Municipal budgetary educational institution Mikheykovskaya secondary school of the Yartsevsky district of the Smolensk region Lesson on the topic “Simple mechanisms. Application of the law of balance of the lever to the block "Grade 7 Compiled and conducted by the teacher of physics of the highest category Sergey Pavlovich Lavnyuzhenkov 2016 - 2017 academic year Lesson objectives (planned learning outcomes): Personal: the formation of skills to manage their learning activities; formation of interest in physics in the analysis of physical phenomena; formation of motivation by setting cognitive tasks; formation of 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; Meta-subject: 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 in organizing work; independently evaluate and analyze their own activities from the standpoint of the results obtained; use various sources to obtain information. Subject: formation of ideas about simple mechanisms; formation of the ability to recognize levers, blocks, inclined planes, gates, wedges; whether simple mechanisms give a gain in strength; formation of the ability to plan and conduct an experiment, formulate a conclusion based on the results of the experiment. Course of the lesson No. p. 1 2 3 4 5 6 7 8 9 Teacher's activity Student's activity Notes Organizational stage Preparation for the lesson Stage of repetition and verification of assimilation of the material covered Work with pictures, work in pairs - oral story According to the plan, mutual verification of knowledge Stage of updating knowledge , goal-setting Organizational-activity stage: assistance and control over the work of students Physical minutes Organizational-activity stage: practical work, updating and goal-setting Stage of practical consolidation of acquired knowledge: problem solving Stage of consolidation of the material covered Introduction of the concept of "simple mechanisms", by Working with a textbook, drawing up a diagram Self-assessment Physical exercises Collection of installations Introduction of the concept of "lever", setting goals Introduction of the concept of "shoulder of power" Experimental confirmation of the balance rule of the lever asks students to highlight something new, interesting, difficult in the lesson Share their impressions orally and in writing Teacher: Today at 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 the beauty of such a science as mechanics. There are several pictures on the screen: What are these people doing? (mechanical work) The Egyptians build a pyramid (lever); A man raises (with the help of a gate) water from a well; People roll a barrel onto a ship (inclined plane); A person lifts a load (block). Teacher: Make a story according to the plan: 1. What conditions are necessary for the performance of mechanical work? 2. Mechanical work is ……………. 3. Symbol of mechanical work 4. Formula of work ... 5. What is taken as a unit of measurement of work? 6. How and after which scientist is it named? 7. In what cases is work positive, negative or equal to zero? Teacher: Now let's look at these pictures again and pay attention to how these people do their work? (people use a long stick, a gate, an inclined plane device, a block) Teacher: Students: Simple mechanisms Teacher: Right! simple mechanisms. What do you think about 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 (recording the topic of the lesson in a notebook, a slide with the topic of the lesson) Let's set ourselves the goals of the lesson: Together with the children: to study what simple mechanisms are; to consider, types of simple mechanisms; equilibrium condition of the lever. Teacher: Guys, what do you think 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 balance, scissors, meat grinder, knife, axe, saw, etc. Teacher: What a simple mechanism the 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: It's a lever. We hang the weights on one of the arms of the lever and, using other weights, balance the lever. Let's see what happened. We see that the shoulders of the weights differ from each other. Let's swing one of the arms of the lever. What do we see? Students: By swinging, the lever returns to the equilibrium position. Teacher: What is called a lever? Students: A lever is a rigid body that can rotate around a fixed axis. Teacher: When is the lever in balance? Students: Option 1: the same number of loads 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 such a dependence in mathematics? Students: Inversely proportional. Teacher: With what force do the weights act on the lever? Students: The weight of the body due to the gravity of the Earth. P = Fstrand = F F  1 F 2 l 2 l 1 where F1 is the modulus of the first force; F2 is the modulus 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. Problem: A worker lifts a 120 kg box with a crowbar. 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) Solving problems (independently with subsequent mutual verification). 1. The first force is 10 N, and the arm of this force is 100 cm. What is the second force equal to if its arm is 10 cm? (Answer: 100 N) 2. A worker using a lever lifts 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 smaller force is 100 cm? (Answer: 50 cm) Summing up. What mechanisms are called simple? What types of simple mechanisms do you know? What is a lever? What is a shoulder of strength? What is the rule for lever balance? What is the importance 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: A simple mechanism in everyday life, in technology Type of a simple mechanism 3. Additionally. Prepare a message about one simple mechanism used in everyday life, technology. Reflection. Complete the sentences: now I know ……………………………………………………………………………………………………………… ……………………… I can……………………………………………………………………. I can find (compare, analyze, etc.) ……………………. I independently correctly performed ………………………………... I applied the studied material in a specific life situation …………. I liked (disliked) the lesson …………………………………

