What is perfect work in physics. Mechanical work and power

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

Since such questions arise, it’s time to remember the definition. When a force is applied to an object and the body moves under its action, mechanical work is performed. This value is proportional to the path traveled by the body and the force applied. There is also an additional dependence on the direction of application of force and the direction of movement 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, which exists in the most general case between them. As an example, we can consider several cases that will allow us to better understand what is meant by this.

When is mechanical work not performed? The truck is standing there, we push it, but it doesn’t move. The force is applied, but there is no movement. The work done is zero. Here is another example - a mother is carrying a child in a stroller, in this case work is done, force is applied, the stroller moves. The difference in the two described cases 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 has accelerated and is calmly rolling along the path, without turning the pedals. The work is being done? No, although there is movement, there is no applied force, the movement is carried out by inertia.

Another example is a horse pulling a cart, with a driver sitting on it. Does it do work? There is movement, there is applied force (the weight of the driver acts on the cart), but the work is not performed. The angle between the direction of movement and the direction of the force is 90 degrees, and the cosine of an angle of 90° is zero.

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

In addition, it must be taken into account that the force acting on the body can be the result of several forces. If this is so, then the work done by all forces applied to the body is equal to the work done by the resultant 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.

From the examples considered, an extremely interesting conclusion can be drawn. When we looked at the driver on the cart, we determined that he was not doing work. Work is done in the horizontal plane because that is where the movement occurs. But the situation changes a little when we consider a pedestrian.

When walking, a person’s center of gravity does not remain stationary, 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 during long walking the body will have to do additional work. So proper gait reduces this extra work and reduces fatigue.

Having analyzed several simple life situations, chosen as examples, and using the knowledge of what mechanical work is, we examined the main situations of its manifestation, as well as when and what kind of work is performed. We determined that the concept of work in everyday life and in physics has a different nature. And they established through the application of physical laws that incorrect gait causes additional fatigue.

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 measured quantity there is a unit in which it is usually measured. Units of measurement are constant and have the same meaning throughout the world.

The reason for this is the following. In nineteen sixty, at the Eleventh General Conference on Weights and Measures, a system of measurements was adopted that 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 determining units of measurement accepted throughout the world and their relationships.

Physical terms and terminology

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

For your information. In physics, everything is interconnected; performing any work involves performing additional actions. As an example, we can take a household fan. When the fan is plugged in, the fan blades begin to rotate. The rotating blades influence the air flow, giving it directional movement. This is the result of the work. But to perform the work, the influence of other external forces is necessary, without which the action is impossible. These include electric current, power, voltage and many other related values.

Electric current, at its core, 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 (Coulomb), named after the French scientist and inventor Charles Coulomb. In the SI system, it is a unit of measurement for the number of charged electrons. 1 C is equal to the volume of charged particles flowing through the cross section of a conductor per unit time. The unit of time is one second. The formula for electric charge is shown in the figure below.

The strength of electric current is indicated by the letter A (ampere). Ampere is a unit in physics that characterizes the measurement of the work of force that is expended to move charges along a conductor. At its core, electric current is the ordered movement of electrons in a conductor under the influence of an electromagnetic field. A conductor is a material or molten salt (electrolyte) that has little resistance to the passage of electrons. The strength of electric current is affected by two physical quantities: voltage and resistance. They will be discussed below. Current strength 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: they need a certain impact to move. This effect is created by creating a potential difference. Electric charge can be positive or negative. Positive charges always tend towards 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 one J (Joule) of work in a period of time of one second. The unit of measurement in physics is designated as W (Watt), in the SI system W (Watt). Since electrical power is considered, here it is the value of the electrical energy expended to perform a certain action in a period of time.

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

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Let the body, which is acted upon by a force, pass, moving along a certain trajectory, a path s. In this case, the force either changes the speed of the body, giving it acceleration, or compensates for the action of another force (or forces) opposing the movement. The action on the path s is characterized by a quantity called work.

