In what units is the work of force measured? The physical meaning of work and mechanical energy

If a force acts on a body, then this force does work to move this body. Before giving a definition of work in the curvilinear motion of a material point, consider special cases:

In this case, mechanical work A is equal to:

A= F s cos=
,

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 build a graph of the projection of force on the direction of movement F S as a function of displacement s. We represent the total displacement as the sum of n small displacements
. For small i -th displacement
work is

or the area of the shaded trapezoid in the figure.

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

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

- basic work.

We break the trajectory of the motion of a material point into infinitesimal displacements

and the work of the force

by moving a material point from a point 1 exactly 2 defined as a curvilinear integral:

–work with curvilinear motion.

Example 1: The 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 a complete displacement . .

If we denote the height of the point 1 from the earth's surface through , and the height of the point 2 through , then

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 in a closed path is zero:
.

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

Example 2 : The work of the 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 of the friction force is always negative and cannot be equal to zero on a closed path. The work done per unit of time is called power. If in time
work is done
, then the power is

–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 watt: 1 W = 1 J / s.

mechanical energy.

Energy is a general quantitative measure of the movement of the 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 binds together all phenomena in nature. In accordance with 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 at the expense of the energy reserve and, conversely, by doing work, it is possible to increase the energy reserve in any device. In other words, work is a quantitative measure of the change in energy:

Energy as well as work in SI is measured in joules: [ E]=1 J.

Mechanical energy is of two types - kinetic and potential.

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

When calculating
using Newton's second law
, as well as
- velocity modulus of a material point. Then
can be represented as:

- kinetic energy of a moving material point.

Multiplying and dividing this expression by
, and taking into account that
, we get

- relationship 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 of gravity
with curvilinear motion of a material point
can be represented as the difference between the values of the function
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 way 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 is equal to the loss of potential energy.

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

the value , 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 mentioned above, is equal to:

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

The horse pulls the cart with some force, let's denote it F traction. Grandpa, who is sitting on the cart, presses on her with some force. Let's denote it F pressure The cart moves in the direction of the horse's pulling force (to the right), but in the direction of the grandfather's pressure force (down), the cart does not move. Therefore, in physics they say that F traction does work on the cart, and F the pressure does not do work on the cart.

So, work done by a force on a body mechanical work- a physical quantity, the modulus of which is equal to the product of the force and the path traveled by the body along the direction of action of this force s:

In honor of the English scientist D. Joule, the unit of mechanical work was named 1 joule(according to the formula, 1 J = 1 N m).

If a certain force acts on the considered body, then a certain body acts on it. So the work of a force on a body and the work of a body on a body are complete synonyms. However, the work of the first body on the second and the work of the second body on the first are 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 signs of work in more detail.

Numerical values of force and path are always non-negative values. In contrast, mechanical work can have both positive and negative signs. If the direction of the force coincides with the direction of motion of the body, then the work done by the force is considered positive. If the direction of the force is opposite to the direction of motion of the body, the work done by the force is considered negative.(we take "-" from the "±" formula). If the direction of motion of the body is perpendicular to the direction of the force, then such a force does no work, that is, A = 0.

Consider three illustrations on three aspects of mechanical work.

Doing work by force may look different from the point of view of different observers. Consider an example: a girl rides in an elevator up. Does it do mechanical work? A girl can do work only on those bodies on which she acts by force. There is only one such body - the elevator car, as the girl presses on her floor with her weight. Now we need to find out if the cabin goes some way. Consider two options: with a stationary and moving observer.

Let the observer boy sit on the ground first. In relation to it, the elevator car moves up and goes some way. The weight of the girl is directed in the opposite direction - down, therefore, the girl performs negative mechanical work on the cabin: A virgins< 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 = 0.

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.

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System of International Units

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 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 with a mass of one kg (kilogram) at an acceleration of one m/s2 (meter per second) in the direction of the force.

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The formula for finding a job

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.

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The formula for finding electric charge

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, an electric current is an ordered movement of electrons in a conductor under the influence of an 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.

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The formula for finding the current strength

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. The electrical charge can be positive or negative. Positive charges always tend to 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.

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The formula for finding 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 electrical power is considered, here it is the value of the electrical energy expended to perform a certain action in a period of time.

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The formula for finding electrical power

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.

Video

Do you know what work is? Without any doubt. What is work, every person knows, 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 idea of \u200b\u200bthis process. But it's not about them now. Even fewer people have any idea what mechanical work from the point of view of physics. In physics, mechanical work is not the work of a person for the sake of food, it is a physical quantity that can be completely unrelated to either a person or any other living being. How so? Now let's figure it out.

Mechanical work in physics

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

Definition of mechanical work

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

Mechanical work formula

The mechanical work is determined by the formula:

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

So, despite all the heroism of the tired roof holder, the work done by him is equal to 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 are applying 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 by the distance 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 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 the 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 motion of the body in any way, then the force produced by this work is equal to zero.

III. Tasks for independent work on the topic under study.

The work of all forces acting on the particle goes to the increment of the kinetic energy of the particle:

A 12 = T 2 - T 1

In the presence of a gravitational field (or, in general, any potential field), the gas molecules are acted upon by gravity. As a result, the concentration of gas molecules turns out to be height dependent in accordance with the law Boltzmann distributions:

n = n 0 exp(- mgh / kT)

where n- concentration of molecules at height h, n 0 - concentration of molecules at the initial level h= 0, m is the mass of particles, g- acceleration of gravity, k is the Boltzmann constant, T- temperature.

