The block can be fixed and movable. A fixed block has an axle fixed, and it does not move when lifting or lowering a load. The fixed block helps to change the direction of the force. Having thrown a rope over such a block suspended at the top, we can lift the load up, while being at the same time at the bottom. However, the use of a fixed block does not give us a gain in strength. We can imagine the block as a lever rotating around a fixed support - the axis of the block. Then the radius of the block will be equal to the shoulders of the forces applied from both sides - the traction force of our rope with a load on one side and the gravity of the load on the other. The shoulders will be equal, respectively, there is no gain in strength.

The situation is different with the movable unit. The movable block moves with the load, as if it lies on the rope. In this case, the fulcrum at each moment of time will be at the point of contact of the block with the rope on one side, the impact of the load will be applied to the center of the block, where it is attached to the axle, and the traction force will be applied at the point of contact with the rope on the other side of the block. ... That is, the shoulder of the body weight will be the radius of the block, and the shoulder of our traction force will be the diameter. The diameter, as you know, is twice the radius, respectively, the shoulders differ in length by two times, and the strength gain obtained with the help of the movable block is equal to two. In practice, a combination of a fixed block with a movable one is used. A fixed block at the top does not give a gain in strength, but it helps to lift the load while standing below. And the movable block, moving with the load, doubles the applied force, helping to lift large loads to a height.

The golden rule of mechanics

The question arises: do the devices used give a gain in work? Work is the product of the distance traveled by the applied force. Consider a lever with arms that differ by half in the length of the arm. This leverage will give us twice the strength gain, however, twice the shoulder will travel twice the distance. That is, despite the gain in strength, the work done will be the same. This is the equality of work when using simple mechanisms: how many times we gain in strength, how many times we lose in distance. This rule is called the golden rule of mechanics., and it applies to absolutely all simple mechanisms. Therefore, simple mechanisms facilitate the work of a person, but do not diminish the work he does. They simply help to translate some types of efforts into others that are more convenient in a particular situation.

A lever is a rigid body that can rotate around a fixed point.

The fixed point is called the fulcrum.

A familiar example of a lever is a swing (fig. 25.1).

When do two on a swing balance each other? Let's start with observations. You, of course, have noticed that two people on a swing balance each other if they have approximately the same weight and are approximately the same distance from the fulcrum (Fig. 25.1, a).

Rice. 25.1. The condition for the balance of the swing: a - people of equal weight balance each other when they sit at equal distances from the fulcrum; b - people of different weights balance each other when the heavier one sits closer to the fulcrum

If these two are very different in weight, they balance each other only on the condition that the heavier one sits much closer to the fulcrum (Fig. 25.1, b).

Let us now pass from observations to experiments: we will find experimentally the conditions for the equilibrium of the lever.

Let's put experience

Experience shows that weights of equal weight balance the lever if they are suspended at equal distances from the fulcrum (Fig. 25.2, a).

If the loads have different weights, then the lever is in equilibrium when the heavier load is as many times closer to the fulcrum as its weight is greater than the weight of the light load (Figure 25.2, b, c).

Rice. 25.2. Experiments on finding the equilibrium condition of the lever

Lever equilibrium condition. The distance from the fulcrum to the straight line along which the force acts is called the shoulder of this force. Let us denote by F 1 and F 2 the forces acting on the lever from the side of the weights (see the diagrams on the right side of Fig. 25.2). The shoulders of these forces will be denoted by l 1 and l 2, respectively. Our experiments have shown that the lever is in equilibrium if the forces F 1 and F 2 applied to the lever tend to rotate it in opposite directions, and the moduli of the forces are inversely proportional to the arms of these forces:

F 1 / F 2 = l 2 / l 1.

This condition for the balance of the lever was established experimentally by Archimedes in the 3rd century BC. e.

You can study the condition of equilibrium of the lever experimentally in laboratory work No. 11.

