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
Note. 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, an electric current is an ordered movement of electrons in a conductor under the influence of an 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. The electrical 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.
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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 electrical power is considered, here it is the value of the electrical energy expended 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
If a force acts on a body, then this force does work to move this body. Before giving a definition of work in the curvilinear motion of a material point, consider special cases:
In this case, mechanical work A is equal to:
A=
F s cos
=
,
or A=Fcos
×
s = F S ×
s ,
whereF S
– projection
strength 
to move. In this case F s =
const, and the geometric meaning of the work A is the area of the rectangle constructed in coordinates F S ,
,
s.
Let's build a graph of the projection of force on the direction of movement F S as a function of displacement s. We represent the total displacement as the sum of n small displacements 
. For small i
-th displacement 
work is 
or the area of the shaded trapezoid in the figure.
.
The value under the integral will represent the elementary work on an infinitesimal displacement 
:
- basic work.
and the work of the force 
by moving a material point from a point 1
exactly 2
defined as a curvilinear integral:
–work with curvilinear motion.
Example 1:
The work of gravity
during curvilinear motion of a material point.
.Further 
as a constant value can be taken out of the integral sign, and the integral 
according to the figure will represent a complete displacement 
.
.
If we denote the height of the point 1
from the earth's surface through 
, and the height of the point 2
through 
, then
We see that in this case the work is determined by the position of the material point at the initial and final moments of time and does not depend on the shape of the trajectory or path. The work done by gravity in a closed path is zero: 
.
Forces whose work on a closed path is zero is calledconservative .
Example 2 : The work of the friction force.
This is an example of a non-conservative force. To show this, it is enough to consider the elementary work of the friction force:
,
those. the work of the friction force is always negative and cannot be equal to zero on a closed path. The work done per unit of time is called power. If in time 
work is done 
, then the power is
–mechanical power.
Taking 
as
,
we get the expression for power:
.
The SI unit of work is the joule: 
= 1 J = 1 N 
1 m, and the unit of power is watt: 1 W = 1 J / s.
mechanical energy.
Energy is a general quantitative measure of the movement of the interaction of all types of matter. Energy does not disappear and does not arise from nothing: it can only pass from one form to another. The concept of energy binds together all phenomena in nature. In accordance with the various forms of motion of matter, different types of energy are considered - mechanical, internal, electromagnetic, nuclear, etc.
The concepts of energy and work are closely related to each other. It is known that work is done at the expense of the energy reserve and, conversely, by doing work, it is possible to increase the energy reserve in any device. In other words, work is a quantitative measure of the change in energy:
.
Energy as well as work in SI is measured in joules: [ E]=1 J.
Mechanical energy is of two types - kinetic and potential.
Kinetic energy
(or the energy of motion) is determined by the masses and velocities of the considered bodies. Consider a material point moving under the action of a force 
. The work of this force increases the kinetic energy of a material point 
. Let us calculate in this case a small increment (differential) of the kinetic energy:
When calculating 
using Newton's second law 
, as well as 
- velocity modulus of a material point. Then 
can be represented as:
-
- kinetic energy of a moving material point.
Multiplying and dividing this expression by 
, and taking into account that 
, we get
-
- relationship between momentum and kinetic energy of a moving material point.
Potential energy ( or the energy of the position of bodies) is determined by the action of conservative forces on the body and depends only on the position of the body .
We have seen that the work of gravity 
with curvilinear motion of a material point 
can be represented as the difference between the values of the function 
taken at the point 1
and at the point 2
:
.
It turns out that whenever the forces are conservative, the work of these forces on the way 1
2
can be represented as:
.
Function
,
which depends only on the position of the body - is called potential energy.
Then for elementary work we get
–work is equal to the loss of potential energy.
Otherwise, we can say that the work is done due to the potential energy reserve.
the value 
, equal to the sum of the kinetic and potential energies of the particle, is called the total mechanical energy of the body:
–total mechanical energy of the body.
In conclusion, we note that using Newton's second law 
, kinetic energy differential 
can be represented as:
.
Potential energy differential 
, as mentioned above, is equal to:
.
Thus, if the power 
is a conservative force and there are no other external forces, then 
, i.e. in this case, the total mechanical energy of the body is conserved.
