Mechanical work si. Mechanical work
Electric current is generated in order to be used in the future for certain purposes, to perform some kind of work. Thanks to electricity, all devices, devices and equipment function. The work itself represents a certain effort applied to move an electric charge over a set distance. Conventionally, such work within a section of the circuit will be equal to the numerical value of the voltage in this section.
To perform the necessary calculations, you need to know how the work of the current is measured. All calculations are carried out on the basis of initial data obtained using measuring instruments. The larger the charge, the more effort is required to move it, and the more work will be done.
What is the work of current called?
Electric current, as a physical quantity, in itself has no practical significance. Most important factor is the action of the current, characterized by the work it performs. The work itself represents certain actions during which one type of energy is transformed into another. For example, electrical energy is converted into mechanical energy by rotating the motor shaft. The work itself electric current consists in the movement of charges in a conductor under the influence of an electric field. In fact, all the work of moving charged particles is done by the electric field.
In order to perform calculations, a formula for the operation of electric current must be derived. To compile formulas, you will need parameters such as current strength and. Since the work done by an electric current and the work done by an electric field are the same thing, it will be expressed as the product of the voltage and the charge flowing in the conductor. That is: A = Uq. This formula was derived from the relationship that determines the voltage in the conductor: U = A/q. It follows that voltage represents the work done by the electric field A to transport a charged particle q.
The charged particle or charge itself is displayed as the product of the current strength and the time spent on the movement of this charge along the conductor: q = It. In this formula, the relation for the current strength in the conductor was used: I = q/t. That is, it is the ratio of the charge to the period of time during which the charge passes through the cross section of the conductor. In its final form, the formula for the work of electric current will look like the product of known quantities: A = UIt.
In what units is the work of electric current measured?
Before directly addressing the question of how the work of electric current is measured, it is necessary to collect the units of measurement of all physical quantities with which this parameter is calculated. Any work, therefore, the unit of measurement of this quantity will be 1 Joule (1 J). Voltage is measured in volts, current is measured in amperes, and time is measured in seconds. This means the unit of measurement will look like this: 1 J = 1V x 1A x 1s.
Based on the obtained units of measurement, the work of electric current will be determined as the product of the current strength in a section of the circuit, the voltage at the ends of the section and the period of time during which the current flows through the conductor.
Measurements are carried out using a voltmeter and a clock. These devices allow you to effectively solve the problem of how to find the exact value of a given parameter. When connecting an ammeter and a voltmeter to a circuit, it is necessary to monitor their readings for a specified period of time. The obtained data is inserted into the formula, after which the final result is displayed.
The functions of all three devices are combined in electric meters that take into account the energy consumed, and in fact the work done by electric current. Here another unit is used - 1 kW x h, which also means how much work was done during a unit of time.
To be able to characterize the energy characteristics of movement, the concept of mechanical work was introduced. And it is to her in her different manifestations the article is devoted to. The topic is both easy and quite difficult to understand. The author sincerely tried to make it more understandable and accessible to understanding, and one can only hope that the goal has been achieved.
What is mechanical work called?
What is it called? If some force works on a body, and as a result of its action the body moves, then this is called mechanical work. When approached from the point of view scientific philosophy here several additional aspects can be highlighted, but the article will cover the topic from the point of view of physics. Mechanical work is not difficult if you think carefully about the words written here. But the word “mechanical” is usually not written, and everything is shortened to the word “work.” But not every job is mechanical. Here is a man sitting and thinking. Does it work? Mentally yes! But is this mechanical work? No. What if a person walks? If a body moves under the influence of a force, then it is mechanical work. It's simple. In other words, a force acting on a body does (mechanical) work. And one more thing: it is work that can characterize the result of the action of a certain force. So, if a person walks, then certain forces (friction, gravity, etc.) perform mechanical work on the person, and as a result of their action, the person changes his point of location, in other words, moves.
Work as a physical quantity is equal to the force that acts on the body, multiplied by the path that the body has made under the influence of this force and in the direction indicated by it. We can say that mechanical work was done if 2 conditions were simultaneously met: a force acted on the body, and it moved in the direction of its action. But it did not occur or does not occur if the force acted and the body did not change its location in the coordinate system. Here are small examples when mechanical work is not performed:
- So a person can lean on a huge boulder in order to move it, but there is not enough strength. The force acts on the stone, but it does not move, and no work occurs.
- The body moves in the coordinate system, and the force is equal to zero or they have all been compensated. This can be observed while moving by inertia.
- When the direction in which a body moves is perpendicular to the action of the force. When a train moves along a horizontal line, gravity does not do its work.
