How is elastic force measured? Deformations

Hooke's law was discovered in the 17th century by the Englishman Robert Hooke. This discovery about the stretching of a spring is one of the laws of elasticity theory and plays an important role in science and technology.

Definition and formula of Hooke's law

The formulation of this law is as follows: the elastic force that appears at the moment of deformation of a body is proportional to the elongation of the body and is directed opposite to the movement of particles of this body relative to other particles during deformation.

The mathematical notation of the law looks like this:

Rice. 1. Formula of Hooke's law

Where Fupr– accordingly, the elastic force, x– elongation of the body (the distance by which the original length of the body changes), and k– proportionality coefficient, called body rigidity. Force is measured in Newtons, and elongation of a body is measured in meters.

To reveal the physical meaning of stiffness, you need to substitute the unit in which elongation is measured in the formula for Hooke’s law - 1 m, having previously obtained an expression for k.

Rice. 2. Body stiffness formula

This formula shows that the stiffness of a body is numerically equal to the elastic force that occurs in the body (spring) when it is deformed by 1 m. It is known that the stiffness of a spring depends on its shape, size and the material from which the body is made.

Elastic force

Now that we know what formula expresses Hooke’s law, it is necessary to understand its basic value. The main quantity is the elastic force. It appears at a certain moment when the body begins to deform, for example, when a spring is compressed or stretched. It is sent to reverse side from gravity. When the elastic force and the force of gravity acting on the body become equal, the support and the body stop.

Deformation is an irreversible change that occurs in the size of the body and its shape. They are associated with the movement of particles relative to each other. If a person sits in a soft chair, then deformation will occur to the chair, that is, its characteristics will change. It happens different types: bending, stretching, compression, shear, torsion.

Since the elastic force is related in origin to electromagnetic forces, you should know that it arises due to the fact that molecules and atoms - smallest particles, from which all bodies are composed, attract each other and repel each other. If the distance between the particles is very small, then they are affected by the repulsive force. If this distance is increased, then the force of attraction will act on them. Thus, the difference between attractive and repulsive forces manifests itself in elastic forces.

The elastic force includes the ground reaction force and body weight. The strength of the reaction is of particular interest. This is the force that acts on a body when it is placed on any surface. If the body is suspended, then the force acting on it is called the tension force of the thread.

Features of elastic forces

As we have already found out, the elastic force arises during deformation, and it is aimed at restoring the original shapes and sizes strictly perpendicular to the deformed surface. Elastic forces also have a number of features.

• they occur during deformation;
• they appear in two deformable bodies simultaneously;
• they are perpendicular to the surface in relation to which the body is deformed.
• they are opposite in direction to the displacement of body particles.

Application of the law in practice

Hooke's law is applied both in technical and high-tech devices, and in nature itself. For example, elastic forces are found in watch mechanisms, in shock absorbers in transport, in ropes, rubber bands, and even in human bones. The principle of Hooke's law underlies the dynamometer, a device used to measure force.

The word “power” is so comprehensive that giving it a clear concept is an almost impossible task. The variety from muscle strength to mind strength does not cover the entire spectrum of concepts included in it. Force considered as physical quantity, has a clearly defined meaning and definition. The force formula specifies a mathematical model: the dependence of force on basic parameters.

The history of the study of forces includes the determination of dependence on parameters and experimental proof of the dependence.

Power in Physics

Force is a measure of the interaction of bodies. The mutual action of bodies on each other fully describes the processes associated with changes in speed or deformation of bodies.

As a physical quantity, force has a unit of measurement (in the SI system - Newton) and a device for measuring it - a dynamometer. The principle of operation of the force meter is based on comparing the force acting on the body with the elastic force of the dynamometer spring.

A force of 1 newton is taken to be the force under which a body weighing 1 kg changes its speed by 1 m in 1 second.

Strength as defined:

• direction of action;
• application point;
• module, absolute value.

When describing interaction, be sure to indicate these parameters.

Types of natural interactions: gravitational, electromagnetic, strong, weak. Gravitational universal gravity with its variety - gravity) exist due to the influence of gravitational fields surrounding any body with mass. The study of gravitational fields has not yet been completed. It is not yet possible to find the source of the field.

A larger number of forces arise due to the electromagnetic interaction of the atoms that make up the substance.

Pressure force

When a body interacts with the Earth, it exerts pressure on the surface. The force of which has the form: P = mg, is determined by body mass (m). Gravity acceleration (g) has different meanings at different latitudes of the Earth.

