mechanical activity. Physical terms and terminology

« Physics - Grade 10 "

The law of conservation of energy is a fundamental law of nature that allows describing most of the phenomena that occur.

The description of the motion of bodies is also possible with the help of such concepts of dynamics as work and energy.

Remember what work and power are in physics.

Do these concepts coincide with everyday ideas about them?

All our daily activities boil down to the fact that with the help of muscles we either set the surrounding bodies in motion and maintain this movement, or we stop the moving bodies.

These bodies are tools (hammer, pen, saw), in games - balls, pucks, chess pieces. In production and agriculture people also set tools in motion.

The use of machines greatly increases labor productivity due to the use of engines in them.

The purpose of any engine is to set the bodies in motion and maintain this movement, despite braking by both ordinary friction and “working” resistance (the cutter must not only slide over the metal, but, crashing into it, remove chips; the plow must loosen land, etc.). In this case, a force must act on the moving body from the side of the engine.

Work is always done in nature when a force (or several forces) from another body (other bodies) acts on a body in the direction of its movement or against it.

The gravitational force does work when rain drops or a stone fall from a cliff. At the same time, the work is done by the resistance force acting on the falling drops or on the stone from the side of the air. The elastic force also does work when a tree bent by the wind straightens.

Job definition.

Newton's second law in impulsive form ∆=∆t allows you to determine how the speed of the body changes in absolute value and direction, if a force acts on it during the time Δt.

The impact on bodies of forces, leading to a change in the modulus of their velocity, is characterized by a value that depends both on the forces and on the displacements of the bodies. This quantity in mechanics is called work of force.

Modulo change of speed is possible only when the projection of the force F r on the direction of body movement is nonzero. It is this projection that determines the action of the force that changes the velocity of the body modulo. She does the work. Therefore, the work can be considered as the product of the projection of the force F r by the displacement modulus |Δ| (Fig. 5.1):

А = F r |Δ|. (5.1)

If the angle between force and displacement is denoted by α, then F r = Fcosα.

Therefore, the work is equal to:

A = |Δ|cosα. (5.2)

Our everyday concept of work differs from the definition of work in physics. You are holding a heavy suitcase, and it seems to you that you are doing work. However, from the point of view of physics, your work is equal to zero.

The work of a constant force is equal to the product of the modules of force and the displacement of the point of application of the force and the cosine of the angle between them.

In the general case, when a rigid body moves, the displacements of its different points are different, but when determining the work of a force, we Δ understand the movement of its point of application. In the translational motion of a rigid body, the displacement of all its points coincides with the displacement of the point of application of the force.

Work, unlike force and displacement, is not a vector, but a scalar quantity. It can be positive, negative or zero.

The sign of work is determined by the sign of the cosine of the angle between force and displacement. If α< 90°, то А >0 since the cosine sharp corners positive. For α > 90°, the work is negative, since the cosine obtuse corners negative. At α = 90° (the force is perpendicular to the displacement), no work is done.

If several forces act on the body, then the projection is equal to operating force per displacement is equal to the sum of the projections of individual forces:

F r = F 1r + F 2r + ... .

Therefore, for the work of the resultant force, we obtain

A = F 1r |Δ| + F 2r |Δ| + ... = A 1 + A 2 + .... (5.3)

If several forces act on the body, then the total work ( algebraic sum work of all forces) is equal to the work of the resultant force.

The work done by force can be represented graphically. Let us explain this by depicting in the figure the dependence of the projection of the force on the coordinate of the body when it moves in a straight line.

Let the body move along the OX axis (Fig. 5.2), then

Fcosα = F x , |Δ| = Δ x.

For the work of the force, we get

А = F|Δ|cosα = F x Δx.

Obviously, the area of ​​the rectangle shaded in Figure (5.3, a) is numerically equal to the work done when moving the body from a point with coordinate x1 to a point with coordinate x2.

Formula (5.1) is valid when the projection of the force on the displacement is constant. In the case of a curved trajectory, constant or variable force, we divide the trajectory into small segments, which can be considered rectilinear, and the projection of the force on a small displacement Δ - permanent.

Unit of work.

The unit of work can be set using the basic formula (5.2). If, when moving a body per unit length, a force acts on it, the modulus of which is equal to one, and the direction of the force coincides with the direction of movement of its point of application (α = 0), then the work will be equal to one. In the International System (SI), the unit of work is the joule (denoted J):

1 J = 1 N 1 m = 1 N m.

Joule is the work done by a force of 1 N at a displacement of 1 if the directions of the force and displacement coincide.

