Physics work force power. Mechanical work: definition and formula
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 is a physical quantity whose modulus is equal to the product force on 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 Nm).
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.
« Physics - Grade 10 "
The law of conservation of energy is a fundamental law of nature that allows describing most of the phenomena that occur.
The description of the motion of bodies is also possible with the help of 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 boil down to the fact that with the help of muscles we either set the surrounding bodies in motion and maintain this movement, or we 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 greatly increases labor productivity due to the use of engines in them.
The purpose of any engine is to set the bodies in motion and maintain this movement, despite braking by both ordinary friction and “working” resistance (the cutter must not only slide over the metal, but, crashing into it, remove chips; the plow must loosen land, etc.). In this case, a force must act on the moving body from the side of the engine.
Work is always done in nature when a force (or several forces) from another body (other bodies) acts on a body in the direction of its movement or against it.
The gravitational force does work when rain drops or a stone fall from a cliff. At the same time, the work is done by the resistance force acting on the falling drops or on the stone from the side of the air. The elastic force also does work when a tree bent by the wind straightens.
Job definition.
Newton's second law in impulsive form ∆=∆t allows you to determine how the speed of the body changes in absolute value and direction, if a force acts on it during the time Δt.
The impact on bodies of forces, leading to a change in the modulus of their velocity, is characterized by a value that depends both on the forces and on the displacements of the bodies. This quantity in mechanics is called work of force.
Modulo change of speed is possible only when the projection of the force F r on the direction of body movement is nonzero. It is this projection that determines the action of the force that changes the velocity of the body modulo. She does the work. Therefore, the work can be considered as the product of the projection of the force F r by the displacement modulus |Δ| (Fig. 5.1):
А = F r |Δ|. (5.1)
If the angle between force and displacement is denoted by α, then F r = Fcosα.
Therefore, the work is equal to:
A = |Δ|cosα. (5.2)
Our everyday concept 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 the point of view of physics, your work is equal to zero.
The work of a constant force is equal to the product of the modules of force and the displacement of the point of application of the force and the cosine of the angle between them.
In general, when moving solid body the displacements of its different points are different, but when determining the work of a force, we Δ understand the movement of its point of application. In the translational motion of a rigid body, the displacement of all its points coincides with the displacement of the point of application of the force.
Work, unlike force and displacement, is not a vector, but a scalar quantity. It can be positive, negative or zero.
The sign of 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° (the force is perpendicular to the displacement), no work is done.
If several forces act on the 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 the body, then full work(the algebraic sum of the work of all forces) is equal to the work of the resultant force.
The work done by force can be represented graphically. Let us explain this by depicting in the figure the dependence of the projection of the force on the coordinate 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 the force, we get
А = 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 the body moves from a point with coordinate x1 to a point with coordinate x2.
Formula (5.1) is valid when the projection of the force on the displacement is constant. In the case of a curved trajectory, constant or variable force, we divide the trajectory into small segments, which can be considered rectilinear, and the projection of the force on a small displacement Δ - permanent.
Then, calculating the work done on each displacement 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 set using the basic formula (5.2). If, when a body moves per unit length, a force acts on it, the modulus of which 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. In the International System (SI), the unit of work is the joule (denoted J):
1 J = 1 N 1 m = 1 N m.
Joule is the work done by a force of 1 N at a displacement of 1 if the directions of the force and displacement coincide.
Multiple units of work are often used - kilojoule and mega joule:
1 kJ = 1000 J,
1 MJ = 1000000 J.
Work can be done in a long period of time, or in a very small one. In practice, however, it is far from indifferent whether work can be done quickly or slowly. The time during which work is done determines the performance of any engine. Very great job can make a tiny electric motor, but it will take a lot of time. Therefore, along with work, a value is introduced that characterizes the speed with which it is produced - power.
Power is the ratio of work A to the time interval Δt for which this work is done, i.e. power is the rate of work:
Substituting in formula (5.4) instead of work A its expression (5.2), we obtain
Thus, if the force and speed of the body are constant, then the power is equal to the product of the modulus of the force vector by the modulus of the velocity vector and the cosine of the angle between the directions of these vectors. If these quantities are variables, then by formula (5.4) one can determine the average power similarly to the definition average speed body movements.
The concept of power is introduced to evaluate the work per unit of time performed by some mechanism (pump, crane, machine motor, etc.). Therefore, in formulas (5.4) and (5.5), by always means the thrust force.
In SI, power is expressed in terms of watts (W).
The power is 1 W if the work equal to 1 J is done 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.
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 that 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
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.
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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, 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. 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. Electric charge can be positive or negative. positive charges always tend towards 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 the electric power is considered, here it is the value of the spent electrical energy 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 measurement 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
One of the most important concepts in mechanics work force .
Force work
All physical bodies in the world around us are driven by force. If a moving body in the same or opposite direction is affected by a force or several forces from one or more bodies, then they say that work is done .
That is, mechanical work is done by the force acting on the body. Thus, the traction force of an electric locomotive sets the entire train in motion, thereby performing mechanical work. The bicycle is propelled by the muscular strength of the cyclist's legs. Therefore, this force also does mechanical work.
In physics work of force called a physical quantity equal to the product of the modulus of force, the modulus of displacement of the point of application of force and the cosine of the angle between the vectors of force and displacement.
A = F s cos (F, s) ,
Where F modulus of force,
s- movement module .
Work is always done if the angle between the winds of force and displacement is not zero. If the force acts in the opposite direction to the direction of motion, the amount of work is negative.
Work is not done if no forces act on the body, or if the angle between the applied force and the direction of motion is 90 o (cos 90 o \u003d 0).
If the horse pulls the cart, then the muscular force of the horse, or the traction force directed in the direction of the cart, does the work. And the force of gravity, with which the driver presses on the cart, does no work, since it is directed downward, perpendicular to the direction of movement.
The work of a force is a scalar quantity.
SI unit of work - joule. 1 joule is the work done by a force of 1 newton at a distance of 1 m if the direction of force and displacement are the same.
If several forces act on a body or material point, then they talk about the work done by their resultant force.
If the applied force is not constant, then its work is calculated as an integral:
Power
The force that sets the body in motion does mechanical work. But how this work is done, quickly or slowly, is sometimes very important to know in practice. For the same work can be done in different time. The work that a large electric motor does can be done by small motor. But it will take him much longer to do so.
In mechanics, there is a quantity that characterizes the speed of work. This value is called power.
Power is the ratio of the work done in a certain period of time to the value of this period.
N= A /∆ t
A-priory A = F s cos α , A s/∆ t = v , hence
N= F v cos α = F v ,
Where F - force, v speed, α is the angle between the direction of the force and the direction of the velocity.
That is power - This scalar product of the force vector to the velocity vector of the body.
IN international system SI power is measured in watts (W).
The power of 1 watt is the work of 1 joule (J) done in 1 second (s).
Power can be increased by increasing the force that does the work, or the rate at which this work is done.
