Almost everyone, without hesitation, will answer: in the second. And they will be wrong. The opposite is true. In physics, mechanical work is described with the following definitions: Mechanical work is performed when a force acts on a body and it moves. Mechanical work is directly proportional to the force applied and the distance traveled.
Mechanical work formula
Mechanical work is determined by the formula:
where A is work, F is force, s is the distance traveled.
POTENTIAL(potential function), a concept that characterizes a wide class of physical force fields (electric, gravitational, etc.) and fields in general physical quantities, represented by vectors (fluid velocity field, etc.). IN general case vector field potential a( x,y,z) is such a scalar function u(x,y,z) that a=grad
35. Conductors in an electric field. Electrical capacity.Conductors in an electric field. Conductors are substances characterized by the presence in them of a large number of free charge carriers that can move under the influence of an electric field. Conductors include metals, electrolytes, and coal. In metals, the carriers of free charges are the electrons of the outer shells of atoms, which, when the atoms interact, completely lose connections with “their” atoms and become the property of the entire conductor as a whole. Free electrons participate in thermal motion like gas molecules and can move through the metal in any direction. Electrical capacity- characteristic of a conductor, a measure of its ability to accumulate electrical charge. In theory electrical circuits capacitance is the mutual capacitance between two conductors; parameter of a capacitive element of an electrical circuit, presented in the form of a two-terminal network. This capacity is defined as the ratio of the quantity electric charge to the potential difference between these conductors
36. Capacitance of a parallel-plate capacitor.
Capacitance of a parallel plate capacitor.
That. The capacitance of a flat capacitor depends only on its size, shape and dielectric constant. To create a high-capacity capacitor, it is necessary to increase the area of the plates and reduce the thickness of the dielectric layer.
37. Magnetic interaction of currents in a vacuum. Ampere's law.Ampere's law. In 1820, Ampere (French scientist (1775-1836)) experimentally established a law by which one can calculate force acting on a conductor element of length carrying current.
where is the vector of magnetic induction, is the vector of the element of the length of the conductor drawn in the direction of the current.
Force modulus , where is the angle between the direction of the current in the conductor and the direction of the magnetic field induction. For a straight conductor of length carrying current in a uniform field
The direction of the acting force can be determined using left hand rules:
If the palm of the left hand is positioned so that the normal (to the current) component magnetic field entered the palm, and the four extended fingers are directed along the current, then the thumb will indicate the direction in which the Ampere force acts.
38. Magnetic field strength. Biot-Savart-Laplace LawMagnetic field strength(standard designation N ) - vector physical quantity, equal to the difference of the vector magnetic induction B And magnetization vector J .
IN International System of Units (SI): 
Where- magnetic constant.
BSL Law. The law determining the magnetic field of an individual current element 
39. Applications of the Bio-Savart-Laplace law. For direct current field
For a circular turn.
And for the solenoid
40. Magnetic field induction A magnetic field is characterized by a vector quantity, which is called magnetic field induction (a vector quantity that is a force characteristic of the magnetic field at a given point in space). MI. (B) this is not a force acting on the conductors, it is a quantity that is found through this force using the following formula: B=F / (I*l) (Verbally: MI vector module. (B) is equal to the ratio of the modulus of force F, with which the magnetic field acts on a current-carrying conductor located perpendicular to the magnetic lines, to the current strength in the conductor I and the length of the conductor l. Magnetic induction depends only on the magnetic field. In this regard, induction can be considered a quantitative characteristic of a magnetic field. It determines with what force (Lorentz force) the magnetic field acts on a charge moving at speed. 
MI is measured in teslas (1 Tesla). In this case, 1 T=1 N/(A*m). MI has a direction. Graphically it can be sketched in the form of lines. In a uniform magnetic field, the MI lines are parallel, and the MI vector will be directed in the same way at all points. In the case of a non-uniform magnetic field, for example, a field around a current-carrying conductor, the magnetic induction vector will change at every point in space around the conductor, and tangents to this vector will create concentric circles around the conductor.
