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.
The reason for this is the following. In 1960, at the eleventh general conference on weights and measures, a system of measurements was adopted, which 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.
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 strength electric current, power, voltage and many other related 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, Cl (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.
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.
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.
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.
In conclusion, it should be noted that the unit of measure 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
To be able to characterize the energy characteristics of motion, the concept of mechanical work was introduced. And it is to her in her various manifestations that the article is devoted. To understand the topic is both easy and quite complex. The author sincerely tried to make it more understandable and understandable, and one can only hope that the goal has been achieved.
What is mechanical work?
What is it called? If some force works on the body, and as a result of the action of this force, the body moves, then this is called mechanical work. When approached from the point of view scientific philosophy here we can highlight several additional aspects, 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 reduced to the word "work". But not every job is mechanical. Here a man sits and thinks. Does it work? Mentally yes! But is it mechanical work? No. What if the person is walking? If the body moves under the influence of a force, then this is mechanical work. Everything is simple. In other words, the force acting on the 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 a person, and as a result of their action, a person changes his point of location, in other words, he moves.
Work as a physical quantity is equal to the force that acts on the body, multiplied by the path that the body 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: the force acted on the body, and it moved in the direction of its action. But it was not performed or is not performed if the force acted, and the body did not change its location in the coordinate system. Here are small examples where mechanical work is not done:
- So a person can fall 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 work does not occur.
- The body moves in the coordinate system, and the force is equal to zero or they are all compensated. This can be observed during inertial motion.
- When the direction in which the body moves is perpendicular to the force. When the train moves along a horizontal line, the force of gravity does not do its work.
Depending on certain conditions, mechanical work can be negative and positive. So, if the directions and forces, and the movements of the body are the same, then positive work occurs. An example of 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 up and gravity, which does negative work. When a body is subjected to the influence of several forces, such work is called "resultant force work".
Features of practical application (kinetic energy)
We pass from theory to practical part. Separately, we should talk about mechanical work and its use in physics. As many probably remembered, 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 is equal to the total energy, and its kinetic energy is zero. When the movement begins, the potential energy begins to decrease, the kinetic energy 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 the force that accelerated the point from zero to the value H, and in formula form, the kinetics of the body is ½ * M * H, where M is the 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 in the 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 multiplied by volume. This approach is applicable not only in cases where there is an exact function of volume, but also to all processes that can be displayed in the pressure/volume plane. The knowledge of mechanical work is also applied not only to gases, but to everything 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, these are projections. She also gives her own definition for various formulas of mechanical work (an example of the definition for the Rimmer integral): the limit to which the sum of all the forces of elementary work tends when the fineness of the partition tends to zero is called the work of the force along the curve. Probably difficult? But nothing, with theoretical mechanics everything. Yes, and all the mechanical work, physics and other difficulties are over. Further there will be only examples and a conclusion.
Mechanical work units
The SI uses joules to measure work, while the GHS uses ergs:
- 1 J = 1 kg m²/s² = 1 Nm
- 1 erg = 1 g cm²/s² = 1 dyn cm
- 1 erg = 10 −7 J
Examples of mechanical work
In order to finally understand such a concept as mechanical work, you should study a few separate examples that will allow you to consider it from many, but not all, sides:
- When a person lifts a stone with his hands, then 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 shoot from it, then thanks to the pressure force that the powder gases will create, 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;
- There is also mechanical work when the friction force acts on the 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 want 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 such 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 watt. A watt is equal to the power that does the work of one joule in one second: 1 W = 1J \ 1s.
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 a crane lifts a load above the ground with a cable, the work of gravity is negative (and the work of the cable's upward force, on the contrary, is positive).
Suppose, when performing construction work, 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 job can be done in different time
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 of the numerical value of the force and 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.
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 equal to 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. After all, the same work can be done in different times. The work that a large electric motor does can be done by a 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
By definition A = F s cos α , a s/∆ t = v , Consequently
N= F v cos α = F v ,
where F - strength, v speed, α is the angle between the direction of the force and the direction of the velocity.
That is power - is the scalar product of the force vector and the velocity vector of the body.
In the international SI system, 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.
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 force 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 motors have powers ranging from hundredths and tenths of a kilowatt (an electric razor motor, sewing machine) up 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, it is necessary to multiply the power by the time during which this work was performed.
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 * 600s = 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.
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 pyramids in Ancient Egypt they moved and lifted heavy stone slabs to a great height.
In many cases, instead of raising heavy load to a certain height, it can be rolled in or dragged to the same height along 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 shoulder 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 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. Cutting scissors 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 operating force have to increase significantly. 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 different kind many cars have. 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.
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 animal and human bodies. 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.
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 slightly more 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).
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. When 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 greater the height the ball rolls, the greater its speed and the farther 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 the dam, the 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. |