Simple lever mechanisms are the golden rule of mechanics. What is the "Golden Rule of Mechanics"

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The "golden rule" of mechanics and the law of conservation of energy

The time has long passed when a person must do any work directly with his own hands. Now mechanisms help people to lift loads, move them on land, water and in the air, perform construction work and much more. At the dawn of the development of civilization, man used simple mechanisms for his activities - a lever, a block, an inclined plane, a wedge, a collar. With their help, unique structures were created, some of which have survived to this day.

And today, simple mechanisms are widely used both by themselves and as parts of complex mechanisms.

When using simple mechanisms, you can get a gain in strength, but it is certainly accompanied by a loss in movement. It is possible, on the contrary, to get a gain in movement, but we will certainly lose in strength.

Archimedes established by experience that when using simple mechanisms, we either gain in strength as many times as we lose in displacement, or we win in displacement as many times as we lose in strength.

This statement has been called the "golden rule" of mechanics. It was most clearly formulated by Galileo, specifying that it is valid when friction can be neglected.

For a long time, the "golden rule" of mechanics was regarded as an "independent" law of nature. And only after the discovery of the law of conservation of energy, it turned out that the "golden rule" of mechanics is one of the manifestations of the law of conservation of energy:

when using any simple mechanism, you can not get a gain in work.

A much more general statement also follows from the law of conservation of energy, concerning any mechanisms, not only simple, but also arbitrarily complex: it is impossible to have a so-called “perpetual motion machine”, the purpose of which would be to perform work forever without consuming energy.

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The golden rule of mechanics

You already know that levers, blocks and presses allow you to gain strength. However, is such a gain given “for free”? Take a look at the drawing. It clearly shows that when using the lever, its longer end travels a greater distance. Thus, having received a gain in strength, we get a loss in distance. This means that by lifting a large load with a small force, we are forced to make a large displacement.

Even the ancients knew the rule that applies not only to the lever, but to all mechanisms: how many times the mechanism gives a gain in strength, the same number of times the loss in distance is obtained. This law is called the "golden rule" of mechanics.

Let us illustrate it now with the example of a movable block. Let us now try to confirm it not only from a qualitative point of view, but also from a quantitative one. To do this, let's do an experiment. Let, for example, we have a load weighing 10 N. Attach it to the hook of the movable block and start lifting it up. Since the block is movable, it will give us a 2-fold gain in strength, that is, the dynamometer attached to the thread will show not 10 N, but only 5 N. Let's say we want to lift the load to a height of 4 meters (say, through the window of the second floors). By doing this action, we will find that we have pulled not 4, but as many as 8 meters of rope through the window. So, having won twice in strength, we lost in the distance by the same number of times.

The "golden rule" of mechanics applies not only to mechanisms consisting of solid bodies. In the previous paragraph, we considered a liquid-filled mechanism - a hydraulic press.

Let's make one important observation. Take a look at the drawing. By lowering the handle of the small piston to a certain height, we find that the large piston rises to a lower height. That is, having received a gain in strength, we get a loss in distance.

If the experiment with the press is set up in such a way that the forces acting on the pistons and the displacements of the pistons can be measured, then we will also obtain a quantitative conclusion: the small piston moves a distance so many times greater than the large piston moves, how many times the force acting on a larger piston, more force acting on a smaller one.

The last equality means that the work done by a small force is equal to the work done by a large force. This conclusion applies not only to the press, but also to any other mechanism, if friction is not taken into account. Therefore, summarizing, we will say: the use of any mechanism does not allow you to get a gain in work; that is, the efficiency of any mechanism cannot be more than 100%.

Technological map of the lesson "The Golden Rule of Mechanics" with a presentation

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Description of the presentation on individual slides:

Chinese proverb “Tell me and I will forget, show me and I will remember, let me try and I will understand” Author Borkova T.B., physics teacher, Lyceum No. 1, Tutaev

To lift the same load, two systems of blocks are used. With what force must the end of the rope be pulled in each case in order to lift a load whose weight is 250 N? (block weight is not taken into account)

What force F2 must be applied to the lever at point A in order to lift the load and keep the lever in balance? Load weight 6 kg (weight of the lever is not taken into account). 2

Is it possible to get a gain in work with the help of a simple mechanism?