Sections: Physics

Lesson type: a lesson in mastering new material

Lesson objectives:

• Educational:
  • acquaintance with the use of simple mechanisms in nature and technology;
  • develop skills in analyzing information sources;
  • to establish experimentally the rule of equilibrium of the lever;
  • to form the ability of students to conduct experiments (experiments) and draw conclusions from them.
• Developing:
  • develop the ability to observe, analyze, compare, generalize, classify, draw up diagrams, formulate conclusions based on the material studied;
  • develop cognitive interest, independence of thinking and intelligence;
  • develop competent oral speech;
  • develop practical skills.
• Educational:
  • moral education: love of nature, a sense of comradely mutual assistance, ethics of group work;
  • education of culture in the organization of educational work.

Basic concepts:

• mechanisms
• lever arm
• shoulder strength
• block
• gate
• inclined plane
• wedge
• screw

Equipment: computer, presentation, handouts (work cards), a lever on a tripod, a set of weights, a laboratory set on the topic "Mechanics, simple mechanisms".

DURING THE CLASSES

I. Organizational stage

1. Greetings.
2. Determination of the absent.
3. Checking the readiness of students for the lesson.
4. Checking the readiness of the classroom for the lesson.
5. Organization of attention .

II. Homework check phase

1. Revealing the fact of homework being completed by the whole class.
2. Visual check of assignments in the workbook.
3. Clarification of the reasons for non-fulfillment of the assignment by individual students.
4. Questions about homework.

III. The stage of preparing students for the active and conscious assimilation of new material

"I could turn the Earth with a lever, just give me a fulcrum"

Archimedes

Guess the riddles:

1. Two rings, two ends, and a stud in the middle. ( Scissors)

2. Two sisters swayed - they sought the truth, and when they achieved it, they stopped. ( scales)

3. Bows, bows - comes home - stretches out. ( Axe)

4. What kind of miracle giant?
Reaches out to the clouds
Engaged in labor:
Helps build a house. ( Hoisting crane)

- Look again carefully at the answers and name them in one word. "Tool, machine" translated from Greek means "mechanisms".

Mechanism- from the Greek word "???? v?" - cannon, construction.
Car- from the Latin word " machina " – construction.

- It turns out that an ordinary stick is the simplest mechanism. Who knows what it's called?
- Let's formulate the topic of the lesson together:….
- Open notebooks, write down the number and topic of the lesson: “Simple mechanisms. Lever equilibrium conditions ”.
- What goal should we set with you today in the lesson ...

IV. The stage of assimilation of new knowledge

"I could turn the Earth with a lever, just give me a fulcrum" - these words, which are the epigraph of our lesson, Archimedes said more than 2000 years ago. And people still remember them and pass them on from mouth to mouth. Why? Was Archimedes right?

- Levers began to be used by people in ancient times.
- What do you think, what are they for?
- Of course, to make it easier to work.
- The first person to use the lever was our distant prehistoric ancestor, who used a stick to move heavy stones from their place in search of edible roots or small animals hiding under the roots. Yes, yes, after all, an ordinary stick, which has a fulcrum around which it can be turned, is a real lever.
There is a lot of evidence that in ancient countries - Babylon, Egypt, Greece - builders widely used levers when lifting and transporting statues, columns and huge stones. At that time they had no idea about the law of a lever, but they already knew well that a lever in skillful hands turns a heavy load into a light one.
Lever arm- is an integral part of almost every modern machine, machine tool, mechanism. The excavator digs a ditch - its iron "hand" with a bucket acts as a lever. The chauffeur changes the speed of the car using the gearshift lever. The pharmacist weighs the powders on the pharmaceutical very precise scales, the main part of these scales is the lever.
Digging up the beds in the garden, the shovel in our hands also becomes a lever. All kinds of rocker arms, handles and collars are all levers.

- Let's get acquainted with simple mechanisms.

The class is divided into six experimental groups:

1st is studying the inclined plane.
2nd examines the lever.
3rd studies block.
4th examines the gate.
5th is studying the wedge.
6th is studying the screw.

