What is the work perfect. Mechanical work

With mechanical work (work of force) you are already familiar from the course of physics of the main school. We will remind the definition of mechanical work there for the following cases.

If the force is directed just like the movement of the body, then the work of force

In this case, the work of the force is positive.

If the force is directed opposite to the movement of the body, then the work of force

In this case, the work of the force is negative.

If the force F_VEC is directed perpendicular to the movement of s_vec of the body, then the operation of the force is zero:

Work is a scalar value. The unit of work is called Joule (indicate: J) in honor of the English scientist James Joule, who played an important role in the opening of the law of energy conservation. From formula (1) follows:

1 j \u003d 1 n * m.

1. The bar weighing 0.5 kg moved across the table by 2 m, applying the force of elasticity equal to 4 H (Fig. 28.1). The friction coefficient between the bar and the table is 0.2. What is equal to the work of acting on the bar:
a) gravity m?
b) the forces of normal reaction?
c) the strength of elasticity?
d) friction force slip TR?

The total work of several forces acting on the body can be found in two ways:
1. Find the work of each strength and fold these works with the signs of signs.
2. Find the equal to all the forces attached to the body and calculate the work of the resultant.

Both methods lead to the same result. To make sure that you return to the previous task and answer questions about Questions 2.

2. What is equal to:
a) Am the work of all the forces acting on the bar?
b) the resultant of all forces acting on the bar?
c) work as an equal? In general, (when the force F_VEC is directed at an arbitrary angle to the movement S_VEC) determination of the operation of the force is such.

The operation A permanent strength is equal to the product of the force module F per module of movement S and on the cosine of the angle α between the direction of force and the direction of movement:

A \u003d fs cos α (4)

3. Show that out of the general definition of work follow the conclusions shown in the following scheme. Word them verbally and write down in a notebook.

4. A force is applied to the Bruck on the table, the module of which is 10 N. What is the angle between this force and the movement of the bar, if, when moving the bar on the table, this force made this force: a) 3 J; b) -3 j; c) -3 j; d) -6 J? Make explanatory drawings.

2. Work of gravity

Let the body mass M move vertically from the initial height H H to the ultimate height H to.

If the body moves down (h n\u003e h to, Fig. 28.2, a), the direction of movement coincides with the direction of gravity, so the work of gravity is positive. If the body moves up (H n< h к, рис. 28.2, б), то работа силы тяжести отрицательна.

In both cases, the work of gravity

A \u003d mg (h n - h to). (five)

We will now find the work of gravity when driving at an angle to the vertical.

5. The small lump mass M slipped along the inclined plane of the length S and the height H (Fig. 28.3). The inclined plane is the angle α with a vertical.

a) What is the angle between the direction of gravity and the direction of moving the bar? Make an explanatory drawing.
b) Express the work of gravity through M, G, S, α.
c) Express s via H and α.
d) Express the work of gravity through M, G, H.
e) What is the work of gravity strength when driving along the entire same plane up?

After completing this task, you made sure that the work of gravity is expressed by formula (5) and then when the body moves at an angle to the vertical - both down and up.

But then formula (5) for the operation of gravity is valid when the body moves along any trajectory, because any trajectory (Fig. 28.4, a) can be represented as a combination of small "inclined planes" (Fig. 28.4, b).

In this way,
work of gravity when driving but any trajectory is expressed by the formula

A T \u003d Mg (H H - H to),

where H H is the initial height of the body, H to - its final height.
The work of gravity does not depend on the form of the trajectory.

For example, the work of gravity when moving the body from point A to point B (Fig. 28.5) along the trajectory 1, 2 or 3 is the same. From here, in particular, it follows that the ribot of gravity when moving along a closed trajectory (when the body returns to the starting point) is zero.

6. The ball mass M, hanging on the thread Length L, rejected 90º, holding a strained thread, and released without a push.
a) what is the work of gravity for the time during which the ball moves to the position of equilibrium (Fig. 28.6)?
B) What is the work of the force of the elasticity of the thread for the same time?
c) What is the work of the equal forces attached to the ball, during the same time?