Mechanical work is a scalar quantity equal to the product of the projection of the force on the direction of movement Fs and the path s traversed by the point of application of the force (Fig. 22):

A = Fs*s.(56)

Expression (56) is valid if the magnitude of the projection of the force Fs on the direction of movement (i.e., on the direction of velocity) remains unchanged all the time. In particular, this occurs when the body moves rectilinearly and a force of constant magnitude forms a constant angle α with the direction of movement. Since Fs = F * cos(α), expression (47) can be given the following form:

A = F * s * cos(α).

If is the displacement vector, then the work is calculated as the scalar product of two vectors and :

. (57)

Work is an algebraic quantity. If the force and direction of movement form an acute angle (cos(α) > 0), the work is positive. If the angle α is obtuse (cos(α)< 0), работа отрицательна. При α = π/2 работа равна нулю. Последнее обстоятельство особенно отчетливо показывает, что понятие работы в механике существенно отличается от обыденного представления о работе. В обыденном понимании всякое усилие, в частности и мускульное напряжение, всегда сопровождается совершением работы. Например, для того чтобы держать тяжелый груз, стоя неподвижно, а тем более для того, чтобы перенести этот груз по горизонтальному пути, носильщик затрачивает много усилий, т. е. «совершает работу». Однако это – «физиологическая» работа. Механическая работа в этих случаях равна нулю.

Work when moving under force

If the magnitude of the projection of force on the direction of movement does not remain constant during movement, then the work is expressed as an integral:

. (58)

An integral of this type in mathematics is called a curvilinear integral along the trajectory S. The argument here is a vector variable, which can change both in magnitude and direction. Under the integral sign is the scalar product of the force vector and the elementary displacement vector.

A unit of work is taken to be the work done by a force equal to one and acting in the direction of movement along a path equal to one. In SI The unit of work is the joule (J), which is equal to the work done by a force of 1 newton along a path of 1 meter:

1J = 1N * 1m.

In the CGS, the unit of work is the erg, equal to the work done by a force of 1 dyne along a path of 1 centimeter. 1J = 10 7 erg.

Sometimes the non-systemic unit kilogrammometer (kg*m) is used. This is the work done by a force of 1 kg along a path of 1 meter. 1 kg*m = 9.81 J.

If a force acts on a body, then this force does work to move this body. Before defining work during curvilinear motion of a material point, let us consider special cases:

In this case the mechanical work A is equal to:

A= F scos=
,

or A = Fcos× s = F S × s,

WhereF S – projection strength to move. In this case F s = const, and the geometric meaning of the work A is the area of ​​the rectangle constructed in coordinates F S , , s.

Let's plot the projection of force on the direction of movement F S as a function of displacement s. Let us represent the total displacement as the sum of n small displacements
. For small i -th movement
work is equal

or the area of ​​the shaded trapezoid in the figure.

Complete mechanical work to move from a point 1 exactly 2 will be equal to:

.

The value under the integral will represent the elementary work of infinitesimal displacement
:

- basic work.

We divide the trajectory of a material point into infinitesimal movements and work of force by moving a material point from a point 1 exactly 2 defined as a curvilinear integral:

–work in curved motion.

Example 1: Work of gravity
during curvilinear motion of a material point.

.

Further as a constant value can be taken out of the integral sign, and the integral according to the figure will represent the full displacement . .

If we denote the height of a point 1 from the Earth's surface through , and the height of the point 2 through , That

We see that in this case the work is determined by the position of the material point at the initial and final moments of time and does not depend on the shape of the trajectory or path. The work done by gravity along a closed path is zero:
.

Forces whose work on a closed path is zero are calledconservative .

Example 2 : Work done by friction force.

This is an example of a non-conservative force. To show this, it is enough to consider the elementary work of the friction force:

,

those. The work done by the friction force is always a negative quantity and cannot be equal to zero on a closed path. The work done per unit time is called power. If during the time
work is being done
, then the power is equal

–mechanical power.

Taking
as

,

we get the expression for power:

.

The SI unit of work is the joule:
= 1 J = 1 N 1 m, and the unit of power is the watt: 1 W = 1 J/s.

Mechanical energy.

