Topics of the Unified State Examination codifier: simple mechanisms, mechanism efficiency.

Mechanism - this is a device for converting force (increasing or decreasing it).
Simple mechanisms - a lever and an inclined plane.

Lever arm.

Lever arm is a rigid body that can rotate around a fixed axis. In Fig. 1) shows a lever with an axis of rotation. Forces and are applied to the ends of the lever (points and ). The shoulders of these forces are equal to and respectively.

The equilibrium condition of the lever is given by the rule of moments: , whence

Rice. 1. Lever

From this relationship it follows that the lever gives a gain in strength or distance (depending on the purpose for which it is used) as many times as the larger arm is longer than the smaller one.

For example, to lift a 700 N load with a force of 100 N, you need to take a lever with a 7:1 arm ratio and place the load on the short arm. We will gain 7 times in strength, but will lose the same amount of times in distance: the end of the long arm will describe a 7 times greater arc than the end of the short arm (that is, the load).

Examples of levers that provide a gain in strength are a shovel, scissors, and pliers. The rower's oar is the lever that gives the gain in distance. And ordinary lever scales are an equal-armed lever that does not provide any gain in either distance or strength (otherwise they can be used to weigh customers).

Fixed block.

An important type of lever is block - a wheel fixed in a cage with a groove through which a rope is passed. In most problems, a rope is considered to be a weightless, inextensible thread.

In Fig. Figure 2 shows a stationary block, i.e. a block with a stationary axis of rotation (passing perpendicular to the plane of the drawing through the point ).

At the right end of the thread, a weight is attached to a point. Let us recall that body weight is the force with which the body presses on the support or stretches the suspension. In this case, the weight is applied to the point where the load is attached to the thread.

A force is applied to the left end of the thread at a point.

The force arm is equal to , where is the radius of the block. The weight arm is equal to . This means that the fixed block is an equal-armed lever and therefore does not provide a gain in either force or distance: firstly, we have the equality , and secondly, in the process of moving the load and the thread, the movement of the point is equal to the movement of the load.

Why then do we need a fixed block at all? It is useful because it allows you to change the direction of the effort. Typically a fixed block is used as part of more complex mechanisms.

Movable block.

In Fig. 3 shown moving block, the axis of which moves along with the load. We pull the thread with a force that is applied at a point and directed upward. The block rotates and at the same time also moves upward, lifting a load suspended on a thread.

IN this moment time, the fixed point is the point , and it is around it that the block rotates (it would “roll” over the point ). They also say that the instantaneous axis of rotation of the block passes through the point (this axis is directed perpendicular to the plane of the drawing).

The weight of the load is applied at the point where the load is attached to the thread. The leverage of force is equal to .

But the shoulder of the force with which we pull the thread turns out to be twice as large: it is equal to . Accordingly, the condition for equilibrium of the load is equality (which we see in Fig. 3: the vector is half as long as the vector).

Consequently, the movable block gives a double gain in strength. At the same time, however, we lose by the same two times in distance: in order to raise the load one meter, the point will have to be moved two meters (that is, pull out two meters of thread).

The block in Fig. 3 there is one drawback: pulling the thread up (beyond the point) is not the most best idea. Agree that it is much more convenient to pull the thread down! This is where the stationary block comes to our rescue.

In Fig. Figure 4 shows a lifting mechanism, which is a combination of a moving block and a fixed one. A load is suspended from the movable block, and the cable is additionally thrown over the fixed block, which makes it possible to pull the cable down to lift the load up. The external force on the cable is again symbolized by the vector .

Fundamentally this device is no different from a moving block: with its help we also get a double gain in strength.

Inclined plane.

As we know, it is easier to roll a heavy barrel along inclined walkways than to lift it vertically. The bridges are thus a mechanism that provides gains in strength.

In mechanics, such a mechanism is called an inclined plane. Inclined plane - this is a smooth flat surface located at a certain angle to the horizon. In this case, they say briefly: “inclined plane with an angle.”

Let's find the force that must be applied to a mass load in order to uniformly lift it along a smooth inclined plane with an angle . This force, of course, is directed along the inclined plane (Fig. 5).

Let's select the axis as shown in the figure. Since the load moves without acceleration, the forces acting on it are balanced:

We project on the axis:

This is exactly the force that needs to be applied to move the load up an inclined plane.

To evenly lift the same load vertically, a force equal to . It can be seen that, since . An inclined plane actually gives a gain in strength, and the smaller the angle, the greater the gain.