The "golden rule" of mechanics None of the mechanisms gives a gain in work. How many times we win in strength, how many times we lose on the way.

With the help of a movable block, the load was lifted to a height of 1.5 m. How long was the free end of the rope extended?

The length of the inclined plane is 3 m and the height is 1 m. What is the greatest gain in strength that can be obtained by lifting a load using this plane?

With the help of a fixed block, the load was lifted to a height of 2 m. How long was the free end of the rope extended?

1. Which of the following statements is correct? A. A fixed block gives a gain in work and no gain in strength. B. The movable block does not give a gain either in work or in strength. C. Neither a fixed block nor a movable one give a gain in work D. Both a fixed block and a movable one give a gain in work and strength

2. The worker, applying a force F = 500 N, lifted the load with the help of a movable block to a height of 6 m. What is the work of the applied force? Ignore the forces of friction. A) 6000J; B) 1200 J; C) 600J; D) 9600J.

A) 0.2 N; B) 1.2 N; C) 2 N; D) 12 N. 3. What is the force with which the student uniformly pulls the body up the inclined plane, if we assume that the friction force is negligible? Fstrand H l, m h, m F 5 1 0.4 ?

A) 1 800 J B) 900 J C) 450 J D) 100 J

Check yourself 1. B) Neither a fixed block nor a movable one give a gain in work 2. A) 6000J; C) 2 N; B) 900 J

When lifting a load to a height of 2 m with the help of a movable block, work was done 1800 J. What is the mass of the load?

Homework §60, exercise 31(2), For those who wish: task 19 p.150

Selected document to view Lesson card The golden rule of mechanics Borkova T.B..doc

Technological map of the construction of the lesson
in a system-activity approach

physics teacher Borkova T.B.

MOU lyceum No. 1 of Tutaev, Yaroslavl region

Subject, class, teaching materials

Physics, Grade 7, Teaching Methods Peryshkin A.V.

"Golden Rule of Mechanics"

1) using the experimental method of research, to form in students the concept of useful and complete work, to achieve the assimilation of the "golden rule" of mechanics;
2) to form the ability to apply the "golden rule" of mechanics in solving problems.

3) to consolidate knowledge of the stages of educational activity and their content, to train the ability to independently implement educational activities under the guidance of a teacher.

4) train mental operations: analysis, synthesis, comparison, generalization, develop speech, logical thinking.

Planned learning outcomes

Personal : to form a cognitive interest, independence in acquiring new knowledge and practical skills.

Subject: to form the ability to derive physical laws and rules from experimental facts;

development of theoretical thinking based on the formation of the ability to establish facts, development, the ability to analyze, compare, draw conclusions;

the ability to solve physical problems on the application of an open rule;

to form communication skills to report on the results of their research, briefly and accurately answer questions.

Metasubject : formation of skills for organizing educational activities, setting goals, planning and evaluating the results of their activities;

development of speech, the ability to express one's thoughts;

to form the ability to process and present information in verbal and symbolic forms;

development of skills to work in a group.

Type of teaching aids and equipment used in the lesson

Laboratory equipment: lever, blocks, sets of 1N weights, dynamometers, tripods, ruler and roller from a tribometer.

Multimedia projector, computer.

Stage 1. Organizational. Self-determination to activity

motivating students for learning activities in the classroom

Methods and techniques of work

Listen, participate in the conversation

- Guys, the epigraph of our today's lesson will be the Chinese proverb "Tell me - and I will forget, show - and I will remember, let me try - and I will understand" ( slide 1) ,

since you have to work in groups, conduct experiments. The success of the whole lesson will depend on the success of the work of each group.

And now try to answer my questions and complete the tasks proposed to you.

- educational and cognitive motivation (L);

Stage 2. Updating knowledge and fixing difficulties in activities

1. preparing students for the discovery of new knowledge;

2. performance by students of a trial educational action; 3. fixation of an individual difficulty.

Methods and techniques of work

Participate in a conversation, answer questions, give examples, solve qualitative problems, work with the text of the textbook

Organizes a dialogue aimed at updating knowledge sufficient to build new knowledge:

- What is the purpose of using simple mechanisms?

(- With the help of simple mechanisms, they perform mechanical work and at the same time receive a gain in strength or distance)

- Give examples when, with the help of a simple mechanism, a gain in distance is obtained.