Mechanical work. Units of work.
In everyday life, under the concept of "work" we understand everything.
In physics, the concept Work somewhat different. This is a certain physical quantity, which means that it can be measured. In physics, the study is primarily mechanical work .
Consider examples of mechanical work.
The train moves under the action of the traction force of the electric locomotive, while doing mechanical work. When a gun is fired, the pressure force of the powder gases does work - it moves the bullet along the barrel, while the speed of the bullet increases.
From these examples, it can be seen that mechanical work is done when the body moves under the action of a force. Mechanical work is also performed in the case when the force acting on the body (for example, the friction force) reduces the speed of its movement.
Wanting to move the cabinet, we press on it with force, but if it does not move at the same time, then we do not perform mechanical work. One can imagine the case when the body moves without the participation of forces (by inertia), in this case, mechanical work is also not performed.
So, mechanical work is done only when a force acts on the body and it moves .
It is easy to understand that the greater the force acting on the body and the longer the path that the body passes under the action of this force, the greater the work done.
Mechanical work is directly proportional to the applied force and directly proportional to the distance traveled. .
Therefore, we agreed to measure mechanical work by the product of force and the path traveled in this direction of this force:
work = force × path
where BUT- Work, F- strength and s- distance traveled.
A unit of work is the work done by a force of 1 N on a path of 1 m.
Unit of work - joule (J ) is named after the English scientist Joule. In this way,
1 J = 1N m.
Also used kilojoules (kJ) .
1 kJ = 1000 J.
Formula A = Fs applicable when the power F is constant and coincides with the direction of motion of the body.
If the direction of the force coincides with the direction of motion of the body, then this force does positive work.
If the motion of the body occurs in the direction opposite to the direction of the applied force, for example, the force of sliding friction, then this force does negative work.
If the direction of the force acting on the body is perpendicular to the direction of motion, then this force does no work, the work is zero:
In the future, speaking of mechanical work, we will briefly call it in one word - work.
Example. Calculate the work done when lifting a granite slab with a volume of 0.5 m3 to a height of 20 m. The density of granite is 2500 kg / m 3.
Given:
ρ \u003d 2500 kg / m 3
Solution:
where F is the force that must be applied to evenly lift the plate up. This force is equal in modulus to the force of the strand Fstrand acting on the plate, i.e. F = Fstrand. And the force of gravity can be determined by the mass of the plate: Ftyazh = gm. We calculate the mass of the slab, knowing its volume and density of granite: m = ρV; s = h, i.e. the path is equal to the height of the ascent.
So, m = 2500 kg/m3 0.5 m3 = 1250 kg.
F = 9.8 N/kg 1250 kg ≈ 12250 N.
A = 12,250 N 20 m = 245,000 J = 245 kJ.
Answer: A = 245 kJ.
Levers.Power.Energy
Different engines take different times to do the same work. For example, a crane at a construction site lifts hundreds of bricks to the top floor of a building in a few minutes. If a worker were to move these bricks, it would take him several hours to do this. Another example. A horse can plow a hectare of land in 10-12 hours, while a tractor with a multi-share plow ( ploughshare- part of the plow that cuts the layer of earth from below and transfers it to the dump; multi-share - a lot of shares), this work will be done for 40-50 minutes.
It is clear that a crane does the same work faster than a worker, and a tractor faster than a horse. The speed of work is characterized by a special value called power.
Power is equal to the ratio of work to the time for which it was completed.
To calculate the power, it is necessary to divide the work by the time during which this work is done. power = work / time.
where N- power, A- Work, t- time of work done.
Power is a constant value, when the same work is done for every second, in other cases the ratio A/t determines the average power:
N cf = A/t . The unit of power was taken as the power at which work in J is done in 1 s.
This unit is called the watt ( Tue) in honor of another English scientist Watt.
1 watt = 1 joule/ 1 second, or 1 W = 1 J/s.
Watt (joule per second) - W (1 J / s).
Larger units of power are widely used in engineering - kilowatt (kW), megawatt (MW) .