The work is carried out according to the description offered to each group in the working card. ( Annex 1 )

We draw up a diagram based on the answers of the students. ( Appendix 2 )

- What mechanisms have you met ...
- What are simple mechanisms for? ...

Lever arm- a rigid body that can rotate around a fixed support. In practice, a stick, board, crowbar, etc. can play the role of a lever.
The arm has a fulcrum and a shoulder. Shoulder Is the shortest distance from the fulcrum to the line of action of the force (i.e. the perpendicular dropped from the fulcrum to the line of action of the force).
Usually the forces applied to the lever can be considered the weight of the bodies. We will call one of the forces the resistance force, the other - the driving force.
On the image ( Appendix 4 ) you see an equal arm that is used to balance the forces. An example of such a lever application is a balance. What do you think will happen if one of the forces doubles?
That's right, the scales will go out of balance (I show it on a regular scale).
Do you think there is a way to balance more power with less?

Guys, I suggest you in the course mini experiment deduce the condition of the balance of the lever.

Experiment

There are laboratory levers on the tables. Let's figure out with you when the lever is in balance.
To do this, hang one weight on the hook on the right side at a distance of 15 cm from the axis.

• Balance the lever with one weight. Measure your left shoulder.
• Balance the lever with two weights. Measure your left shoulder.
• Balance the lever with three weights. Measure your left shoulder.
• Balance the lever with four weights. Measure your left shoulder.

- What conclusions can be drawn:

• Where the strength is greater, the shoulder is less.
• How many times the strength has increased, how many times the shoulder has decreased,

- Let's formulate lever equilibrium rule:

The lever is in balance when the forces acting on it are inversely proportional to the shoulders of these forces.

- Now try to write this rule mathematically, that is, the formula:

F 1 l 1 = F 2 l 2 => F 1 / F 2 = l 2 / l 1

The balance rule of the lever was established by Archimedes.
This rule implies that a smaller force can be balanced by a lever with a larger force.

Relaxation: Close your eyes and cover them with your palms. Imagine a sheet of white paper and try to mentally write your first and last name on it. At the end of the recording, put a full stop. Now forget about the letters and remember only the point. It should seem to you moving from side to side with slow and light swaying. You have relaxed ... remove your palms, open your eyes, we are returning to the real world full of strength and energy.

V. The stage of consolidating new knowledge

1. Continue the phrase ...

• The lever is ... rigid body that can rotate about a fixed support
• The lever is in equilibrium if ... the forces acting on him are inversely proportional to the shoulders of these forces.
• The shoulder of strength is ... the shortest distance from the fulcrum to the line of action of the force (i.e. the perpendicular dropped from the fulcrum to the line of action of the force).
• Strength is measured in ...
• The shoulder of force is measured in ...
• Simple mechanisms include ... lever and its varieties: - wedge, screw; inclined plane and its varieties: wedge, screw.
• Simple mechanisms are needed for ... in order to gain the power

2. Fill in the table (by yourself):

Find simple mechanisms in devices

INTERCONTROL

Transfer the assessment after the peer review to the self-assessment card.

Was Archimedes right?

Archimedes was sure that there was no such heavy load that a person could not lift - you just need to use the lever.
Yet Archimedes exaggerated human capabilities... If Archimedes knew how huge the mass of the Earth is, he would probably have refrained from the exclamation attributed to him by legend: "Give me a fulcrum and I will raise the Earth!" Indeed, to move the earth by just 1 cm, Archimedes' hand would have to travel 10 18 km. It turns out that in order to move the Earth by a millimeter, the long lever arm must be larger than the short one at 100,000,000,000 trillion. once! The end of this shoulder would have traveled a path of 1,000,000 trillion. kilometers (approximately). And on such a road it would take a man many millions of years! .. But this is the topic of another lesson.

Vi. Information stage for students about homework, instructions on how to complete it

1. Summing up: what was new learned in the lesson, how the class worked, which of the students worked especially diligently (grades).

2. Homework

Everyone: § 55-56
For those who wish: to compose a crossword puzzle on the topic "Simple mechanisms at my home"
Individually: prepare a message or presentation "Levers in Wildlife", "The Power of Our Hands".

