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You and I know that if a force acts on a body, then the body will move under the influence of this force. For example, a leaf falls to the ground because it is attracted by the Earth. But if a leaf falls on a bench, it does not continue to fall, and does not fall through the bench, but is at rest.

And if the leaf suddenly stops moving, it means that a force must have appeared that counteracts its movement. This force acts in the direction opposite to the attraction of the Earth, and is equal to it in magnitude. In physics, this force, which counteracts the force of gravity, is called the force of elasticity.

What is elastic force?

Puppy Antoshka loves to watch the birds.

For an example explaining what the force of elasticity is, let us also remember the birds and the rope. When the bird sits on the rope, the support, previously stretched horizontally, sags under the weight of the bird and slightly stretches. The bird first moves to the ground along with the rope, then stops. And this happens when another bird is added to the rope. And then another. That is, it is obvious that with an increase in the force of influence on the rope, it is deformed until the moment when the forces of counteracting this deformation become equal to the weight of all the birds. And then the downward movement stops.

When the suspension is stretched, the elastic force will be equal to the force of gravity, then the stretching stops.

In simple terms, the work of the elastic force is to maintain the integrity of objects that we act on by other objects. And if the force of elasticity does not cope, then the body is deformed irrevocably. The rope breaks under the abundance of snow, the handles of the bag break if it is overloaded with food, with large harvests, the branches of the apple tree break, and so on.

When does the force of elasticity arise? At the moment of the beginning of the impact on the body. When the bird sat on the rope. And disappears when the bird takes off. That is, when the impact stops. The point of application of the elastic force is the point at which the impact occurs.

Deformation

The elastic force arises only when the bodies are deformed. If the deformation of the body disappears, then the elastic force also disappears.

Deformations are of different types: tension, compression, shear, bending and torsion.

Stretching - we weigh the body on spring scales, or ordinary elastic band, which stretches under the weight of the body

Compression - we put a heavy object on the spring

Shift - the work of scissors or a saw, a loose chair, where the floor can be taken as the base, and the seat as the plane of application of the load.

Bend - our birds sat on a branch, a horizontal bar with students in a physical education lesson

Definition

The force that occurs as a result of the deformation of the body and trying to return it to its original state is called elastic force.

Most often it is denoted by $(\overline(F))_(upr)$. The elastic force appears only when the body is deformed and disappears if the deformation disappears. If, after removing the external load, the body completely restores its size and shape, then such a deformation is called elastic.

R. Hooke, a contemporary of I. Newton, established the dependence of the elastic force on the magnitude of the deformation. Hooke doubted the validity of his conclusions for a long time. In one of his books, he gave an encrypted formulation of his law. Which meant: "Ut tensio, sic vis" in Latin: what is the stretch, such is the strength.

Consider a spring subject to a tensile force ($\overline(F)$) that is directed vertically downwards (Fig. 1).

The force $\overline(F\ )$ is called the deforming force. Under the influence of a deforming force, the length of the spring increases. As a result, an elastic force ($(\overline(F))_u$) appears in the spring, balancing the force $\overline(F\ )$. If the deformation is small and elastic, then the elongation of the spring ($\Delta l$) is directly proportional to the deforming force:

\[\overline(F)=k\Delta l\left(1\right),\]

where in the coefficient of proportionality is called the stiffness of the spring (coefficient of elasticity) $k$.

Rigidity (as a property) is a characteristic of the elastic properties of a body that is being deformed. Rigidity is considered the ability of a body to resist an external force, the ability to maintain its geometric parameters. The greater the stiffness of the spring, the less it changes its length under the influence of a given force. The stiffness coefficient is the main characteristic of stiffness (as a property of a body).

The coefficient of spring stiffness depends on the material from which the spring is made and its geometric characteristics. For example, the stiffness coefficient of a coiled coil spring, which is wound from round wire and subjected to elastic deformation along its axis, can be calculated as:

where $G$ is the shear modulus (value depending on the material); $d$ - wire diameter; $d_p$ - spring coil diameter; $n$ is the number of coils of the spring.

