INSTRUCTIONS AND PROPHECIES OF THE Blessed MOTHER ALIPIA GOLOSEEVSKY, Kyiv...
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 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.
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.
Every body that moves can be described as work. In other words, it characterizes the action of forces.
Work is defined as:
The product of the modulus of force and the path traveled by the body, multiplied by the cosine of the angle between the direction of force and motion.
Work is measured in Joules:
1 [J] = = [kg* m2/s2]
For example, body A, under the influence of a force of 5 N, has passed 10 m. Determine the work done by the body.
Since the direction of movement and the action of the force are the same, the angle between the force vector and the displacement vector will be 0°. The formula is simplified because the cosine of an angle at 0° is 1.
Substituting the initial parameters into the formula, we find:
A= 15 J.
Consider another example, a body with a mass of 2 kg, moving with an acceleration of 6 m / s2, passed 10 m. Determine the work done by the body if it moved upward along an inclined plane at an angle of 60 °.
To begin with, we calculate what force must be applied to inform the body of an acceleration of 6 m / s2.
F = 2 kg * 6 m/s2 = 12 H.
Under the action of a force of 12H, the body traveled 10 m. The work can be calculated using the already known formula:
Where, a is equal to 30 °. Substituting the initial data into the formula, we get:
A= 103.2 J.
Power
Many machines of mechanisms perform the same work for a different period of time. To compare them, the concept of power is introduced.
Power is a value that shows the amount of work done per unit of time.
Power is measured in watts, after the Scottish engineer James Watt.
1 [Watt] = 1 [J/s].
For example, a large crane lifted a load weighing 10 tons to a height of 30 m in 1 minute. A small crane lifted 2 tons of bricks to the same height in 1 minute. Compare crane capacities.
Define the work performed by cranes. The load rises by 30m, while overcoming the force of gravity, so the force expended on lifting the load will be equal to the force of interaction between the Earth and the load (F = m * g). And work is the product of forces and the distance traveled by the goods, that is, the height.
For a large crane A1 = 10,000 kg * 30 m * 10 m / s2 = 3,000,000 J, and for a small crane A2 = 2,000 kg * 30 m * 10 m / s2 = 600,000 J.
Power can be calculated by dividing work by time. Both cranes lifted the load in 1 min (60 sec).
From here:
N1 = 3,000,000 J/60 s = 50,000 W = 50 kW.
N2 = 600,000 J / 60 s = 10,000 W = 10 kW.
From the above data, it is clearly seen that the first crane is 5 times more powerful than the second.
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 towards opposite side- 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.
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.
The second special case is 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.
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 is force, s is the distance traveled.
POTENTIAL(potential function), a concept that characterizes a wide class of physical force fields (electric, gravitational, etc.) and, in general, fields of physical quantities represented by vectors (fluid velocity field, etc.). In the general case, the potential of the vector field a( x,y,z) is such a scalar function u(x,y,z) that a=grad
35. Conductors in an electric field. Electrical capacity.conductors in an electric field. Conductors are substances characterized by the presence in them of a large number of free charge carriers that can move under the influence of an electric field. Conductors include metals, electrolytes, coal. In metals, the carriers of free charges are the electrons of the outer shells of atoms, which, when atoms interact, completely lose their bonds with “their” atoms and become the property of the entire conductor as a whole. Free electrons participate in thermal motion like gas molecules and can move through the metal in any direction. Electric capacity- a characteristic of a conductor, a measure of its ability to accumulate an electric charge. In theory electrical circuits capacitance is the mutual capacitance between two conductors; parameter of the capacitive element of the electrical circuit, presented in the form of a two-terminal network. This capacity is defined as the ratio of the magnitude electric charge to the potential difference between these conductors
36. Capacitance of a flat capacitor.
Capacitance of a flat capacitor.
That. the capacitance of a flat capacitor depends only on its size, shape and dielectric constant. To create a high-capacity capacitor, it is necessary to increase the area of the plates and reduce the thickness of the dielectric layer.
37. Magnetic interaction of currents in vacuum. Ampere's law.Ampere's law. In 1820, Ampère (a French scientist (1775-1836)) established experimentally a law by which one can calculate force acting on a conductor element of length with current.
where is the vector of magnetic induction, is the vector of the length element of the conductor drawn in the direction of the current.
Force modulus , where is the angle between the direction of the current in the conductor and the direction of the magnetic field. For a straight conductor with current in a uniform field
The direction of the acting force can be determined using left hand rules:
If the palm of the left hand is positioned so that the normal (to the current) component magnetic field entered the palm, and four outstretched fingers are directed along the current, then the thumb will indicate the direction in which the Ampère force acts.
38. Magnetic field strength. Biot-Savart-Laplace lawMagnetic field strength(standard designation H ) - vector physical quantity, equal to the difference of the vector magnetic induction B and magnetization vector J .
AT International System of Units (SI): 
where- magnetic constant.
BSL law. The law that determines the magnetic field of an individual current element 
39. Applications of the Biot-Savart-Laplace law. For direct current field
For a circular loop.
And for the solenoid
40. Magnetic field induction The magnetic field is characterized by a vector quantity, which is called the magnetic field induction (a vector quantity, which is the force characteristic of the magnetic field at a given point in space). MI. (B) this is not a force acting on conductors, it is a quantity that is found through a given force according to the following formula: B \u003d F / (I * l) (Verbally: MI vector modulus. (B) is equal to the ratio of the modulus of force F, with which the magnetic field acts on a current-carrying conductor located perpendicular to the magnetic lines, to the current strength in the conductor I and the length of the conductor l. Magnetic induction depends only on the magnetic field. In this regard, induction can be considered a quantitative characteristic of the magnetic field. It determines with what force (Lorentz Force) the magnetic field acts on a charge moving with speed. 
MI is measured in Tesla (1 T). In this case, 1 Tl \u003d 1 N / (A * m). MI has direction. Graphically, it can be drawn as lines. In a uniform magnetic field, the MIs are parallel, and the MI vector will be directed in the same way at all points. In the case of a non-uniform magnetic field, for example, a field around a conductor with current, the magnetic induction vector will change at each point in space around the conductor, and tangents to this vector will create concentric circles around the conductor.
41. Motion of a particle in a magnetic field. Lorentz force. a) - If a particle flies into a region of a uniform magnetic field, and the vector V is perpendicular to the vector B, then it moves along a circle of radius R=mV/qB, since the Lorentz force Fl=mV^2/R plays the role of a centripetal force. The period of revolution is T=2piR/V=2pim/qB and it does not depend on the speed of the particle (This is true only for V<<скорости света) - Если угол между векторами V и B не равен 0 и 90 градусов, то частица в однородном магнитном поле движется по винтовой линии. - Если вектор V параллелен B, то частица движется по прямой линии (Fл=0). б) Силу, действующую со стороны магнитного поля на движущиеся в нем заряды, называют силой Лоренца.
The L. force is determined by the relation: Fl = q V B sina (q is the magnitude of the moving charge; V is the modulus of its velocity; B is the modulus of the magnetic field induction vector; alpha is the angle between the vector V and the vector B) The Lorentz force is perpendicular to the velocity and therefore it does not do work, does not change the modulus of the speed of the charge and its kinetic energy. But the direction of the speed changes continuously. The Lorentz force is perpendicular to the vectors B and v, and its direction is determined using the same rule of the left hand as the direction of the Ampère force: if the left hand is positioned so that the magnetic induction component B, perpendicular to the charge velocity, enters the palm, and four fingers are directed along the movement of a positive charge (against the movement of a negative one), then the thumb bent 90 degrees will show the direction of the Lorentz force acting on the charge F l. 