Multiple units of work are often used - kilojoule and mega joule:

1 kJ = 1000 J,
1 MJ = 1000000 J.

The work can be done as large gap time, and for very little. In practice, however, it is far from indifferent whether work can be done quickly or slowly. The time during which work is done determines the performance of any engine. A tiny electric motor can do a lot of work, but it will take a lot of time. Therefore, along with work, a value is introduced that characterizes the speed with which it is produced - power.

Power is the ratio of work A to the time interval Δt for which this work is done, i.e. power is the rate of work:

Substituting in formula (5.4) instead of work A its expression (5.2), we obtain

Thus, if the force and speed of the body are constant, then the power is equal to the product of the modulus of the force vector by the modulus of the velocity vector and the cosine of the angle between the directions of these vectors. If these quantities are variable, then by formula (5.4) one can determine the average power similarly to the determination of the average speed of a body.

The concept of power is introduced to evaluate the work per unit of time performed by some mechanism (pump, crane, machine motor, etc.). Therefore, in formulas (5.4) and (5.5), by always means the thrust force.

In SI, power is expressed in terms of watts (W).

The power is 1 W if the work equal to 1 J is done in 1 s.

Along with the watt, larger (multiple) units of power are used:

1 kW (kilowatt) = 1000 W,
1 MW (megawatt) = 1,000,000 W.

The horse pulls the cart with some force, let's denote it F traction. Grandpa, who is sitting on the cart, presses on her with some force. Let's denote it F pressure The cart moves in the direction of the horse's pulling force (to the right), but in the direction of the grandfather's pressure force (down), the cart does not move. Therefore, in physics they say that F traction does work on the cart, and F the pressure does not do work on the cart.

So, work done by a force on a body mechanical work- a physical quantity, the modulus of which is equal to the product of the force and the path traveled by the body along the direction of action of this force s:

In honor of the English scientist D. Joule, the unit of mechanical work was named 1 joule(according to the formula, 1 J = 1 N m).

If a certain force acts on the considered body, then a certain body acts on it. So the work of a force on a body and the work of a body on a body are complete synonyms. However, the work of the first body on the second and the work of the second body on the first are partial synonyms, since the modules of these works are always equal, and their signs are always opposite. That is why the “±” sign is present in the formula. Let's discuss signs of work in more detail.

Numerical values ​​of force and path are always non-negative values. In contrast, mechanical work can have both positive and negative signs. If the direction of the force coincides with the direction of motion of the body, then the work done by the force is considered positive. If the direction of the force is opposite to the direction of motion of the body, the work done by the force is considered negative.(we take "-" from the "±" formula). If the direction of motion of the body is perpendicular to the direction of the force, then such a force does no work, that is, A = 0.

Consider three illustrations on three aspects of mechanical work.

Doing work by force may look different from the point of view of different observers. Consider an example: a girl rides in an elevator up. Does it do mechanical work? A girl can do work only on those bodies on which she acts by force. There is only one such body - the elevator car, as the girl presses on her floor with her weight. Now we need to find out if the cabin goes some way. Consider two options: with a stationary and moving observer.

Let the observer boy sit on the ground first. In relation to it, the elevator car moves up and goes some way. The weight of the girl is directed towards opposite side- down, therefore, the girl performs negative mechanical work on the cabin: A virgins< 0. Вообразим, что мальчик-наблюдатель пересел внутрь кабины движущегося лифта. Как и ранее, вес девочки действует на пол кабины. Но теперь по отношению к такому наблюдателю кабина лифта не движется. Поэтому с точки зрения наблюдателя в кабине лифта девочка не совершает механическую работу: A dev = 0.

The energy characteristics of motion are introduced on the basis of the concept of mechanical work or the work of a force.

Work A performed by a constant force F → is a physical quantity equal to the product of the modules of force and displacement, multiplied by the cosine of the angle α located between force vectors F → and displacement s → .

This definition seen in Figure 1. eighteen . one .

The work formula is written as,

A = F s cos α .

Work is a scalar quantity. This makes it possible to be positive at (0 ° ≤ α< 90 °) , отрицательной при (90 ° < α ≤ 180 °) . Когда задается прямой угол α , тогда совершаемая сила равняется нулю. Единицы измерения работы по системе СИ - джоули (Д ж) .

A joule is equal to the work done by a force of 1 N to move 1 m in the direction of the force.