- Give examples when, with the help of a simple mechanism, a gain in strength is obtained;

- To lift the same load, two systems of blocks are used. With what force must the end of the rope be pulled in each case in order to lift a load whose weight is 250 N? (block weight is not taken into account).

F2-?

(-– In the first system of blocks, a movable block is used. It gives a gain in strength by 2 times, so the force applied to the rope is 125 N. In the second system of blocks, both blocks are motionless, they do not give a gain in strength, which means that the force applied to the rope in this case is equal to 250 N)

What is the purpose of the fixed block?

(- It serves to change the direction of force)

– What is the magnitude of the force F 2 that must be applied to the lever at point A in order to lift the load and keep the lever in balance? Load weight 6 kg (weight of the lever is not taken into account).

With lay 3

(- - The weight of the load is 60 N, and the desired force is 20 N, because this leverage gives a gain in strength of 3 times).

– Why are simple mechanisms used in the considered tasks?

(-– To do work: raise the body to some height and at the same time get a gain in strength or change the direction of the force)

- Guys, when using mechanisms, they distinguish between useful and complete (spent) work. Find using the text of the textbook (paragraph 61 p.150), what kind of work is called useful, how is it designated?

(- Useful work is the work of lifting a load or overcoming any resistance. It is denoted by A p)

(- It is necessary to multiply the force of gravity acting on the body by the height of the lift.)

- Find using the textbook test (paragraph 61 p. 150 ) , what work is called expended, how is it designated?

(- The work done by the force applied to the mechanism is called total or expended. It is denoted by A z.)

- In the problems considered at the beginning of the lesson, what force does the full work?

(- Full work is done by the force F 2, which is applied to the rope or lever to lift the load)

(- It is necessary to multiply the modulus of force F 2 by the path that the point of application of this force passes)

- What other simple mechanism can be used to raise the body to the desired height, gaining strength?

(-– You can use an inclined plane, it also gives a gain in strength)

- The work of what force in this case is full work?

(-– The work of the force F 2 that is applied to the bar)

(- Multiply the magnitude of gravity by the height of the inclined plane)

- At the beginning of the lesson, we remembered that simple mechanisms give a gain in strength or distance. The question arises: (slide 7) do the mechanisms give a gain in work, i.e. could a full job be less useful?

Students express different opinions.

- motivational basis of educational activity (L);

— structuring knowledge (P);

- construction of a logical chain of reasoning (P);

- a fairly complete and accurate expression of one's thoughts in accordance with the tasks and conditions of communication (K);

- conscious and arbitrary construction of a speech statement in oral speech, (P);

- define concepts (P)

- master the basics of introductory, search reading (P)

Stage 3. Statement of the learning task

Determine the location and cause of the problem

lead students to formulate the topic and purpose of the lesson

Methods and techniques of work

Introductory dialogue method

Participate in a dialogue, identify the place and cause of the difficulty, formulate the topic and purpose of the lesson.

Organizes a dialogue leading to the topic and purpose of the lesson:

How many opinions do we have in the class?

- So what is the question?

(- Which of us is right? Do simple mechanisms give a gain in work?) learning problem as a question

So what is the purpose of our lesson? What question are we looking for an answer to?

(- We will find out whether it is possible to get a gain in work using simple mechanisms?)

- setting a learning task in cooperation with the teacher (R);

- educational and cognitive interest (L);

- statement and formulation of the problem (P);

- taking into account different opinions, coordinating different positions in cooperation (K);

- formulating and arguing your opinion and position in communication (K)

- setting a cognitive goal (P);

Stage 4. Discovery of new knowledge

Build and implement a project of educational activities aimed at achieving the goal.

Use the constructed method of action to solve the original problem that caused difficulty.

Clarify the general nature of the new knowledge and record the overcoming of the difficulty that arose earlier

Methods and techniques of work

Lead-in dialogue, frontal experiment

Students in a communicative form consider the project of future educational activities: formulate the purpose of the experiment, draw up an experiment plan, select the necessary equipment, offer a table view to record the results of the experiment.

They work in groups using the research plan that is given to each student in the group, making all necessary notes in this plan.

They report on the research carried out and their results. They draw conclusions. Formulate the topic of the lesson.