41. Motion of a particle in a magnetic field. Lorentz force. a) - If a particle flies into a region of a uniform magnetic field, and the vector V is perpendicular to the vector B, then it moves in a circle of radius R=mV/qB, since the Lorentz force Fl=mV^2/R plays the role of a centripetal force. The period of revolution is equal to T=2piR/V=2pim/qB and it does not depend on the particle speed (This is only true for V<<скорости света) - Если угол между векторами V и B не равен 0 и 90 градусов, то частица в однородном магнитном поле движется по винтовой линии. - Если вектор V параллелен B, то частица движется по прямой линии (Fл=0). б) Силу, действующую со стороны магнитного поля на движущиеся в нем заряды, называют силой Лоренца.
The magnetic force is determined by the relation: Fl = q·V·B·sina (q is the magnitude of the moving charge; V is the modulus of its speed; B is the modulus of the magnetic field induction vector; alpha is the angle between vector V and vector B) The Lorentz force is perpendicular to the speed and therefore it does not do work, does not change the modulus of the charge speed and its kinetic energy. But the direction of speed changes continuously. The Lorentz force is perpendicular to the vectors B and v, and its direction is determined using the same left-hand rule as the direction of the Ampere force: if the left hand is positioned so that the component of magnetic induction B, perpendicular to the speed of the charge, enters the palm, and the four fingers are are directed along the movement of the positive charge (against the movement of the negative), then the thumb bent 90 degrees will show the direction of the Lorentz force F l acting on the charge. 
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 measured quantity there is a unit in which it is usually measured. Units of measurement are constant and have the same meaning throughout the world.
The reason for this is the following. In nineteen sixty, 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 determining units of measurement accepted throughout the world and their relationships.
Physical terms and terminology
In physics, the unit of measurement of the work of force is called J (Joule), in honor of the English physicist James Joule, who made a great contribution to the development of the branch 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 of one kg (kilogram) mass with an acceleration of one m/s2 (meter per second) in the direction of the force.
For your information. In physics, everything is interconnected; performing any work involves performing additional actions. As an example, we can take a household fan. When the fan is plugged in, the fan blades begin to rotate. The rotating blades influence the air flow, giving it directional movement. This is the result of the work. But to perform the work, the influence of other external forces is necessary, without which the action is impossible. These include electric current, power, voltage and many other related values.
Electric current, at its core, 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 (Coulomb), named after the French scientist and inventor Charles Coulomb. In the SI system, it is a unit of measurement for the number of charged electrons. 1 C is equal to the volume of charged particles flowing through the cross section of a conductor per unit time. The unit of time is one second. The formula for electric charge is shown in the figure below.
The strength of electric current is indicated by the letter A (ampere). Ampere is a unit in physics that characterizes the measurement of the work of force that is expended to move charges along a conductor. At its core, electric current is the ordered movement of electrons in a conductor under the influence of an electromagnetic field. A conductor is a material or molten salt (electrolyte) that has little resistance to the passage of electrons. The strength of electric current is affected by two physical quantities: voltage and resistance. They will be discussed below. Current strength 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: they need a certain impact to move. This effect is created by creating a potential difference. Electric charge can be positive or negative. Positive charges always tend towards negative charges. This is necessary for the balance of the system. The difference between the number of positively and negatively charged particles is called electrical voltage.
Power is the amount of energy expended to do one J (Joule) of work in a period of time of one second. The unit of measurement in physics is designated 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.
One of the most important concepts in mechanics is work of force .
Work of force
All physical bodies in the world around us are set in motion by force. If a moving body in the same or opposite direction is acted upon by a force or several forces from one or more bodies, then it is said that work is being done .
That is, mechanical work is performed by a 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 driven by the muscular power of the cyclist's legs. Consequently, this force also does mechanical work.
In physics work of force call a physical quantity equal to the product of the force modulus, the displacement modulus of the point of application of the force and the cosine of the angle between the force and displacement vectors.