1 MW = 1,000,000 W
1 kW = 1000 W
1 mW = 0.001 W
1 W = 0.000001 MW
1 W = 0.001 kW
1 W = 1000 mW
Example. Find the power of the flow of water flowing through the dam, if the height of the water fall is 25 m, and its flow rate is 120 m3 per minute.
Given:
ρ = 1000 kg/m3
Solution:
Mass of falling water: m = ρV,
m = 1000 kg/m3 120 m3 = 120,000 kg (12 104 kg).
The force of gravity acting on water:
F = 9.8 m/s2 120,000 kg ≈ 1,200,000 N (12 105 N)
Work done per minute:
A - 1,200,000 N 25 m = 30,000,000 J (3 107 J).
Flow power: N = A/t,
N = 30,000,000 J / 60 s = 500,000 W = 0.5 MW.
Answer: N = 0.5 MW.
Various engines have powers ranging from hundredths and tenths of a kilowatt (motor of an electric razor, sewing machine) to hundreds of thousands of kilowatts (water and steam turbines).
Table 5
Power of some engines, kW.
Each engine has a plate (engine passport), which contains some data about the engine, including its power.
Human power under normal working conditions is on average 70-80 watts. Making jumps, running up the stairs, a person can develop power up to 730 watts, and in some cases even more.
From the formula N = A/t it follows that
To calculate the work, you need to multiply the power by the time during which this work was done.
Example. The room fan motor has a power of 35 watts. How much work does he do in 10 minutes?
Let's write down the condition of the problem and solve it.
Given:
Solution:
A = 35 W * 600 s = 21,000 W * s = 21,000 J = 21 kJ.
Answer A= 21 kJ.
simple mechanisms.
Since time immemorial, man has been using various devices to perform mechanical work.
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Everyone knows that a heavy object (stone, cabinet, machine), which cannot be moved by hand, can be moved with a fairly long stick - a lever.
At the moment, it is believed that with the help of levers three thousand years ago, during the construction of the pyramids in ancient Egypt, heavy stone slabs were moved and raised to a great height.
In many cases, instead of lifting a heavy load to a certain height, it can be rolled or pulled to the same height on an inclined plane or lifted using blocks.
Devices used to transform power are called mechanisms .
Simple mechanisms include: levers and its varieties - block, gate; inclined plane and its varieties - wedge, screw. In most cases, simple mechanisms are used in order to obtain a gain in strength, i.e., to increase the force acting on the body by several times.
Simple mechanisms are found both in household and in all complex factory and factory machines that cut, twist and stamp large sheets of steel or draw the finest threads from which fabrics are then made. The same mechanisms can be found in modern complex automata, printing and counting machines.
Lever arm. The balance of forces on the lever.
Consider the simplest and most common mechanism - the lever.
The lever is a rigid body that can rotate around a fixed support.
The figures show how a worker uses a crowbar to lift a load as a lever. In the first case, a worker with a force F presses the end of the crowbar B, in the second - raises the end B.
The worker needs to overcome the weight of the load P- force directed vertically downwards. For this, he rotates the crowbar around an axis passing through the only motionless breaking point - its fulcrum O. Strength F, with which the worker acts on the lever, less force P, so the worker gets gain in strength. With the help of a lever, you can lift such a heavy load that you cannot lift it on your own.
The figure shows a lever whose axis of rotation is O(fulcrum) is located between the points of application of forces BUT and AT. The other figure shows a diagram of this lever. Both forces F 1 and F 2 acting on the lever are directed in the same direction.
The shortest distance between the fulcrum and the straight line along which the force acts on the lever is called the arm of the force.
To find the shoulder of the force, it is necessary to lower the perpendicular from the fulcrum to the line of action of the force.The length of this perpendicular will be the shoulder of this force. The figure shows that OA- shoulder strength F 1; OV- shoulder strength F 2. The forces acting on the lever can rotate it around the axis in two directions: clockwise or counterclockwise. Yes, power F 1 rotates the lever clockwise, and the force F 2 rotates it counterclockwise.
The condition under which the lever is in equilibrium under the action of forces applied to it can be established experimentally. At the same time, it must be remembered that the result of the action of a force depends not only on its numerical value (modulus), but also on the point at which it is applied to the body, or how it is directed.