With the help of an introductory dialogue, it helps students to build and implement a project of educational activities aimed at achieving the set goal:

- How can you get an answer to this question?

(-– With the help of experience, it is necessary to determine the useful and complete work done when using any mechanism, and compare them)

- What mechanisms will we investigate, what measuring instruments will be required?

(- We will explore the lever, blocks, an inclined plane. You will need a dynamometer to measure forces and a ruler to measure the path)

– How can the measurement results be recorded?

(– Using a table) Provides a table view.

– Working in groups, each group will explore one of the mechanisms using the research plan.

Supervises the work of groups, answers students' questions, if they have them during the study.

Organizes a group report on the work done:

- So, what general conclusion can be done based on your experiences?

(-– None of the mechanisms gives a gain in work)

How can this be written using a formula?

Write this expression using a proportion.

- Formulate the resulting rule.

(- None of the mechanisms gives a gain in work. How many times we win in strength, how many times we lose in distance)

– This rule is called the “golden rule” of mechanics. It was already known to ancient scientists and is applicable to all mechanisms, because any complex machine is a combination of simple mechanisms. Slide 8

Now, guess the topic of today's lesson.

- awareness of responsibility for the common cause (L);

- analysis, synthesis, comparison, generalization (P);

- volitional self-regulation (P);

— cognitive initiative (P);

- independent creation of activity algorithms (P);

- independent creation of ways to solve problems of a creative nature (P);

— managing the partner's behavior (K);

- planning of educational cooperation (C);

- adequate use of speech means for solving communication problems (K)

- the ability to process information and present it in symbolic form. (P)

- the ability to analyze and process the information received in accordance with the tasks (P)

– planning and organization of activities (P)

- development of monologue and dialogic speech, the ability to express one's thoughts and the ability to listen to the interlocutor (K)

— Formation of skills to work in a group (K)

Stage 5. Primary fastening

Reinforce the “open” rule by solving qualitative problems

Methods and techniques of work

Conversation, frontal work of students

students solve qualitative problems on the "open" rule with pronunciation of the solution algorithm aloud

Organizes problem solving according to the "open" rule:

1. With the help of a movable block, the load was lifted to a height of 1.5 m. How long was the free end of the rope extended?

(-– This block gives a gain in strength by 2 times, which means that they lose in the distance by the same amount, the rope is pulled 3 m)

2. The length of the inclined plane is 3 m, and the height is 1 m. What is the greatest gain in strength that can be obtained by lifting the load using this plane?

(- They lose in distance three times, which means they win in strength by the same number of times)

3. With the help of a fixed block, the load was lifted to a height of 2 m. How long was the free end of the rope extended?

(- This block does not give a gain in strength, which means there is no loss in distance. The rope is pulled 2 m)

- volitional self-regulation (P);

- construction of speech statements (P);

- derivation of consequences (P);

— development of monologue and dialogic speech, the ability to express one's thoughts and the ability to listen to the interlocutor (K);

- the ability to consciously build a verbal statement in oral form (P);

- establishing cause-and-effect relationships, building a logical chain of reasoning (P)

Stage 6. Independent work with self-test according to the standard. Introspection and self-control

To identify the degree of assimilation by students of the "golden" rule of mechanics at the moment

Methods and techniques of work

individual independent work of students

independently perform test tasks and carry out their self-examination, comparing with the standard

Organizes independent work of students with the test (Slides 12-15) and self-assessment of test performance by offering students slide16 with the correct answers, finds out which tasks caused difficulty in completing.

- development of ethical feelings and regulators of moral behavior (L);

- analysis, comparison (P);

- independent consideration of the selected action points in the new educational material (P);

- the use of sign-symbolic means (P);

- volitional self-regulation (P);

- implementation of self-control by the result and by the method of action (P);

- independent adequate assessment of the correctness of the results of the action, making the necessary adjustments (P).

Stage 7. Inclusion of new knowledge in the knowledge system and repetition

Reinforce the "open" rule through a task in which a new course of action is envisaged as an intermediate step.

Methods and techniques of work

Dialogue method, frontal work of students

Frontally perform a task in which a new mode of action is provided as an intermediate step.

Tell how they did the job. They draw up the solution of problems on the board and in notebooks, comment on the solution.