A = F s cos (F, s) ,
Where F force module,
s – travel module .
Work is always done if the angle between the winds of force and displacement is not zero. If the force acts in the direction opposite to the direction of motion, the amount of work is negative.
No work is done if no forces act on the body, or if the angle between the applied force and the direction of movement is 90 o (cos 90 o = 0).
If a horse pulls a cart, then the horse's muscular force, or the traction force directed along the direction of the cart's movement, does work. But the force of gravity with which the driver presses on the cart does not do any work, since it is directed downward, perpendicular to the direction of movement.
The work of force is a scalar quantity.
Unit of work in the SI measurement system - joule. 1 joule is the work done by a force of 1 newton at a distance of 1 m if the directions of the force and displacement coincide.
If several forces act on a body or a material point, then we speak of 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 a 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 completed in different times. The work that a large electric motor does can be done by a small motor. But he will need much more time for this.
In mechanics, there is a quantity that characterizes the speed of work. This quantity is called power.
Power is the ratio of work performed in a certain period of time to the value of this period.
N= A /∆ t
A-priory A = F s cos α , A s/∆ t = v , hence
N= F v cos α = F v ,
Where F - force, v speed, α – the angle between the direction of force and the direction of speed.
That is power – this 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).
1 watt of power is 1 joule (J) of work done in 1 second (s).
Power can be increased by increasing the force doing work or the rate at which this work is done.
In order to be able to characterize the energy characteristics of movement, the concept of mechanical work was introduced. And the article is dedicated to it in its various manifestations. The topic is both easy and quite difficult to understand. The author sincerely tried to make it more understandable and accessible to understanding, and one can only hope that the goal has been achieved.
What is mechanical work called?
What is it called? If some force works on a body, and as a result of its action the body moves, then this is called mechanical work. When approaching from the point of view of scientific philosophy, several additional aspects can be highlighted here, but the article will cover the topic from the point of view of physics. Mechanical work is not difficult if you think carefully about the words written here. But the word “mechanical” is usually not written, and everything is shortened to the word “work.” But not every job is mechanical. Here is a man sitting and thinking. Does it work? Mentally yes! But is this mechanical work? No. What if a person walks? If a body moves under the influence of force, then this is mechanical work. It's simple. In other words, a force acting on a body does (mechanical) work. And one more thing: it is work that can characterize the result of the action of a certain force. So, if a person walks, then certain forces (friction, gravity, etc.) perform mechanical work on the person, and as a result of their action, the person changes his point of location, in other words, moves.
Work as a physical quantity is equal to the force that acts on the body, multiplied by the path that the body has made under the influence of this force and in the direction indicated by it. We can say that mechanical work was done if 2 conditions were simultaneously met: a force acted on the body, and it moved in the direction of its action. But it did not occur or does not occur if the force acted and the body did not change its location in the coordinate system. Here are small examples when mechanical work is not performed:
- So a person can lean on a huge boulder in order to move it, but there is not enough strength. The force acts on the stone, but it does not move, and no work occurs.
- The body moves in the coordinate system, and the force is equal to zero or they have all been compensated. This can be observed while moving by inertia.
- When the direction in which a body moves is perpendicular to the action of the force. When a train moves along a horizontal line, gravity does not do its work.
Depending on certain conditions, mechanical work can be negative and positive. So, if the directions of both the forces and the movements of the body are the same, then positive work occurs. 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 upward and the force of gravity, which does negative work. When a body is subject to the influence of several forces, such work is called “resultant force work.”
Features of practical application (kinetic energy)
Let's move from theory to practical part. Separately, we should talk about mechanical work and its use in physics. As many probably remember, all the energy of the body is divided into kinetic and potential. When an object is in equilibrium and not moving anywhere, its potential energy equals its total energy and its kinetic energy equals zero. When movement begins, potential energy begins to decrease, kinetic energy begins to increase, but in total they are equal to the total energy of the object. For a material point, kinetic energy is defined as the work of a force that accelerates the point from zero to the value H, and in formula form the kinetics of a body is equal to ½*M*N, where M is mass. To find out the kinetic energy of an object that consists of many particles, you need to find the sum of all the kinetic energy of the particles, and this will be the kinetic energy of the body.