Widely used types of inclined plane are wedge and screw.

The golden rule of mechanics.

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

For example, a lever with a leverage ratio of 2:1 gives a double gain in strength. In order to lift a weight on the smaller shoulder, you need to apply force to the larger shoulder. But to raise the load to a height, the larger arm will have to be lowered by , and the work done will be equal to:

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

In the case of an inclined plane, we gain in strength, since we apply a force to the load that is less than the force of gravity. However, in order to raise the load to a height above the initial position, we need to go along the inclined plane. At the same time we do work

i.e. the same as when lifting a load vertically.

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

Golden Rule mechanics. None of the simple mechanisms provide any gains in performance. The number of times we win in strength, the same number of 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.

Efficiency of the mechanism.

In practice, we have to distinguish between useful work A useful, which must be accomplished using a mechanism in ideal conditions absence of any losses, and full time job A full,
which is performed for the same purposes in a real situation.

The total work is equal to the sum:
-useful work;
-work done against friction forces in various parts of the mechanism;
-work done to move the component elements of the mechanism.

So, when lifting a load with a lever, you have to additionally do work to overcome the frictional 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 total work is called the coefficient of performance (efficiency) 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's calculate the efficiency of an inclined plane with an angle in the presence of friction. The coefficient of friction between the surface of the inclined plane and the load is equal to .

Let the mass load rise uniformly along the inclined plane under the action of force from point to point to a height (Fig. 6). In the direction opposite to the movement, the sliding friction force acts on the load.

There is no acceleration, so the forces acting on the load are balanced:

We project on the X axis:

. (1)

We project on the Y axis:

. (2)

Besides,

, (3)

From (2) we have:

Then from (3):

Substituting this into (1), we get:

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

A full=.

The useful work is obviously equal to:

A useful=.

For the required efficiency we obtain:

Bibliographic description: Shumeiko A. V., Vetashenko O. G. Modern look on a simple “block” mechanism, studied in physics textbooks for grade 7 // Young scientist. 2016. No. 2. P. 106-113..07.2019).

Physics textbooks for 7th grade, when studying a simple block mechanism, interpret winning in different ways force when lifting a load from using this mechanism, for example: in Peryshkin's textbook A. B. winnings in strength is achieved with using the wheel of the block, on which the forces of the lever act, and in Gendenstein's textbook L. E. the same winnings are obtained with using a cable, which is subject to the tension force of the cable. Various textbooks, various items And different forces - to receive winnings in force when lifting a load. Therefore, the purpose of this article is to search for objects and strength, with through which the winnings are obtained force, when lifting a load with a simple block mechanism.

Keywords:

First, let’s take a look and compare how gains in strength are obtained when lifting a load with a simple block mechanism, in physics textbooks for the 7th grade. For this purpose, we will place excerpts from textbook texts with the same concepts in a table for clarity.

Peryshkin A.V. Physics. 7th grade.

§ 61. Application of the lever equilibrium rule to the block, pp. 180–183.

Gendenshtein L. E. Physics. 7th grade.

§ 24. Simple mechanisms, pp. 188–196.

"Block It is a wheel with a groove, mounted in a holder. A rope, cable or chain is passed through the block gutter.

"Fixed block they call such a block the axis of which is fixed and does not rise or fall when lifting loads (Fig. 177).

Fixed block can be considered as an equal-arm lever, in which the arms of the forces are equal to the radius of the wheel (Fig. 178): OA=OB=r.

Such a block does not provide a gain in strength

(F1 = F2), but allows you to change the direction of the force."

“Does a stationary block give you a gain in strength? ...in Fig. 24.1a the cable is tensioned by a force applied by the fisherman to the free end of the cable. The tension force of the cable remains constant along the cable, so from the side of the cable to the load (fish ) a force of the same magnitude acts. Therefore, a stationary block does not provide a gain in strength.

6.How can you gain strength using a fixed block? If a person lifts yourself, as shown in Fig. 24.6, then the weight of the person is distributed equally into two parts of the cable (according to different sides block). Therefore, a person lifts himself by applying a force that is half his weight."

« Movable block- this is a block whose axis rises and falls along with the load (Fig. 179).

Figure 180 shows the lever corresponding to it: O is the fulcrum of the lever,

AO - arm of force P and OB - arm of force F.

Since the OB arm is 2 times larger than the OA arm,

then the force F is 2 times less than the force P: F=P/2.