3. Work of elasticity

When the spring returns to an undeformed state, the strength of elasticity is always positive: its direction coincides with the direction of movement (Fig. 28.7).

We find the work of the force of elasticity.
The module of this force is associated with the deformation module X by the ratio (see § 15)

The work of this force can be found graphically.

We first note that the work of constant strength is numerically equal to the area of \u200b\u200bthe rectangle under the chart of the dependence of the force from movement (Fig. 28.8).

Figure 28.9 shows a graph of the dependence f (x) for the force of elasticity. We break mentally all the movement of the body to such small gaps so that on each of them the force can be considered constant.

Then work on each of these gaps is numerically equal to the area of \u200b\u200bthe figure under the appropriate section of the chart. All the work is equal to the amount of work in these areas.

Therefore, in this case, the work is numerically equal to the area of \u200b\u200bthe figure under the graph of the dependence f (x).

7. Using Figure 28.10, prove that

the work of the force of elasticity at the return of the spring to the undeformed state is expressed by the formula

A \u003d (KX 2) / 2. (7)

8. Using a graph in Figure 28.11, prove that when the springs deformation changes from X N to x to the work of the force of elasticity is expressed by the formula

From formula (8) we see that the work of the force of elasticity depends only on the initial and final deformation of the spring, so if the body is first deformed, and then it returns to the initial state, then the work of the force of elasticity is zero. Recall that the work of gravity is also possessed as the same property.

9. In the initial moment, the stretching of the spring with stiffness of 400 N / m is 3 cm. The spring was stretched for another 2 cm.
a) What is the final deformation of the spring?
b) What is the work of the Spring's elasticity force?

10. At the initial moment of the spring, the rigidity of 200 n / m is stretched by 2 cm, and at the end moment it is compressed by 1 cm. What is the operation of the force of elasticity of the spring?

4. Work of friction force

Let the body slides on a fixed support. The gliding friction force acting on the body is always directed opposite to movement and, therefore, the work of the slide friction force is negative at any direction of movement (Fig. 28.12).

Therefore, if you move the bar to the right, and Peg to the same distance left, then, although it will return to the initial position, the total work of the slip of the slip will not be zero. This consists of the most important difference in the work of the friction force of sliding from the work of gravity and the strength of elasticity. Recall that the work of these forces when moving the body on a closed trajectory is zero.

11. Laming weighing 1 kg moved on the table so that its trajectory was the square with a side of 50 cm.
a) whether the bar returned to the starting point?
B) What is the total work of the friction force acting on the bar? The friction coefficient between the bar and the table is 0.3.

5. Power

Not only work performed, but also the speed of work is often important. It is characterized by power.

The power of P is called the ratio of perfect work A by the time interval T, for which this work is done:

(Sometimes the power in mechanics is denoted by the letter n, and in the electrodynamics - the letter P. We consider the same power designation more convenient.)

The power unit is Watt (denotes: W), named after the English inventor James Watt. From formula (9) it follows that

1 W \u003d 1 j / c.

12. What power develops a person evenly raising a water bucket weighing 10 kg to a height of 1 m within 2 s?

Often, the power is convenient to express not through work and time, but through force and speed.

Consider the case when the force is directed along the movement. Then the work of force A \u003d FS. Substituting this expression in formula (9) for power, we get:

P \u003d (FS) / T \u003d F (S / T) \u003d FV. (10)

13. The car rides horizontal road at a speed of 72 km / h. At the same time, its engine develops the power of 20 kW. What is the resistance force of the car's movement?

Prompt. When the car moves along a horizontal road at a constant speed, the thrust force is equal to the module by the power of resistance to the movement of the car.

14. How long is it necessary for a uniform lifting of the concrete block weighing 4 tons to a height of 30 m, if the power of the lifting crane engine is 20 kW, and the efficiency of the electric motor of the lifting crane is 75%?

Prompt. The efficiency of the electric motor is equal to the cost of working on the lifting of the engine to the operation of the engine.