Depending on certain conditions, mechanical work can be negative and positive. So, if the directions of both the forces and the movements of the body are the same, then positive work occurs. Example positive work is the effect of gravity on a falling drop of water. But if the force and direction of movement are opposite, then negative mechanical work occurs. An example of such an option is a balloon rising upward and the force of gravity, which does negative work. When a body is subject to the influence of several forces, such work is called “resultant force work.”
Features of practical application (kinetic energy)
Let's move from theory to practical part. Separately, we should talk about mechanical work and its use in physics. As many probably remember, all the energy of the body is divided into kinetic and potential. When an object is in equilibrium and not moving anywhere, its potential energy equals its total energy and its kinetic energy equals zero. When movement begins, potential energy begins to decrease, kinetic energy begins to increase, but in total they are equal to the total energy of the object. For a material point, kinetic energy is defined as the work of a force that accelerates the point from zero to the value H, and in formula form the kinetics of a body is equal to ½*M*N, where M is mass. To find out the kinetic energy of an object that consists of many particles, you need to find the sum of all the kinetic energy of the particles, and this will be the kinetic energy of the body.
Features of practical application (potential energy)
In the case when all the forces acting on the body are conservative, and the potential energy is equal to the total, then no work is done. This postulate is known as the law of conservation of mechanical energy. Mechanical energy in a closed system is constant over a time interval. The conservation law is widely used to solve problems from classical mechanics.
Features of practical application (thermodynamics)
In thermodynamics, the work done by a gas during expansion is calculated by the integral of pressure times volume. This approach is applicable not only in cases where there is an exact volume function, but also to all processes that can be displayed in the pressure/volume plane. It also applies knowledge of mechanical work not only to gases, but to anything that can exert pressure.
Features of practical application in practice (theoretical mechanics)
In theoretical mechanics, all the properties and formulas described above are considered in more detail, in particular projections. She also gives her own definition for various formulas of mechanical work (an example of a definition for the Rimmer integral): the limit to which the sum of all forces tends basic work, when the fineness of the partition tends to zero, is called the work of force along the curve. Probably difficult? But nothing, s theoretical mechanics All. Yes, all the mechanical work, physics and other difficulties are over. Further there will be only examples and a conclusion.
Units of measurement of mechanical work
The SI uses joules to measure work, while the GHS uses ergs:
- 1 J = 1 kg m²/s² = 1 N m
- 1 erg = 1 g cm²/s² = 1 dyne cm
- 1 erg = 10 −7 J
Examples of mechanical work
In order to finally understand such a concept as mechanical work, you should study several individual examples that will allow you to consider it from many, but not all, sides:
- When a person lifts a stone with his hands, mechanical work occurs with the help of the muscular strength of the hands;
- When a train travels along the rails, it is pulled by the traction force of the tractor (electric locomotive, diesel locomotive, etc.);
- If you take a gun and fire from it, then thanks to the pressure force created by the powder gases, work will be done: the bullet is moved along the barrel of the gun at the same time as the speed of the bullet itself increases;
- Mechanical work also exists when the friction force acts on a body, forcing it to reduce the speed of its movement;
- The above example with balls, when they rise in the opposite direction relative to the direction of gravity, is also an example of mechanical work, but in addition to gravity, the Archimedes force also acts, when everything that is lighter than air rises up.
What is power?
Finally, I would like to touch on the topic of power. The work done by a force in one unit of time is called power. In fact, power is a physical quantity that is a reflection of the ratio of work to a certain period of time during which this work was done: M=P/B, where M is power, P is work, B is time. The SI unit of power is 1 W. A watt is equal to the power that does one joule of work in one second: 1 W=1J\1s.
The energy characteristics of motion are introduced on the basis of the concept of mechanical work or work of force.
Definition 1Work A performed by a constant force F → is a physical quantity equal to the product of the force and displacement modules multiplied by the cosine of the angle α , located between the force vectors F → and the displacement s →.
This definition discussed in Figure 1. 18 . 1 .
The work formula is written as,
A = F s cos α .
Work is a scalar quantity. This makes it possible to be positive at (0° ≤ α< 90 °) , отрицательной при (90 ° < α ≤ 180 °) . Когда задается прямой угол α , тогда совершаемая сила равняется нулю. Единицы измерения работы по системе СИ - джоули (Д ж) .
A joule is equal to the work done by a force of 1 N to move 1 m in the direction of the force.
Picture 1 . 18 . 1 . Work of force F →: A = F s cos α = F s s
When projecting F s → force F → onto the direction of movement s → the force does not remain constant, and the calculation of work for small movements Δ s i is summed up and produced according to the formula:
A = ∑ ∆ A i = ∑ F s i ∆ s i .
This amount of work is calculated from the limit (Δ s i → 0) and then goes into the integral.