Thus, the movable block gives a gain offorce 2 times".

"5. Why does a moving block give a win inin forcetwice?

When the load is lifted uniformly, the moving block also moves uniformly. This means that the resultant of all forces applied to it is zero. If the mass of the block and the friction in it can be neglected, then we can assume that three forces are applied to the block: the weight of the load P, directed downward, and two identical tension forces of the cable F, directed upward. Since the resultant of these forces is zero, then P = 2F, that is the weight of the load is 2 times the tension force of the cable. But the tension force of the cable is precisely the force that is applied when lifting the load with the help of a movable block. Thus we have proven that the movable block gives a gain in force 2 times".

“Usually in practice they use a combination of a fixed block and a movable one (Fig. 181).

The fixed block is used for convenience only. It does not give a gain in strength, but it changes the direction of the force, for example, it allows you to lift a load while standing on the ground.

Fig. 181. A combination of movable and fixed blocks - a chain hoist."

“12.Figure 24.7 shows the system

blocks. How many movable blocks does it have and how many fixed ones?

What gain in strength does such a system of blocks give if friction and

can the mass of the blocks be neglected? .

Fig.24.7. Answer on page 240: “12. Three moving blocks and one fixed; 8 times."

Let’s summarize the review and comparison of texts and pictures in textbooks:

The proof of obtaining a gain in strength in the textbook by A. V. Peryshkin is carried out on the wheel of the block and the acting force is the force of the lever; When lifting a load, a stationary block does not provide a gain in strength, but a movable block provides a 2-fold gain in force. There is no mention of a cable on which a load hangs on a fixed block and a movable block with a load.

On the other hand, in the textbook by Gendenstein L.E., the proof of the gain in force is carried out on a cable on which a load or a movable block with a load hangs and the acting force is the tension force of the cable; when lifting a load, a stationary block can give a 2-fold increase in strength, but there is no mention in the text of the lever on the block wheel.

A search for literature describing the gain in force using a block and a cable led to the “Elementary Textbook of Physics”, edited by Academician G. S. Landsberg, in §84. Simple machines on pp. 168–175 describe: “simple block, double block, gate, pulley and differential block.” Indeed, by its design, “a double block gives a gain in strength when lifting a load, due to the difference in the length of the radii of the blocks” with the help of which the load is lifted, and “a pulley block gives a gain in strength when lifting a load, due to the rope , on several parts of which a load hangs.” Thus, it was possible to find out why a block and a cable (rope) give a gain in strength when lifting a load, but it was not possible to find out how the block and cable interact with each other and transfer the weight of the load to each other, since the load can be suspended on a cable , and the cable is thrown over the block or the load can hang on the block, and the block hangs on the cable. It turned out that the tension force of the cable is constant and acts along the entire length of the cable, so the transfer of the weight of the load by the cable to the block will be at each point of contact between the cable and the block, as well as the transfer of the weight of the load suspended on the block to the cable. To clarify the interaction of the block with the cable, we will conduct experiments to obtain a gain in force with a moving block when lifting a load, using the equipment of a school physics classroom: dynamometers, laboratory blocks and a set of weights in 1H (102 g). Let's start the experiments with a moving block, because we have three different versions obtaining a gain in power with this block. The first version is “Fig.180. A moving block as a lever with unequal arms" - textbook by A. V. Peryshkin, the second "Fig. 24.5... two equal tension forces of the cable F" - according to the textbook by L. E. Gendenstein and finally the third "Fig. 145. Pull Block" . Lifting a load with a movable clip of a pulley on several parts of one rope - according to the textbook by G. S. Landsberg.

Experience No. 1. "Fig. 183"

To carry out experiment No. 1, obtaining a gain in strength on the movable block “with a lever with unequal shoulders OAB Fig. 180” according to the textbook by A. V. Peryshkin, on the movable block “Fig. 183” position 1, draw a lever with unequal shoulders OAB, as in “Fig. 180”, and begin lifting the load from position 1 to position 2. At the same instant, the block begins to rotate, counterclockwise, around its axis at point A, and point B, the end of the lever behind which the lift occurs, comes out beyond the semicircle along which the cable goes around the moving block from below. Point O - the fulcrum of the lever, which should be stationary, goes down, see “Fig. 183” - position 2, i.e. a lever with unequal shoulders OAB changes like a lever with equal shoulders (points O and B pass through the same paths).