Features of practical application (potential energy)
In the case when all the forces acting on the body are conservative, and the potential energy is equal to the total, then no work is done. This postulate is known as the law of conservation of mechanical energy. Mechanical energy in a closed system is constant over a time interval. The conservation law is widely used to solve problems from classical mechanics.
Features of practical application (thermodynamics)
In thermodynamics, the work done by a gas during expansion is calculated by the integral of pressure times volume. This approach is applicable not only in cases where there is an exact volume function, but also to all processes that can be displayed in the pressure/volume plane. It also applies knowledge of mechanical work not only to gases, but to anything that can exert pressure.
Features of practical application in practice (theoretical mechanics)
In theoretical mechanics, all the properties and formulas described above are considered in more detail, in particular projections. It also gives its definition for various formulas of mechanical work (an example of a definition for the Rimmer integral): the limit to which the sum of all forces of elementary work tends, when the fineness of the partition tends to zero, is called the work of force along the curve. Probably difficult? But nothing, everything is fine with theoretical mechanics. Yes, all the mechanical work, physics and other difficulties are over. Further there will be only examples and a conclusion.
Units of measurement of mechanical work
The SI uses joules to measure work, while the GHS uses ergs:
- 1 J = 1 kg m²/s² = 1 N m
- 1 erg = 1 g cm²/s² = 1 dyne cm
- 1 erg = 10 −7 J
Examples of mechanical work
In order to finally understand such a concept as mechanical work, you should study several individual examples that will allow you to consider it from many, but not all, sides:
- When a person lifts a stone with his hands, mechanical work occurs with the help of the muscular strength of his hands;
- When a train travels along the rails, it is pulled by the traction force of the tractor (electric locomotive, diesel locomotive, etc.);
- If you take a gun and fire from it, then thanks to the pressure force created by the powder gases, work will be done: the bullet is moved along the barrel of the gun at the same time as the speed of the bullet itself increases;
- Mechanical work also exists when the friction force acts on a body, forcing it to reduce the speed of its movement;
- The above example with balls, when they rise in the opposite direction relative to the direction of gravity, is also an example of mechanical work, but in addition to gravity, the Archimedes force also acts, when everything that is lighter than air rises up.
What is power?
Finally, I would like to touch on the topic of power. The work done by a force in one unit of time is called power. In fact, power is a physical quantity that is a reflection of the ratio of work to a certain period of time during which this work was done: M=P/B, where M is power, P is work, B is time. The SI unit of power is 1 W. A watt is equal to the power that does one joule of work in one second: 1 W=1J\1s.
Mechanical work. Units of work.
In everyday life, we understand everything by the concept of “work”.
In physics, the concept Job somewhat different. It is a definite physical quantity, which means it can be measured. In physics it is studied primarily mechanical work .
Let's look at examples of mechanical work.
The train moves under the traction force of an electric locomotive, and mechanical work is performed. When a gun is fired, the pressure force of the powder gases does work - it moves the bullet along the barrel, and the speed of the bullet increases.
From these examples it is clear that mechanical work is performed when a body moves under the influence of force. Mechanical work is also performed in the case when a force acting on a body (for example, friction force) reduces the speed of its movement.
Wanting to move the cabinet, we press hard on it, but if it does not move, then we do not perform mechanical work. One can imagine a case when a 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 a body and it moves .
It is not difficult to understand that the greater the force acts on the body and the longer the path that the body travels under the influence of this force, the greater the work done.
Mechanical work is directly proportional to the force applied and directly proportional to the distance traveled .
Therefore, we agreed to measure mechanical work by the product of force and the path traveled along this direction of this force:
work = force × path
Where A- Job, F- strength and s- distance traveled.