Picture 1 . eighteen . one . Work force F → : A = F s cos α = F s s

When projecting F s → force F → onto the direction of movement s → the force does not remain constant, and the calculation of work for small displacements Δ s i summed up and produced according to the formula:

A = ∑ ∆ A i = ∑ F s i ∆ s i .

This amount of work is calculated from the limit (Δ s i → 0), after which it goes into the integral.

The graphic image of the work is determined from the area of ​​the curvilinear figure located under the graph F s (x) of Figure 1. eighteen . 2.

Picture 1 . eighteen . 2. Graphic definition of work Δ A i = F s i Δ s i .

An example of a coordinate-dependent force is the elastic force of a spring, which obeys Hooke's law. To stretch the spring, it is necessary to apply a force F → , the modulus of which is proportional to the elongation of the spring. This can be seen in Figure 1. eighteen . 3 .

Picture 1 . eighteen . 3 . Stretched spring. Direction external force F → coincides with the direction of movement s → . F s = k x , where k is the stiffness of the spring.

F → y p p = - F →

The dependence of the module of the external force on the coordinates x can be shown on the graph using a straight line.

Picture 1 . eighteen . 4 . Dependence of the module of the external force on the coordinate when the spring is stretched.

From the above figure, it is possible to find work on the external force of the right free end of the spring, using the area of ​​the triangle. The formula will take the form

This formula is applicable to express the work done by an external force when a spring is compressed. Both cases show that the elastic force F → y p p is equal to the work of the external force F → , but with the opposite sign.

Definition 2

If several forces act on the body, then the formula for the total work will look like the sum of all the work done on it. When a body moves forward, the points of application of forces move in the same way, that is general work of all forces will be equal to the work of the resultant of the applied forces.

Picture 1 . eighteen . 5 . model of mechanical work.

Determination of power

Power is the work done by a force per unit of time.

The record of the physical quantity of power, denoted N, takes the form of the ratio of work A to the time interval t of the work performed, that is:

Definition 4

The SI system uses the watt (Wt) as the unit of power, which is equal to the power of a force that does work of 1 J in 1 s.

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To be able to characterize the energy characteristics of motion, the concept of mechanical work was introduced. And it is to her in her various manifestations that the article is devoted. To understand the topic is both easy and quite complex. The author sincerely tried to make it more understandable and understandable, and one can only hope that the goal has been achieved.

What is mechanical work?

What is it called? If some force works on the body, and as a result of the action of this force, the body moves, then this is called mechanical work. When approached from the point of view of scientific philosophy, several additional aspects can be distinguished here, but the article will cover the topic from the point of view of physics. mechanical work- it's not difficult if you think carefully about the words written here. But the word "mechanical" is usually not written, and everything is reduced to the word "work". But not every job is mechanical. Here a man sits and thinks. Does it work? Mentally yes! But is it mechanical work? No. What if the person is walking? If the body moves under the influence of a force, then this is mechanical work. Everything is simple. In other words, the force acting on the body does (mechanical) work. And one more thing: it is work that can characterize the result of the action of a certain force. So if a person walks, then certain forces (friction, gravity, etc.) perform mechanical work on a person, and as a result of their action, a person changes his point of location, in other words, he moves.

Work as a physical quantity is equal to the force that acts on the body, multiplied by the path that the body made under the influence of this force and in the direction indicated by it. We can say that mechanical work was done if 2 conditions were simultaneously met: the force acted on the body, and it moved in the direction of its action. But it was not performed or is not performed if the force acted, and the body did not change its location in the coordinate system. Here small examples when no mechanical work is done:

1. So a person can fall on a huge boulder in order to move it, but there is not enough strength. The force acts on the stone, but it does not move, and work does not occur.
2. The body moves in the coordinate system, and the force is equal to zero or they are all compensated. This can be observed during inertial motion.
3. When the direction in which the body moves is perpendicular to the force. When the train moves along a horizontal line, the force of gravity does not do its work.

Depending on certain conditions, mechanical work can be negative and positive. So, if the directions and forces, and the movements of the body are the same, then positive work occurs. An example of positive work is the effect of gravity on a falling drop of water. But if the force and direction of movement are opposite, then negative mechanical work occurs. An example of such an option is the rising balloon and the force of gravity, which does negative work. When a body is subjected to the influence of several forces, such work is called "resultant force work".