Based on the data obtained in experiment No. 1 on changes in the position of the OAB lever on the moving block when lifting a load from position 1 to position 2, we can conclude that the representation of the moving block as a lever with unequal arms in “Fig. 180”, when lifting load, with the rotation of the block around its axis, corresponds to a lever with equal arms, which does not provide a gain in strength when lifting the load.

We will begin experiment No. 2 by attaching dynamometers to the ends of the cable, on which we will hang a moving block with a load weighing 102 g, which corresponds to a gravity force of 1 N. We will fix one of the ends of the cable on a suspension, and using the other end of the cable we will lift the load on the moving block. Before the ascent, the readings of both dynamometers were 0.5 N each; at the beginning of the ascent, the readings of the dynamometer for which the ascent occurred changed to 0.6 N, and remained so during the ascent; at the end of the ascent, the readings returned to 0.5 N. The readings of the dynamometer, fixed for a fixed suspension did not change during the rise and remained equal to 0.5 N. Let us analyze the results of the experiment:

Before lifting, when a load of 1 N (102 g) hangs on a movable block, the weight of the load is distributed over the entire wheel and transferred to the cable, which goes around the block from below, using the entire semicircle of the wheel.
Before lifting, the readings of both dynamometers are 0.5 N, which indicates the distribution of the weight of a load of 1 N (102 g) into two parts of the cable (before and after the block) or that the tension force of the cable is 0.5 N, and is the same along the entire length of the cable (the same at the beginning, the same at the end of the cable) - both of these statements are true.

Let's compare the analysis of experiment No. 2 with the textbook versions about obtaining a 2-fold gain in strength using a moving block. Let's start with the statement in the textbook by Gendenstein L.E. “... that three forces are applied to the block: the weight of the load P, directed downward, and two identical tension forces of the cable, directed upward (Fig. 24.5).” It would be more accurate to say that the weight of the load in “Fig. 14.5" was distributed into two parts of the cable, before and after the block, since the tension force of the cable is one. It remains to analyze the signature under “Fig. 181” from the textbook by A. V. Peryshkin “Combination of movable and fixed blocks - pulley block.” A description of the device and the gain in strength when lifting a load with a pulley is given in the Elementary Textbook of Physics, ed. Lansberg G.S. where it is said: “Each piece of rope between the blocks will act on a moving load with a force T, and all pieces of rope will act with a force nT, where n is the number of separate sections of rope connecting both parts of the block.” It turns out that if we apply to “Fig. 181” the gain in force with a “rope connecting both parts” of the pulley from the Elementary Textbook of Physics by G. S. Landsberg, then the description of the gain in force with a moving block in “Fig. 179” and, accordingly, Fig. 180" would be an error.

Having analyzed four physics textbooks, we can conclude that the existing description of how a simple block mechanism produces a gain in force does not correspond to the real state of affairs and therefore requires a new description of the operation of a simple block mechanism.

Simple lifting mechanism consists of a block and a cable (rope or chain).

The blocks of this lifting mechanism are divided into:

by design into simple and complex;

according to the method of lifting loads into movable and stationary ones.

Let's start getting acquainted with the design of blocks with simple block, which is a wheel rotating around its axis, with a groove around the circumference for a cable (rope, chain) Fig. 1 and it can be considered as an equal-armed lever in which the arms of forces are equal to the radius of the wheel: OA=OB=r. Such a block does not provide a gain in strength, but allows you to change the direction of movement of the cable (rope, chain).

Double block consists of two blocks of different radii, rigidly fastened together and mounted on common axis Fig.2. The radii of the blocks r1 and r2 are different and, when lifting a load, they act like a lever with unequal shoulders, and the gain in force will be equal to the ratio of the lengths of the radii of the block of larger diameter to the block of smaller diameter F = Р·r1/r2.

Gate consists of a cylinder (drum) and a handle attached to it, which acts as a block large diameter, The gain in force given by the collar is determined by the ratio of the radius of the circle R described by the handle to the radius of the cylinder r on which the rope is wound F = Р·r/R.

Let's move on to the method of lifting a load with blocks. From the design description, all blocks have an axis around which they rotate. If the axis of the block is fixed and does not rise or fall when lifting loads, then such a block is called fixed block single block, double block, gate.

U moving block the axle rises and falls together with the load (Fig. 10) and it is intended mainly to eliminate the bending of the cable at the place where the load is suspended.