Offers a task in which a new course of action is envisaged as an intermediate step.
Slide 17
When lifting a load to a height of 2 m with the help of a movable block, work was done 1,800 J. What is the mass of the load?

- analysis, synthesis, comparison (P);

- the use of sign-symbolic means (P);

- the use of general methods for solving problems (P);

- construction of speech statements (P)

- posing questions (K);

Stage 8. Reflection of activity (the result of the lesson)

To fix the new content studied in the lesson, reflection and self-assessment by students of their own learning activities.

Correlation of the purpose of educational activity and its result, fixing the degree of their compliance.

Methods and techniques of work

They answer questions, correlate the purpose and results of their educational activities and fix the degree of their compliance.

Organizes reflection and self-assessment by students of their learning activities in the classroom.

Have we achieved the goal set at the beginning of the lesson?

- How did you achieve this?

What is the rule you discovered?

- What did you learn to determine with the help of this rule?

Are you satisfied with your work in class?

- the internal position of the student (L);

- self-assessment based on the criterion of success (L);

- reflection of the methods and conditions of action (P);

- an adequate understanding of the reasons for success or failure in educational activities (L);

— control and evaluation of the process and results of activities (P);

Final control, debriefing

The teacher evaluates the work of students in the lesson. Gives homework

§ 60, exercise 31 (2). For those who wish: assignment 19 p. 150

Lever study plan.

State the purpose of the research……………..

Suspend from one part of the lever, for example, 3 weights, and from the other 1 weight, achieve balance of the lever.

O
tilt the vertical plane lever and measure the paths traveled by the gravity application points.

Calculate the useful and total work. Record the results of measurements and calculations in the table:

Definition of the golden rule of mechanics

TOPIC 3. OPERATION AND POWER

Students should learn that:

♦ simple mechanisms do not give a gain in work: Fs = F 1 s 1 .

Students must learn:

♦ find the force with which to act on a block or system of blocks in a particular situation;

♦ establish the "golden rule" of mechanics;

♦ formulate the efficiency of the lever.

The "golden rule" of mechanics

PZ 11. On what and how does the efficiency of the lever depend?

U. It is necessary to assume on what factors the efficiency of the lever may depend, to check experimentally the dependence on each factor. Then explore the type of dependency.

P. We have created a certain stock of knowledge about the lever, so we will try to solve the problem of efficiency theoretically, that is, derive a formula, and then conduct its experimental verification. (Writes down the solution method.) I will derive the formula for the efficiency of the lever.

Determinant formula for efficiency

Useful work is the work of the force F to move the load a distance s. Useful work formula: A p \u003d Fs.

The work expended is the work of the force F 1 to move the lever with the load a distance s 1. The formula for the work expended: A s \u003d F 1 s 1.

Then the efficiency of the mechanism

Gain in leverage

The relationship between s and s 1 can be expressed in terms of l and l 1 from similar triangles. (Hatches triangles - see "View of the board.") or 100%. How does this conclusion agree with experimental data?

U. The efficiency of any mechanism is less than 1, the conclusion is contrary to experience.

Think about why the work actually spent is more useful? You have 1 min. (If students find it difficult to identify the reasons, refer them to the second paragraph of § 24 of the textbook.)

U. We did not take into account that the lever itself had to be moved, that is, we did not take into account the gravity force of the lever, as well as the friction force between the support and the solid body. It is necessary to act on the lever with a force that balances not only the force F, but also the force of friction. This means that the work spent will always be more useful.

P. Let's write down this explanation.

Now let's formulate the answer. What is the formula for calculating the efficiency of a lever in a real situation?

P. We got two results. First, the theoretical conclusion that the lever cannot give a gain in work. If losses are not taken into account, then A p \u003d A 3 or Fs \u003d F 1 s 1. How many times we win in strength, how many times we lose in distance. This conclusion applies to all simple mechanisms and is called the "golden rule" of mechanics. Let's write it down.

Second, for real leverage

1 You can immediately set the task “Why is the efficiency of mechanisms less than 1?” Then the material in square brackets can be omitted. However, it should be remembered that then there will be difficulties with the derivation of efficiency formulas in the next lesson.

The golden rule of mechanics

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With the help of this video tutorial, you can independently study the topic "Golden Rule of Mechanics". You will learn how the "golden rule" of mechanics is formulated and what the essence of this rule is. Consider the law of lever balance and learn how it applies to blocks. Get acquainted with the experimental confirmation of this rule.