- The lesson is over! Goodbye, all the best to you!

Since time immemorial, humanity has been using various mechanisms that are designed to facilitate physical labor. One of them is the lever. That he is a presenter ...

Lever equilibrium condition. The rule of the moments. Simple mechanisms. Challenges and solutions

From Masterweb

Since time immemorial, humanity has been using various mechanisms that are designed to facilitate physical labor. One of them is the lever. What it is, what is the idea of ​​its use, and also what is the condition for the equilibrium of the lever, this article is devoted to all these issues.

When did humanity begin to apply the principle of leverage?

It is difficult to answer this question precisely, since simple mechanisms were already known to the ancient Egyptians and the inhabitants of Mesopotamia as early as three thousand BC.

One of these mechanisms is the so-called crane lever. It was represented by a long pole, which was located on a support. The latter was installed closer to one end of the pole. A vessel was tied to the end, which was further from the reference point, and some counterweight, for example, a stone, was placed on the other. The system was adjusted so that a half-filled vessel would bring the pole to a horizontal position.

The crane-lever was used to raise water from a well, river or other depression to the level where a person was. Applying a small force to the vessel, the person lowered it to the source of water, the vessel was filled with liquid, and then, applying a slight force to the other end of the counterbalanced pole, the indicated vessel could be raised.

The Legend of Archimedes and the Ship

Everyone knows the ancient Greek philosopher from the city of Syracuse, Archimedes, who in his writings not only described the principle of operation of simple mechanisms (lever, inclined board), but also gave the corresponding mathematical formulas. Until now, his phrase remains famous:

Give me a foothold and I will move this world!

As you know, no one provided him with such support, and the Earth remained in its place. However, what Archimedes was really able to move was the ship. One of Plutarch's legends (work "Parallel Lives") says the following: Archimedes, in a letter to his friend, Tsar Hieron of Syracuse, said that he could single-handedly move as much weight as desired, under certain conditions. Hieron was surprised by this statement of the philosopher and asked him to demonstrate what he was talking about. Archimedes agreed. One day the ship of Hieron, which was at the dock, was loaded with people and barrels filled with water. The philosopher, located at some distance from the ship, was able to lift it above the water by pulling on the ropes, while applying a little effort.

Lever components

Despite the fact that we are talking about a fairly simple mechanism, it still has a certain device. Physically, it consists of two main parts: a pole or beam and a support. When considering tasks, the pole is considered as an object consisting of two (or one) shoulders. The shoulder is the portion of the pole that is relative to the support on one side. It is the length of the arm that plays an important role in the principle of operation of the mechanism under consideration.

When a lever is considered in operation, two additional elements arise: the applied force and the force of opposition to it. The first seeks to set in motion an object that creates a reaction force.

Equilibrium condition for a lever in physics

Having got acquainted with the device of this mechanism, we will give a mathematical formula, using which, we can say which of the arms of the lever will move and in which direction, or, conversely, the whole device will be at rest. The formula is:

where F1 and F2 are the forces of action and reaction, respectively, l1 and l2 are the lengths of the arms to which these forces are applied.

This expression allows one to investigate the equilibrium conditions for a lever having an axis of rotation. So, if the shoulder l1 is greater than l2, then a smaller value of F1 is needed to balance the force F2. Conversely, if l2> l1, then a large F1 will be required to counter the force F2. These conclusions can be obtained by rewriting the expression above in the following form:

As you can see, the forces involved in the formation of the balance are inversely related to the length of the lever arms.

What are the gains and losses when using leverage?

An important conclusion follows from the above formulas: with the help of a long arm and low effort, objects with a huge mass can be moved. This is true, and many might think that leverage leads to gains in performance. But this is not the case. Work is an energetic quantity that cannot be created out of nothing.