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

Looks 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 holder with a hook attached to the wheel axle. The block can be fixed or movable. The fixed block has a fixed axle, and it does not move when the load is raised or lowered. The immovable 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 ourselves being at the bottom. However, the use of a fixed block does not give us a gain in strength. We can imagine a 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 applied on both sides of the forces - 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 moving block. The movable block moves along with the load, as if it lies on a 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 load will be applied to the center of the block, where it is attached to the axis, 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 the force of our thrust will be the diameter. The diameter, as you know, is twice the radius, respectively, the arms differ in length by a factor of two, and the gain in strength obtained using the movable block is two. In practice, a combination of a fixed block with a movable block is used. An immovable block fixed at the top does not give a gain in strength, but it helps to lift the load while standing below. And the moving block, moving along 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 times the applied force. Consider a lever with arms that differ by a factor of two in the length of the arm. This leverage will give us a gain in strength twice, however, twice as much leverage will travel twice as far. 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 have a gain in strength, so 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 reduce the work done by him. They simply help to translate one type of effort into another, 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 well-known example of a lever is a swing (Fig. 25.1).

When two people on a swing balance each other? Let's start with observations. Of course, you 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. Seesaw balance condition: 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: let us find experimentally the conditions for the equilibrium of the lever.

Let's put experience

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

If the loads have different weights, then the lever is in equilibrium when the heavier load is so many times closer to the fulcrum, how many times its weight is greater than the weight of the light load (Fig. 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 F 1 and F 2 denote the forces acting on the lever from the side of the loads (see diagrams on the right side of Fig. 25.2). Let us denote the shoulders of these forces as 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 modules of the forces are inversely proportional to the shoulders of these forces:

F 1 / F 2 \u003d l 2 / l 1.

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

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

Sections: Physics

Lesson type: learning lesson

Lesson Objectives:

• Educational:
  • familiarity with the use of simple mechanisms in nature and technology;
  • to form the skills of analyzing sources of information;
  • 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 on the studied material;
  • develop cognitive interest, independence of thinking and intellect;
  • develop competent oral speech;
  • develop practical skills.
• Educational:
  • moral education: love for nature, a sense of comradely mutual assistance, the ethics of group work;
  • education of culture in the organization of educational work.

Basic concepts:

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

Equipment: computer, presentation, handout (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. Greeting.
2. Determination of absentees.
3. Checking the readiness of students for the lesson.
4. Checking the preparedness of the classroom for the lesson.
5. Organization of attention .

II. Homework check step

1. Revealing the fact that homework was done by the whole class.
2. Visual check of tasks in the workbook.
3. Finding out the reasons for the non-fulfillment of the task by individual students.
4. Questions on homework.

III. The stage of preparing students for 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 carnations in the middle. ( Scissors)

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

3. Bows, bows - will come home - stretch out. ( Axe)

4. What kind of miracle giant?
Stretches his hand to the clouds
Doing work:
Helps build a house. ( Crane)

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

Mechanism- from the Greek word "????v?" - tool, building.
The car- from the Latin word " machine" – building.

- 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 date and the topic of the lesson: “Simple mechanisms. Lever equilibrium conditions.
- What is the goal we should set with you today in the lesson ...