The unit of measure for the stiffness coefficient in the International System of Units (SI) is the newton divided by the meter:

\[\left=\left[\frac(F_(upr\ ))(x)\right]=\frac(\left)(\left)=\frac(H)(m).\]

The stiffness coefficient is equal to the amount of force that must be applied to the spring to change its length per unit distance.

Spring stiffness formula

Let $N$ springs be connected in series. Then the stiffness of the entire joint is equal to:

\[\frac(1)(k)=\frac(1)(k_1)+\frac(1)(k_2)+\dots =\sum\limits^N_(\ i=1)(\frac(1) (k_i)\left(3\right),)\]

where $k_i$ is the stiffness of the $i-th$ spring.

When the springs are connected in series, the stiffness of the system is determined as:

Examples of problems with a solution

Example 1

Exercise. The spring in the absence of load has a length $l=0.01$ m and a stiffness equal to 10 $\frac(N)(m).\ $What will be the stiffness of the spring and its length if the force acting on the spring is $F$= 2 N ? Assume that the deformation of the spring is small and elastic.

Solution. The stiffness of the spring under elastic deformations is a constant value, which means that in our problem:

Under elastic deformations, Hooke's law is fulfilled:

From (1.2) we find the elongation of the spring:

\[\Delta l=\frac(F)(k)\left(1.3\right).\]

The length of the stretched spring is:

Calculate the new length of the spring:

Answer. 1) $k"=10\ \frac(Н)(m)$; 2) $l"=0.21$ m

Example 2

Exercise. Two springs with stiffnesses $k_1$ and $k_2$ are connected in series. What will be the elongation of the first spring (Fig. 3) if the length of the second spring is increased by $\Delta l_2$?

Solution. If the springs are connected in series, then the deforming force ($\overline(F)$) acting on each of the springs is the same, that is, it can be written for the first spring:

For the second spring we write:

If the left parts of expressions (2.1) and (2.2) are equal, then the right parts can also be equated:

From equality (2.3) we obtain the elongation of the first spring:

\[\Delta l_1=\frac(k_2\Delta l_2)(k_1).\]

Answer.$\Delta l_1=\frac(k_2\Delta l_2)(k_1)$

It is necessary to know the point of application and the direction of each force. It is important to be able to determine exactly what forces act on the body and in what direction. Force is denoted as , measured in Newtons. In order to distinguish between forces, they are designated as follows

Below are the main forces acting in nature. It is impossible to invent non-existent forces when solving problems!

There are many forces in nature. Here we consider the forces that are considered in the school physics course when studying dynamics. Other forces are also mentioned, which will be discussed in other sections.

Gravity

Every body on the planet is affected by the Earth's gravity. The force with which the Earth attracts each body is determined by the formula

The point of application is at the center of gravity of the body. Gravity always pointing vertically down.

Friction force

Let's get acquainted with the force of friction. This force arises when bodies move and two surfaces come into contact. The force arises as a result of the fact that the surfaces, when viewed under a microscope, are not smooth as they seem. The friction force is determined by the formula:

A force is applied at the point of contact between two surfaces. Directed in the direction opposite to the movement.

Support reaction force

Imagine a very heavy object lying on a table. The table bends under the weight of the object. But according to Newton's third law, the table acts on the object with exactly the same force as the object on the table. The force is directed opposite to the force with which the object presses on the table. That is up. This force is called the support reaction. The name of the force "speaks" react support. This force arises whenever there is an impact on the support. The nature of its occurrence at the molecular level. The object, as it were, deformed the usual position and connections of the molecules (inside the table), they, in turn, tend to return to their original state, "resist".

Absolutely any body, even a very light one (for example, a pencil lying on a table), deforms the support at the micro level. Therefore, a support reaction occurs.

There is no special formula for finding this force. They designate it with the letter, but this force is just a separate type of elastic force, so it can also be denoted as

The force is applied at the point of contact of the object with the support. Directed perpendicular to the support.