A unit of work is taken to be the work done by a force of 1N over a path of 1 m.
Unit of work - joule (J ) named after the English scientist Joule. Thus,
1 J = 1N m.
Also used kilojoules (kJ) .
1 kJ = 1000 J.
Formula A = Fs applicable when the force F constant and coincides with the direction of movement 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 body moves in the direction opposite to the direction of the applied force, for example, the sliding friction force, then this force does negative work.
If the direction of the force acting on the body is perpendicular to the direction of movement, then this force does no work, the work is zero:
In the future, speaking about 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/m3.
Given:
ρ = 2500 kg/m 3
Solution:
where F is the force that must be applied to uniformly lift the slab up. This force is equal in modulus to the force Fstrand acting on the slab, i.e. F = Fstrand. And the force of gravity can be determined by the mass of the slab: Fweight = gm. Let's calculate the mass of the slab, knowing its volume and the density of granite: m = ρV; s = h, i.e. the path is equal to the lifting height.
So, m = 2500 kg/m3 · 0.5 m3 = 1250 kg.
F = 9.8 N/kg · 1250 kg ≈ 12,250 N.
A = 12,250 N · 20 m = 245,000 J = 245 kJ.
Answer: A =245 kJ.
Levers.Power.Energy
Different engines require different times to complete 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 these bricks were moved by a worker, 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-ploughshare - many ploughshares), this work will be completed in 40-50 minutes.
It is clear that a crane does the same work faster than a worker, and a tractor does the same work faster than a horse. The speed of work is characterized by a special quantity called power.
Power is equal to the ratio of work to the time during which it was performed.
To calculate power, you need to divide the work by the time during which this work was done. power = work/time.
Where N- power, A- Job, t- time of work completed.
Power is a constant quantity when the same work is done every second; in other cases the ratio A/t determines the average power:
N avg = A/t . The unit of power is taken to be the power at which J of work is done in 1 s.
This unit is called the watt ( W) 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 technology - 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 water flow 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).
Gravity acting on water:
F = 9.8 m/s2 120,000 kg ≈ 1,200,000 N (12 105 N)
Work done by flow 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 indicates some information about the engine, including its power.
Human power under normal operating conditions is on average 70-80 W. When jumping or running up stairs, a person can develop power up to 730 W, 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 conditions 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 used various devices to perform mechanical work.
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Everyone knows that a heavy object (a stone, a cabinet, a machine tool), which cannot be moved by hand, can be moved with the help of a sufficiently 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 great heights.
In many cases, instead of lifting a heavy load to a certain height, it can be rolled or pulled to the same height along an inclined plane or lifted using blocks.
Devices used to convert force 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 to gain strength, that is, to increase the force acting on the body several times.
Simple mechanisms are found both in household and in all complex industrial and industrial 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 automatic machines, printing and counting machines.
Lever arm. Balance of forces on the lever.
Let's consider the simplest and most common mechanism - the lever.
A lever is a rigid body that can rotate around a fixed support.
The pictures show how a worker uses a crowbar as a lever to lift a load. In the first case, the worker with 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. To do this, he turns the crowbar around an axis passing through the only motionless the breaking point is the point of its support ABOUT. Force F with which the worker acts on the lever is less force P, thus the worker receives gain in strength. Using 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 ABOUT(fulcrum) is located between the points of application of forces A And IN. Another picture shows a diagram of this lever. Both forces F 1 and F 2 acting on the lever are directed in one direction.
The shortest distance between the fulcrum and the straight line along which the force acts on the lever is called the arm of force.
To find the arm of the force, you need to lower the perpendicular from the fulcrum to the line of action of the force.The length of this perpendicular will be the arm of this force. The figure shows that OA- shoulder strength F 1; OB- shoulder strength F 2. The forces acting on the lever can rotate it around its axis in two directions: clockwise or counterclockwise. Yes, strength 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 influence of forces applied to it can be established experimentally. 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 figure) 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 force modules and their shoulders are measured. From the experience shown in Figure 154, it is clear that force 2 N balances the force 4 N. In this case, as can be seen from the figure, the shoulder of lesser strength is 2 times larger than the shoulder of greater strength.