Features of practical application (kinetic energy)

We pass from theory to practical part. Separately, we should talk about mechanical work and its use in physics. As many probably remembered, all the energy of the body is divided into kinetic and potential. When an object is in equilibrium and not moving anywhere, its potential energy is equal to the total energy, and its kinetic energy is zero. When the movement begins, the potential energy begins to decrease, the kinetic energy to increase, but in total they are equal to the total energy of the object. For a material point, kinetic energy is defined as the work of the force that accelerated the point from zero to the value H, and in formula form, the kinetics of the body is ½ * M * H, where M is the mass. To find out the kinetic energy of an object that consists of many particles, you need to find the sum of all the kinetic energy of the particles, and this will be the kinetic energy of the body.

Features of practical application (potential energy)

In the case when all the forces acting on the body are conservative, and the potential energy is equal to the total, then no work is done. This postulate is known as the law of conservation of mechanical energy. Mechanical energy in closed system is constant over time. The conservation law is widely used to solve problems from classical mechanics.

Features of practical application (thermodynamics)

In thermodynamics, the work done by a gas during expansion is calculated by the integral of pressure multiplied by volume. This approach is applicable not only in cases where there is an exact function of volume, but also to all processes that can be displayed in the pressure/volume plane. The knowledge of mechanical work is also applied not only to gases, but to everything that can exert pressure.

Features of practical application in practice (theoretical mechanics)

In theoretical mechanics, all the properties and formulas described above are considered in more detail, in particular, these are projections. She also gives her own definition for various formulas of mechanical work (an example of the definition for the Rimmer integral): the limit to which the sum of all the forces of elementary work tends when the fineness of the partition tends to zero is called the work of the force along the curve. Probably difficult? But nothing, with theoretical mechanics everything. Yes, and all the mechanical work, physics and other difficulties are over. Further there will be only examples and a conclusion.

Mechanical work units

The SI uses joules to measure work, while the GHS uses ergs:

1. 1 J = 1 kg m²/s² = 1 Nm
2. 1 erg = 1 g cm²/s² = 1 dyn cm
3. 1 erg = 10 −7 J

Examples of mechanical work

In order to finally understand such a concept as mechanical work, you should study a few separate examples that will allow you to consider it from many, but not all, sides:

1. When a person lifts a stone with his hands, then mechanical work occurs with the help of the muscular strength of the hands;
2. When a train travels along the rails, it is pulled by the traction force of the tractor (electric locomotive, diesel locomotive, etc.);
3. If you take a gun and shoot from it, then thanks to the pressure force that the powder gases will create, work will be done: the bullet is moved along the barrel of the gun at the same time as the speed of the bullet itself increases;
4. There is also mechanical work when the friction force acts on the body, forcing it to reduce the speed of its movement;
5. The above example with balls, when they rise in the opposite direction relative to the direction of gravity, is also an example of mechanical work, but in addition to gravity, the Archimedes force also acts when everything that is lighter than air rises up.

What is power?

Finally, I want to touch on the topic of power. The work done by a force in one unit of time is called power. In fact, power is such a physical quantity that is a reflection of the ratio of work to a certain period of time during which this work was done: M = P / B, where M is power, P is work, B is time. The SI unit of power is 1 watt. A watt is equal to the power that does the work of one joule in one second: 1 W = 1J \ 1s.

Mechanical work. Units of work.

In everyday life, under the concept of "work" we understand everything.

In physics, the concept Work somewhat different. This is a certain physical quantity, which means that it can be measured. In physics, the study is primarily mechanical work .

Consider examples of mechanical work.

The train moves under the action of the traction force of the electric locomotive, while doing mechanical work. When a gun is fired, the pressure force of the powder gases does work - it moves the bullet along the barrel, while the speed of the bullet increases.

From these examples, it can be seen that mechanical work is done when the body moves under the action of a force. Mechanical work is also performed in the case when the force acting on the body (for example, the friction force) reduces the speed of its movement.

Wanting to move the cabinet, we press on it with force, but if it does not move at the same time, then we do not perform mechanical work. One can imagine the case when the body moves without the participation of forces (by inertia), in this case, mechanical work is also not performed.

So, mechanical work is done only when a force acts on the body and it moves .

It is easy to understand that the greater the force acting on the body and the longer the path that the body passes under the action of this force, the greater the work done.

Mechanical work is directly proportional to the applied force and directly proportional to the distance traveled. .

Therefore, we agreed to measure mechanical work by the product of force and the path traveled in this direction of this force:

work = force × path

where A- Work, F- strength and s- distance traveled.

A unit of work is the work done by a force of 1 N on a path of 1 m.

Unit of work - joule (J ) is named after the English scientist Joule. In this way,

1 J = 1N m.

Also used kilojoules (kJ) .

1 kJ = 1000 J.