History of the golden rule of mechanics

When people began to use blocks, levers, gates, they discovered that the movements made during the operation of simple mechanisms turned out to be associated with the forces developed by these mechanisms.

This rule in antiquity was formulated as follows: what we gain in strength, we lose on the way. This provision is general, but very important, and has received the name of the golden rule of mechanics.

Proof of the golden rule of mechanics

We balance the lever with the help of two forces with different modulus. Shoulder l 1 force is acting F 1 , on the shoulder l 2 force is acting F 2 , under the action of these forces, the lever is in equilibrium. Then we set the lever in motion. At the same time, the point of application of force F 1 will pass the path S 1, and the point of application of force F 2 will pass the path S 2 (Fig. 1).

If we measure the modules of these forces and the paths traversed by the points of application of forces, then we get the equality: .

From this equality, we see how many times the forces applied to the lever differ, the paths made by the points of application of the force will differ in the same number of times inversely.

Using the proportion properties, we translate this expression into another form: - the product of the force F 1 on the path S 1 is equal to the product of the force F 2 on the path S 2. The product of the force on the path is called work, in this case the work is equal to A 1 \u003d A 2. The lever does not give a gain in work, the same conclusion can be drawn about any other simple mechanism.

The golden rule of mechanics: no mechanism gives a gain in work. Winning in strength, we lose on the road and vice versa.

The golden rule of mechanics as applied to blocks

Consider a fixed block. We fix the block in the axis and attach two weights to the ropes of the block, then we move one weight down, the weight moved down went the distance S, and the weight that moved up went the same distance S.

The forces are equal, the paths traveled by the bodies are also equal, which means that the work is also equal, and a fixed block does not give a gain in work.

Consider a moving block. We fix one end of the rope, pass it through the movable block and attach the other end to the dynamometer, hang loads from the block. Note the position of the weights on the tripod, lift the weights to a distance S 1, also mark and return to their original position, now mark the position of the dynamometer hook on the tripod. Again we raise the loads to a distance S 1 and note the position of the dynamometer hook in this case (Fig. 2).

To lift the load to a height S 1, it was necessary to pull out the rope, which was almost twice as different from the distance that the load had traveled. The movable block gives a gain in strength, but in work it does not give, how many times we gain in strength, how many times we lose on the way.

Problem solution example

Condition. With the help of a movable block, the loader lifted the box with tools to a height S 1 = 7 m, applying a force F 2 = 160 N. What work did the loader A 2 do?

In order to find a job, you need the following: .

S 2 - the amount of movement of the rope.

How many times we win in strength, how many times we lose on the way, therefore, then.

Answer: the work done by the loader, 2.24 kJ.

Conclusion

Centuries-old practice proves that not a single simple mechanism gives a gain in work, it is possible, gaining in strength, to lose on the way and vice versa - depending on the conditions of the problem to be solved.

1. Lukashik V.I., Ivanova E.V. Collection of tasks in physics for grades 7–9 of educational institutions. – 17th ed. - M .: Education, 2004.
2. Peryshkin A.V. Physics. 7 cells - 14th ed., stereotype. – M.: Bustard, 2010.
3. Peryshkin A.V. Collection of problems in physics, grades 7–9: 5th ed., stereotype. - M: Publishing house "Exam", 2010.

Homework

1. Why use simple mechanisms if they do not give a gain in work?
2. A 200 kg mass is lifted with a lever. To what height was the load lifted if the force acting on the long arm of the lever did the work 400 J.
3. With the help of a movable block, the load was raised by 3 m. How far did the free end of the rope have to be pulled out?