The vertical pressure force is equal in magnitude and opposite in direction to the elastic force arising in the support. The formula of force changes depending on the movement of the body.

Change in body weight

The action of a body on support due to interaction with the Earth is often called body weight. Interestingly, the amount of body weight depends on the acceleration of movement in the vertical direction. In the case where the direction of acceleration is opposite to the acceleration of gravity, an increase in weight is observed. If the acceleration of the body coincides with the direction of free fall, then the weight of the body decreases. For example, being in an ascending elevator, at the beginning of the ascent a person feels an increase in weight for some time. There is no need to say that its mass changes. At the same time, we separate the concepts of “body weight” and its “mass”.

Elastic force

When the shape of a body changes (its deformation), a force appears that tends to return the body to its original shape. This force was given the name "elastic force". It arises due to electrical interaction particles that make up a body.

Let's consider the simplest deformation: tension and compression. Tension is accompanied by an increase in the linear dimensions of bodies, compression - by their decrease. The quantity characterizing these processes is called body elongation. Let's denote it "x". The elastic force formula is directly related to elongation. Each body undergoing deformation has its own geometric and physical parameters. The dependence of the elastic resistance to deformation on the properties of the body and the material from which it is made is determined by the elasticity coefficient, let's call it rigidity (k).

The mathematical model of elastic interaction is described by Hooke's law.

The force arising during deformation of the body is directed against the direction of displacement of individual parts of the body and is directly proportional to its elongation:

• F y = -kx (in vector notation).

The “-” sign indicates the opposite direction of deformation and force.

In scalar form negative sign absent. The elastic force, the formula of which is next view F y = kx, used only for elastic deformations.

Interaction of magnetic field with current

Influence magnetic field for direct current is described. In this case, the force with which the magnetic field acts on a conductor with current placed in it is called the Ampere force.

The interaction of the magnetic field with causes force manifestation. Ampere's force, the formula of which is F = IBlsinα, depends on (B), the length of the active part of the conductor (l), (I) in the conductor and the angle between the direction of the current and the magnetic induction.

Thanks to the last dependence, it can be argued that the vector of action of the magnetic field can change when the conductor is rotated or the direction of the current changes. The left hand rule allows you to establish the direction of action. If left hand positioned so that the magnetic induction vector enters the palm, four fingers are directed along the current in the conductor, then bent 90 ° thumb will show the direction of action of the magnetic field.

Mankind has found applications for this effect, for example, in electric motors. Rotation of the rotor is caused by a magnetic field created by a powerful electromagnet. The force formula allows you to judge the possibility of changing engine power. As the current or field strength increases, the torque increases, which leads to an increase in motor power.

Particle trajectories

The interaction of a magnetic field with a charge is widely used in mass spectrographs in the study of elementary particles.

The action of the field in this case causes the appearance of a force called the Lorentz force. When a charged particle moving at a certain speed enters a magnetic field, the formula of which is F = vBqsinα, causes the particle to move in a circle.

In this mathematical model v is the particle velocity module, electric charge of which - q, B - magnetic field induction, α - angle between the directions of speed and magnetic induction.

The particle moves in a circle (or arc of a circle), since the force and speed are directed at an angle of 90 ° to each other. Changing the direction of linear velocity causes acceleration to appear.

The rule of the left hand, discussed above, also occurs when studying the Lorentz force: if the left hand is positioned in such a way that the magnetic induction vector enters the palm, four fingers extended in a line are directed along the speed of a positively charged particle, then bent by 90 ° the thumb will indicate the direction of the force.

Plasma problems

The interaction of a magnetic field and matter is used in cyclotrons. Problems associated with laboratory study plasma, do not allow it to be kept in closed vessels. High can only exist when high temperatures. Plasma can be kept in one place in space using magnetic fields, twisting the gas in the form of a ring. Controlled ones can also be studied by twisting high-temperature plasma into a cord using magnetic fields.

An example of the effect of a magnetic field under natural conditions on ionized gas is the Aurora Borealis. This majestic spectacle is observed above the Arctic Circle at an altitude of 100 km above the surface of the earth. The mysterious colorful glow of the gas could only be explained in the 20th century. The earth's magnetic field near the poles cannot prevent the solar wind from entering the atmosphere. The most active radiation, directed along magnetic induction lines, causes ionization of the atmosphere.

