Mechanical work. Power

Mechanical work. Units of work.

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

In physics, the concept Job 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 BUT- Job, 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. Thus,

1 J = 1N m.

Also used kilojoules (kJ) .

1 kJ = 1000 J.

Formula A = Fs applicable when the force 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

Decision:

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

Different engines take different times to do the same work. For example, a crane at a construction site 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- Job, 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

Decision:

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 engines have powers ranging from hundredths and tenths of a kilowatt (motor of an electric razor, sewing machine) 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 under normal working conditions is on average 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:

Decision:

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.

At the 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 by several times.

Simple mechanisms are found both in household and in all complex factory and factory machines that cut, twist and stamp large sheets of steel or draw 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. Force 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 BUT and AT. 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.

To find the shoulder of the force, it is necessary to lower the perpendicular from the fulcrum to the line of action 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:

Decision:

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 shoulder of the smaller force must be longer than the shoulder of the greater force.

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. It is better to unscrew the nut with a long wrench than with a short one. 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. Scissors for cutting sheet metal (Fig.) have handles much longer than the blades, since the resistance force of the metal is large and to balance it, the arm of the acting force must 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 of various types are available on many machines. 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 of a 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 . AT 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 of the body of animals and humans. 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 .

Thus, 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. BUT 1 = BUT 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.

Thus, 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. Various mechanisms are used in order to win in strength 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. under these ideal conditions, the 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:

Up< Аз или Ап / Аз < 1.

The ratio of useful work to total 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 by the Greek letter η, 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 of the driving force dropped 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 :

Decision :

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 the "golden rule" is fulfilled 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).