Additional questions and tasks

15. The ball weighing 200 g was thrown from a balcony with a height of 10 and at an angle of 45º to the horizon. Having reached a maximum height of 15 m in flight, the ball fell to the ground.
a) what is the work of gravity when lifting the ball?
b) What is the work of gravity, when the ball is descending?
B) What is the work of gravity for all the time of the ball?
d) Is there any extra data on the condition?

16. The ball with a mass of 0.5 kg is suspended to the rigidity of 250 N / m and is in equilibrium. The ball is raised so that the spring becomes undeformed, and they are released without a push.
a) What height raised the ball?
b) What is the work of gravity for the time during which the ball is moving towards the position of equilibrium?
c) What is the work of the force of elasticity for the time during which the ball moves to the position of equilibrium?
d) What is the work equal to the equality of all the forces attached to the ball during the time during which the ball moves to the position of equilibrium?

17. Sanki weighing 10 kg moves without initial speed from a snowy mountain with an angle of inclination α \u003d 30º and some distance along the horizontal surface (Fig. 28.13). The friction coefficient between sledding and snow 0.1. Mountain base length L \u003d 15 m.

a) What is the friction force module when the skew is moving along the horizontal surface?
b) What is the work of the friction force when the Sanok moves along the horizontal surface on the way 20 m?
c) What is the friction force module when the sled is moving on the mountain?
d) What is the work of the friction force during the descent of the Sanok?
e) What is the work of gravity for the descent of the Sanok?
e) What is the work of the automatic forces acting on Sanki, when they are descending from the mountain?

18. The car weighing 1 t is moving at a speed of 50 km / h. The engine develops a power of 10 kW. Gasoline consumption is 8 liters per 100 km. The density of gasoline is 750 kg / m 3, and its specific heat combustion of 45 MJ / kg. What is the engine kpd? Is there any extra data in the condition?
Prompt. The efficiency of the thermal engine is equal to the ratio of the engine performed by the engine to the amount of heat, which was separated during the combustion of the fuel.

The horse pulls the cart with some force, we denote it F.traction. Grandfather sitting on the cart presses on her with some force. Denote it F.pressure. The cart moves along the direction of the thrust force of the horse (right), and in the direction of the pressure force of the grandfather (down) the cart does not move. Therefore, in physics they say that F.thrust makes work on the cart, and F.pressure does not work on the cart.

So, work of power over body or mechanical work - physical quantity, the module of which is equal to the work of force on the path traveled by the body along the direction of the action of this forces:

In honor of the English scientist, D.Joul, a unit of mechanical work was named 1 joule (According to the formula, 1 j \u003d 1 n · m).

If some force acts on the body under consideration, it means that some body acts on it. therefore Work of force over the body and body work over the body - complete synonyms. However, the first body work over the second and the work of the second body over the first is 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 the work signs in more detail.

Numerical values \u200b\u200bof force and paths are always non-negative values. Unlike them, mechanical work can have both positive and negative signs. If the direction of force coincides with the direction of the body movement, then The work of the force is considered positive. If the direction of force is opposite to the direction of the body movement, the work of the force consider negative (Take the "-" from "±" formula). If the direction of the body movement is perpendicular to the direction of force, then Such force does not perform work, that is, a \u003d 0.

Consider three illustrations of three aspects of mechanical work.

The performance of work may look different from the points of view of various observers. Consider an example: a girl rides in an elevator up. Does it make mechanical work? The girl can work only on those bodies that act by force. Such a body is only one thing - the cabin of the elevator, as the girl presses its weight on her floor. Now we need to find out if the cabin passes some way. Consider two options: with a fixed and moving observer.

Let first the observer boy sits on the ground. In relation to it, the elevator cabin moves up and passes some path. The weight of the girl is directed in the opposite side - down, therefore, the girl performs over the cabin negative mechanical work: A.virgin< 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 \u003d 0.

In our daily experience, the word "work" is found very often. But physiological and work in the point of view of physics should be distinguished. When you come from lessons, you say: "Oh, as I'm tired!". This is a physiological work. Or, for example, the work of the team in the folk fairy tale "Rack".

