Before revealing the topic “How work is measured”, it is necessary to make a small digression. Everything in this world obeys the laws of physics. Each process or phenomenon can be explained on the basis of certain laws of physics. For each measurable quantity, there is a unit in which it is customary to measure it. Units of measurement are fixed and have the same meaning throughout the world.

The reason for this is the following. In 1960, at the eleventh general conference on weights and measures, a system of measurements was adopted, which is recognized throughout the world. This system was named Le Système International d'Unités, SI (SI System International). This system has become the basis for the definitions of units of measurement accepted throughout the world and their ratio.

Physical terms and terminology

In physics, the unit for measuring the work of a force is called J (Joule), in honor of the English physicist James Joule, who made a great contribution to the development of the section of thermodynamics in physics. One Joule equals work, performed by a force of one N (Newton), when its application moves one M (meter) in the direction of the force. One N (Newton) equal to strength, with a mass of one kg (kilogram), with an acceleration of one m/s2 (meter per second) in the direction of the force.

Note. In physics, everything is interconnected, the performance of any work is associated with the performance of additional actions. An example is a household fan. When the fan is switched on, the fan blades begin to rotate. Rotating blades act on the air flow, giving it a directional movement. This is the result of work. But to perform the work, the influence of other external forces is necessary, without which the performance of the action is impossible. These include the strength of the electric current, power, voltage and many other interrelated values.

Electric current, in its essence, is the ordered movement of electrons in a conductor per unit time. Electric current is based on positively or negatively charged particles. They are called electric charges. Denoted by the letters C, q, Kl (Pendant), named after the French scientist and inventor Charles Coulomb. In the SI system, it is a unit of measure for the number of charged electrons. 1 C is equal to the volume of charged particles flowing through the cross section of the conductor per unit time. The unit of time is one second. The formula for electric charge is shown below in the figure.

The strength of the electric current is denoted by the letter A (ampere). An ampere is a unit in physics that characterizes the measurement of the work of a force that is expended to move charges along a conductor. At its core, electricity is the ordered movement of electrons in a conductor under the influence of electromagnetic field. By conductor is meant a material or molten salt (electrolyte) that has little resistance to the passage of electrons. Two physical quantities affect the strength of an electric current: voltage and resistance. They will be discussed below. Current is always directly proportional to voltage and inversely proportional to resistance.

As mentioned above, electric current is the ordered movement of electrons in a conductor. But there is one caveat: for their movement, a certain impact is needed. This effect is created by creating a potential difference. Electric charge can be positive or negative. positive charges always striving for negative charges. This is necessary for the balance of the system. The difference between the number of positively and negatively charged particles is called electrical voltage.

Power is the amount of energy expended to do work of one J (Joule) in a period of time of one second. The unit of measurement in physics is denoted as W (Watt), in the SI system W (Watt). Since the electric power is considered, here it is the value of the spent electrical energy to perform a certain action in a period of time.

In conclusion, it should be noted that the unit of measure of work is a scalar quantity, has a relationship with all sections of physics and can be considered from the side of not only electrodynamics or heat engineering, but also other sections. The article briefly considers the value that characterizes the unit of measurement of the work of force.

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« Physics - Grade 10 "

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

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

Remember what work and power are in physics.

Do these concepts coincide with everyday ideas about them?

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

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

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

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

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

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

Job definition.

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

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

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

А = F r |Δ|. (5.1)

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

Therefore, the work is equal to:

A = |Δ|cosα. (5.2)

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

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

In general, when moving solid body move it different points are different, but when determining the work of a force, we Δ understand the movement of its point of application. At forward movement of a rigid body, the movement of all its points coincides with the movement of the point of application of the force.

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

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

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

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

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

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

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

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

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

Fcosα = F x , |Δ| = Δ x.

For the work of the force, we get

А = F|Δ|cosα = F x Δx.

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

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

Unit of work.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

In our everyday experience, the word "work" is very common. But one should distinguish between physiological work and work from the point of view of the science of physics. When you come home from class, you say: “Oh, how tired I am!”. This is a physiological job. Or, for example, the work of the team in the folk tale "Turnip".

Fig 1. Work in the everyday sense of the word

We will talk here about work from the point of view of physics.

Mechanical work is done when a force moves a body. Work is denoted by the Latin letter A. A more rigorous definition of work is as follows.

The work of force is called physical quantity, equal to the product of the magnitude of the force by the distance traveled by the body in the direction of the force.

Fig 2. Work is a physical quantity

The formula is valid when a constant force acts on the body.

AT international system SI units work is measured in joules.

This means that if a body moves 1 meter under the action of a force of 1 newton, then 1 joule of work is done by this force.

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

Figure 3. James Prescott Joule (1818 - 1889)

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

The first case is when a force acts on the body, but the body does not move. For example, a huge force of gravity acts on a house. But she does no work, because the house is motionless.

The second case is when the body moves by inertia, that is, no forces act on it. For example, spaceship moving in intergalactic space.

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

Fig 4. Three cases when the work is equal to zero

It should also be said that the work of a force can be negative. So it will be if the movement of the body occurs against the direction of the force. For example, when a crane lifts a load above the ground with a cable, the work of gravity is negative (and the work of the cable's upward force, on the contrary, is positive).

Suppose, when performing construction work, the pit must be covered with sand. An excavator would need several minutes to do this, and a worker with a shovel would have to work for several hours. But both the excavator and the worker would have performed the same job.