Phenomena associated with charge movement

Historically, the main quantity characterizing the flow of current in a conductor is called current strength. It is interesting that this concept has nothing to do with force in physics. The current strength, the formula of which includes the charge flowing per unit time through the cross section of the conductor, has the form:

• I = q/t, where t is the flow time of charge q.

In fact, current is the amount of charge. Its unit of measurement is Ampere (A), as opposed to N.

Definition of work of force

The force exerted on a substance is accompanied by the performance of work. Work of force is a physical quantity, numerically equal to the product force on the displacement passed under its action, and the cosine of the angle between the directions of force and displacement.

The required work of force, the formula of which is A = FScosα, includes the magnitude of the force.

The action of a body is accompanied by a change in the speed of the body or deformation, which indicates simultaneous changes in energy. The work done by a force directly depends on the magnitude.

Nature, being a macroscopic manifestation of intermolecular interaction. In the simplest case of tension/compression of a body, the elastic force is directed opposite to the displacement of the particles of the body, perpendicular to the surface.

The force vector is opposite to the direction of deformation of the body (displacement of its molecules).

Hooke's law

In the simplest case of one-dimensional small elastic deformations, the formula for the elastic force has the form:

,

where is the rigidity of the body, is the magnitude of the deformation.

In its verbal formulation, Hooke's law sounds like this:

The elastic force that arises during deformation of a body is directly proportional to the elongation of the body and is directed opposite to the direction of movement of particles of the body relative to other particles during deformation.

Nonlinear deformations

As the amount of deformation increases, Hooke's law ceases to apply, and the elastic force begins to depend in a complex way on the amount of stretching or compression.

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See what “Elasticity force” is in other dictionaries: elastic force - elastic energy - Topics oil and gas industry Synonyms elastic energy EN elastic energy ...

See what “Elasticity force” is in other dictionaries: Technical Translator's Guide - tamprumo jėga statusas T sritis Standartizacija ir metrologija apibrėžtis Vidinės kūno jėgos, veikiančios prieš jį deformuojančias išorines jėgas ir iš dlies ar visiškai atkuriančios deformuotojo kūno (skys čių, dujų) tūrį ir (kietojo kūno) formą …

See what “Elasticity force” is in other dictionaries: Penkiakalbis aiškinamasis metrologijos terminų žodynas

- tamprumo jėga statusas T sritis fizika atitikmenys: engl. elastic force vok. elastische Kraft, f rus. elastic force, f; elastic force, f pranc. force élastique, f … Fizikos terminų žodynas FORCE - vector quantity is a measure of the mechanical impact on the body from other bodies, as well as the intensity of other physical forces. processes and fields. Forces are different: (1) C. Ampere, the force with which (see) acts on a conductor carrying current; direction of the force vector... ...

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The query "strength" redirects here; see also other meanings. Force Dimension LMT−2 SI units ... Wikipedia

The query "strength" redirects here; see also other meanings. Force Dimension LMT−2 SI units newton ... Wikipedia Noun, g., used. max. often Morphology: (no) what? strength, why? strength, (see) what? strength, what? by force, about what? about strength; pl. What? strength, (no) what? strength, what? strength, (see) what? strength, what? forces, about what? about forces 1. Strength is the ability of living things... ... Dictionary

Dmitrieva A branch of mechanics in which displacements, deformations and stresses that arise in elastic bodies at rest or in motion under the influence of load are studied. U. t. the basis for calculations of strength, deformability and stability in construction, business, aviation and... ...

A branch of mechanics in which displacements, deformations and stresses that arise in elastic bodies at rest or in motion under the influence of load are studied. U. t. theoretical. the basis for calculations of strength, deformability and stability in construction. in fact...... A branch of mechanics in which displacements, deformations and stresses that arise in elastic bodies at rest or in motion under the influence of load are studied. U. t. the basis for calculations of strength, deformability and stability in construction, business, aviation and... ...

A branch of mechanics (See Mechanics) that studies the displacements, deformations and stresses that arise in elastic bodies at rest or in motion under the influence of a load. U.t. theoretical basis calculations for strength, deformability and... ... Great Soviet Encyclopedia

Books

• Strength and deformation. Applied Theory of Elasticity Volume 2, A. Feppl. PREFACE BY THE EDITOR OF THE RUSSIAN TRANSLATION TO THE SECOND VOLUME. The publication of the second volume of the book by A. Feppl and L. Feppl was delayed so much that the initial assumptions about the placement of the series...