Formula A = Fs applicable when the power F is constant and coincides with the direction of motion of the body.

If the direction of the force coincides with the direction of motion of the body, then this force does positive work.

If the motion of the body occurs in the direction opposite to the direction of the applied force, for example, the force of sliding friction, then this force does negative work.

If the direction of the force acting on the body is perpendicular to the direction of motion, then this force does no work, the work is zero:

In the future, speaking of mechanical work, we will briefly call it in one word - work.

Example. Calculate the work done when lifting a granite slab with a volume of 0.5 m3 to a height of 20 m. The density of granite is 2500 kg / m 3.

Given:

ρ \u003d 2500 kg / m 3

Solution:

where F is the force that must be applied to evenly lift the plate up. This force is equal in modulus to the force of the strand Fstrand acting on the plate, i.e. F = Fstrand. And the force of gravity can be determined by the mass of the plate: Ftyazh = gm. We calculate the mass of the slab, knowing its volume and density of granite: m = ρV; s = h, i.e. the path is equal to the height of the ascent.

So, m = 2500 kg/m3 0.5 m3 = 1250 kg.

F = 9.8 N/kg 1250 kg ≈ 12250 N.

A = 12,250 N 20 m = 245,000 J = 245 kJ.

Answer: A = 245 kJ.

Levers.Power.Energy

It takes different engines to do the same work. different time. For instance, crane at a construction site, he lifts hundreds of bricks to the top floor of a building in a few minutes. If a worker were to move these bricks, it would take him several hours to do this. Another example. A horse can plow a hectare of land in 10-12 hours, while a tractor with a multi-share plow ( ploughshare- part of the plow that cuts the layer of earth from below and transfers it to the dump; multi-share - a lot of shares), this work will be done for 40-50 minutes.

It is clear that a crane does the same work faster than a worker, and a tractor faster than a horse. The speed of work is characterized by a special value called power.

Power is equal to the ratio of work to the time for which it was completed.

To calculate the power, it is necessary to divide the work by the time during which this work is done. power = work / time.

where N- power, A- Work, t- time of work done.

Power is a constant value, when the same work is done for every second, in other cases the ratio A/t determines the average power:

N cf = A/t . The unit of power was taken as the power at which work in J is done in 1 s.

This unit is called the watt ( Tue) in honor of another English scientist Watt.

1 watt = 1 joule/ 1 second, or 1 W = 1 J/s.

Watt (joule per second) - W (1 J / s).

Larger units of power are widely used in engineering - kilowatt (kW), megawatt (MW) .

1 MW = 1,000,000 W

1 kW = 1000 W

1 mW = 0.001 W

1 W = 0.000001 MW

1 W = 0.001 kW

1 W = 1000 mW

Example. Find the power of the flow of water flowing through the dam, if the height of the water fall is 25 m, and its flow rate is 120 m3 per minute.

Given:

ρ = 1000 kg/m3

Solution:

Mass of falling water: m = ρV,

m = 1000 kg/m3 120 m3 = 120,000 kg (12 104 kg).

The force of gravity acting on water:

F = 9.8 m/s2 120,000 kg ≈ 1,200,000 N (12 105 N)

Work done per minute:

A - 1,200,000 N 25 m = 30,000,000 J (3 107 J).

Flow power: N = A/t,

N = 30,000,000 J / 60 s = 500,000 W = 0.5 MW.

Answer: N = 0.5 MW.

Various motors have powers ranging from hundredths and tenths of a kilowatt (an electric razor motor, sewing machine) up to hundreds of thousands of kilowatts (water and steam turbines).

Table 5

Power of some engines, kW.

Each engine has a plate (engine passport), which contains some data about the engine, including its power.

Human power at normal conditions work on average is 70-80 watts. Making jumps, running up the stairs, a person can develop power up to 730 watts, and in some cases even more.

From the formula N = A/t it follows that

To calculate the work, you need to multiply the power by the time during which this work was done.

Example. The room fan motor has a power of 35 watts. How much work does he do in 10 minutes?

Let's write down the condition of the problem and solve it.

Given:

Solution:

A = 35 W * 600 s = 21,000 W * s = 21,000 J = 21 kJ.

Answer A= 21 kJ.

simple mechanisms.

Since time immemorial, man has been using various devices to perform mechanical work.

Everyone knows that a heavy object (stone, cabinet, machine), which cannot be moved by hand, can be moved with a fairly long stick - a lever.

On the this moment it is believed that with the help of levers three thousand years ago, during the construction of the pyramids in ancient Egypt, heavy stone slabs were moved and raised to a great height.