Various weights are suspended from the lever (see Fig.) on both sides of the fulcrum so that each time the lever remains in balance. The forces acting on the lever are equal to the weights of these loads. For each case, the modules of forces and their shoulders are measured. From the experience shown in Figure 154, it can be seen that the force 2 H balances power 4 H. In this case, as can be seen from the figure, the shoulder of lesser force is 2 times larger than the shoulder of greater force.
On the basis of such experiments, the condition (rule) of the balance of the lever was established.
The lever is in equilibrium when the forces acting on it are inversely proportional to the shoulders of these forces.
This rule can be written as a formula:
F 1/F 2 = l 2/ l 1 ,
where F 1and F 2 - forces acting on the lever, l 1and l 2 , - the shoulders of these forces (see Fig.).
The rule for the balance of the lever was established by Archimedes around 287-212. BC e. (But didn't the last paragraph say that the levers were used by the Egyptians? Or is the word "established" important here?)
It follows from this rule that a smaller force can be balanced with a leverage of a larger force. Let one arm of the lever be 3 times larger than the other (see Fig.). Then, applying a force of, for example, 400 N at point B, it is possible to lift a stone weighing 1200 N. In order to lift an even heavier load, it is necessary to increase the length of the lever arm on which the worker acts.
Example. Using a lever, a worker lifts a slab weighing 240 kg (see Fig. 149). What force does he apply to the larger arm of the lever, which is 2.4 m, if the smaller arm is 0.6 m?
Let's write down the condition of the problem, and solve it.
Given:
Solution:
According to the lever equilibrium rule, F1/F2 = l2/l1, whence F1 = F2 l2/l1, where F2 = P is the weight of the stone. Stone weight asd = gm, F = 9.8 N 240 kg ≈ 2400 N
Then, F1 = 2400 N 0.6 / 2.4 = 600 N.
Answer: F1 = 600 N.
In our example, the worker overcomes a force of 2400 N by applying a force of 600 N to the lever. But at the same time, the arm on which the worker acts is 4 times longer than that on which the weight of the stone acts ( l 1 : l 2 = 2.4 m: 0.6 m = 4).
By applying the rule of leverage, a smaller force can balance a larger force. In this case, the shoulder of the smaller force must be longer than the shoulder of the greater force.
Moment of power.
You already know the lever balance rule:
F 1 / F 2 = l 2 / l 1 ,
Using the property of proportion (the product of its extreme terms is equal to the product of its middle terms), we write it in this form:
F 1l 1 = F 2 l 2 .
On the left side of the equation is the product of the force F 1 on her shoulder l 1, and on the right - the product of the force F 2 on her shoulder l 2 .
The product of the modulus of the force rotating the body and its arm is called moment of force; it is denoted by the letter M. So,
A lever is in equilibrium under the action of two forces if the moment of force rotating it clockwise is equal to the moment of force rotating it counterclockwise.
This rule is called moment rule , can be written as a formula:
M1 = M2
Indeed, in the experiment we have considered, (§ 56) the acting forces were equal to 2 N and 4 N, their shoulders, respectively, were 4 and 2 lever pressures, i.e., the moments of these forces are the same when the lever is in equilibrium.
The moment of force, like any physical quantity, can be measured. A moment of force of 1 N is taken as a unit of moment of force, the shoulder of which is exactly 1 m.
This unit is called newton meter (N m).
The moment of force characterizes the action of the force, and shows that it depends simultaneously on the modulus of the force and on its shoulder. Indeed, we already know, for example, that the effect of a force on a door depends both on the modulus of the force and on where the force is applied. The door is easier to turn, the farther from the axis of rotation the force acting on it is applied. It is better to unscrew the nut with a long wrench than with a short one. The easier it is to lift a bucket from the well, the longer the handle of the gate, etc.
Levers in technology, everyday life and nature.
The lever rule (or the rule of moments) underlies the action of various kinds of tools and devices used in technology and everyday life where a gain in strength or on the road is required.