The more deformation a body is subjected to, the greater the elastic force generated in it. This means that deformation and elastic force are interrelated, and by changing one value one can judge the change in the other. Thus, knowing the deformation of a body, it is possible to calculate the elastic force arising in it. Or, knowing the elastic force, determine the degree of deformation of the body.

If you hang it from a spring different quantities weights of the same mass, then the more of them are suspended, the more the spring will stretch, that is, deform. The more a spring is stretched, the greater the elastic force generated in it. Moreover, experience shows that each subsequent suspended weight increases the length of the spring by the same amount.

So, for example, if the original length of the spring was 5 cm, and hanging one weight on it increased it by 1 cm (i.e., the spring became 6 cm long), then hanging two weights will increase it by 2 cm (the total length will be 7 cm ), and three - by 3 cm (the length of the spring will be 8 cm).

Even before experiment, it is known that weight and the elastic force arising under its action are directly proportional to each other. A multiple increase in weight will increase the elasticity strength by the same amount. Experience shows that deformation also depends on weight: a multiple increase in weight increases the changes in length by the same amount. This means that, by eliminating weight, it is possible to establish a directly proportional relationship between the elastic force and deformation.

If we denote the elongation of a spring as a result of its stretching as x or as ∆l (l 1 – l 0, where l 0 is the initial length, l 1 is the length of the stretched spring), then the dependence of the elastic force on stretching can be expressed by the following formula:

F control = kx or F control = k∆l, (∆l = l 1 – l 0 = x)

The formula uses the coefficient k. It shows the exact relationship between elastic force and elongation. After all, elongation by every centimeter can increase the elastic force of one spring by 0.5 N, the second by 1 N, and the third by 2 N. For the first spring, the formula will look like F control = 0.5x, for the second - F control = x, for the third - F control = 2x.

The coefficient k is called rigidity springs. The stiffer the spring, the more difficult it is to stretch it, and the more higher value will have k. And the larger k, the greater the elastic force (F control) will be with equal elongations (x) of different springs.

Stiffness depends on the material from which the spring is made, its shape and size.

The unit of measurement for hardness is N/m (newton per meter). Stiffness shows how many newtons (how much force) must be applied to the spring to stretch it 1 m. Or how many meters the spring will stretch if a force of 1 N is applied to stretch it. For example, a force of 1 N is applied to the spring, and it stretches by 1 cm (0.01 m). This means that its stiffness is 1 N / 0.01 m = 100 N/m.

Also, if you pay attention to the units of measurement, it will become clear why stiffness is measured in N/m. The elastic force, like any force, is measured in newtons, and the distance is measured in meters. To equalize the left and right sides of the equation F control = kx in units of measurement, you need to reduce the meters on the right side (that is, divide by them) and add newtons (that is, multiply by them).

The relationship between the elastic force and the deformation of an elastic body, described by the formula F control = kx, was discovered by the English scientist Robert Hooke in 1660, so this relationship bears his name and is called Hooke's law.

Elastic deformation is one when, after the cessation of forces, the body returns to its original state. There are bodies that are almost impossible to subject to elastic deformation, while for others it can be quite large. For example, placing a heavy object on a piece soft clay, you will change its shape, and this piece itself will not return to its original state. However, if you stretch the rubber band, it will return to its original size when you release it. It should be remembered that Hooke's law is applicable only for elastic deformations.

The formula F control = kx makes it possible to calculate the third from two known quantities. So, knowing the applied force and elongation, you can find out the rigidity of the body. Knowing the stiffness and elongation, find the elastic force. And knowing the elastic force and rigidity, calculate the change in length.

What is elastic force?

The elastic force is a force that arises through deformation of a body and is directed in the direction opposite to the movements of body particles during deformation.

For more clear example, to better understand what elastic force is, let’s take shining example from Everyday life. Imagine that in front of you is an ordinary clothesline on which you have hung wet laundry. If we hang wet laundry on a well-stretched horizontal rope, we will see how, under the weight of things, this rope begins to bend and stretch.

First, you and I hang one wet thing on a rope and see how it bends to the ground together with the rope, and then stops. Then we hang the next thing and see that the same action is repeated and the rope bends even more.

In this case, the conclusion suggests itself that as the force acting on the rope increases, deformation will occur until the forces opposing this deformation are equal to the weight of all things. And only after this the downward movement will stop.

It should be noted that the work of the elastic force is to maintain the integrity of objects on which we act with other objects. If the elastic forces are not able to cope with this, then the body is deformed irrevocably, that is, the rope may simply break.

