What is the work of the force. How is work measured?

mechanical work is the energy characteristic of motion physical bodies, which has a scalar form. It is equal to the modulus of the force acting on the body, multiplied by the modulus of displacement caused by this force and the cosine of the angle between them.

Formula 1 - Mechanical work.

F - Force acting on the body.

s - body movement.

cosa - Cosine of the angle between force and displacement.

This formula has general form. If the angle between the applied force and the displacement is zero, then the cosine is 1. Accordingly, the work will only be equal to the product of the force and the displacement. Simply put, if the body moves in the direction of application of the force, then the mechanical work is equal to the product of the force and the displacement.

Second special case when the angle between the force acting on the body and its displacement is 90 degrees. In this case, the cosine of 90 degrees is equal to zero, respectively, the work will be equal to zero. And indeed, what happens is we apply force in one direction, and the body moves perpendicular to it. That is, the body is obviously not moving under the influence of our force. Thus, the work of our force to move the body is zero.

Figure 1 - The work of forces when moving the body.

If more than one force acts on the body, then the total force acting on the body is calculated. And then it is substituted into the formula as the only force. A body under the action of a force can move not only in a straight line, but also along an arbitrary trajectory. In this case, the work is calculated for a small section of movement, which can be considered straight and then summed up along the entire path.

Work can be both positive and negative. That is, if the displacement and force coincide in direction, then the work is positive. And if the force is applied in one direction, and the body moves in the other, then the work will be negative. An example of negative work is the work of the friction force. Since the friction force is directed against the movement. Imagine a body moving along a plane. A force applied to a body pushes it in a certain direction. This force does positive work to move the body. But at the same time, the friction force does negative work. It slows down the movement of the body and is directed towards its movement.

Figure 2 - Force of movement and friction.

Work in mechanics is measured in Joules. One Joule is the work done by a force of one Newton when a body moves one meter. In addition to the direction of movement of the body, the magnitude of the applied force can also change. For example, when a spring is compressed, the force applied to it will increase in proportion to the distance traveled. In this case, the work is calculated by the formula.

Formula 2 - Work of compression of a spring.

k is the stiffness of the spring.

x - move coordinate.

Note that work and energy have the same unit of measurement. This means that work can be converted into energy. For example, in order to lift a body to a certain height, then it will have potential energy, a force is needed that will do this work. The work of the lifting force will be converted into potential energy.

The rule for determining work according to the dependency graph F(r): work is numerically equal to the area of the figure under the graph of force versus displacement.

Angle between force vector and displacement

1) Correctly determine the direction of the force that does the work; 2) We depict the displacement vector; 3) We transfer the vector to one point, we get the desired angle.

In the figure, the body is affected by gravity (mg), support reaction (N), friction force (Ftr) and rope tension force F, under the influence of which the body moves r.

The work of gravity

Support reaction work

The work of the friction force

Rope tension work

The work of the resultant force

The work of the resultant force can be found in two ways: 1 way - as the sum of the work (taking into account the signs "+" or "-") of all forces acting on the body, in our example
Method 2 - first of all, find the resultant force, then directly its work, see figure

The work of the elastic force

To find the work done by the elastic force, it is necessary to take into account that this force changes, since it depends on the elongation of the spring. From Hooke's law it follows that with an increase in absolute elongation, the force increases.

To calculate the work of the elastic force during the transition of a spring (body) from an undeformed state to a deformed one, use the formula

Power

A scalar value that characterizes the speed of doing work (an analogy can be drawn with acceleration, which characterizes the speed of change in speed). Determined by the formula

Efficiency

efficiency is the ratio useful work, perfect by the machine, to all the work expended (energy supplied) for the same time

Coefficient useful action expressed as a percentage. The closer this number is to 100%, the better the performance of the machine. There cannot be an efficiency greater than 100, since it is impossible to do more work with less energy.

The efficiency of an inclined plane is the ratio of the work done by gravity to the work expended in moving along an inclined plane.

The main thing to remember

1) Formulas and units of measurement;
2) Work is done by force;
3) Be able to determine the angle between the vectors of force and displacement

If the work of a force when moving a body along a closed path is zero, then such forces are called conservative or potential. The work of the friction force when moving a body along a closed path is never equal to zero. The force of friction, in contrast to the force of gravity or the force of elasticity, is non-conservative or non-potential.

There are conditions under which the formula cannot be used
If the force is variable, if the trajectory of motion is a curved line. In this case, the path is divided into small sections for which these conditions are met, and elementary work on each of these sections is calculated. The total work in this case is equal to the algebraic sum of elementary works:

The value of the work of some force depends on the choice of the reference system.

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 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.

In the international SI system of 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 crane lifts the load above the ground with the help of a cable, the work of the force of gravity is negative (and the work of the upward force of the cable, on the contrary, is positive).

Let's assume that when executing construction works 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 numerical value force on 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

Lukashik V.I., Ivanova E.V. Collection of tasks in physics for grades 7-9 of educational institutions. - 17th ed. - M.: Enlightenment, 2004.
Peryshkin A.V. Physics. 7 cells - 14th ed., stereotype. - M.: Bustard, 2010.
Peryshkin A.V. Collection of problems in physics, grades 7-9: 5th ed., stereotype. - M: Exam Publishing House, 2010.

Internet portal Physics.ru ().
Internet portal Festival.1september.ru ().
Internet portal Fizportal.ru ().
Internet portal Elkin52.narod.ru ().

Homework

When is work equal to zero?
What is the work done on the path traveled in the direction of the force? In the opposite direction?
What work is done by the friction force acting on the brick when it moves 0.4 m? The friction force is 5 N.

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 person who holds outstretched hands heavy object, for example, holds a cracked roof over a porch country house from falling while his wife and children frantically search for something to support her. 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 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 putting a lot of effort. 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 given 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.