Based on such experiments, the condition (rule) of lever equilibrium was established.
A lever is in equilibrium when the forces acting on it are inversely proportional to the arms 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 figure).
The rule of lever equilibrium was established by Archimedes around 287 - 212. BC e. (but in the last paragraph it was said that the levers were used by the Egyptians? Or does the word “established” play an important role here?)
From this rule it follows that a smaller force can be used to balance a larger force using a lever. Let one arm of the lever be 3 times larger than the other (see figure). Then, by applying a force of, for example, 400 N at point B, you can lift a stone weighing 1200 N. To lift an even heavier load, you need 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 lever arm of 2.4 m if the smaller arm is 0.6 m?
Let's write down the conditions 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, applying a force of 600 N to the lever. But in this case, the arm on which the worker acts is 4 times longer than the one 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 lesser force should be longer than the shoulder of greater strength.
Moment of power.
You already know the rule of lever equilibrium:
F 1 / F 2 = l 2 / l 1 ,
Using the property of proportion (the product of its extreme members is equal to the product of its middle members), we write it in this form:
F 1l 1 = F 2 l 2 .
On the left side of the equation is the product of force F 1 on her shoulder l 1, and on the right - the product of force F 2 on her shoulder l 2 .
The product of the modulus of the force rotating the body and its shoulder is called moment of force; it is designated by the letter M. This means
A lever is in equilibrium under the action of two forces if the moment of the force rotating it clockwise is equal to the moment of the force rotating it counterclockwise.
This rule is called rule of moments , can be written as a formula:
M1 = M2
Indeed, in the experiment we considered (§ 56), the acting forces were equal to 2 N and 4 N, their shoulders respectively amounted to 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. The unit of moment of force is taken to be a moment of force of 1 N, the arm of which is exactly 1 m.
This unit is called newton meter (N m).
The moment of force characterizes the action of a force, and shows that it depends simultaneously on both the modulus of the force and its leverage. Indeed, we already know, for example, that the action of a force on a door depends both on the magnitude of the force and on where the force is applied. The easier it is to turn the door, 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 rule of leverage (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 travel is required.
We have a gain in strength when working with scissors. Scissors - this is a lever(fig), 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 gripping the scissors. Counterforce F 2 is the resistance force of the material being cut with scissors. Depending on the purpose of the scissors, their design varies. Office scissors, designed for cutting paper, have long blades and handles that are almost the same length. Cutting paper does not require much force, and a long blade makes it easier to cut in a straight line. Shears 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 arm of the acting force has to be significantly increased. The difference between the length of the handles and the distance of the cutting part and the axis of rotation is even greater wire cutters(Fig.), designed for cutting wire.
Many machines have different types of levers. The handle of a sewing machine, the pedals or handbrake of a bicycle, the pedals of a car and tractor, and the keys of a piano 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 scales is based on the principle of the lever (Fig.). The training scales shown in Figure 48 (p. 42) act as equal-arm lever . IN decimal scales The shoulder from which the cup with weights is suspended is 10 times longer than the shoulder carrying the load. This makes weighing large loads much easier. When weighing a load on a decimal scale, you should multiply the mass of the weights by 10.
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The device of scales for weighing freight cars of cars is also based on the rule of leverage.
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 (by reading a book about insects and the structure of their bodies), birds, and in the structure of plants.
Application of the law of equilibrium of a lever to a block.
Block It is a wheel with a groove, mounted in a holder. A rope, cable or chain is passed through the block groove.
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Fixed block This is called a block whose axis is fixed and does not rise or fall when lifting loads (Fig.).