IV. 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 from mouth to mouth. Why? Was Archimedes right?

- Levers began to be used by people in ancient times.
What do you think they are for?
- Of course, to make it easier to work.
- The first person to use the lever was our distant prehistoric ancestor, who moved heavy stones with a stick in search of edible roots or small animals hiding under the roots. Yes, yes, because an ordinary stick that has a fulcrum around which it can be turned is the 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 did not know about the law of the lever, but they already knew well that the lever in capable 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 "arm" with a bucket acts as a lever. The driver changes the speed of the car using the gearshift lever. The pharmacist hangs the powders on a very precise pharmacy scales, the main part of these scales is the lever.
Digging up beds in the garden, the shovel in our hands also becomes a lever. All kinds of rocker arms, handles and gates are all levers.

- Let's get acquainted with simple mechanisms.

The class is divided into six experimental groups:

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

The work is carried out according to the description proposed to each group in the work card. ( Appendix 1 )

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

- What mechanisms did you get acquainted with ...
What are simple machines 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 lever has a fulcrum and a shoulder. Shoulder- this 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. One of the forces we will call the force of resistance, the other - the driving force.
On the image ( Appendix 4 ) you see an equal-arm lever that is used to balance forces. An example of such an application of a lever is a scale. What do you think will happen if one of the forces doubles?
That's right, the scales will go out of balance (I show on ordinary scales).
Do you think there is a way to balance the greater power with the lesser?

Guys, I suggest you during mini experiment derive the equilibrium condition for the lever.

Experiment

There are laboratory levers on the tables. Let's find out together with you when the lever will be in balance.
To do this, hang one load 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, but with two weights. Measure your left shoulder.
• Balance the lever, but with three weights. Measure your left shoulder.
• Balance the lever, but with four weights. Measure your left shoulder.

– What conclusions can be drawn:

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

- Let's formulate lever balance rule:

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

- And now try to write down this rule mathematically, that is, the formula:

F 1 l 1 = F 2 l 2 => F 1 / F 2 \u003d l 2 / l 1

The rule of equilibrium for a lever was established by Archimedes.
From this rule follows that a smaller force can be balanced by a leverage of 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 name and surname on it. Put a period at the end of the entry. Now forget about the letters and remember only the dot. It should appear to you as moving from side to side in slow, gentle wiggles. You are relaxed… remove your palms, open your eyes, we are returning to the real world full of strength and energy.

V. Stage of consolidation of new knowledge

1. Continue the phrase ...

• The lever is... a rigid body that can rotate around a fixed support
• The lever is in balance if... the forces acting on it are inversely proportional to the shoulders of these forces.
• The arm 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 leverage is measured in...
• Simple machines are... lever and its varieties: - wedge, screw; inclined plane and its varieties: wedge, screw.
• Simple mechanisms are needed for ... in order to get a gain in strength

2. Fill in the table (on your own):

Find simple mechanisms in devices

MUTUAL CONTROL

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

Was Archimedes right?

Archimedes was sure that there is no such heavy load that a person would not lift - you just need to use the lever.
And yet Archimedes exaggerated the possibilities of man. 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 point of support, and I will lift the Earth!”. After all, in order to move the earth by only 1 cm, the hand of Archimedes would have to travel a distance of 10 18 km. It turns out that in order to move the Earth by a millimeter, the long arm of the lever must be greater than the short arm of 100,000,000,000 trillion. once! The end of this shoulder would have traveled 1,000,000 trillion. kilometers (approx.). And such a journey would take a man many millions of years!.. But this is the topic of another lesson.

VI. The stage of information to students about homework, instructions on how to complete it

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

2. Homework

To all: § 55-56
For those who wish: make a crossword puzzle on the topic “Simple mechanisms in my house”
Individually: prepare messages or a presentation "Leverage in wildlife", "The strength of our hands".

- Lesson completed! Goodbye, all the best to you!

Since time immemorial, mankind has used various mechanisms that are designed to facilitate physical labor. One of them is the lever. What does he represent...

Lever equilibrium condition. Moment rule. simple mechanisms. Challenges and Solutions

By Masterweb

Since time immemorial, mankind has used 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 what is the equilibrium condition of the lever, this article is devoted to the consideration of all these issues.