Let's get acquainted with the device and method of lifting a load; the second part of a simple lifting mechanism is a cable, rope or chain. The cable is made of steel wires, the rope is made of threads or strands, and the chain consists of links connected to each other.

Methods for hanging a load and gaining strength when lifting a load with a cable:

In Fig. 4, the load is fixed at one end of the cable, and if you lift the load by the other end of the cable, then to lift this load you will need a force slightly greater than the weight of the load, since a simple block of gain in strength does not give F = P.

In Fig. 5, the worker lifts the load by a cable that goes around a simple block from above; at one end of the first part of the cable there is a seat on which the worker sits, and by the second part of the cable the worker lifts himself with a force 2 times less than his weight, because the worker’s weight was distributed into two parts of the cable, the first - from the seat to the block, and the second - from the block to the worker’s hands F = P/2.

In Fig. 6, the load is lifted by two workers using two cables and the weight of the load will be distributed equally between the cables and therefore each worker will lift the load with a force of half the weight of the load F = P/2.

In Fig. 7, workers are lifting a load that hangs on two parts of one cable and the weight of the load will be distributed equally between the parts of this cable (as between two cables) and each worker will lift the load with a force equal to half the weight of the load F = P/2.

In Fig. 8, the end of the cable, by which one of the workers was lifting the load, was secured on a stationary suspension, and the weight of the load was distributed into two parts of the cable, and when the worker lifted the load by the second end of the cable, the force with which the worker would lift the load was doubled less than the weight of the load F = P/2 and lifting the load will be 2 times slower.

In Fig. 9, the load hangs on 3 parts of one cable, one end of which is fixed and the gain in force when lifting the load will be equal to 3, since the weight of the load will be distributed over three parts of the cable F = P/3.

To eliminate the bend and reduce the friction force, a simple block is installed in the place where the load is suspended and the force required to lift the load has not changed, since a simple block does not provide a gain in strength (Fig. 10 and Fig. 11), and the block itself will be called moving block, since the axis of this block rises and falls along with the load.

Theoretically, a load can be suspended on an unlimited number of parts of one cable, but in practice they are limited to six parts and such a lifting mechanism is called chain hoist, which consists of fixed and movable clips with simple blocks, which are alternately wrapped around a cable, one end of which is fixed to a fixed clip, and the load is lifted using the other end of the cable. The gain in strength depends on the number of parts of the cable between the fixed and movable cages; as a rule, it is 6 parts of the cable and the gain in strength is 6 times.

The article examines the real-life interactions between the blocks and the cable when lifting a load. The existing practice in determining that “a fixed block does not give a gain in strength, but a movable block gives a gain in force by 2 times” erroneously interpreted the interaction of the cable and the block in lifting mechanism and did not reflect the full diversity of block designs, which led to the development of one-sided erroneous ideas about the block. Compared to the existing volumes of material for studying a simple block mechanism, the volume of the article has increased by 2 times, but this made it possible to clearly and intelligibly explain the processes occurring in a simple lifting mechanism not only to students, but also to teachers.

Literature:

Pyryshkin, A.V. Physics, 7th grade: textbook / A.V. Pyryshkin. - 3rd ed., additional - M.: Bustard, 2014, - 224 p.,: ill. ISBN 978–5-358–14436–1. § 61. Application of the lever equilibrium rule to the block, pp. 181–183.
Gendenstein, L. E. Physics. 7th grade. In 2 hours. Part 1. Textbook for educational institutions / L. E. Gendenshten, A. B. Kaidalov, V. B. Kozhevnikov; edited by V. A. Orlova, I. I. Roizen. - 2nd ed., revised. - M.: Mnemosyne, 2010.-254 p.: ill. ISBN 978–5-346–01453–9. § 24. Simple mechanisms, pp. 188–196.
Elementary textbook of physics, edited by academician G. S. Landsberg Volume 1. Mechanics. Heat. Molecular physics. - 10th ed. - M.: Nauka, 1985. § 84. Simple machines, pp. 168–175.
Gromov, S. V. Physics: Textbook. for 7th grade general education institutions / S. V. Gromov, N. A. Rodina. - 3rd ed. - M.: Education, 2001.-158 p.,: ill. ISBN-5–09–010349–6. §22. Block, pp.55 -57.

Keywords: block, double block, fixed block, movable block, pulley block..