Let's analyze the operation of a simple lever with two heals l1 and l2. Let a weight of weight P (F2 = P) be placed at the end of the arm l2. At the end of the other shoulder, the person applies force F1 and lifts this weight to a height h. Now, let's calculate the work of each force and equate the results. We get:

Force F2 acted along a vertical trajectory of length h, in turn F1 also acted along the vertical, but was already applied to the other arm, the end of which moved by an unknown value x. To find it, it is necessary to substitute in the last expression the formula for the connection between the forces and the arms of the lever. Expressing x, we have:

x = F2 * h / F1 = l1 * h / l2.

This equality shows that if l1> l2, then F2> F1 and x> h, that is, applying a small force, you can lift a load with a large weight, but you will have to move the corresponding lever arm (l1) a greater distance. Conversely, if l1

Thus, the lever does not give a gain in work, it only allows it to be redistributed either in favor of a smaller applied force, or in favor of a greater amplitude of the object's movement. In the discussed topic of physics, a general philosophical principle works: any gain is compensated by some loss.

Types of levers

Depending on the points of application of the force and on the position of the support, the following types of this mechanism are distinguished:

• The first kind: the pivot point is between the two forces F1 and F2, so the leverage will depend on the length of the arms. An example is regular scissors.
• The second kind. Here the force against which the work is done is located between the support and the applied force. This type of construction means that it will always yield gains in strength and losses in travel and speed. An example of this is the garden wheelbarrow.
• The third kind. The last option that remains to be realized in this simple structure is the position of the applied force between the support and the reaction force. In this case, there is a gain along the way, but a loss in power. An example is tweezers.

The concept of the moment of force

Any problems in mechanics that involve the concept of an axis or a point of rotation are handled by the rule of moments of force. Since the support of the lever is also the axis (point) around which the system rotates, the moment of force is also used to assess the balance of this mechanism. It is understood as a quantity in physics equal to the product of the shoulder and the effective force, that is:

Taking this definition into account, the condition for the equilibrium of the lever can be rewritten as follows:

M1 = M2, where M1 = l1 * F1 and M2 = l2 * F2.

The moment M is additive, which means that the total moment of force for the system under consideration can be obtained by the usual addition of all the moments Mi acting on it. However, in this case, their sign should be taken into account (the force causing the system to rotate counterclockwise creates a positive moment + M, and vice versa). With that said, the moment rule for a lever in equilibrium would look like this:

The lever loses its balance when M1 ≠ M2.

Where is the principle of leverage used?

Some examples of the use of this simple and well-known mechanism from ancient times have already been given above. Here are just a few additional examples:

• Pliers: A 1st class lever that allows enormous forces to be generated due to the short arm length l2 where the tool teeth are located.
• Bottle and can opener: This is a 2nd class lever, so it always pays off in the effort involved.
• Fishing Rod: A 3rd class lever that allows you to move the rod end with float, sinker and hook to large amplitudes. The loss in strength is felt when the fisherman finds it difficult to pull the fish out of the water, even if its weight does not exceed 0.5 kg.

The person himself, with his joints, muscles, bones and tendons, is a prime example of a system with many different levers.

The solution of the problem

The equilibrium condition of the lever, considered in the article, is used to solve a simple problem. It is necessary to calculate the approximate length of the lever arm, applying an effort to the end of which, Archimedes was able to lift the ship, as described by Plutarch.

For the solution, we introduce the following assumptions: take into account the Greek trireme of 90 tons with a displacement and assume that the support of the lever was 1 meter from its center of mass. Since Archimedes, according to legend, could easily lift the ship, we will assume that for this he applied a force equal to half his weight, that is, about 400 N (for a mass of 82 kg). Then, applying the condition of equilibrium of the lever, we obtain:

F1 * l1 = F2 * l2 => l1 = F2 * l2 / F1 = m * g * l2 / F1 = 90,000 * 9.81 * 1/400 ≈ 2.2 km.

Even if you increase the applied force to the value of the weight of Archimedes himself and bring the support two times closer, you get the value of the arm length of about 500 meters, which is also a large value. Most likely, Plutarch's legend is an exaggeration to demonstrate the effectiveness of the lever, and Archimedes did not actually raise the ship above the water.

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