A compressed spring (rice), straightening out, does work, lifts a load to a height, or makes a cart move. An immovable load raised above the ground does not do work, but if this load falls, it can do work (for example, it can drive a pile into the ground). Every moving body has the ability to do work. So, a steel ball A (rice) rolled down from an inclined plane, hitting a wooden block B, moves it a certain distance. In doing so, work is being done. If a body or several interacting bodies (a system of bodies) can do work, it is said that they have energy. Energy - a physical quantity showing what work a body (or several bodies) can do. Energy is expressed in the SI system in the same units as work, i.e. in joules. The more work a body can do, the more energy it has. When work is done, the energy of bodies changes. The work done is equal to the change in energy. Potential and kinetic energy. Potential (from lat. potency - possibility) energy is called energy, which is determined by the mutual position of interacting bodies and parts of the same body. Potential energy, for example, has a body raised relative to the surface of the Earth, because the energy depends on the relative position of it and the Earth. and their mutual attraction. If we consider the potential energy of a body lying on the Earth to be equal to zero, then the potential energy of a body raised to a certain height will be determined by the work done by gravity when the body falls to the Earth. Denote the potential energy of the body E n because E = A, and the work, as we know, is equal to the product of the force and the path, then A = Fh, where F- gravity. Hence, the potential energy En is equal to: E = Fh, or E = gmh, where g- acceleration of gravity, m- body mass, h- the height to which the body is raised. The water in the rivers held by dams has a huge potential energy. Falling down, the water does work, setting in motion the powerful turbines of power plants. The potential energy of a copra hammer (Fig.) is used in construction to perform the work of driving piles. By opening a door with a spring, work is done to stretch (or compress) the spring. Due to the acquired energy, the spring, contracting (or straightening), does the work, closing the door. The energy of compressed and untwisted springs is used, for example, in wrist watches, various clockwork toys, etc. Any elastic deformed body possesses potential energy. The potential energy of compressed gas is used in the operation of heat engines, in jackhammers, which are widely used in the mining industry, in the construction of roads, excavation of solid soil, etc. The energy possessed by a body as a result of its movement is called kinetic (from the Greek. cinema - movement) energy. The kinetic energy of a body is denoted by the letter E to. Moving water, driving the turbines of hydroelectric power plants, expends its kinetic energy and does work. Moving air also has kinetic energy - the wind. What does kinetic energy depend on? Let us turn to experience (see Fig.). If you roll ball A from different heights, you will notice that the greater the height the ball rolls, the greater its speed and the farther it advances the bar, i.e., it does more work. This means that the kinetic energy of a body depends on its speed. Due to the speed, a flying bullet has a large kinetic energy. The kinetic energy of a body also depends on its mass. Let's do our experiment again, but we will roll another ball - a larger mass - from an inclined plane. Block B will move further, i.e., more work will be done. This means that the kinetic energy of the second ball is greater than the first. The greater the mass of the body and the speed with which it moves, the greater its kinetic energy. In order to determine the kinetic energy of a body, the formula is applied: Ek \u003d mv ^ 2 / 2, where m- body mass, v is the speed of the body. The kinetic energy of bodies is used in technology. The water retained by the dam has, as already mentioned, a large potential energy. When falling from a dam, water moves and has the same large kinetic energy. It drives a turbine connected to an electric current generator. Due to the kinetic energy of water, electrical energy is generated. The energy of moving water is of great importance in the national economy. This energy is used by powerful hydroelectric power plants. The energy of falling water is an environmentally friendly source of energy, unlike fuel energy. All bodies in nature, relative to the conditional zero value, have either potential or kinetic energy, and sometimes both. For example, a flying plane has both kinetic and potential energy relative to the Earth. We got acquainted with two types of mechanical energy. Other types of energy (electrical, internal, etc.) will be considered in other sections of the physics course. The transformation of one type of mechanical energy into another. The phenomenon of the transformation of one type of mechanical energy into another is very convenient to observe on the device shown in the figure. Winding the thread around the axis, raise the disk of the device. The disk raised up has some potential energy. If you let it go, it will spin and fall. As it falls, the potential energy of the disk decreases, but at the same time its kinetic energy increases. At the end of the fall, the disk has such a reserve of kinetic energy that it can again rise almost to its previous height. (Part of the energy is expended working against friction, so the disk does not reach its original height.) Having risen up, the disk falls again, and then rises again. In this experiment, when the disk moves down, its potential energy is converted into kinetic energy, and when moving up, kinetic energy is converted into potential. The transformation of energy from one type to another also occurs when two elastic bodies hit, for example, a rubber ball on the floor or a steel ball on a steel plate. If you lift a steel ball (rice) over a steel plate and release it from your hands, it will fall. As the ball falls, its potential energy decreases, and its kinetic energy increases, as the speed of the ball increases. When the ball hits the plate, both the ball and the plate will be compressed. The kinetic energy that the ball possessed will turn into the potential energy of the compressed plate and the compressed ball. Then, due to the action of elastic forces, the plate and the ball will take their original shape. The ball will bounce off the plate, and their potential energy will again turn into the kinetic energy of the ball: the ball will bounce upward with a speed almost equal to the speed that it had at the moment of impact on the plate. As the ball rises, the speed of the ball, and hence its kinetic energy, decreases, and the potential energy increases. bouncing off the plate, the ball rises to almost the same height from which it began to fall. At the top of the ascent, all its kinetic energy will again turn into potential energy. Natural phenomena are usually accompanied by the transformation of one type of energy into another. Energy can also be transferred from one body to another. So, for example, when shooting from a bow, the potential energy of a stretched bowstring is converted into the kinetic energy of a flying arrow.

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 is 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 are small examples where mechanical work is not 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 a balloon rising up and 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 a closed system is constant in the time interval. 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.

Basic theoretical information

mechanical work

The energy characteristics of motion are introduced on the basis of the concept mechanical work or force work. Work done 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 between the force vectors F and displacement S:

Work is a scalar quantity. It can be either positive (0° ≤ α < 90°), так и отрицательна (90° < α ≤ 180°). At α = 90° the work done by the force is zero. In the SI system, work is measured in joules (J). A joule is equal to the work done by a force of 1 newton to move 1 meter in the direction of the force.