Since the body is represented as a material point, the force can be depicted from the center

Elastic force

This force arises as a result of deformation (changes in the initial state of matter). For example, when we stretch a spring, we increase the distance between the molecules of the spring material. When we compress the spring, we decrease it. When we twist or shift. In all these examples, a force arises that prevents deformation - the elastic force.

Hooke's Law

The elastic force is directed opposite to the deformation.

Since the body is represented as a material point, the force can be depicted from the center

When connected in series, for example, springs, the stiffness is calculated by the formula

When connected in parallel, the stiffness

Sample stiffness. Young's modulus.

Young's modulus characterizes the elastic properties of a substance. This is a constant value that depends only on the material, its physical state. Characterizes the ability of a material to resist tensile or compressive deformation. The value of Young's modulus is tabular.

Learn more about the properties of solids.

Body weight

Body weight is the force with which an object acts on a support. You say it's gravity! The confusion occurs in the following: indeed, often the weight of the body is equal to the force of gravity, but these forces are completely different. Gravity is the force that results from interaction with the Earth. Weight is the result of interaction with the support. The force of gravity is applied at the center of gravity of the object, while the weight is the force that is applied to the support (not to the object)!

There is no formula for determining weight. This force is denoted by the letter .

The support reaction force or elastic force arises in response to the impact of an object on a suspension or support, therefore the body weight is always numerically the same as the elastic force, but has the opposite direction.

The reaction force of the support and the weight are forces of the same nature, according to Newton's 3rd law they are equal and oppositely directed. Weight is a force that acts on a support, not on a body. The force of gravity acts on the body.

Body weight may not be equal to gravity. It can be either more or less, or it can be such that the weight is zero. This state is called weightlessness. Weightlessness is a state when an object does not interact with a support, for example, the state of flight: there is gravity, but the weight is zero!

It is possible to determine the direction of acceleration if you determine where the resultant force is directed

Note that weight is a force, measured in Newtons. How to correctly answer the question: "How much do you weigh"? We answer 50 kg, naming not weight, but our mass! In this example, our weight is equal to gravity, which is approximately 500N!

Overload- the ratio of weight to gravity

Strength of Archimedes

Force arises as a result of the interaction of a body with a liquid (gas), when it is immersed in a liquid (or gas). This force pushes the body out of the water (gas). Therefore, it is directed vertically upwards (pushes). Determined by the formula:

In the air, we neglect the force of Archimedes.

If the Archimedes force is equal to the force of gravity, the body floats. If the Archimedes force is greater, then it rises to the surface of the liquid, if it is less, it sinks.

electrical forces

There are forces of electrical origin. Occur in the presence of an electric charge. These forces, such as the Coulomb force, Ampère force, Lorentz force, are discussed in detail in the Electricity section.

Schematic designation of the forces acting on the body

Often the body is modeled by a material point. Therefore, in the diagrams, various points of application are transferred to one point - to the center, and the body is schematically depicted as a circle or rectangle.

In order to correctly designate the forces, it is necessary to list all the bodies with which the body under study interacts. Determine what happens as a result of interaction with each: friction, deformation, attraction, or maybe repulsion. Determine the type of force, correctly indicate the direction. Attention! The number of forces will coincide with the number of bodies with which the interaction takes place.

The main thing to remember

1) Forces and their nature;
2) Direction of forces;
3) Be able to identify the acting forces

Distinguish between external (dry) and internal (viscous) friction. External friction occurs between solid surfaces in contact, internal friction occurs between layers of liquid or gas during their relative motion. There are three types of external friction: static friction, sliding friction and rolling friction.

Rolling friction is determined by the formula

The resistance force arises when a body moves in a liquid or gas. The magnitude of the resistance force depends on the size and shape of the body, the speed of its movement and the properties of the liquid or gas. At low speeds, the resistance force is proportional to the speed of the body

At high speeds it is proportional to the square of the speed

Consider the mutual attraction of an object and the Earth. Between them, according to the law of gravity, a force arises

Now let's compare the law of gravity and the force of gravity

The value of free fall acceleration depends on the mass of the Earth and its radius! Thus, it is possible to calculate with what acceleration objects on the Moon or on any other planet will fall, using the mass and radius of that planet.