We have a gain in strength when working with scissors. Scissors - it's a lever(rice), the axis of rotation of which occurs through a screw connecting both halves of the scissors. acting force F 1 is the muscular strength of the hand of the person squeezing the scissors. Opposing force F 2 - the resistance force of such a material that is cut with scissors. Depending on the purpose of the scissors, their device is different. Office scissors, designed for cutting paper, have long blades and handles that are almost the same length. It does not require much force to cut paper, and it is more convenient to cut in a straight line with a long blade. Scissors for cutting sheet metal (Fig.) have handles much longer than the blades, since the resistance force of the metal is large and to balance it, the shoulder of the acting force must be significantly increased. Even more difference between the length of the handles and the distance of the cutting part and the axis of rotation in wire cutters(Fig.), Designed for wire cutting.
Levers of various types are available on many machines. A sewing machine handle, bicycle pedals or hand brakes, car and tractor pedals, piano keys are all examples of levers used in these machines and tools.
Examples of the use of levers are the handles of vices and workbenches, the lever of a drilling machine, etc.
The action of lever balances is also based on the principle of the lever (Fig.). The training scale shown in figure 48 (p. 42) acts as equal-arm lever . AT decimal scales the arm to which the cup with weights is suspended is 10 times longer than the arm carrying the load. This greatly simplifies the weighing of large loads. When weighing a load on a decimal scale, multiply the weight of the weights by 10.
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The device of scales for weighing freight wagons of cars is also based on the rule of the lever.
Levers are also found in different parts of the body of animals and humans. These are, for example, arms, legs, jaws. Many levers can be found in the body of insects (having read a book about insects and the structure of their body), birds, in the structure of plants.
Application of the law of balance of the lever to the block.
Block is a wheel with a groove, reinforced in the holder. A rope, cable or chain is passed along the gutter of the block.
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Fixed block such a block is called, the axis of which is fixed, and when lifting loads it does not rise and does not fall (Fig.
A fixed block can be considered as an equal-arm lever, in which the arms of forces are equal to the radius of the wheel (Fig.): OA = OB = r. Such a block does not give a gain in strength. ( F 1 = F 2), but allows you to change the direction of the force. Movable block is a block. the axis of which rises and falls along with the load (Fig.). The figure shows the corresponding lever: O- fulcrum of the lever, OA- shoulder strength R and OV- shoulder strength F. Since the shoulder OV 2 times the shoulder OA, then the force F 2 times less power R:
F = P/2 .
In this way, the movable block gives a gain in strength by 2 times .
This can also be proved using the concept of moment of force. When the block is in equilibrium, the moments of forces F and R are equal to each other. But the shoulder of strength F 2 times the shoulder strength R, which means that the force itself F 2 times less power R.
Usually, in practice, a combination of a fixed block with a movable one is used (Fig.). The fixed block is used for convenience only. It does not give a gain in strength, but changes the direction of the force. For example, it allows you to lift a load while standing on the ground. It comes in handy for many people or workers. However, it gives a power gain of 2 times more than usual!
Equality of work when using simple mechanisms. The "golden rule" of mechanics.
The simple mechanisms we have considered are used in the performance of work in those cases when it is necessary to balance another force by the action of one force.
Naturally, the question arises: giving a gain in strength or path, do not simple mechanisms give a gain in work? The answer to this question can be obtained from experience.
Having balanced on the lever two forces of different modulus F 1 and F 2 (fig.), set the lever in motion. It turns out that for the same time, the point of application of a smaller force F 2 goes a long way s 2, and the point of application of greater force F 1 - smaller path s 1. Having measured these paths and force modules, we find that the paths traversed by the points of application of forces on the lever are inversely proportional to the forces:
s 1 / s 2 = F 2 / F 1.
Thus, acting on the long arm of the lever, we win in strength, but at the same time we lose the same amount on the way.
Product of force F on the way s there is work. Our experiments show that the work done by the forces applied to the lever are equal to each other:
F 1 s 1 = F 2 s 2, i.e. BUT 1 = BUT 2.
So, when using the leverage, the win in the work will not work.
By using the lever, we can win either in strength or in distance. Acting by force on the short arm of the lever, we gain in distance, but lose in strength by the same amount.
There is a legend that Archimedes, delighted with the discovery of the rule of the lever, exclaimed: "Give me a fulcrum, and I will turn the Earth!".