Energy is a general quantitative measure of the movement of interaction of all types of matter. Energy does not disappear and does not arise from nothing: it can only pass from one form to another. The concept of energy links together all phenomena in nature. In accordance with the various forms of motion of matter, different types of energy are considered - mechanical, internal, electromagnetic, nuclear, etc.

The concepts of energy and work are closely related to each other. It is known that work is done due to the energy reserve and, conversely, by doing work, you can increase the energy reserve in any device. In other words, work is a quantitative measure of energy change:

.

Energy, like work, is measured in SI in joules: [ E]=1 J.

Mechanical energy is of two types - kinetic and potential.

Kinetic energy (or energy of motion) is determined by the masses and velocities of the bodies in question. Consider a material point moving under the influence of a force . The work of this force increases the kinetic energy of a material point
. In this case, let us calculate the small increment (differential) of kinetic energy:

When calculating
Newton's second law was used
, and
- module of the velocity of the material point. Then
can be represented as:

-

- kinetic energy of a moving material point.

Multiplying and dividing this expression by
, and given that
, we get

-

- connection between momentum and kinetic energy of a moving material point.

Potential energy ( or the energy of the position of bodies) is determined by the action of conservative forces on the body and depends only on the position of the body .

We have seen that the work done by gravity
with curvilinear motion of a material point
can be represented as the difference in function values
, taken at the point 1 and at the point 2 :

.

It turns out that whenever the forces are conservative, the work of these forces on the path 1
2 can be represented as:

.

Function , which depends only on the position of the body is called potential energy.

Then for elementary work we get

–work equals loss of potential energy.

Otherwise, we can say that work is done due to the reserve of potential energy.

Size , equal to the sum of the kinetic and potential energies of the particle, is called the total mechanical energy of the body:

–total mechanical energy of the body.

In conclusion, we note that using Newton's second law
, kinetic energy differential
can be represented as:

.

Potential energy differential
, as indicated above, is equal to:

.

Thus, if the force – conservative force and there are no other external forces, then , i.e. in this case, the total mechanical energy of the body is conserved.

In our everyday experience, the word “work” appears very often. 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, I’m so tired!” This is physiological work. Or, for example, the work of the team in the folk tale “Turnip”.

Figure 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 performed if a body moves under the influence of a force. Work is designated by the Latin letter A. A more strict definition of work sounds like this.

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

Figure 2. Work is a physical quantity

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

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

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

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

Fig 3. James Prescott Joule (1818 - 1889)

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

The first case is when a force acts on a body, but the body does not move. For example, a house is subject to a huge force of gravity. But she does not do any 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, a spaceship is moving in intergalactic space.

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

Figure 4. Three cases when work is zero

It should also be said that the work done by a force can be negative. This will happen if the body moves against the direction of the force. For example, when a crane lifts a load above the ground using a cable, the work done by the force of gravity is negative (and the work done by the elastic force of the cable directed upward, on the contrary, is positive).

Let’s assume that when performing construction work, the pit needs to be filled with sand. It would take a few minutes for an excavator to do this, but a worker with a shovel would have to work for several hours. But both the excavator and the worker would have completed the same job.

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

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

Power is a physical quantity equal to the ratio of work to the time it is performed.

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

Fig 6. James Watt (1736 - 1819)

Let's combine the formula for calculating work with the formula for calculating power.

Let us now remember that the ratio of the path traveled by the body is S, by the time of movement t represents the speed of movement of the body v.

Thus, 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 with a known speed.

Bibliography

1. Lukashik V.I., Ivanova E.V. Collection of problems in physics for grades 7-9 of general education institutions. - 17th ed. - M.: Education, 2004.
2. Peryshkin A.V. Physics. 7th grade - 14th ed., stereotype. - M.: Bustard, 2010.
3. Peryshkin A.V. Collection of problems in physics, grades 7-9: 5th ed., stereotype. - M: Publishing House “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 work equal to zero?
2. How is the work done along the path traveled in the direction of the force? In the opposite direction?
3. How much work is done by the frictional force acting on the brick when it moves 0.4 m? The friction force is 5 N.