A fixed block can be considered as an equal-armed lever, in which the arms of forces are equal to the radius of the wheel (Fig): OA = OB = r. Such a block does not provide a gain in strength. ( F 1 = F 2), but allows you to change the direction of the force. Movable block - this is a block. the axis of which rises and falls along with the load (Fig.). The figure shows the corresponding lever: ABOUT- fulcrum point of the lever, OA- shoulder strength R And OB- shoulder strength F. Since the shoulder OB 2 times the shoulder OA, then the strength F 2 times less force R:
F = P/2 .
Thus, the movable block gives a 2-fold gain in strength .
This can be proven using the concept of moment of force. When the block is in equilibrium, the moments of forces F And R equal to each other. But the shoulder of strength F 2 times the leverage R, and, therefore, the power itself F 2 times less force R.
Usually in practice a combination of a fixed block and a movable one is used (Fig.). The fixed block is used for convenience only. It does not give a gain in force, but it changes the direction of the force. For example, it allows you to lift a load while standing on the ground. This comes in handy for many people or workers. However, it gives a gain in strength 2 times greater than usual!
Equality of work when using simple mechanisms. "Golden rule" of mechanics.
The simple mechanisms we have considered are used when performing work in cases where it is necessary to balance another force through the action of one force.
Naturally, the question arises: while giving a gain in strength or path, don’t simple mechanisms give a gain in work? The answer to this question can be obtained from experience.
By balancing two different magnitude forces on a lever F 1 and F 2 (fig.), set the lever in motion. It turns out that at the same time the point of application of the smaller force F 2 goes further s 2, and the point of application of the greater force F 1 - shorter 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 gain in strength, but at the same time we lose by the same amount along 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 is equal to each other:
F 1 s 1 = F 2 s 2, i.e. A 1 = A 2.
So, When using leverage, you won’t be able to win at work.
By using leverage, we can gain either power or distance. By applying force to the short arm of the lever, we gain in distance, but lose by the same amount in strength.
There is a legend that Archimedes, delighted with the discovery of the rule of leverage, exclaimed: “Give me a fulcrum and I will turn the Earth over!”
Of course, Archimedes could not cope with such a task even if he had been given a fulcrum (which should have been outside the Earth) and a lever of the required length.
To raise the earth just 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!
A stationary block does not give any gain in work, which is easy to verify experimentally (see figure). Paths traversed by the points of application of forces F And F, are the same, the forces are the same, which means the work is the same.
You can measure and compare the work done with the help of a moving block. In order to lift a load to a height h using 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.
Thus, getting a 2-fold gain in strength, they lose 2-fold on the way, therefore, the movable block does not give a gain in work.
Centuries-old practice has shown that None of the mechanisms gives a gain in performance. They use various mechanisms in order to win in strength or in travel, depending on the working conditions.
Already ancient scientists knew a rule applicable to all mechanisms: no matter how many times we win in strength, the same number of times we lose in distance. This rule has been called the "golden rule" of mechanics.
Efficiency of the mechanism.
When considering the design 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 full), is equal to useful work on lifting loads or overcoming any resistance.
In practice, the total work done by a mechanism is always slightly greater than the useful work.
Part of the work is done against the frictional force in the mechanism and by moving its individual parts. So, when using a movable block, you have to additionally do work to lift the block itself, the rope and determine the friction force in the axis of the block.
Whatever mechanism we take, the useful work done with its help always constitutes only a part of the total work. This means, denoting useful work by the letter Ap, total (expended) 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.
The efficiency factor is abbreviated as efficiency.
Efficiency = Ap / Az.
Efficiency is usually expressed as a percentage and is denoted by the Greek letter η, read as “eta”:
η = Ap / Az · 100%.
Example: A load weighing 100 kg is suspended on the short arm of a lever. To lift it, a force of 250 N is applied to the long arm. The load is raised to a height of h1 = 0.08 m, while the point of application of the driving force drops to a height of h2 = 0.4 m. Find the efficiency of the lever.
Let's write down the conditions of the problem and solve it.
Given :
Solution :
η = Ap / Az · 100%.
Total (expended) work Az = Fh2.
Useful work Ap = Рh1
P = 9.8 100 kg ≈ 1000 N.