Annotation: Physics textbooks for the 7th grade, when studying a simple block mechanism, interpret in different ways the gain in force when lifting a load using this mechanism, for example: in the textbook by A. V. Peryshkin, the gain in force is achieved using the wheel of the block, on which the forces of the lever act, and in the textbook by Gendenstein L.E. the same gain is obtained with the help of a cable, which is acted upon by the tension force of the cable. Different textbooks, different objects and different forces - to obtain a gain in strength when lifting a load. Therefore, the purpose of this article is to search for objects and forces with the help of which a gain in strength is obtained when lifting a load with a simple block mechanism.

ITEM: Physics

CLASS: 7

LESSON TOPIC: Inclined plane. "The Golden Rule of Mechanics."

Physics teacher

TYPE OF LESSON: Combined.

THE PURPOSE OF THE LESSON: Update your knowledge on the topic "Simple mechanisms"

and learn the general position for all varieties of simple

mechanisms, which is called the “golden rule” of mechanics.

LESSON OBJECTIVES:

EDUCATIONAL:

- deepen knowledge about the condition of equilibrium of a rotating body, about moving and stationary blocks;

Prove that simple mechanisms used in work provide a gain in strength, and on the other hand, allow you to change the direction of body movement under the influence of force;

Develop practical skills in selecting reasoned material.

EDUCATIONAL:

To cultivate intellectual culture in leading students to understand the basic rules of simple mechanisms;

To introduce the functions of using levers in everyday life, in technology, in a school workshop, in nature.

DEVELOPMENT OF THINKING:

Develop the ability to generalize known data based on highlighting the main thing;

Form elements of creative search based on the technique of generalization.

EQUIPMENT: Instruments (levers, set of weights, ruler, blocks, inclined plane, dynamometer), table “Levers in Wildlife”, computers, handouts (tests, task cards), textbook, blackboard, chalk.

DURING THE CLASSES.

STRUCTURAL ELEMENTS OF A LESSON ACTIVITIES OF THE TEACHER AND STUDENTS

STATEMENT OF THE LESSON OBJECTIVE The teacher addresses the class:

Covering the whole world from earth to heaven,

Having alarmed more than one generation,

Scientific progress is sweeping across the planet.

Nature has fewer and fewer secrets.

How to use knowledge is people's concern.

Today guys, let's meet general position simple mechanisms called "golden rule" of mechanics.

QUESTION FOR STUDENTS (GROUP OF LINGUISTS)

Why do you think the rule is called "golden"?

ANSWER: " Golden Rule " - one of the oldest moral commandments contained in folk proverbs and sayings: “Do not do to others what you do not want to be done to you,” said the ancient eastern sages.

GROUP OF EXPERTS ANSWER: ”“Golden” is the basis of all foundations.

IDENTIFICATION OF KNOWLEDGE. PERFORMANCE OF THE WORK AND POWER TEST

(on a computer, test attached)

TRAINING TASKS AND QUESTIONS.

1.What is a lever?

2. What is called the shoulder of strength?

3. Lever balance rule.

4. Formula for the rule of lever equilibrium.

5. Find the error in the picture.

6. Using the lever equilibrium rule, find F2

d1=2cm d2=3cm

7. Will the lever be in equilibrium?

d1=4cm d2=3cm

A group of linguists performs № 1, 3, 5.

A group of precision workers perform № 2, 4, 6, 7.

EXPERIMENTAL TASK FOR STUDENT GROUP

1. Balance the lever

2. Hang two weights on the left side of the lever at a distance of 12 cm from the axis of rotation

3. Balance these two weights:

a) one load_ _ _ shoulder_ _ _ cm.

b) two weights_ _ _ shoulder_ _ _ cm.

c) three weights_ _ _shoulder _ _ _ cm.

A consultant works with students

In the world of interesting things.

"Levers in nature"

(prizewinner of the Biology Olympiad Marina Minakova speaks)

WORK ON Demonstration of experiments (consultant)

STUDIES No. 1 Application of the law of equilibrium of a lever to a block.

MATERIAL. a) Fixed block.

Previously updated Students should explain that a fixed block can be learned consider like an equal-armed lever and winning in

knowledge about simple does not give strength

mechanisms. No. 2 Balance of forces on a moving block.

Based on experiments, students conclude that the mobile
the block gives a double gain in strength and the same loss in
ways.

STUDYING

NEW MATERIAL. More than 2000 years have passed since Archimedes died, but also
today the memory of people preserves his words: “Give me a point of support, and
I will lift up the whole world for you.” So said the outstanding ancient Greek
scientist - mathematician, physicist, inventor, having developed a theory
lever and understanding its capabilities.

