Mechanical work and power in brief. Mechanical work. Formula. Formulation of the definition. Ground reaction work

Mechanical work is an energy characteristic of the movement of physical bodies, which has a scalar form. It is equal to the modulus of the force acting on the body, multiplied by the modulus of the displacement caused by this force and by the cosine of the angle between them.

Formula 1 - Mechanical work.

F - Force acting on the body.

s - Body movement.

cosa - Cosine of the angle between force and displacement.

This formula has a general form. If the angle between the applied force and the displacement is zero, then the cosine is equal to 1. Accordingly, the work will be equal only to the product of the force and the displacement. Simply put, if a body moves in the direction of application of force, then mechanical work is equal to the product of force and displacement.

The second special case is when the angle between the force acting on the body and its displacement is 90 degrees. In this case, the cosine of 90 degrees is equal to zero, so the work will be equal to zero. And indeed, what happens is that we apply force in one direction, and the body moves perpendicular to it. That is, the body clearly does not move under the influence of our force. Thus, the work done by our force to move the body is zero.

Figure 1 - Work of forces when moving a body.

If more than one force acts on a body, then the total force acting on the body is calculated. And then it is substituted into the formula as the only force. A body under the influence of force can move not only rectilinearly, but also along an arbitrary trajectory. In this case, the work is calculated for a small section of movement, which can be considered rectilinear, and then summed up along the entire path.

Work can be both positive and negative. That is, if the displacement and force coincide in direction, then the work is positive. And if a force is applied in one direction, and the body moves in another, then the work will be negative. An example of negative work is the work of a frictional force. Since the friction force is directed counter to the movement. Imagine a body moving along a plane. A force applied to a body pushes it in a certain direction. This force does positive work to move the body. But at the same time, the friction force does negative work. It slows down the movement of the body and is directed towards its movement.

Figure 2 - Force of motion and friction.

Mechanical work is measured in Joules. One Joule is the work done by a force of one Newton when moving a body one meter. In addition to the direction of movement of the body, the magnitude of the applied force can also change. For example, when a spring is compressed, the force applied to it will increase in proportion to the distance traveled. In this case, the work is calculated using the formula.

Formula 2 - Work of compression of a spring.

k is the spring stiffness.

x - moving coordinate.

Class

Lesson #27

Mechanical work. Power Their units of measurement.

Learning new material

Job". This word has been familiar to us since childhood. It accompanies us throughout our lives; with this word we call any type of human activity: physical, mental or creative. We know that throughout life the heart does work. This work of the heart is equivalent to the work that needs to be done to lift a train up the highest mountain in Europe - Mont Blanc (4810 m). All living things are constantly moving, a person only develops and achieves his results through his activities. This is an important concept.

But physics puts a slightly different content into this concept. In physics, mechanical work is primarily studied. And a very important fact when doing work is its speed. We always want to do something not only better, but also faster.

At this point, I will ask you to demonstrate performing some work in your field. Tell me, please, what is a necessary condition for doing the work?

Yes, the presence of applied force and movement.

Mechanical work is a physical quantity that characterizes the movement of a body under the influence of force.

Like any other physical quantity, mechanical work has units of measurement and a formula for calculation.

[A] = 1 J

Mechanical work is equal to the product of force and displacement.

« This is interesting!" The SI unit of work is named after the 19th century English scientist J. Joule. J. Joule (1818-1889) was born in England into the family of a brewery owner. Due to poor health, James did not attend school until he was 15. But at the age of 15, under the guidance of the famous chemist John Dalton, he successfully mastered mathematics, physics and chemistry. After the death of his father, having sold his part of the inheritance, Joule began independent scientific research, investing all his money in it. In his lifetime, Joule conducted a thousand experiments in the fields of mechanics, electromagnetism and thermal phenomena, which were successful.

Now let's look at this example of doing the job. The area needs to be dug up. How to do this work faster - with a shovel or a tractor? Will the work done be the same?

Yes, the work is the same; but different amounts of time will be spent: with a tractor this work will be completed faster.

We will go up to the 10th floor faster by elevator than by stairs. A crane lifts heavy bricks to the height of the house being built in a few minutes, while workers would spend a whole day doing the same job. The mechanism that does the work faster is considered more powerful.

Power is a physical quantity that characterizes the speed of work.

Power is equal to the ratio of mechanical work to the time during which this work is performed.