In many cases, instead of lifting a heavy load to a certain height, it can be rolled or pulled to the same height on an inclined plane or lifted with blocks.

Devices used to transform power are called mechanisms .

Simple mechanisms include: levers and its varieties - block, gate; inclined plane and its varieties - wedge, screw. In most cases simple mechanisms are used in order to obtain a gain in strength, i.e., to increase the force acting on the body several times.

Simple mechanisms are found in household and all complex factory and factory machines that cut, twist and stamp large sheets steel or pull out the finest threads, from which fabrics are then made. The same mechanisms can be found in modern complex automata, printing and counting machines.

Lever arm. The balance of forces on the lever.

Consider the simplest and most common mechanism - the lever.

The lever is a rigid body that can rotate around a fixed support.

The figures show how a worker uses a crowbar to lift a load as a lever. In the first case, a worker with a force F presses the end of the crowbar B, in the second - raises the end B.

The worker needs to overcome the weight of the load P- force directed vertically downwards. For this, he rotates the crowbar around an axis passing through the only motionless breaking point - its fulcrum O. Power F, with which the worker acts on the lever, less force P, so the worker gets gain in strength. With the help of a lever, you can lift such a heavy load that you cannot lift it on your own.

The figure shows a lever whose axis of rotation is O(fulcrum) is located between the points of application of forces A and V. The other figure shows a diagram of this lever. Both forces F 1 and F 2 acting on the lever are directed in the same direction.

The shortest distance between the fulcrum and the straight line along which the force acts on the lever is called the arm of the force.

The length of this perpendicular will be the shoulder of this force. The figure shows that OA- shoulder strength F 1; OV- shoulder strength F 2. The forces acting on the lever can rotate it around the axis in two directions: clockwise or counterclockwise. Yes, power F 1 rotates the lever clockwise, and the force F 2 rotates it counterclockwise.

The condition under which the lever is in equilibrium under the action of forces applied to it can be established experimentally. At the same time, it must be remembered that the result of the action of a force depends not only on its numerical value (modulus), but also on the point at which it is applied to the body, or how it is directed.

Various weights are suspended from the lever (see Fig.) on both sides of the fulcrum so that each time the lever remains in balance. The forces acting on the lever are equal to the weights of these loads. For each case, the modules of forces and their shoulders are measured. From the experience shown in Figure 154, it can be seen that the force 2 H balances power 4 H. In this case, as can be seen from the figure, the shoulder of lesser force is 2 times larger than the shoulder of greater force.

On the basis of such experiments, the condition (rule) of the balance of the lever was established.

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

This rule can be written as a formula:

F 1/F 2 = l 2/ l 1 ,

where F 1and F 2 - forces acting on the lever, l 1and l 2 , - the shoulders of these forces (see Fig.).

The rule for the balance of the lever was established by Archimedes around 287-212. BC e. (But didn't the last paragraph say that the levers were used by the Egyptians? Or is the word "established" important here?)

It follows from this rule that a smaller force can be balanced with a leverage of a larger force. Let one arm of the lever be 3 times larger than the other (see Fig.). Then, applying a force of, for example, 400 N at point B, it is possible to lift a stone weighing 1200 N. In order to lift an even heavier load, it is necessary to increase the length of the lever arm on which the worker acts.

Example. Using a lever, a worker lifts a slab weighing 240 kg (see Fig. 149). What force does he apply to the larger arm of the lever, which is 2.4 m, if the smaller arm is 0.6 m?

Let's write down the condition of the problem, and solve it.

Given:

Solution:

According to the lever equilibrium rule, F1/F2 = l2/l1, whence F1 = F2 l2/l1, where F2 = P is the weight of the stone. Stone weight asd = gm, F = 9.8 N 240 kg ≈ 2400 N

Then, F1 = 2400 N 0.6 / 2.4 = 600 N.

Answer: F1 = 600 N.

In our example, the worker overcomes a force of 2400 N by applying a force of 600 N to the lever. But at the same time, the arm on which the worker acts is 4 times longer than that on which the weight of the stone acts ( l 1 : l 2 = 2.4 m: 0.6 m = 4).

By applying the rule of leverage, a smaller force can balance a larger force. In this case, the arm of lesser force should be longer than the arm greater strength.

Moment of power.

You already know the lever balance rule:

F 1 / F 2 = l 2 / l 1 ,

Using the property of proportion (the product of its extreme terms is equal to the product of its middle terms), we write it in this form:

F 1l 1 = F 2 l 2 .