Ap = 1000 N · 0.08 = 80 J.
Az = 250 N · 0.4 m = 100 J.
η = 80 J/100 J 100% = 80%.
Answer : η = 80%.
But the “golden rule” applies in this case as well. 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%. When designing mechanisms, people strive to increase their efficiency. To achieve 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 (Fig.), when straightened, does work, raises a load to a height, or makes a cart move. A stationary 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. Thus, a steel ball A (fig) rolling down from an inclined plane, hitting a wooden block B, moves it a certain distance. At the same time, work is done. If a body or several interacting bodies (a system of bodies) can do work, they are said to have energy. Energy - a physical quantity showing how much 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. Work done is equal to the change in energy. Potential and kinetic energy.Potential (from lat. potency - possibility) energy is the energy that is determined by the relative position of interacting bodies and parts of the same body. Potential energy, for example, is possessed by 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 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. Let us denote the potential energy of the body E n, because E = A, and work, as we know, is equal to the product of force and path, then A = Fh, Where F- gravity. This means that 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. Water in rivers held by dams has enormous potential energy. Falling down, the water does work, driving powerful turbines of power plants. The potential energy of a copra hammer (Fig.) is used in construction to carry out 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 work, closing the door. The energy of compressed and untwisted springs is used, for example, in watches, various wind-up toys, etc. Any elastic deformed body has 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 road construction, excavation of hard soil, etc. The energy that a body possesses as a result of its movement is called kinetic (from the Greek. kinema - 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, the wind, also has kinetic energy. What does kinetic energy depend on? Let's turn to experience (see figure). If you roll ball A from different heights, you will notice that the greater the height the ball rolls from, the greater its speed and the further it moves the block, i.e., it does more work. This means that the kinetic energy of a body depends on its speed. Due to its speed, a flying bullet has high kinetic energy. The kinetic energy of a body also depends on its mass. Let's do our experiment again, but we'll roll another ball of greater mass from the inclined plane. Bar 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 a body and the speed at which it moves, the greater its kinetic energy. In order to determine the kinetic energy of a body, the formula is used: Ek = mv^2 /2, Where m- body mass, v- speed of body movement. The kinetic energy of bodies is used in technology. The water retained by the dam has, as already mentioned, great potential energy. When water falls from a dam, it moves and has the same high 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 using 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 conventional zero value, have either potential or kinetic energy, and sometimes both together. For example, a flying airplane has both kinetic and potential energy relative to the Earth. We became acquainted with two types of mechanical energy. Other types of energy (electrical, internal, etc.) will be discussed in other sections of the physics course. Conversion of one type of mechanical energy into another. The phenomenon of transformation of one type of mechanical energy into another is very convenient to observe on the device shown in the figure. By winding the thread onto the axis, the device disk is lifted. A disk raised upward has some potential energy. If you let go of it, it will spin and begin to 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 rise again to almost its previous height. (Part of the energy is spent working against the frictional force, 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 downward, its potential energy turns into kinetic energy, and when it moves up, the kinetic energy turns into potential energy. The transformation of energy from one type to another also occurs when two elastic bodies collide, for example, a rubber ball on the floor or a steel ball on a steel plate. If you lift a steel ball (rice) above 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 had will turn into potential energy of the compressed plate and the compressed ball. Then, thanks to the action of elastic forces, the plate and the ball will take their original shape. The ball will bounce off the slab, and their potential energy will again turn into the kinetic energy of the ball: the ball will bounce up at a speed almost equal to the speed it had at the moment it hit the slab. As the ball rises upward, the speed of the ball, and therefore its kinetic energy, decreases, while the potential energy increases. Having bounced off the plate, the ball rises to almost the same height from which it began to fall. At the top point of the rise, all its kinetic energy will again turn into potential. Natural phenomena are usually accompanied by the transformation of one type of energy into another. Energy can be transferred from one body to another. For example, when archery, the potential energy of a drawn bowstring is converted into the kinetic energy of a flying arrow. |
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