Of course, Archimedes could not have coped with such a task even if he had been given a fulcrum (which would have to be outside the Earth) and a lever of the required length.
To raise the earth by only 1 cm, the long arm of the lever would have to describe an arc of enormous length. It would take millions of years to move the long end of the lever along this path, for example, at a speed of 1 m/s!
Does not give a gain in work and a fixed block, which is easy to verify by experience (see Fig.). Paths traversed by points of application of forces F and F, are the same, the same are the forces, which means that the work is the same.
It is possible to measure and compare with each other the work done with the help of a movable block. In order to lift the load to a height h with the help of a movable block, it is necessary to move the end of the rope to which the dynamometer is attached, as experience shows (Fig.), to a height of 2h.
In this way, getting a gain in strength by 2 times, they lose 2 times on the way, therefore, the movable block does not give a gain in work.
Centuries of practice has shown that none of the mechanisms gives a gain in work. Various mechanisms are used in order to win in strength or on the way, depending on the working conditions.
Already ancient scientists knew the rule applicable to all mechanisms: how many times we win in strength, how many times we lose in distance. This rule has been called the "golden rule" of mechanics.
The efficiency of the mechanism.
Considering the device and action of the lever, we did not take into account friction, as well as the weight of the lever. under these ideal conditions, the work done by the applied force (we will call this work complete), is equal to useful lifting loads or overcoming any resistance.
In practice, the total work done by the mechanism is always somewhat greater than the useful work.
Part of the work is done against the friction force in the mechanism and by moving its individual parts. So, using a movable block, you have to additionally perform work on lifting the block itself, the rope and determining the friction force in the axis of the block.
Whatever mechanism we choose, the useful work accomplished with its help is always only a part of the total work. So, denoting the useful work by the letter Ap, the full (spent) work by the letter Az, we can write:
Up< Аз или Ап / Аз < 1.
The ratio of useful work to total work is called the efficiency of the mechanism.
Efficiency is abbreviated as efficiency.
Efficiency = Ap / Az.
Efficiency is usually expressed as a percentage and denoted by the Greek letter η, it is read as "this":
η \u003d Ap / Az 100%.
Example: A 100 kg mass is suspended from the short arm of the lever. To lift it, a force of 250 N was applied to the long arm. The load was lifted to a height h1 = 0.08 m, while the point of application of the driving force dropped to a height h2 = 0.4 m. Find the efficiency of the lever.
Let's write down the condition of the problem and solve it.
Given :
Solution :
η \u003d Ap / Az 100%.
Full (spent) work Az = Fh2.
Useful work Ап = Рh1
P \u003d 9.8 100 kg ≈ 1000 N.
Ap \u003d 1000 N 0.08 \u003d 80 J.
Az \u003d 250 N 0.4 m \u003d 100 J.
η = 80 J/100 J 100% = 80%.
Answer : η = 80%.
But the "golden rule" is fulfilled in this case too. Part of the useful work - 20% of it - is spent on overcoming friction in the axis of the lever and air resistance, as well as on the movement of the lever itself.
The efficiency of any mechanism is always less than 100%. By designing mechanisms, people tend to increase their efficiency. To do this, friction in the axes of the mechanisms and their weight are reduced.
Energy.
In factories and factories, machines and machines are driven by electric motors, which consume electrical energy (hence the name).