And here a rhetorical question arises. At what moment did the elastic force arise? And it arises when we just begin to hang up our laundry, that is, at the moment of the initial impact on the body. And when the laundry is dry and we take it off, the elasticity disappears.

Types of deformations

Now we already know that the elastic force appears as a result of deformation.

Let's remember what deformation is? Deformation is a change in the volume or shape of a body under the influence of external forces.

And the reason for the occurrence of deformation is that different parts of the body do not move in the same way, but in different ways. With the same movement, the body would always have its original shape and size, that is, it would not be deformed.

Let's look at the question of what types of deformation we can observe.

Types of deformation can be divided according to the nature of the change in their shape.

In addition, deformation is divided into two types. In this case, the deformation can be elastic or plastic deformation.

If, for example, you take and stretch a spring, and then release it, then after such deformation the spring will restore its previous size and shape. This will be an example of elastic deformation.

That is, if we see that after the action on the body ceases, the deformation completely disappears, then such deformation is elastic.

Now let's give another example. Let's take a piece of plasticine and squeeze it or mold some kind of figure. You and I see that even after the action ceased, the plasticine did not change shape, that is, it remained deformed. This inelastic deformation is plastic.

During plastic deformation, it persists even when external forces cease to act on it.

This type of deformation is used in addition to modeling from clay or plasticine and in the technical processes of forging and stamping.

Exercise: Describe what types of deformation you see in the image?

Elastic force and Hooke's law

The magnitude of the elastic force also depends on the amount of deformation to which any body is subjected. Consequently, deformation and elastic force are closely related. If one quantity has undergone changes, it means that changes have appeared in the other.

Therefore, if we know the deformation of a body, then we can calculate the elastic force that has arisen in this body. Conversely, if we know the elastic force, we can easily determine the degree of deformation of the body.

When, for example, you take a spring and hang an equal mass of weights from it, you can see that with each subsequent suspended load, the spring stretches more and more. And you will notice that the more this spring is deformed, the greater the elastic force becomes.

And if you take into account the fact that the weights have the same mass, then hanging them one by one, you will notice that with each new hanging, the length of the spring increases by exactly the same amount.

To find the relationship between the elastic force and the deformation of an elastic body, you need to use the formula that was discovered by the famous English scientist Robert Guk.

The scientist established a simple connection between the increase in body length and the elastic force that was caused by this elongation.

In this formula, delta denotes the changes that occur to a quantity.

Hooke's law states that for small deformations, the elastic force is directly proportional to the elongation of the body.

That is, the greater the deformation appears, the great strength elasticity we can observe.

But it should also be noted that Hooke's law is valid only where elastic deformation is present.

The force of elasticity in nature

The force of elasticity plays a fairly significant role in nature. After all, only thanks to this force, the tissues of plants, animals and humans are able to withstand enormous loads without breaking or collapsing.

You have probably seen more than once how plants bend under a gust of wind or tree branches bend under the weight of snow, and as a result of the action of elasticity they return to their previous shape.

Also, each of you could observe how, under the pressure of a strong hurricane wind, tree branches were breaking. And we can observe such a result when the action of the wind force exceeds the elastic force of the tree itself.

All bodies on Earth are capable of withstanding force. atmospheric pressure only due to the force of elasticity. Inhabitants of deep reservoirs are able to withstand even greater loads. Therefore, we can come to the logical conclusion that only thanks to the force of elasticity, all living organisms in nature have the ability not only to endure mechanical loads, but also to maintain their shape intact.

Flocks of birds sitting on tree branches, bunches of grapes hanging on bushes, huge caps of snow on spruce paws - this is a clear demonstration of the forces of elasticity in nature.

Hooke's famous law applies in almost all areas of our lives. It is impossible to do without it, either in everyday life or in architecture. This law is used in the construction of houses and cars. Ego is even used in trading.

But, probably, not every one of you could imagine that the force of elasticity could be applied in the circus arena. Back in the century before last, the famous Franconi Circus performed an act called “Bomb Man.”

To do this, a huge cannon was installed in the circus arena, from which a man fired. The spectators were shocked by this number, as they did not suspect that the shot was fired not by powder gases, but by a spring. A powerful elastic spring was placed in the cannon barrel and after the command “fire!” a spring from the barrel threw the artist into the arena. Well, the roar, smoke and fire only enhanced the effect of this act and terrified the audience.

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