When did mankind 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 3000 BC.

One of these mechanisms is the so-called lever-crane. It was 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 kind of counterweight, for example, a stone, was placed on the other. The system was set up in such a way that a half-filled vessel would lead to a horizontal position of the pole.

The lever-crane served to raise water from a well, river or other depression to the level where the 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 small force to the other end of the pole with a counterweight, it was possible to raise the specified vessel.

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 (the work "Parallel Lives") says the following: Archimedes, in a letter to his friend, King Hieron of Syracuse, said that he could single-handedly move an arbitrarily large weight, under certain conditions. Hiero was surprised by this statement of the philosopher and asked him to demonstrate what he was talking about. Archimedes agreed. One day, Hieron's ship, which was in the dock, was loaded with people and barrels filled with water. The philosopher, having settled down at some distance from the ship, was able to raise it above the water by pulling on the ropes, while applying a little effort.

Components of a lever

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 the tasks, the pole is considered as an object consisting of two (or one) shoulder. Shoulder - this is the part of the pole, which is located relative to the support on one side. An important role in the principle of operation of the mechanism under consideration is played by the length of the arm.

When considering a lever at work, there are two additional elements: the applied force and the force opposing it. The first seeks to set in motion an object that creates a counterforce.

Lever equilibrium condition in physics

Having become 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 and in which direction will move or, conversely, the entire device will be at rest. The formula looks like:

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

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

As can be seen, the forces involved in the process of equilibrium formation are inversely related to the length of the lever arms.

What are the gains and losses of leverage?

An important conclusion follows from the above formulas: with the help of a long arm and a small effort, objects with a huge mass can be moved. This is true, and many may think that the use of leverage leads to a gain in work. But it's not. Work is an energy quantity that cannot be created from nothing.

Let us analyze the operation of a simple lever having two arms l1 and l2. Let a weight P (F2 = P) be placed at the end of the arm l2. At the end of the other shoulder, a person applies force F1 and lifts this load to a height h. Now, we 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 amount 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, by 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 you to redistribute it either in favor of a smaller applied force, or in favor of a greater amplitude of movement of the object. In the topic of physics under discussion, a general philosophical principle works: every gain is compensated by some loss.

Types of levers

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

• The first kind: the fulcrum is between the two forces F1 and F2, so the length of the arms will depend on what benefits such a lever gives. An example is ordinary scissors.
• Second kind. Here the force against which the work is done is located between the support and the applied force. This type of design means that it will always give a gain in strength and a loss in travel and speed. An example is a garden wheelbarrow.
• Third kind. The last option that remains to be implemented in this simple design is the position of the applied force between the support and the reaction force. In this case, there is a gain on the way, but a loss in force. An example is tweezers.

The concept of the moment of force

Consideration of any problems in mechanics, which include the concepts of an axis or a point of rotation, is carried out using the rule of moments of forces. Since the lever support 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 acting force, that is:

Given this definition, the equilibrium condition of the lever can be rewritten in the following form:

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 simply adding all the moments Mi acting on it. However, their sign should be taken into account (the force that causes 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: Lever of the 1st kind, which allows you to create huge forces due to the small length of the shoulders l2, where the teeth of the tool are located.
• Can and bottle cap opener: This is a type 2 lever, so it will always give you a gain in effort.
• Rod: 3rd class lever that allows you to move the end of the rod with a float, sinker and hook to large amplitudes. At the same time, the loss in strength is felt when it is difficult for the fisherman to pull the fish out of the water, even if its mass 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 arm of the lever, applying force to the end of which, Archimedes was able to raise the ship, as described by Plutarch.

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

F1 * l1 = F2 * l2 => l1 = F2 * l2 / F1 = m * g * l2 / F1 = 90000 * 9.81 * 1/400 ≈ 2.2 km.

Even if we increase the applied force to the value of the weight of Archimedes himself and bring the support two more times closer, we will get a shoulder length value 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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