The graphical representation of the work is determined from the area of the curvilinear figure located under the graph F s (x) in Figure 1. 18 . 2.
Picture 1 . 18 . 2. Graphic definition of work Δ A i = F s i Δ s i .
An example of a force that depends on the coordinate is the elastic force of a spring, which obeys Hooke's law. To stretch a spring, it is necessary to apply a force F →, the modulus of which is proportional to the elongation of the spring. This can be seen in Figure 1. 18 . 3.
Picture 1 . 18 . 3. Stretched spring. The direction of the external force F → coincides with the direction of movement s →. F s = k x , where k denotes the spring stiffness.
F → y p = - F →
The dependence of the external force modulus on the x coordinates can be plotted using a straight line.
Picture 1 . 18 . 4 . Dependence of the external force modulus on the coordinate when the spring is stretched.
From the above figure, it is possible to find the work done on the external force of the right free end of the spring, using the area of the triangle. The formula will take the form
This formula is applicable to express the work done by an external force when compressing a spring. Both cases show that the elastic force F → y p is equal to the work of the external force F → , but with the opposite sign.
Definition 2
If several forces act on a body, then the formula for the total work will look like the sum of all the work done on it. When a body moves translationally, the points of application of forces move equally, that is general work of all forces will be equal to the resultant work of the applied forces.
Picture 1 . 18 . 5 . Model of mechanical work.
Power determination
Definition 3Power is called the work done by a force per unit time.
Recording the physical quantity of power, denoted N, takes the form of the ratio of work A to the time period t of the work performed, that is:
Definition 4
The SI system uses the watt (W t) as a unit of power, equal to the power of the force that does 1 J of work in 1 s.
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« Physics - 10th grade"
The law of conservation of energy is a fundamental law of nature that allows us to describe most occurring phenomena.
Description of the movement of bodies is also possible using such concepts of dynamics as work and energy.
Remember what work and power are in physics.
Do these concepts coincide with everyday ideas about them?
All our daily actions come down to the fact that we, with the help of muscles, either set the surrounding bodies in motion and maintain this movement, or stop the moving bodies.
These bodies are tools (hammer, pen, saw), in games - balls, pucks, chess pieces. In production and agriculture people also set tools in motion.
The use of machines increases labor productivity many times due to the use of engines in them.
The purpose of any engine is to set bodies in motion and maintain this movement, despite braking by both ordinary friction and “working” resistance (the cutter should not just slide over the metal, but, cutting into it, remove chips; the plow should loosen land, etc.). In this case, a force must act on the moving body from the side of the engine.
Work is performed in nature whenever a force (or several forces) from another body (other bodies) acts on a body in the direction of its movement or against it.
The force of gravity does work when raindrops or stones fall from a cliff. At the same time, work is also done by the resistance force acting on the falling drops or on the stone from the air. The elastic force also performs work when a tree bent by the wind straightens.
Definition of work.
Newton's second law in impulse form Δ = Δt allows you to determine how the speed of a body changes in magnitude and direction if a force acts on it during a time Δt.
The influence of forces on bodies that lead to a change in the modulus of their velocity is characterized by a value that depends on both the forces and the movements of the bodies. In mechanics this quantity is called work of force.
A change in speed in absolute value is possible only in the case when the projection of the force F r on the direction of movement of the body is different from zero. It is this projection that determines the action of the force that changes the velocity of the body modulo. She does the work. Therefore, work can be considered as the product of the projection of force F r by the displacement modulus |Δ| (Fig. 5.1):
A = F r |Δ|. (5.1)
If the angle between force and displacement is denoted by α, then Fr = Fcosα.
Therefore, the work is equal to:
A = |Δ|cosα. (5.2)
Our everyday idea of work differs from the definition of work in physics. You are holding a heavy suitcase, and it seems to you that you are doing work. However, from a physical point of view, your work is zero.
The work of a constant force is equal to the product of the moduli of the force and the displacement of the point of application of the force and the cosine of the angle between them.
IN general case when driving solid moving it different points are different, but when determining the work of force we are under Δ we understand the movement of its point of application. During the translational motion of a rigid body, the movement of all its points coincides with the movement of the point of application of the force.
Work, unlike force and displacement, is not vector, but scalar quantity. It can be positive, negative or zero.
The sign of the work is determined by the sign of the cosine of the angle between force and displacement. If α< 90°, то А >0, since the cosine of acute angles is positive. For α > 90°, the work is negative, since the cosine of obtuse angles is negative. At α = 90° (force perpendicular to displacement) no work is done.
If several forces act on a body, then the projection of the resultant force on the displacement is equal to the sum of the projections of the individual forces:
F r = F 1r + F 2r + ... .