The unit of power measurement is named after the English scientist James Watt. He was called the "Archimedes" of the 18th century. But there is a non-systemic unit of measurement of power - horsepower. The fact is that at the dawn of mechanical engineering, it was more familiar and clearer to potential consumers that the power of this mechanism was 20 horsepower, that is, the mechanism was capable of replacing 20 horses.

« This is interesting!" The average power of an adult with sufficiently long work is approximately 35 - 75 W. But in a fairly short time, a person can develop more power than a horse. For example, athletes who push a barbell weighing more than 200 kg to a height of 1.8 m in 1 second develop a power of approximately 3500 W.

You can check this fact using calculations in your notebooks.

And the power of an insect in flight is approximately 0.00001 W.

Consolidation of new material.

The solution of the problem

What power does a weightlifter develop if he lifts a barbell weighing 125 kg to a height of 70 cm in 0.3 s?

Given: SI Solution

t=125kg

h=70cm 0.7m N= but A=FS and F=mg, and S=h.

t=0.3s So N=

N-? N= 2916.7 W

[N] = = = =W

Answer: 2916.7 W.

Homework

8-a: learn paragraphs 17 and 19 (point 3); answer questions in writing.

8-b: learn paragraphs 41 and 47; answer questions in writing.

Questions

1. Give examples when a force acts on a body, but it does not do work.

2. Two cargoes of equal weight were delivered by bus to a suburban village of Donetsk and to the center of Donetsk. Was the work done the same in the first and second cases? Why?

3. Why did they begin to build faster in the 20th and 21st centuries than before?

4. Two boys of different weights raced to the third floor of the house, showing the same time. Did they develop the same power?

Do you know what work is? Without any doubt. Every person knows what work is, provided that he was born and lives on planet Earth. What is mechanical work?

This concept is also known to most people on the planet, although some individuals have a rather vague understanding of this process. But we are not talking about them now. Even fewer people have any idea what it is mechanical work from the point of view of physics. In physics, mechanical work is not human labor for food, it is a physical quantity that may be completely unrelated to either a person or any other living creature. How so? Let's figure it out now.

Mechanical work in physics

Let's give two examples. In the first example, the waters of the river, faced with an abyss, noisily fall down in the form of a waterfall. The second example is a man who holds a heavy object in his outstretched arms, for example, holding the broken roof over the porch of a country house from falling, while his wife and children are frantically looking for something to support it with. When is mechanical work performed?

Definition of mechanical work

Almost everyone, without hesitation, will answer: in the second. And they will be wrong. The opposite is true. In physics, mechanical work is described with the following definitions: Mechanical work is performed when a force acts on a body and it moves. Mechanical work is directly proportional to the force applied and the distance traveled.

Mechanical work formula

Mechanical work is determined by the formula:

where A is work,
F - strength,
s is the distance traveled.

So, despite all the heroism of the tired roof holder, the work he has done is zero, but the water, falling under the influence of gravity from a high cliff, does the most mechanical work. That is, if we push a heavy cabinet unsuccessfully, then the work we have done from the point of view of physics will be equal to zero, despite the fact that we apply a lot of force. But if we move the cabinet a certain distance, then we will do work equal to the product of the applied force and the distance over which we moved the body.

The unit of work is 1 J. This is the work done by a force of 1 Newton to move a body over a distance of 1 m. If the direction of the applied force coincides with the direction of movement of the body, then this force does positive work. An example is when we push a body and it moves. And in the case when a force is applied in the direction opposite to the movement of the body, for example, friction force, then this force does negative work. If the applied force does not affect the movement of the body in any way, then the force performed by this work is equal to zero.

In order to be able to characterize the energy characteristics of movement, the concept of mechanical work was introduced. And the article is dedicated to it in its various manifestations. The topic is both easy and quite difficult to understand. The author sincerely tried to make it more understandable and accessible to understanding, and one can only hope that the goal has been achieved.

What is mechanical work called?

What is it called? If some force works on a body, and as a result of its action the body moves, then this is called mechanical work. When approaching from the point of view of scientific philosophy, several additional aspects can be highlighted 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 shortened to the word “work.” But not every job is mechanical. Here is a man sitting and thinking. Does it work? Mentally yes! But is this mechanical work? No. What if a person walks? If a body moves under the influence of force, then this is mechanical work. It's simple. In other words, a force acting on a 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 the person, and as a result of their action, the person changes his point of location, in other words, moves.