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Mechanical work and power1. Mechanical work \u003d product of force on the path.
2. Mechanical work can be performed only when the body moves under the action of a force, and the force must either promote the movement or hinder it.
Work is positive when the force is directed in the direction of motion of the body. Otherwise, the work is negative.
3. Power is the speed of doing work.
Power shows how much work is done per unit of time.
Simple Mechanisms 4. The "golden rule" of mechanics: if, when doing work, they gain in strength several times, then they lose in the distance by the same amount.
Mechanisms (lever, gate, inclined plane) - devices that allow you to convert force.
5. Lever - a solid body with an axis of rotation.
The rule of equilibrium for a lever is this: the lever is in equilibrium when the moment of force rotating it clockwise is equal to the moment of force rotating the lever counterclockwise.
Arm of the force = distance from the axis of rotation to the straight line along which the force acts.
Moment of force = product of force on her shoulder.
6. A block is a wheel with a groove into which a cable (chain, belt, rope) is passed.
The immovable block only changes the direction of the force, while the movable block still gives a twofold gain in strength.
7. Coefficient of performance (COP) = the ratio of useful work to full.
When using a mechanism, the total work done is always greater than the useful work. In other words, the efficiency is always less than 100%.
Energy 8. Energy is the ability to do work.
The greater the energy of the body, the more work it can do. When work is done, the energy of the body decreases.
9. Kinetic energy is the energy of motion of a body or system of bodies.
The greater the mass and the greater the speed of a given body, the greater its kinetic energy.
10. Potential energy is the energy of interaction of bodies (or parts of one body) depending on their relative position.
The potential energy of a body of mass m raised to a height h is equal to the product mgh.
11. Mechanical energy can be transferred from one form to another.

A mechanism in physics is a device for transforming force (its increase or decrease). For example, by applying a small force in one place of the mechanism, you can get a much larger force in another place.

We have already met one type of mechanism: it is a hydraulic press. Here we consider the so-called simple lever and inclined plane mechanisms.

17.1 Lever

A lever is a rigid body that can rotate around a fixed axis. On fig. fifty

From this relation it follows that the lever gives a benefit
rysh in strength or in distance (depending on how
purpose it is used) as many times as it hurts
neck shoulder is longer than the smaller one.
For example, in order to lift a load with a weight of 100 N		Rice. 50. Lever

700 N, you need to take a lever with an arm ratio of 7: 1 and put a load on the short arm. We will win in strength by 7 times, but we will lose by the same number of times

in distance: the end of the long arm will describe a 7 times larger arc than the end of the short arm (that is, the load).

Examples of a lever that gives a gain in strength are a shovel, scissors, pliers. The rower's oar is a lever that gives a gain in distance. And conventional balance scales are an equal-armed lever that does not give a gain either in distance or in strength (otherwise they can be used to weigh buyers).

		Fixed block
	An important type of lever is a reinforced block
	a wheel in a cage with a groove through which a rope is passed
	ka. In most problems, the rope is considered to be weightless
	heavy thread.
	On fig. 51 shows a fixed block, i.e. a block with a non-
	moving axis of rotation (passing perpendicular to the plane
	drawing bones through point O).
	A load of weight P is fixed at the right end of the thread at point D.
	Recall that the weight of the body is the force with which the body presses on
	support or stretch the suspension. In this case, the weight P applied
	wives to point D, where the weight is attached to the thread.
	A force F is applied to the left end of the thread at point C.
			Rice. 51. Fixed block
	The arm of the force F is OA = r, where r is the radius of the block. Shoulder
	weight P is equal to OB = r. So the fixed block is
	equal-armed lever and therefore does not give a gain either in strength or in distance: firstly,

	we have the equality F = P , and secondly, in the process of movement of the load and the thread, the movement of the point C
	equal to the movement of the load.
	Why, then, is a fixed block needed at all? It is useful in that it allows you to change
	thread direction of effort. Usually a fixed block is used as part of more complex
	mechanisms.
		Movable block
	On fig. 52 shows a movable block, the axis of which is moved
	rolls along with the load. We pull the thread with force F, which
	applied at point C and directed upward. The block rotates and
	at the same time it also moves upward, lifting the load suspended
	on the OD thread.
	At this point in time, the fixed point is
	point A, and it is around it that the block rotates (it would
	rolls¿ through point A). They also say that through point A
	passes the instantaneous axis of rotation of the block (this axis is directed
	perpendicular to the drawing plane).
	The weight of the load P is applied at the point D of the attachment of the load to the thread.
	The shoulder of the force P is equal to AO = r.
	But the shoulder of the force F, with which we pull the thread, is
	is twice as large: it is equal to AB = 2r. Respectively,
	the equilibrium condition for the load is the equality F = P=2 (which
	we see in Fig. 52 : the length of the vector F is half
	the length of the vector P).
	Therefore, the movable block gives a gain in strength in		Rice. 52. Movable block
	twice. At the same time, however, we lose in the same two times
	vaem in the distance. Indeed, it is easy to see that
	to lift the load by one meter, point C will have to be moved up by two meters (that is,
	pull out two meters of thread).
	The block in Fig. 52 there is one drawback: pull the thread up
	(for point C) not the best idea. Agree that th-
	much more convenient to pull the thread down! This is where it comes to the rescue
	fixed block.
	On fig. 53 shows a lifting mechanism that pre-
	is a combination of a movable block with a fixed
	nym. A load is suspended from the movable block, and the cable is additionally
	thrown over a fixed block, which makes it possible
	ability to pull the cable down to lift the load up. External
	the force on the rope is again denoted by the vector F.
	Fundamentally, this device is no different from		Rice. 53. Block combination
	moving block: with its help, we also get two-
	multiple win in force.