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A compressed spring (rice), straightening out, does work, lifts a load to a height, or makes a cart move. An immovable load raised above the ground does not do work, but if this load falls, it can do work (for example, it can drive a pile into the ground). Every moving body has the ability to do work. So, a steel ball A (rice) rolled down from an inclined plane, hitting a wooden block B, moves it a certain distance. In doing so, work is being done. If a body or several interacting bodies (a system of bodies) can do work, it is said that they have energy. Energy - a physical quantity showing what work a body (or several bodies) can do. Energy is expressed in the SI system in the same units as work, i.e. in joules. The more work a body can do, the more energy it has. When work is done, the energy of bodies changes. The work done is equal to the change in energy. Potential and kinetic energy.Potential (from lat. potency - possibility) energy is called energy, which is determined by the mutual position of interacting bodies and parts of the same body. Potential energy, for example, has a body raised relative to the surface of the Earth, because the energy depends on the relative position of it and the Earth. and their mutual attraction. If we consider the potential energy of a body lying on the Earth to be equal to zero, then the potential energy of a body raised to a certain height will be determined by the work done by gravity when the body falls to the Earth. Denote the potential energy of the body E n because E = A, and the work, as we know, is equal to the product of the force and the path, then A = Fh, where F- gravity. Hence, the potential energy En is equal to: E = Fh, or E = gmh, where g- acceleration of gravity, m- body mass, h- the height to which the body is raised. The water in the rivers held by dams has a huge potential energy. Falling down, the water does work, setting in motion the powerful turbines of power plants. The potential energy of a copra hammer (Fig.) is used in construction to perform the work of driving piles. By opening a door with a spring, work is done to stretch (or compress) the spring. Due to the acquired energy, the spring, contracting (or straightening), does the work, closing the door. The energy of compressed and untwisted springs is used, for example, in wrist watches, various clockwork toys, etc. Any elastic deformed body possesses potential energy. The potential energy of compressed gas is used in the operation of heat engines, in jackhammers, which are widely used in the mining industry, in the construction of roads, excavation of solid soil, etc. The energy possessed by a body as a result of its movement is called kinetic (from the Greek. cinema - movement) energy. The kinetic energy of a body is denoted by the letter E to. Moving water, driving the turbines of hydroelectric power plants, expends its kinetic energy and does work. Moving air also has kinetic energy - the wind. What does kinetic energy depend on? Let us turn to experience (see Fig.). If you roll ball A from different heights, you will notice that the higher the ball rolls from, the greater its speed and the further it advances the bar, i.e., it does more work. This means that the kinetic energy of a body depends on its speed. Due to the speed, a flying bullet has a large kinetic energy. The kinetic energy of a body also depends on its mass. Let's do our experiment again, but we will roll another ball - a larger mass - from an inclined plane. Block B will move further, i.e., more work will be done. This means that the kinetic energy of the second ball is greater than the first. The greater the mass of the body and the speed with which it moves, the greater its kinetic energy. In order to determine the kinetic energy of a body, the formula is applied: Ek \u003d mv ^ 2 / 2, where m- body mass, v is the speed of the body. The kinetic energy of bodies is used in technology. The water retained by the dam has, as already mentioned, a large potential energy. When falling from a dam, water moves and has the same large kinetic energy. It drives a turbine connected to an electric current generator. Due to the kinetic energy of water, electrical energy is generated. The energy of moving water is of great importance in the national economy. This energy is used by powerful hydroelectric power plants. The energy of falling water is an environmentally friendly source of energy, unlike fuel energy. All bodies in nature, relative to the conditional zero value, have either potential or kinetic energy, and sometimes both. For example, a flying plane has both kinetic and potential energy relative to the Earth. We got acquainted with two types of mechanical energy. Other types of energy (electrical, internal, etc.) will be considered in other sections of the physics course. The transformation of one type of mechanical energy into another. The phenomenon of the transformation of one type of mechanical energy into another is very convenient to observe on the device shown in the figure. Winding the thread around the axis, raise the disk of the device. The disk raised up has some potential energy. If you let it go, it will spin and fall. As it falls, the potential energy of the disk decreases, but at the same time its kinetic energy increases. At the end of the fall, the disk has such a reserve of kinetic energy that it can again rise almost to its previous height. (Part of the energy is expended working against friction, so the disk does not reach its original height.) Having risen up, the disk falls again, and then rises again. In this experiment, when the disk moves down, its potential energy is converted into kinetic energy, and when moving up, kinetic energy is converted into potential. The transformation of energy from one type to another also occurs when two elastic bodies hit, for example, a rubber ball on the floor or a steel ball on a steel plate. If you lift a steel ball (rice) over a steel plate and release it from your hands, it will fall. As the ball falls, its potential energy decreases, and its kinetic energy increases, as the speed of the ball increases. When the ball hits the plate, both the ball and the plate will be compressed. The kinetic energy that the ball possessed will turn into the potential energy of the compressed plate and the compressed ball. Then, due to the action of elastic forces, the plate and the ball will take their original shape. The ball will bounce off the plate, and their potential energy will again turn into the kinetic energy of the ball: the ball will bounce upward with a speed almost equal to the speed that it had at the moment of impact on the plate. As the ball rises, the speed of the ball, and hence its kinetic energy, decreases, and the potential energy increases. bouncing off the plate, the ball rises to almost the same height from which it began to fall. At the top of the ascent, all its kinetic energy will again turn into potential energy. Natural phenomena are usually accompanied by the transformation of one type of energy into another. Energy can also be transferred from one body to another. So, for example, when shooting from a bow, the potential energy of a stretched bowstring is converted into the kinetic energy of a flying arrow. |
"Work" - Examples of mechanical work. A task. The load has not moved, the distance traveled is 0. Who has traveled the longest distance. A bag of potatoes was dragged 2m. James Prescott Joule. What work must be done to put the dumbbell on the table. Formula for calculating work. The internal energy of a gas does not depend on the volume it occupies.