On the left side of the equation is the product of the force F 1 on her shoulder l 1, and on the right - the product of the force F 2 on her shoulder l 2 .

The product of the modulus of the force rotating the body and its arm is called moment of force; it is denoted by the letter M. So,

A lever is in equilibrium under the action of two forces if the moment of force rotating it clockwise is equal to the moment of force rotating it counterclockwise.

This rule is called moment rule , can be written as a formula:

M1 = M2

Indeed, in the experiment we have considered, (§ 56) the acting forces were equal to 2 N and 4 N, their shoulders, respectively, were 4 and 2 lever pressures, i.e., the moments of these forces are the same when the lever is in equilibrium.

The moment of force, like any physical quantity, can be measured. A moment of force of 1 N is taken as a unit of moment of force, the shoulder of which is exactly 1 m.

This unit is called newton meter (N m).

The moment of force characterizes the action of the force, and shows that it depends simultaneously on the modulus of the force and on its shoulder. Indeed, we already know, for example, that the effect of a force on a door depends both on the modulus of the force and on where the force is applied. The door is easier to turn, the farther from the axis of rotation the force acting on it is applied. Nut, it is better to unscrew the long wrench than short. The easier it is to lift a bucket from the well, the longer the handle of the gate, etc.

Levers in technology, everyday life and nature.

The lever rule (or the rule of moments) underlies the action of various kinds of tools and devices used in technology and everyday life where a gain in strength or on the road is required.

We have a gain in strength when working with scissors. Scissors - it's a lever(rice), the axis of rotation of which occurs through a screw connecting both halves of the scissors. acting force F 1 is the muscular strength of the hand of the person squeezing the scissors. Opposing force F 2 - the resistance force of such a material that is cut with scissors. Depending on the purpose of the scissors, their device is different. Office scissors, designed for cutting paper, have long blades and handles that are almost the same length. It does not require much force to cut paper, and it is more convenient to cut in a straight line with a long blade. Cutting scissors sheet metal(Fig.) have handles much longer than the blades, since the resistance force of the metal is large and to balance it, the shoulder of the acting force has to be significantly increased. Even more difference between the length of the handles and the distance of the cutting part and the axis of rotation in wire cutters(Fig.), Designed for wire cutting.

Levers different kind many cars have. A sewing machine handle, bicycle pedals or hand brakes, car and tractor pedals, piano keys are all examples of levers used in these machines and tools.

Examples of the use of levers are the handles of vices and workbenches, the lever drilling machine etc.

The action of lever balances is also based on the principle of the lever (Fig.). The training scale shown in figure 48 (p. 42) acts as equal-arm lever . V decimal scales the arm to which the cup with weights is suspended is 10 times longer than the arm carrying the load. This greatly simplifies the weighing of large loads. When weighing a load on a decimal scale, multiply the weight of the weights by 10.

The device of scales for weighing freight wagons of cars is also based on the rule of the lever.

Levers are also found in different parts animal and human bodies. These are, for example, arms, legs, jaws. Many levers can be found in the body of insects (having read a book about insects and the structure of their body), birds, in the structure of plants.

Application of the law of balance of the lever to the block.

Block is a wheel with a groove, reinforced in the holder. A rope, cable or chain is passed along the gutter of the block.

Fixed block such a block is called, the axis of which is fixed, and when lifting loads it does not rise and does not fall (Fig.

A fixed block can be considered as an equal-arm lever, in which the arms of forces are equal to the radius of the wheel (Fig.): OA = OB = r. Such a block does not give a gain in strength. ( F 1 = F 2), but allows you to change the direction of the force. Movable block is a block. the axis of which rises and falls along with the load (Fig.). The figure shows the corresponding lever: O- fulcrum of the lever, OA- shoulder strength R and OV- shoulder strength F. Since the shoulder OV 2 times the shoulder OA, then the force F 2 times less power R:

F = P/2 .

In this way, the movable block gives a gain in strength by 2 times .

This can also be proved using the concept of moment of force. When the block is in equilibrium, the moments of forces F and R are equal to each other. But the shoulder of strength F 2 times the shoulder strength R, which means that the force itself F 2 times less power R.

Usually, in practice, a combination of a fixed block with a movable one is used (Fig.). The fixed block is used for convenience only. It does not give a gain in strength, but changes the direction of the force. For example, it allows you to lift a load while standing on the ground. It comes in handy for many people or workers. However, it gives a power gain of 2 times more than usual!

Equality of work when using simple mechanisms. The "golden rule" of mechanics.