17.4 Inclined plane

As we know, it is easier to roll a heavy barrel along inclined walkways than to lift it vertically. Bridges are thus a mechanism that gives a gain in strength.

In mechanics, such a mechanism is called an inclined plane. An inclined plane is a flat, level surface at some angle to the horizontal. In such

case, they briefly say: ¾inclined plane with angle ¿.

Find the force that must be applied to a load of mass m in order to lift it uniformly along

smooth inclined plane with angle. This force F, of course, is directed along the inclined plane (Fig. 54).

Projecting on the X axis:

It is this force that must be applied to move the load up the inclined plane. To evenly lift the same load vertically, you need to apply a force to it,

equal to mg. It can be seen that F< mg, поскольку sin < 1. Наклонная плоскость действительно даёт выигрыш в силе, и тем больший, чем меньше угол.

Widely used varieties of the inclined plane are the wedge and the screw.

17.5 The golden rule of mechanics

A simple mechanism may give a gain in strength or distance, but it cannot give a gain in work.

For example, a lever with a leverage ratio of 2:1 gives a gain in strength twice. In order to lift a weight P on the smaller arm, a force P=2 must be applied to the larger arm. But to raise the load to a height h, the larger arm will have to be lowered by 2h, and the work done will be equal to

A = P 2 2h = P h;

t. e. the same value as without using the lever.

AT In the case of an inclined plane, we win in strength, since we apply a force F = mg sin to the load, which is less than the force of gravity. However, in order to lift the load to a height h above the initial position, we need to travel the path l = h= sin along an inclined plane. At the same time, we are doing the work

A = mg sin sin h = mgh;

i.e. the same as for the vertical lifting of the load.

These facts serve as manifestations of the so-called golden rule of mechanics.

The golden rule of mechanics. None of the simple mechanisms gives a gain in work. How many times we win in strength, how many times we lose in distance, and vice versa.

The golden rule of mechanics is nothing more than a simple version of the law of conservation of energy.

17.6 Machine efficiency

In practice, one has to distinguish between the useful work Auseful, which must be done by the mechanism in ideal conditions without any losses, and the total work Afull, which is performed for the same purposes in a real situation.

The total work is equal to the sum:

useful work;

the work done against the forces of friction in various parts of the mechanism;

work done to move the constituent elements of the mechanism.

So, when lifting a load with a lever, in addition, work has to be done to overcome the friction force in the axis of the lever and to move the lever itself, which has some weight.

Full work is always more useful. The ratio of useful work to complete work is called

efficiency factor (COP) of the mechanism:

A useful:

A full

Efficiency is usually expressed as a percentage. The efficiency of real mechanisms is always less than 100%. Let us calculate the efficiency of an inclined plane with an angle in the presence of friction. Friction coefficient

between the surface of the inclined plane and the load is equal.

Let a load of mass m rise uniformly along an inclined plane under the action of

forces ~ from point to point to height (Fig. 55). In the direction opposite to the

displacement, the sliding friction force acts on the load ~ . f

From (80 ) we have:

Then from (81 ):

Substituting this into (79 ), we get:

F = mg sin + f = mg sin + mg cos = mg(sin + cos):

The total work is equal to the product of the force F and the path traveled by the body along the surface

inclined plane:

Atot = F P Q = mg(sin + cos)

The useful work is obviously equal to:

Auseful = mgh:

For the desired efficiency, we get:

A useful

A full

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