In physics conservative forces(potential forces) - forces, the work of which does not depend on the shape of the trajectory (depends only on the initial and final points of application of forces). This implies the following definition: conservative forces are those forces whose work along any closed trajectory is equal to 0.

Potential energy- the work that must be done to move the body from a certain reference point to a given point in the field of conservative forces.

Potential energy is measured from a certain point in space, the choice of which is determined by the convenience of further calculations. The process of choosing a given point is called potential energy normalization. It is also clear that the correct definition of potential energy can only be given in the field of forces, the work of which depends only on the initial and final positions of the bodies, but not on the path of their movement. Such forces are called conservative.

For example, the potential energy of a body near the Earth's surface is calculated by the formula , where m- body mass, g - value of free fall acceleration, h- height, the surface of the Earth is taken as zero.

degree of freedom - the minimum number of variables that describe the movement of a molecule in space.

Theorem:

If the system of molecules is in equilibrium at temperature T, then Wk of the motion of molecules will be distributed uniformly over the degrees of freedom, with each st. freedom has an energy of 1\2kT.

Thermal motion- the process of chaotic (random) movement of particles that form a substance. The thermal motion of atoms and molecules is most often considered.

Law of conservation of mechanical energy- the mechanical energy of a conservative mechanical system is conserved in time. Simply put, in the absence of dissipative forces (for example, friction forces), mechanical energy does not arise from nothing and cannot disappear anywhere.

Forces of sliding friction- forces that arise between contacting bodies during their relative motion. If there is no liquid or gaseous layer (lubrication) between the bodies, then such friction is called dry. Otherwise, the friction is called "liquid". A characteristic distinguishing feature of dry friction is the presence of static friction.

Maxwell distribution is a probability distribution encountered in physics and chemistry. It underlies the kinetic theory of gases, which explains many of the fundamental properties of gases, including pressure and diffusion. The Maxwell distribution is also applicable to electronic transport processes and other phenomena. The Maxwell distribution applies to a variety of properties of individual molecules in a gas. It is usually thought of as the energy distribution of molecules in a gas, but it can also be applied to the distribution of velocities, momenta, and momentum modulus of molecules. It can also be expressed as a discrete distribution over a set of discrete energy levels, or as a continuous distribution over some energy continuum.

Law of energy conservation- the basic law of nature, which consists in the fact that the energy of an isolated (closed) system is conserved in time. In other words, energy cannot arise from nothing and cannot disappear into nowhere, it can only pass from one form to another. The law of conservation of energy is found in various branches of physics and manifests itself in the conservation of various types of energy. For example, in classical mechanics, the law manifests itself in]] the law of conservation of energy is called the first law of thermodynamics and says

Probability

The statistical distribution function (distribution function in statistical physics) is one of the fundamental concepts of statistical physics. Knowledge of the distribution function completely determines the probabilistic properties of the system under consideration.

The mechanical state of any system is uniquely determined by the coordinates q i and impulses pi its particles ( i=1,2,…, d; d is the number of degrees of freedom of the system). The set of quantities and form the phase space. The probability of the system being in an element of the phase space (with dot q, p inside) is given by the formula:

The function is called the full statistical distribution function (or simply the distribution function). In fact, it is a density of representing points in the phase space.

Variance of a random variable- a measure of the spread of a given random variable, i.e. its deviation from the mathematical expectation. Denoted D[X] in Russian literature and (eng. variance) in foreign countries. In statistics, the designation or is often used. The square root of the variance is called the standard deviation, standard deviation, or standard spread.

Let be a random variable defined on some probability space. Then

where symbol M stands for mathematical expectation.

In classical mechanics, harmonic oscillator- a system that, when displaced from an equilibrium position, experiences the action of a restoring force F, proportional to the displacement x(according to Hooke's law):

where k is a positive constant describing the rigidity of the system.

If a F- the only force acting on the system, then the system is called simple or conservative harmonic oscillator. Free oscillations of such a system represent a periodic movement around the equilibrium position (harmonic oscillations). The frequency and amplitude are constant, and the frequency does not depend on the amplitude.

If there is also a friction force (attenuation) proportional to the speed of movement (viscous friction), then such a system is called fading or dissipative oscillator. If the friction is not too great, then the system performs an almost periodic motion - sinusoidal oscillations with a constant frequency and an exponentially decreasing amplitude. The frequency of free oscillations of a damped oscillator turns out to be somewhat lower than that of a similar oscillator without friction.

If the oscillator is left to itself, then it is said that it performs free oscillations. If there is an external force (depending on time), then we say that the oscillator experiences forced oscillations.

Random event- subset of outcomes random experiment; when a random experiment is repeated many times, the frequency of the occurrence of an event serves as an estimate of its probability.

A random event that is never realized as a result of a random experiment is called impossible and is denoted by the symbol . A random event, which is always realized as a result of a random experiment, is called reliable and is denoted by the symbol Ω.

Probability(probability measure) - a measure of the reliability of a random event. An estimate of the probability of an event can be the frequency of its occurrence in a long series of independent repetitions of a random experiment. According to the definition of P. Laplace, a measure of probability is a fraction, the numerator of which is the number of all favorable cases, and the denominator is the number of all possible cases.