If the force changes over time, then to find the work, they build a graph of the dependence of the force on the displacement and find the area of ​​\u200b\u200bthe figure under the graph - this is the work:

An example of a force whose modulus depends on the coordinate (displacement) is the elastic force of a spring, which obeys Hooke's law ( F extr = kx).

Power

The work done by a force per unit of time is called power. Power P(sometimes referred to as N) is a physical quantity equal to the ratio of work A to the time span t during which this work was completed:

This formula calculates average power, i.e. power generally characterizing the process. So, work can also be expressed in terms of power: A = Pt(unless, of course, the power and time of doing the work are known). The unit of power is called the watt (W) or 1 joule per second. If the motion is uniform, then:

With this formula, we can calculate instant power(power at a given time), if instead of speed we substitute the value of instantaneous speed into the formula. How to know what power to count? If the task asks for power at a point in time or at some point in space, then it is considered instantaneous. If you are asking about power over a certain period of time or a section of the path, then look for the average power.

Efficiency - efficiency factor, is equal to the ratio of useful work to spent, or useful power to spent:

What work is useful and what is spent is determined from the condition of a particular task by logical reasoning. For example, if a crane does work to lift a load to a certain height, then the work of lifting the load will be useful (since the crane was created for it), and the work done by the crane's electric motor will be spent.

So, useful and expended power do not have a strict definition, and are found by logical reasoning. In each task, we ourselves must determine what in this task was the purpose of doing the work (useful work or power), and what was the mechanism or way of doing all the work (expended power or work).

In the general case, the efficiency shows how efficiently the mechanism converts one type of energy into another. If the power changes over time, then the work is found as the area of ​​​​the figure under the graph of power versus time:

Kinetic energy

A physical quantity equal to half the product of the body's mass and the square of its speed is called kinetic energy of the body (energy of motion):

That is, if a car with a mass of 2000 kg moves at a speed of 10 m/s, then it has a kinetic energy equal to E k \u003d 100 kJ and is capable of doing work of 100 kJ. This energy can be converted into heat (when the car brakes, the tires of the wheels, the road and the brake discs heat up) or can be spent on deforming the car and the body that the car collided with (in an accident). When calculating kinetic energy, it does not matter where the car is moving, since energy, like work, is a scalar quantity.

A body has energy if it can do work. For example, a moving body has kinetic energy, i.e. the energy of motion, and is capable of doing work to deform bodies or impart acceleration to bodies with which a collision occurs.

The physical meaning of kinetic energy: in order for a body at rest with mass m began to move at a speed v it is necessary to do work equal to the obtained value of kinetic energy. If the body mass m moving at a speed v, then to stop it, it is necessary to do work equal to its initial kinetic energy. During braking, the kinetic energy is mainly (except for cases of collision, when the energy is used for deformation) “taken away” by the friction force.

Kinetic energy theorem: the work of the resultant force is equal to the change in the kinetic energy of the body:

The kinetic energy theorem is also valid in the general case when the body moves under the action of a changing force, the direction of which does not coincide with the direction of movement. It is convenient to apply this theorem in problems of acceleration and deceleration of a body.

Potential energy

Along with the kinetic energy or the energy of motion in physics, an important role is played by the concept potential energy or energy of interaction of bodies.

Potential energy is determined by the mutual position of the bodies (for example, the position of the body relative to the Earth's surface). The concept of potential energy can be introduced only for forces whose work does not depend on the trajectory of the body and is determined only by the initial and final positions (the so-called conservative forces). The work of such forces on a closed trajectory is zero. This property is possessed by the force of gravity and the force of elasticity. For these forces, we can introduce the concept of potential energy.

Potential energy of a body in the Earth's gravity field calculated by the formula:

The physical meaning of the potential energy of the body: the potential energy is equal to the work done by the force of gravity when lowering the body to the zero level ( h is the distance from the center of gravity of the body to the zero level). If a body has potential energy, then it is capable of doing work when this body falls from a height h down to zero. The work of gravity is equal to the change in the potential energy of the body, taken with the opposite sign:

Often in tasks for energy, you have to find work to lift (turn over, get out of the pit) the body. In all these cases, it is necessary to consider the movement not of the body itself, but only of its center of gravity.