Therefore, for the work of the resultant force we obtain
A = F 1r |Δ| + F 2r |Δ| + ... = A 1 + A 2 + .... (5.3)
If several forces act on a body, then the total work (the algebraic sum of the work of all forces) is equal to the work of the resultant force.
The work done by a force can be represented graphically. Let us explain this by depicting in the figure the dependence of the projection of force on the coordinates of the body when it moves in a straight line.
Let the body move along the OX axis (Fig. 5.2), then
Fcosα = F x , |Δ| = Δ x.
For the work of force we get
A = F|Δ|cosα = F x Δx.
Obviously, the area of the rectangle shaded in Figure (5.3, a) is numerically equal to the work done when moving a body from a point with coordinate x1 to a point with coordinate x2.
Formula (5.1) is valid in the case when the projection of the force onto the displacement is constant. In the case of a curvilinear trajectory, constant or variable force, we divide the trajectory into small segments, which can be considered rectilinear, and the projection of the force at a small displacement Δ - constant.
Then, calculating the work on each movement Δ
and then summing up these works, we determine the work of the force on the final displacement (Fig. 5.3, b). Unit of work.
The unit of work can be established using the basic formula (5.2). If, when moving a body by a unit length, a force acts on it, the modulus of which is equal to one, and the direction of the force coincides with the direction of movement of its point of application (α = 0), then the work will be equal to one. The International System (SI) unit of work is the joule (denoted by J):
1 J = 1 N 1 m = 1 N m.
Joule- this is the work done by a force of 1 N on displacement 1 if the directions of force and displacement coincide.
Multiple units of work are often used: kilojoule and megajoule:
1 kJ = 1000 J,
1 MJ = 1000000 J.
Work can be completed either in a large period of time or in a very short one. In practice, however, it is far from indifferent whether work can be done quickly or slowly. The time during which work is performed determines the performance of any engine. Very great job A tiny electric motor can do this, but it will take a lot of time. Therefore, along with work, a quantity is introduced that characterizes the speed with which it is produced - power.
Power is the ratio of work A to the time interval Δt during which this work is done, i.e. power is the speed of work:
Substituting into formula (5.4) instead of work A its expression (5.2), we obtain
Thus, if the force and speed of a body are constant, then the power is equal to the product of the magnitude of the force vector by the magnitude of the velocity vector and the cosine of the angle between the directions of these vectors. If these quantities are variable, then using formula (5.4) one can determine the average power in a similar way to determining the average speed of a body.
The concept of power is introduced to evaluate the work per unit of time performed by any mechanism (pump, crane, machine motor, etc.). Therefore, in formulas (5.4) and (5.5), traction force is always meant.
In SI, power is expressed in watt (W).
Power is equal to 1 W if work equal to 1 J is performed in 1 s.
Along with the watt, larger (multiple) units of power are used:
1 kW (kilowatt) = 1000 W,
1 MW (megawatt) = 1,000,000 W.
IN Everyday life I often come across such a concept as work. What does this word mean in physics and how to determine the work of the elastic force? You will find out the answers to these questions in the article.
Mechanical work
Work is a scalar algebraic quantity that characterizes the relationship between force and displacement. If the direction of these two variables coincides, it is calculated using the following formula:
- F- module of the force vector that does the work;
- S- displacement vector module.
A force that acts on a body does not always do work. For example, the work done by gravity is zero if its direction is perpendicular to the movement of the body.
If the force vector forms a non-zero angle with the displacement vector, then another formula should be used to determine the work:
A=FScosα
α - the angle between the force and displacement vectors.
Means, mechanical work is the product of the projection of force on the direction of displacement and the module of displacement, or the product of the projection of displacement on the direction of force and the module of this force.
Mechanical work sign
Depending on the direction of the force relative to the movement of the body, the work A can be:
- positive (0°≤ α<90°);
- negative (90°<α≤180°);
- equal to zero (α=90°).
If A>0, then the speed of the body increases. An example is an apple falling from a tree to the ground. At A<0 сила препятствует ускорению тела. Например, действие силы трения скольжения.
The SI (International System of Units) unit of work is Joule (1N*1m=J). A joule is the work done by a force, the value of which is 1 Newton, when a body moves 1 meter in the direction of the force.
Work of elastic force
The work of force can also be determined graphically. To do this, calculate the area of the curvilinear figure under the graph F s (x).
Thus, from the graph of the dependence of the elastic force on the elongation of the spring, one can derive the formula for the work of the elastic force.
It is equal to:
A=kx 2 /2
- k- rigidity;
- x- absolute elongation.
What have we learned?
Mechanical work is performed when a force is applied to a body, which leads to movement of the body. Depending on the angle that occurs between the force and the displacement, the work can be zero or have a negative or positive sign. Using the example of elastic force, you learned about a graphical method for determining work.