Figure 1. Work in the daily sense of the word

We will talk here about work in terms of physics.

The mechanical work is performed if the body moves under the action of force. The work is denoted by the Latin letter A. More strictly determining the work sounds like this.

The work of the force is the physical value equal to the product of the amount of force at the distance traveled by the body in the direction of force.

Figure 2. Work is a physical value

The formula is valid when constant power is on the body.

In the international system of units of SI, work is measured in Joules.

This means that if under the action of force in 1 Newton, the body moved to 1 meter, then 1 Joule was working for this force.

The unit of work is named after the English scientist James Prescotta Joule.

Figure 3. James Prescott Joule (1818 - 1889)

From the formula for calculating the work it follows that three cases are possible when the work is zero.

The first case - when force acts on the body, but the body does not move. For example, the house has a huge force of gravity. But it does not make work, since the house is still.

The second case - when the body moves along the inertia, that is, there are no forces on it. For example, a spacecraft moves in intergalactic space.

The third case - when the body acts on the body, perpendicular to the direction of the body movement. In this case, although the body moves, and the force on it acts, but there is no body movement in the direction of force.

Figure 4. Three cases when the work is zero

It should also be said that the work of strength may be negative. So it will be if the movement of the body occurs against the direction of force. For example, when the lifting valve with a cable lifts the cargo above the ground, the work of gravity is negative (and the work of the force of elasticity of the cable, directed upward, on the contrary, is positive).

Suppose, when performing construction works, you need to float sand. The excavator for this will need a few minutes, and the worker with the help of the shovel would have to work for several hours. But also the excavator, and the worker would fulfill same work.

Figure 5. The same work can be performed at different times.

In order to characterize the speed of execution of work in physics, a value called power is used.

Power is a physical value equal to the ratio of its implementation.

Power is denoted by the Latin letter N..

Unit of power measurement I system SI is watt.

One watt is a power at which the work in one joule is performed in one second.

The power unit is named after the English scientist, the inventor of the James Watt steam car.

Figure 6. James Watt (1736 - 1819)

We combine the formula for calculating work with the formula for calculating the power.

Recall now that the attitude of the path traveled by the body, S.by movement t. represents the speed of the body v..

In this way, power is equal to the product of the numerical value of force on the body speed in the direction of force.

This formula is convenient to use when solving problems in which force acts on the body moving at a certain speed.

Bibliography

1. Lukashik V.I., Ivanova E.V. Collection of tasks in physics for 7-9 classes of general educational institutions. - 17th ed. - M.: Enlightenment, 2004.
2. Pryrickin A.V. Physics. 7 cl. - 14th ed., Stereotype. - M.: Drop, 2010.
3. Pryrickin A.V. Collection of tasks in physics, 7-9 cl.: 5th ed., Stereotype. - M: Publishing "Exam", 2010.

1. Internet portal Physics.ru ().
2. Internet portal Festival 1September.ru ().
3. Internet portal Fizportal.ru ().
4. Internet portal ELKIN52.NAROD.RU ().

Homework

1. In what cases is the work equal to zero?
2. How is the work on the way traveled in the direction of force? In the opposite direction?
3. What kind of work does the force of friction acting on the brick, when it moves 0.4 m? The friction force is 5 N.

Before disclosing the topic "What is measured by work", it is necessary to make a slight retreat. Everything in this world is subject to the laws of physics. Each process or phenomenon can be explained on the basis of certain laws of physics. For each measured value there is a unit in which it is accepted. Units of measurements are unchanged and have a single value throughout the world.

The reason for this is the following. In nine hundred and sixtieth year, a measurement system was adopted at the eleventh General Conference on measures and weights. This system has received the name of Le Système International D'Unités, Si (SI intermenimal system). This system has become the basic for the definitions of the units of measurement and their relations taken throughout the world.

Physical Terms and Terminology

In physics, the unit of measurement of the work is called J (Joule), in honor of the English scientist James Joule, who made a great contribution to the development of the section of thermodynamics in physics. One Joule is equal to the work performed by force in one H (Newton), when it moves its application to one m (meter) in the direction of force. One H (Newton) is equal to force, weighing one kg (kilogram), while accelerating in one m / s2 (meter per second) in the direction of force.