The potential energy Ep depends on the choice of the zero level, that is, on the choice of the origin of the OY axis. In each problem, the zero level is chosen for reasons of convenience. It is not the potential energy itself that has physical meaning, but its change when the body moves from one position to another. This change does not depend on the choice of the zero level.

Potential energy of a stretched spring calculated by the formula:

where: k- spring stiffness. A stretched (or compressed) spring is capable of setting in motion a body attached to it, that is, imparting kinetic energy to this body. Therefore, such a spring has a reserve of energy. Stretch or Compression X must be calculated from the undeformed state of the body.

The potential energy of an elastically deformed body is equal to the work of the elastic force during the transition from a given state to a state with zero deformation. If in the initial state the spring was already deformed, and its elongation was equal to x 1 , then upon transition to a new state with elongation x 2, the elastic force will do work equal to the change in potential energy, taken with the opposite sign (since the elastic force is always directed against the deformation of the body):

Potential energy during elastic deformation is the energy of interaction of individual parts of the body with each other by elastic forces.

The work of the friction force depends on the distance traveled (this type of force whose work depends on the trajectory and the distance traveled is called: dissipative forces). The concept of potential energy for the friction force cannot be introduced.

Efficiency

Efficiency factor (COP)- a characteristic of the efficiency of a system (device, machine) in relation to the conversion or transfer of energy. It is determined by the ratio of useful energy used to the total amount of energy received by the system (the formula has already been given above).

Efficiency can be calculated both in terms of work and in terms of power. Useful and expended work (power) is always determined by simple logical reasoning.

In electric motors, efficiency is the ratio of the performed (useful) mechanical work to the electrical energy received from the source. In heat engines, the ratio of useful mechanical work to the amount of heat expended. In electrical transformers, the ratio of electromagnetic energy received in the secondary winding to the energy consumed by the primary winding.

Due to its generality, the concept of efficiency makes it possible to compare and evaluate from a unified point of view such different systems as nuclear reactors, electric generators and engines, thermal power plants, semiconductor devices, biological objects, etc.

Due to the inevitable energy losses due to friction, heating of surrounding bodies, etc. The efficiency is always less than unity. Accordingly, the efficiency is expressed as a fraction of the energy expended, that is, as a proper fraction or as a percentage, and is a dimensionless quantity. Efficiency characterizes how efficiently a machine or mechanism works. The efficiency of thermal power plants reaches 35-40%, internal combustion engines with supercharging and pre-cooling - 40-50%, dynamos and high-power generators - 95%, transformers - 98%.

The task in which you need to find the efficiency or it is known, you need to start with a logical reasoning - what work is useful and what is spent.

Law of conservation of mechanical energy

full mechanical energy the sum of kinetic energy (i.e., the energy of motion) and potential (i.e., the energy of interaction of bodies by the forces of gravity and elasticity) is called:

If mechanical energy does not pass into other forms, for example, into internal (thermal) energy, then the sum of kinetic and potential energy remains unchanged. If mechanical energy is converted into thermal energy, then the change in mechanical energy is equal to the work of the friction force or energy losses, or the amount of heat released, and so on, in other words, the change in total mechanical energy is equal to the work of external forces:

The sum of the kinetic and potential energies of the bodies that make up a closed system (i.e., one in which no external forces act, and their work is equal to zero, respectively) and interacting with each other by gravitational forces and elastic forces, remains unchanged:

This statement expresses law of conservation of energy (LSE) in mechanical processes. It is a consequence of Newton's laws. The law of conservation of mechanical energy is fulfilled only when the bodies in a closed system interact with each other by forces of elasticity and gravity. In all problems on the law of conservation of energy there will always be at least two states of the system of bodies. The law says that the total energy of the first state will be equal to the total energy of the second state.