In front of the eyes of the ruler of Syracuse, Archimedes, taking advantage

complex
using a device made of levers, he single-handedly lowered the ship. Motto
everyone who finds something new is served the famous “Eureka!”

One of the simple mechanisms that gives a gain in strength is
inclined plane. Let us determine the work done using
inclined plane.

DEMONSTRATION OF EXPERIENCE:

Work of forces on an inclined plane.

We measure the height and length of the inclined plane and

We compare their ratio with the gain of power on

F plane.

L A) repeat the experiment by changing the angle of the board.

Conclusion from experience: inclined plane gives

h the gain in strength is as many times as its length

More height. =

2. The golden rule of mechanics is also true for

lever

When rotating the lever how many times

we win in strength, we lose by the same amount

in motion.

IMPROVEMENT Quality assignments.

AND APPLICATION No. 1. Why drivers avoid stopping trains at

KNOWLEDGE. rising? (answers a group of linguists).

No. 2 The block in position B slides down an inclined

plane, overcoming friction. Will it

slide the block in position A? (the answer is given

exacts).

Answer: It will be, because the valueF friction of the block on the plane is not
depends on the area of contacting surfaces.

Calculation tasks.

No. 1. Find the force acting parallel to the length of an inclined plane, the height of which is 1 m, length 8 m, in order to hold a load weighing 1.6 * 10³ N on the inclined plane

Given: Solution:

h = 1m F= F=

Answer: 2000N

No. 2. To hold a sled with a rider weighing 480 N on an ice mountain, a force of 120 N is needed. The slope of the slide is constant along its entire length. What is the length of the mountain if its height is 4 m?

Given: Solution:

h = 4m l =

Answer: 16m

No. 3. A car weighing 3*104 N moves uniformly on a rise 300 m long and 30 m high. Determine the traction force of the car if the friction force of the wheels on the ground is 750 N. What work does the engine do along this path?

Given: Solution:

P = 3*104H Force required for lifting
Ftr = 750H of the car without taking into account friction

l = 300m F= F=

h =30m Traction force is equal to: Fthrust= F+Ftr=3750H

Fthrust-?, A -? Engine operation: A= Fthrust*L

A=3750H*300m=1125*103J

Answer: 1125kJ

Summing up the lesson, assessing the work of students by consultants using a map of an intra-differentiated approach to the types of activities in the lesson.

HOMEWORK § 72 rep. § 69.71. With. 197 USD 41 No. 5

IN modern technology For the transfer of goods at construction sites and enterprises, lifting mechanisms are widely used, which are indispensable components which can be called simple mechanisms. Among them are the most ancient inventions of mankind: the block and the lever. The ancient Greek scientist Archimedes made man's work easier by giving him a gain in strength when using his invention, and taught him to change the direction of force.

A block is a wheel with a groove around its circumference for a rope or chain, the axis of which is rigidly attached to a wall or ceiling beam.

Lifting devices usually use not one, but several blocks. A system of blocks and cables designed to increase load capacity is called a chain hoist.

The movable and fixed block are the same ancient simple mechanisms as the lever. Already in 212 BC, with the help of hooks and grapples connected to blocks, the Syracusans captured siege equipment from the Romans. The construction of military vehicles and the defense of the city was led by Archimedes.

Archimedes considered a fixed block as an equal-armed lever.

The moment of force acting on one side of the block is equal to the moment of force applied on the other side of the block. The forces that create these moments are also the same.

There is no gain in strength, but such a block allows you to change the direction of the force, which is sometimes necessary.

Archimedes took the movable block as an unequal-armed lever, which gives a 2-fold gain in force. Relative to the center of rotation, moments of forces act, which in equilibrium must be equal.

Archimedes studied the mechanical properties of the moving block and applied it in practice. According to Athenaeus, “many methods were invented to launch the gigantic ship built by the Syracusan tyrant Hieron, but the mechanic Archimedes, using simple mechanisms, alone managed to move the ship with the help of a few people. Archimedes came up with a block and with the help of it launched a huge ship.” .

The block does not give any gain in work, confirming the golden rule of mechanics. This is easy to verify by paying attention to the distances traveled by the hand and the weight.

Sports sailing ships, like the sailboats of the past, cannot do without blocks when setting and controlling the sails. Modern ships need blocks for lifting signals and boats.