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. That's why 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.

Definition

In the event that under the influence of a force there is a change in the modulus of the velocity of the body, then they say that the force makes work. It is believed that if the speed increases, then the work is positive, if the speed decreases, then the work done by the force is negative. The change in the kinetic energy of a material point in the course of its movement between two positions is equal to the work done by the force:

The action of a force on a material point can be characterized not only by changing the speed of the body, but by using the magnitude of the displacement that the body in question makes under the action of force ().

elementary work

The elementary work of some force is defined as the scalar product:

Radius is the vector of the point to which the force is applied, is the elementary movement of the point along the trajectory, is the angle between the vectors and . If the work is an obtuse angle, the work is less than zero, if the angle is acute, then the work is positive, with

IN Cartesian coordinates formula (2) has the form:

where F x ,F y ,F z are vector projections onto Cartesian axes.

When considering the work of a force applied to a material point, you can use the formula:

where is the velocity of the material point, is the momentum of the material point.

If several forces simultaneously act on a body (mechanical system), then the elementary work that these forces perform on the system is equal to:

where the summation of the elementary work of all forces is carried out, dt is a small period of time during which elementary work is performed on the system.

The resulting work of internal forces, even if solid moving is zero.

Let a rigid body rotate around a fixed point - the origin of coordinates (or a fixed axis that passes through this point). In this case, the elementary work of all external forces(assuming that their number is n) that act on the body is equal to:

where is the resulting moment of forces relative to pivot points, is the elementary rotation vector, is the instantaneous angular velocity.

The work of the force on the final section of the trajectory

If the force does work to move the body in the final section of the trajectory of its movement, then the work can be found as:

In the event that the force vector is a constant value over the entire segment of the movement, then:

where is the projection of the force on the tangent to the trajectory.

Work units

The basic unit of measurement of the moment of work in the SI system is: [A] \u003d J \u003d N m

In CGS: [A]=erg=dyn cm

1J=10 7 erg

Examples of problem solving

Example

The task. Material point moves in a straight line (Fig. 1) under the influence of a force, which is given by the equation: . The force is directed along the motion of the material point. What is the work of this force on the segment of the path from s=0 to s=s 0 ?

Solution. As a basis for solving the problem, we take the formula for calculating the work of the form:

where , the same as according to the condition of the problem . We substitute the expression for the force modulus given by the conditions, take the integral:

Answer.

Example

The task. The material point moves in a circle. Its speed changes according to the expression: . In this case, the work of the force that acts on a point is proportional to time: . What is the value of n?

DEFINITION

mechanical work is the product of a force applied to an object times the displacement made by that force.

- work (can be denoted as), - force, - displacement.

Unit of measure of work − J (joule).

This formula is applicable to a body moving in a straight line and constant value force acting on it. If there is an angle between the force vector and the straight line describing the trajectory of the body, then the formula takes the form:

In addition, the concept of work can be defined as a change in the energy of a body:

It is this application of this concept that is most often found in problems.

Examples of solving problems on the topic "Mechanical work"

EXAMPLE 1

EXAMPLE 2

mechanical work is a scalar physical quantity that characterizes a change in the position of a body under the action of a force and is equal to the product of the modulus of force and the modulus of displacement (path).

A = Fs

per unit of measure work adopted in SI 1 joule.

[A] = 1N×1m = 1 J

Analysis of the mechanical work formula:

1. The work of the force is positive
A > 0, if the direction of the force and the direction of displacement are the same;

Example: A cat falls off a roof. Direction of movement of the cat matches with the direction of gravity. Means, work done by gravity is positive.

2. The work of the force is negative
BUT< 0 , if the direction of force and the direction of movement are directed in opposite directions;

Example: the cat was thrown up. Direction of movement of the cat opposite direction of gravity. Means, work done by gravity is negative.

3. The work of the force is zero
A = 0, if
1. under the action of a force, the body does not move, that is, when s = 0
2. the magnitude of the force is zero, i.e. F=0
3. injection between directions of movement and force equals 90°.

Example: the cat is just walking along the path. The direction of movement of the cat is perpendicular to the direction of gravity. Means, work done by gravity is zero.

If we build a graph of the dependence of the force value on the displacement (path) traversed by the body, then this graph will be a straight line segment parallel to the axis of displacement (path).

It can be seen from the figure that the shaded area under the graph is a rectangle with sides F and s. The area of ​​this rectangle is F s.
The geometric meaning of mechanical work is that the work of the force numerically equal to the area of ​​​​the figure under the graph of the dependence of force on the displacement of the body.

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 huge contribution in 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) 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.

For your information. 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. The strength of the electric current is affected by two physical quantities: 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 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.

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.

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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