Algorithm for solving problems on the law of conservation of energy:

1. Find the points of the initial and final position of the body.
2. Write down what or what energies the body has at these points.
3. Equate the initial and final energy of the body.
4. Add other necessary equations from previous physics topics.
5. Solve the resulting equation or system of equations using mathematical methods.

It is important to note that the law of conservation of mechanical energy made it possible to obtain a connection between the coordinates and velocities of the body at two different points of the trajectory without analyzing the law of motion of the body at all intermediate points. The application of the law of conservation of mechanical energy can greatly simplify the solution of many problems.

In real conditions, almost always moving bodies, along with gravitational forces, elastic forces and other forces, are acted upon by friction forces or resistance forces of the medium. The work of the friction force depends on the length of the path.

If friction forces act between the bodies that make up a closed system, then mechanical energy is not conserved. Part of the mechanical energy is converted into internal energy of bodies (heating). Thus, the energy as a whole (i.e. not only mechanical energy) is conserved in any case.

In any physical interactions, energy does not arise and does not disappear. It only changes from one form to another. This experimentally established fact expresses the fundamental law of nature - law of conservation and transformation of energy.

One of the consequences of the law of conservation and transformation of energy is the assertion that it is impossible to create a “perpetual motion machine” (perpetuum mobile) - a machine that could do work indefinitely without consuming energy.

Miscellaneous work tasks

If you need to find mechanical work in the problem, then first select the method for finding it:

1. Jobs can be found using the formula: A = FS cos α . Find the force that does the work and the amount of displacement of the body under the action of this force in the selected reference frame. Note that the angle must be chosen between the force and displacement vectors.
2. The work of an external force can be found as the difference between the mechanical energy in the final and initial situations. Mechanical energy is equal to the sum of the kinetic and potential energies of the body.
3. The work done to lift a body at a constant speed can be found by the formula: A = mgh, where h- the height to which it rises center of gravity of the body.
4. Work can be found as the product of power and time, i.e. according to the formula: A = Pt.
5. Work can be found as the area of ​​a figure under a graph of force versus displacement or power versus time.

The law of conservation of energy and the dynamics of rotational motion

The tasks of this topic are quite complex mathematically, but with knowledge of the approach they are solved according to a completely standard algorithm. In all problems you will have to consider the rotation of the body in the vertical plane. The solution will be reduced to the following sequence of actions:

1. It is necessary to determine the point of interest to you (the point at which it is necessary to determine the speed of the body, the force of the thread tension, weight, and so on).
2. Write down Newton's second law at this point, given that the body rotates, that is, it has centripetal acceleration.
3. Write down the law of conservation of mechanical energy so that it contains the speed of the body at that very interesting point, as well as the characteristics of the state of the body in some state about which something is known.
4. Depending on the condition, express the speed squared from one equation and substitute it into another.
5. Carry out the rest of the necessary mathematical operations to obtain the final result.

When solving problems, remember that:

• The condition for passing the upper point during rotation on the threads at a minimum speed is the reaction force of the support N at the top point is 0. The same condition is met when passing through the top point of the dead loop.
• When rotating on a rod, the condition for passing the entire circle is: the minimum speed at the top point is 0.
• The condition for the separation of the body from the surface of the sphere is that the reaction force of the support at the separation point is zero.

Inelastic Collisions

The law of conservation of mechanical energy and the law of conservation of momentum make it possible to find solutions to mechanical problems in cases where the acting forces are unknown. An example of such problems is the impact interaction of bodies.

Impact (or collision) It is customary to call the short-term interaction of bodies, as a result of which their velocities experience significant changes. During the collision of bodies, short-term impact forces act between them, the magnitude of which, as a rule, is unknown. Therefore, it is impossible to consider the impact interaction directly with the help of Newton's laws. The application of the laws of conservation of energy and momentum in many cases makes it possible to exclude the process of collision from consideration and obtain a relationship between the velocities of bodies before and after the collision, bypassing all intermediate values ​​of these quantities.

One often has to deal with the impact interaction of bodies in everyday life, in technology and in physics (especially in the physics of the atom and elementary particles). In mechanics, two models of impact interaction are often used - absolutely elastic and absolutely inelastic impacts.