Work as a physical quantity is equal to the force that acts on the body, multiplied by the path that the body has 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: a force acted on the body, and it moved in the direction of its action. But it did not occur or does not occur if the force acted and the body did not change its location in the coordinate system. Here are small examples when mechanical work is not performed:

1. So a person can lean 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 no work occurs.
2. The body moves in the coordinate system, and the force is equal to zero or they have all been compensated. This can be observed while moving by inertia.
3. When the direction in which a body moves is perpendicular to the action of the force. When a train moves along a horizontal line, gravity does not do its work.

Depending on certain conditions, mechanical work can be negative and positive. So, if the directions of both the 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 upward and the force of gravity, which does negative work. When a body is subject to the influence of several forces, such work is called “resultant force work.”

Features of practical application (kinetic energy)

Let's move from theory to practical part. Separately, we should talk about mechanical work and its use in physics. As many probably remember, 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 equals its total energy and its kinetic energy equals zero. When movement begins, potential energy begins to decrease, kinetic energy begins 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 a force that accelerates the point from zero to the value H, and in formula form the kinetics of a body is equal to ½*M*N, where M is 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 over a 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 times volume. This approach is applicable not only in cases where there is an exact volume function, but also to all processes that can be displayed in the pressure/volume plane. It also applies knowledge of mechanical work not only to gases, but to anything 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 projections. It also gives its definition for various formulas of mechanical work (an example of a definition for the Rimmer integral): the limit to which the sum of all forces of elementary work tends, when the fineness of the partition tends to zero, is called the work of force along the curve. Probably difficult? But nothing, everything is fine with theoretical mechanics. Yes, all the mechanical work, physics and other difficulties are over. Further there will be only examples and a conclusion.

Units of measurement of mechanical work

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

1. 1 J = 1 kg m²/s² = 1 N m
2. 1 erg = 1 g cm²/s² = 1 dyne 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 several individual examples that will allow you to consider it from many, but not all, sides:

1. When a person lifts a stone with his hands, mechanical work occurs with the help of the muscular strength of his 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 fire from it, then thanks to the pressure force created by the powder gases, 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. Mechanical work also exists when the friction force acts on a 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 would like 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 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 W. A watt is equal to the power that does one joule of work in one second: 1 W=1J\1s.

What does it mean?

In physics, “mechanical work” is the work of some force (gravity, elasticity, friction, etc.) on a body, as a result of which the body moves.

Often the word “mechanical” is simply not written.
Sometimes you can come across the expression “the body has done work,” which in principle means “the force acting on the body has done work.”

I think - I'm working.

I'm going - I'm working too.

Where is the mechanical work here?

If a body moves under the influence of a force, then mechanical work is performed.

They say that the body does work.
Or more precisely, it will be like this: the work is done by the force acting on the body.

Work characterizes the result of a force.

The forces acting on a person perform mechanical work on him, and as a result of the action of these forces, the person moves.

Work is a physical quantity equal to the product of the force acting on a body and the path made by the body under the influence of a force in the direction of this force.

A - mechanical work,
F - strength,
S - distance traveled.

Work is done, if 2 conditions are met simultaneously: a force acts on the body and it
moves in the direction of the force.

No work is done(i.e. equal to 0), if:
1. The force acts, but the body does not move.

For example: we exert force on a stone, but cannot move it.

2. The body moves, and the force is zero, or all forces are compensated (i.e., the resultant of these forces is 0).
For example: when moving by inertia, no work is done.
3. The direction of the force and the direction of movement of the body are mutually perpendicular.

For example: when a train moves horizontally, gravity does no work.

Work can be positive and negative

1. If the direction of the force and the direction of motion of the body coincide, positive work is done.

For example: the force of gravity, acting on a drop of water falling down, does positive work.

2. If the direction of force and movement of the body is opposite, negative work is done.

For example: the force of gravity acting on a rising balloon does negative work.

If several forces act on a body, then the total work done by all forces is equal to the work done by the resulting force.

Units of work

In honor of the English scientist D. Joule, the unit of work was named 1 Joule.

In the International System of Units (SI):
[A] = J = N m
1J = 1N 1m

Mechanical work is equal to 1 J if, under the influence of a force of 1 N, a body moves 1 m in the direction of this force.

When flying from a person's thumb to his index finger
the mosquito does work - 0.000 000 000 000 000 000 000 000 001 J.

The human heart performs approximately 1 J of work per contraction, which corresponds to the work done when lifting a load weighing 10 kg to a height of 1 cm.

GET TO WORK, FRIENDS!