For your information. In physics, everything is interconnected, the execution of any work is associated with the implementation of additional actions. As an example, you can take a household fan. When the fan is turned on, the fan blade is started to rotate. Rotating blades affect the air flow by giving him directional movement. This is the result of work. But to perform work, the impact of other third-party forces is necessary, without which the performance is impossible. These include electric current, power, voltage and many other interrelated values.

Electric current, in essence, is an ordered movement of electrons in the conductor per unit of time. The electric current is based on positively or negatively charged particles. They are called electrical charges. Denoted by the letters C, Q, CL (pendant), named after the French scientist and the inventor Charles Kulon. In the system C is a unit of measurement of the number of charged electrons. 1 CL is equal to the volume of charged particles flowing through the cross-section of the conductor per unit of time. A unit of time is meant one second. The electric charge formula is shown below in the figure.

The power of the electric current is denoted by the letter A (ampere). Ampere is a unit in physics, characterizing the measurement of the work of force, which is spent to move charges by conductor. In essence, the electric current is an ordered electron movement in the conductor under the influence of an electromagnetic field. Under the conductor means material or melt salts (electrolyte) having a small resistance to the passage of electrons. For electric current, two physical quantities affect: voltage and resistance. They will be discussed below. The current is always directly proportional to the voltage and inversely proportional to the resistance.

As mentioned above, the electric current is an ordered electron movement in the conductor. But there is one nuance: for their movement you need a certain impact. This impact is created by creating a potential difference. Electric charge can be positive or negative. Positive charges always strive for negative charges. This is necessary for the equilibrium of the system. The difference between the number of positive and negatively charged particles is called electrically voltage.

Power is the amount of energy spent on the execution of work in one J (JOUL) over the time interval of one second. The unit of measurement in physics is indicated as W (Watt), in the SI W (WATT) system. Since the power is considered, here it is the value of the expended electrical energy to perform a certain action in a period of time.

In everyday life often have to meet with such a concept as work. What does this word mean in physics and how to determine the work of the force of elasticity? Answers to these questions you will learn in the article.

Mechanical work

Work is a scalar algebraic value that characterizes the relationship between strength and movement. When the direction of these two variables coincides, it is calculated according to the following formula:

• F. - module of the power vector that makes work;
• S. - Module of movement vector.

Not always the force that acts on the body makes work. For example, the work of gravity is zero if its direction is perpendicular to the movement of the body.

If the power vector forms a different angle from zero with a movement vector, another formula should be used to determine the operation:

A \u003d FSCOSα.

α - The angle between the versions of strength and movement.

It means mechanical work - This is a product of the projection of force towards the direction of movement and the movement module, or the product of the projection of movement to the direction of force and the module of this force.

Sign of mechanical work

Depending on the direction of force relative to the movement of the body, work a may be:

• positive (0°≤ α<90°);
• negative (90 °<α≤180°);
• equal to zero (α \u003d 90 °).

If a\u003e 0, then the body speed increases. An example is the fall of the apple from the tree to the ground. With A.<0 сила препятствует ускорению тела. Например, действие силы трения скольжения.

Unit of measurement of work in SI (International Units) - Joule (1N * 1m \u003d J). Joule is the work of strength, the value of which is 1 Newton, when moving the body by 1 meter in the direction of force.

Work of strength of elasticity

The work of the force can be determined and graphically. For this, the area of \u200b\u200bthe curvilinear figure under the graph F s (x) is calculated.

Thus, according to the chart of the dependence of the force of elasticity from the extension of the spring, it is possible to derive the formula for the operation of the force of elasticity.

It is equal:

A \u003d kx 2/2

• k. - rigidity;
• x. - Absolute elongation.

What did we know?

Mechanical work is performed under action on the body of the force, which leads to the movement of the body. Depending on the angle that occurs between force and movement, the work can be zero or have a negative or positive sign. On the example of the strength of the elasticity, you learned about the graphic method of determining work.