Absolutely inelastic impact Such a shock interaction is called, in which the bodies are connected (stick together) with each other and move on as one body.

In a perfectly inelastic impact, mechanical energy is not conserved. It partially or completely passes into the internal energy of bodies (heating). To describe any impacts, you need to write down both the law of conservation of momentum and the law of conservation of mechanical energy, taking into account the released heat (it is highly desirable to draw a drawing beforehand).

Absolutely elastic impact

Absolutely elastic impact is called a collision in which the mechanical energy of a system of bodies is conserved. In many cases, collisions of atoms, molecules and elementary particles obey the laws of absolutely elastic impact. With an absolutely elastic impact, along with the law of conservation of momentum, the law of conservation of mechanical energy is fulfilled. A simple example of a perfectly elastic collision would be the central impact of two billiard balls, one of which was at rest before the collision.

center punch balls is called a collision, in which the speeds of the balls before and after the impact are directed along the line of centers. Thus, using the laws of conservation of mechanical energy and momentum, it is possible to determine the velocities of the balls after the collision, if their velocities before the collision are known. The central impact is very rarely realized in practice, especially when it comes to collisions of atoms or molecules. In non-central elastic collision, the velocities of particles (balls) before and after the collision are not directed along the same straight line.

A special case of a non-central elastic impact is the collision of two billiard balls of the same mass, one of which was stationary before the collision, and the speed of the second was not directed along the line of the centers of the balls. In this case, the velocity vectors of the balls after elastic collision are always directed perpendicular to each other.

Conservation laws. Difficult tasks

Multiple bodies

In some tasks on the law of conservation of energy, the cables with which some objects move can have mass (that is, not be weightless, as you might already be used to). In this case, the work of moving such cables (namely, their centers of gravity) must also be taken into account.

If two bodies connected by a weightless rod rotate in a vertical plane, then:

1. choose a zero level for calculating potential energy, for example, at the level of the axis of rotation or at the level of the lowest point where one of the loads is located and make a drawing;
2. the law of conservation of mechanical energy is written, in which the sum of the kinetic and potential energies of both bodies in the initial situation is written on the left side, and the sum of the kinetic and potential energies of both bodies in the final situation is written on the right side;
3. take into account that the angular velocities of the bodies are the same, then the linear velocities of the bodies are proportional to the radii of rotation;
4. if necessary, write down Newton's second law for each of the bodies separately.

Projectile burst

In the event of a projectile burst, explosive energy is released. To find this energy, it is necessary to subtract the mechanical energy of the projectile before the explosion from the sum of the mechanical energies of the fragments after the explosion. We will also use the momentum conservation law written in the form of the cosine theorem (vector method) or in the form of projections onto selected axes.

Collisions with a heavy plate

Let towards a heavy plate that moves at a speed v, a light ball of mass moves m with speed u n. Since the momentum of the ball is much less than the momentum of the plate, the plate's speed will not change after impact, and it will continue to move at the same speed and in the same direction. As a result of elastic impact, the ball will fly off the plate. Here it is important to understand that the speed of the ball relative to the plate will not change. In this case, for the final speed of the ball we get:

Thus, the speed of the ball after impact is increased by twice the speed of the wall. A similar reasoning for the case when the ball and the plate were moving in the same direction before the impact leads to the result that the speed of the ball is reduced by twice the speed of the wall:

In physics and mathematics, among other things, three essential conditions must be met:

1. Study all the topics and complete all the tests and tasks given in the study materials on this site. To do this, you need nothing at all, namely: to devote three to four hours every day to preparing for the CT in physics and mathematics, studying theory and solving problems. The fact is that the CT is an exam where it is not enough just to know physics or mathematics, you also need to be able to quickly and without failures solve a large number of problems on various topics and varying complexity. The latter can only be learned by solving thousands of problems.
2. Learn all formulas and laws in physics, and formulas and methods in mathematics. In fact, it is also very simple to do this, there are only about 200 necessary formulas in physics, and even a little less in mathematics. In each of these subjects there are about a dozen standard methods for solving problems of a basic level of complexity, which can also be learned, and thus, completely automatically and without difficulty, solve most of the digital transformation at the right time. After that, you will only have to think about the most difficult tasks.
3. Attend all three stages of rehearsal testing in physics and mathematics. Each RT can be visited twice to solve both options. Again, on the DT, in addition to the ability to quickly and efficiently solve problems, and knowledge of formulas and methods, it is also necessary to be able to properly plan time, distribute forces, and most importantly fill out the answer form correctly, without confusing either the numbers of answers and problems, or your own name. Also, during the RT, it is important to get used to the style of posing questions in tasks, which may seem very unusual to an unprepared person on the DT.

Successful, diligent and responsible implementation of these three points will allow you to show an excellent result on the CT, the maximum of what you are capable of.

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

Definition 1

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 is discussed 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. The direction of the external force F → coincides with the direction of displacement 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 the body moves forward, the points of application of forces move in the same way, that is, the total 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

Definition 3

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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Everyone knows. Even children work, in kindergarten - kids. However, the generally accepted, everyday idea is far from the same as the concept of mechanical work in physics. Here, for example, a man stands and holds a bag in his hands. In the usual sense, he does work by holding the load. However, from the point of view of physics, he does nothing of the kind. What's the matter here?

Since such questions arise, it's time to recall the definition. When a force acts on an object, and under its action the body moves, then mechanical work is performed. This value is proportional to the path traveled by the body and the applied force. There is an additional dependence on the direction of application of force and the direction of motion of the body.

Thus, we introduced such a concept as mechanical work. Physics defines it as the product of the magnitude of force and displacement, multiplied by the value of the cosine of the angle that exists in the most general case between them. As an example, we can consider several cases that will allow you to better understand what is meant by this.

When is mechanical work not done? There is a truck, we push it, but it does not move. The force is applied, but there is no movement. The work done is zero. And here is another example - a mother is carrying a child in a stroller, in this case the work is done, force is applied, the stroller moves. The difference in the two cases described is the presence of movement. And accordingly, the work is done (example with a stroller) or not done (example with a truck).

Another case - a boy on a bicycle accelerated and calmly rolls along the path, does not pedal. The work is being done? No, although there is movement, but there is no applied force, the movement is carried out by inertia.

Another example - a horse is pulling a cart, a driver is sitting on it. Does he get the job done? There is displacement, there is applied force (the driver's weight acts on the cart), but no work is done. The angle between the direction of movement and the direction of the force is 90 degrees, and the cosine of the 90° angle is zero.

The examples given make it clear that mechanical work is not just a product of two quantities. It must also take into account how these quantities are directed. If the direction of movement and the direction of the force are the same, then the result will be positive, if the direction of movement occurs against the direction of application of the force, then the result will be negative (for example, the work done by the friction force when moving the load).

In addition, it must be taken into account that the force acting on the body can be the resultant of several forces. If so, then the work of all forces applied to the body is equal to the work done by the resulting force. Work is measured in joules. One joule is equal to the work done by a force of one newton when moving a body one meter.

An extremely curious conclusion can be drawn from the considered examples. When we examined the driver on the cart, we determined that he did not do the work. The work is done in the horizontal plane, because that is where the movement takes place. But the situation will change a little when we consider a pedestrian.

When walking, the center of gravity of a person does not remain motionless, he moves in a vertical plane and, therefore, does work. And since the movement is directed against, the work will occur against the direction of action. Even if the movement is small, but with a long walk, the body will have to do additional work. So the correct gait reduces this extra work and reduces fatigue.

After analyzing a few simple life situations chosen as examples, and using the knowledge of what mechanical work is, we considered the main situations of its manifestation, as well as when and what kind of work is performed. It was determined that such a concept as work in everyday life and in physics is of a different nature. And it was established by the application of physical laws that an incorrect gait causes additional fatigue.