Fig 5. The same work can be done in different times

To characterize the speed of work in physics, a quantity called power is used.

Power is a physical quantity equal to the ratio of work to the time of its execution.

Power is indicated by a Latin letter N.

The SI unit of power is the watt.

One watt is the power at which one joule of work is done in one second.

The unit of power is named after the English scientist and inventor of the steam engine James Watt.

Figure 6. James Watt (1736 - 1819)

Combine the formula for calculating work with the formula for calculating power.

Recall now that the ratio of the path traveled by the body, S, by the time of movement t is the speed of the body v.

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

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

Bibliography

1. Lukashik V.I., Ivanova E.V. Collection of tasks in physics for grades 7-9 educational institutions. - 17th ed. - M.: Enlightenment, 2004.
2. Peryshkin A.V. Physics. 7 cells - 14th ed., stereotype. - M.: Bustard, 2010.
3. Peryshkin A.V. Collection of problems in physics, grades 7-9: 5th ed., stereotype. - M: Exam Publishing House, 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. When is work equal to zero?
2. What is the work done on the path traveled in the direction of the force? In the opposite direction?
3. What work is done by the friction force acting on the brick when it moves 0.4 m? The friction force is 5 N.

AT Everyday life We often come across the concept of work. What does this word mean in physics and how to determine the work of an elastic force? You will find the answers to these questions in the article.

mechanical work

Work is a scalar algebraic quantity that characterizes the relationship between force and displacement. If the direction of these two variables coincides, it is calculated by the following formula:

• F- modulus of the force vector that does the work;
• S- displacement vector modulus.

The force that acts on the body does not always do work. For example, the work of gravity is zero if its direction is perpendicular to the movement of the body.

If the force vector forms a non-zero angle with the displacement vector, then another formula should be used to determine the work:

A=FScosα

α - angle between force and displacement vectors.

Means, mechanical work is the product of the projection of the force on the direction of displacement and the module of displacement, or the product of the projection of the displacement on the direction of the force and the module of this force.

mechanical work sign

Depending on the direction of the force relative to the displacement of the body, the work A can be:

• positive (0°≤ α<90°);
• negative (90°<α≤180°);
• zero (α=90°).

If A>0, then the speed of the body increases. An example is an apple falling from a tree to the ground. For A<0 сила препятствует ускорению тела. Например, действие силы трения скольжения.

The unit of measure for work in SI (International System of Units) is the Joule (1N*1m=J). Joule is the work of a force, the value of which is 1 Newton, when a body moves 1 meter in the direction of the force.

The work of the elastic force

The work of a force can also be determined graphically. For this, the area of ​​the curvilinear figure under the graph F s (x) is calculated.

So, according to the graph of the dependence of the elastic force on the elongation of the spring, it is possible to derive the formula for the work of the elastic force.

It is equal to:

A=kx 2 /2

• k- rigidity;
• x- absolute elongation.

What have we learned?

Mechanical work is performed when a force acts on a body, which leads to the displacement of the body. Depending on the angle that occurs between the force and the displacement, the work can be zero or have a negative or positive sign. Using the elastic force as an example, you learned about a graphical way to determine work.

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One of the most important concepts in mechanics work force .

Force work

All physical bodies in the world around us are driven by force. If a moving body in the same or opposite direction is affected by a force or several forces from one or more bodies, then they say that work is done .

That is, mechanical work is done by the force acting on the body. Thus, the traction force of an electric locomotive sets the entire train in motion, thereby performing mechanical work. The bicycle is propelled by the muscular strength of the cyclist's legs. Therefore, this force also does mechanical work.

In physics work of force called a physical quantity equal to the product of the modulus of force, the modulus of displacement of the point of application of force and the cosine of the angle between the vectors of force and displacement.

A = F s cos (F, s) ,

where F modulus of force,

s- movement module .

Work is always done if the angle between the winds of force and displacement is not equal to zero. If the force acts in the opposite direction to the direction of motion, the amount of work is negative.

Work is not done if no forces act on the body, or if the angle between the applied force and the direction of motion is 90 o (cos 90 o \u003d 0).

If the horse pulls the cart, then the muscular force of the horse, or the traction force directed in the direction of the cart, does the work. And the force of gravity, with which the driver presses on the cart, does no work, since it is directed downward, perpendicular to the direction of movement.

The work of a force is a scalar quantity.

SI unit of work - joule. 1 joule is the work done by a force of 1 newton at a distance of 1 m if the direction of force and displacement are the same.

If several forces act on a body or material point, then they talk about the work done by their resultant force.

If the applied force is not constant, then its work is calculated as an integral:

Power

The force that sets the body in motion does mechanical work. But how this work is done, quickly or slowly, is sometimes very important to know in practice. After all, the same work can be done in different times. The work that a large electric motor does can be done by a small motor. But it will take him much longer to do so.

In mechanics, there is a quantity that characterizes the speed of work. This value is called power.

Power is the ratio of the work done in a certain period of time to the value of this period.

N= A /∆ t

By definition A = F s cos α , a s/∆ t = v , Consequently

N= F v cos α = F v ,

where F - strength, v speed, α is the angle between the direction of the force and the direction of the velocity.

That is power - is the scalar product of the force vector and the velocity vector of the body.

In the international SI system, power is measured in watts (W).

The power of 1 watt is the work of 1 joule (J) done in 1 second (s).

Power can be increased by increasing the force that does the work, or the rate at which this work is done.