The simple mechanisms we have considered are used in the performance of work in those cases when it is necessary to balance another force by the action of one force.

Naturally, the question arises: giving a gain in strength or path, do not simple mechanisms give a gain in work? The answer to this question can be obtained from experience.

Having balanced on the lever two forces of different modulus F 1 and F 2 (fig.), set the lever in motion. It turns out that for the same time, the point of application of a smaller force F 2 goes a long way s 2, and the point of application of greater force F 1 - smaller path s 1. Having measured these paths and force modules, we find that the paths traversed by the points of application of forces on the lever are inversely proportional to the forces:

s 1 / s 2 = F 2 / F 1.

Thus, acting on the long arm of the lever, we win in strength, but at the same time we lose the same amount on the way.

Product of force F on the way s there is work. Our experiments show that the work done by the forces applied to the lever are equal to each other:

F 1 s 1 = F 2 s 2, i.e. A 1 = A 2.

So, when using the leverage, the win in the work will not work.

By using the lever, we can win either in strength or in distance. Acting by force on the short arm of the lever, we gain in distance, but lose in strength by the same amount.

There is a legend that Archimedes, delighted with the discovery of the rule of the lever, exclaimed: "Give me a fulcrum, and I will turn the Earth!".

Of course, Archimedes could not have coped with such a task even if he had been given a fulcrum (which would have to be outside the Earth) and a lever of the required length.

To raise the earth by only 1 cm, the long arm of the lever would have to describe an arc of enormous length. It would take millions of years to move the long end of the lever along this path, for example, at a speed of 1 m/s!

Does not give a gain in work and a fixed block, which is easy to verify by experience (see Fig.). Paths traversed by points of application of forces F and F, are the same, the same are the forces, which means that the work is the same.

It is possible to measure and compare with each other the work done with the help of a movable block. In order to lift the load to a height h with the help of a movable block, it is necessary to move the end of the rope to which the dynamometer is attached, as experience shows (Fig.), to a height of 2h.

In this way, getting a gain in strength by 2 times, they lose 2 times on the way, therefore, the movable block does not give a gain in work.

Centuries of practice has shown that none of the mechanisms gives a gain in work. Apply the same various mechanisms in order to win in force or on the way, depending on the working conditions.

Already ancient scientists knew the rule applicable to all mechanisms: how many times we win in strength, how many times we lose in distance. This rule has been called the "golden rule" of mechanics.

The efficiency of the mechanism.

Considering the device and action of the lever, we did not take into account friction, as well as the weight of the lever. in these ideal conditions work done by the applied force (we will call this work complete), is equal to useful lifting loads or overcoming any resistance.

In practice, the total work done by the mechanism is always somewhat greater than the useful work.

Part of the work is done against the friction force in the mechanism and by moving its individual parts. So, using a movable block, you have to additionally perform work on lifting the block itself, the rope and determining the friction force in the axis of the block.

Whatever mechanism we choose, the useful work accomplished with its help is always only a part of the total work. So, denoting the useful work by the letter Ap, the full (spent) work by the letter Az, we can write:

Ap< Аз или Ап / Аз < 1.

The ratio of useful work to full work is called the efficiency of the mechanism.

Efficiency is abbreviated as efficiency.

Efficiency = Ap / Az.

Efficiency is usually expressed as a percentage and denoted Greek letterη, it is read as "this":

η \u003d Ap / Az 100%.

Example: A 100 kg mass is suspended from the short arm of the lever. To lift it, a force of 250 N was applied to the long arm. The load was lifted to a height h1 = 0.08 m, while the point of application driving force descended to a height h2 = 0.4 m. Find the efficiency of the lever.

Let's write down the condition of the problem and solve it.

Given :

Solution :

η \u003d Ap / Az 100%.

Full (spent) work Az = Fh2.

Useful work Ап = Рh1

P \u003d 9.8 100 kg ≈ 1000 N.

Ap \u003d 1000 N 0.08 \u003d 80 J.

Az \u003d 250 N 0.4 m \u003d 100 J.

η = 80 J/100 J 100% = 80%.

Answer : η = 80%.

But " Golden Rule" is performed in this case too. Part of the useful work - 20% of it - is spent on overcoming friction in the axis of the lever and air resistance, as well as on the movement of the lever itself.

The efficiency of any mechanism is always less than 100%. By designing mechanisms, people tend to increase their efficiency. To do this, friction in the axes of the mechanisms and their weight are reduced.

Energy.

In factories and factories, machines and machines are driven by electric motors, which consume electrical energy (hence the name).