"Energy and work" - Potential energy. Powder gases act only at a distance of 1m. An example of the action of kinetic energy. Forms of energy. An example of the action of potential energy. From a vertically placed cannon 1 m long, a 1 kg cannon ball flies out. An example of the action of thermal energy. How to make a kilogrammeter work.
"Physics" Power, energy, work "" - Work. The work is equal to the scalar product. The man moves the sled. The sum of kinetic and potential energies. Work, power, energy. The person is in good physical shape. The concept of power. Movement speed after inelastic impact. Electronovolt. Work done by a conservative force. Kinetic energy.
"Mechanical work of a physicist" - The unit of work is the joule (J). The meaning of the word "work". Mechanical work. The concept of work in physics. 1 MJ \u003d 1,000,000J. Inertia movement. A unit of work is the work done by a force of 1N over a distance of 1m. 1 kJ = 1000J. Units of work. Mechanical work is directly proportional to the applied force and the distance traveled.
"Tasks for work and power" - Condition. When connected in series, the currents are the same. Boiler efficiency 80%. Parallel connection. Formulas for work and power of electric current. Boiler with an efficiency of 80% is made of nichrome wire. Expressed the length of the wire from the formula. Which resistor generates the most heat?
The energy characteristics of motion are introduced on the basis of the concept of mechanical work or the work of a force.
Definition 1Work A performed by a constant force F → is a physical quantity equal to the product of the modules of force and displacement, multiplied by the cosine of the angle α located between force vectors F → and displacement s → .
This definition is discussed in Figure 1 . eighteen . one .
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 . eighteen . one . Work 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 displacements Δ s i 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), after which it goes into the integral.
The graphic image of the work is determined from the area of the curvilinear figure located under the graph F s (x) of Figure 1. eighteen . 2.
Picture 1 . eighteen . 2. Graphic definition of work Δ A i = F s i Δ s i .
An example of a coordinate-dependent force is the elastic force of a spring, which obeys Hooke's law. To stretch the 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. eighteen . 3 .
Picture 1 . eighteen . 3 . Stretched spring. The direction of the external force F → coincides with the direction of displacement s → . F s = k x , where k is the stiffness of the spring.
F → y p p = - F →
The dependence of the module of the external force on the coordinates x can be shown on the graph using a straight line.
Picture 1 . eighteen . four . Dependence of the module of the external force on the coordinate when the spring is stretched.
From the above figure, it is possible to find work 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 a spring is compressed. Both cases show that the elastic force F → y p p is equal to the work of the external force F → , but with the opposite sign.
Definition 2
If several forces act on the body, then the formula for the total work will look like the sum of all the work done on it. When the body moves forward, the points of application of forces move in the same way, that is, the total work of all forces will be equal to the work of the resultant of the applied forces.
Picture 1 . eighteen . 5 . model of mechanical work.
Determination of power
Definition 3Power is the work done by a force per unit of time.
The record of the physical quantity of power, denoted N, takes the form of the ratio of work A to the time interval t of the work performed, that is:
Definition 4
The SI system uses the watt (Wt) as the unit of power, which is equal to the power of a force that does work of 1 J in 1 s.
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