The distance from the center of the Earth to the poles is less than to the equator. Therefore, the acceleration of free fall at the equator is slightly less than at the poles. At the same time, it should be noted that the main reason for the dependence of the acceleration of free fall on the latitude of the area is the fact that the Earth rotates around its axis.

When moving away from the surface of the Earth, the force of gravity and the acceleration of free fall change inversely with the square of the distance to the center of the Earth.

Topics of the USE codifier: forces in mechanics, elastic force, Hooke's law.

As we know, on the right side of Newton's second law is the resultant (that is, the vector sum) of all forces applied to the body. Now we have to study the forces of interaction of bodies in mechanics. There are three types: elastic force, gravitational force and friction force. Let's start with elasticity.

Deformation.

Elastic forces arise during deformations of bodies. Deformation is a change in the shape and size of the body. Deformations include tension, compression, torsion, shear and bending.
Deformations are elastic and plastic. Elastic deformation completely disappears after the termination of the action of the external forces causing it, so that the body completely restores its shape and size. Plastic deformation is preserved (perhaps partially) after the removal of the external load, and the body no longer returns to its previous size and shape.

The particles of the body (molecules or atoms) interact with each other by attractive and repulsive forces of electromagnetic origin (these are the forces acting between the nuclei and electrons of neighboring atoms). The forces of interaction depend on the distances between the particles. If there is no deformation, then the forces of attraction are compensated by the forces of repulsion. During deformation, the distances between the particles change, and the balance of interaction forces is disturbed.

For example, when a rod is stretched, the distances between its particles increase, and attractive forces begin to prevail. On the contrary, when the rod is compressed, the distances between the particles decrease, and the repulsive forces begin to predominate. In any case, a force arises that is directed in the direction opposite to the deformation, and tends to restore the original configuration of the body.

Elastic force - this is the force that arises during the elastic deformation of the body and is directed in the direction opposite to the displacement of the particles of the body in the process of deformation. Elastic force:

1. acts between adjacent layers of a deformed body and is applied to each layer;
2. acts from the side of the deformed body on the body in contact with it, causing deformation, and is applied at the point of contact of these bodies perpendicular to their surfaces (a typical example is the support reaction force).

The forces arising from plastic deformations do not belong to the elastic forces. These forces do not depend on the magnitude of the deformation, but on the rate of its occurrence. The study of such forces
goes far beyond the curriculum.

In school physics, tensions of threads and cables, as well as tensions and compressions of springs and rods are considered. In all these cases, the elastic forces are directed along the axes of these bodies.

Hooke's law.

The deformation is called small if the change in body size is much less than its original size. At small deformations, the dependence of the elastic force on the magnitude of the deformation turns out to be linear.

Hooke's Law . The absolute value of the elastic force is directly proportional to the magnitude of the deformation. In particular, for a spring compressed or stretched by an amount , the elastic force is given by the formula:

(1)

where is the spring constant.

The stiffness coefficient depends not only on the material of the spring, but also on its shape and dimensions.

From formula (1) it follows that the graph of the dependence of the elastic force on (small) deformation is a straight line (Fig. 1):

Rice. 1. Hooke's law

The stiffness coefficient is about the angular coefficient in the straight line equation. Therefore, the equality is true:

where is the angle of inclination of this straight line to the abscissa axis. This equality is convenient to use when experimentally finding the quantity .

We emphasize once again that Hooke's law of the linear dependence of the elastic force on the magnitude of the deformation is valid only for small deformations of the body. When the deformations cease to be small, this dependence ceases to be linear and acquires a more complex form. Accordingly, the straight line in Fig. 1 is only a small initial part of the curvilinear graph describing the dependence on for all values ​​of strain .

Young's modulus.

In the particular case of small deformations rods there is a more detailed formula that refines the general form ( 1 ) of Hooke's law.

Namely, if the rod length and cross-sectional area stretch or compress
by the value , then the formula is valid for the elastic force:

Here - Young's modulus rod material. This coefficient no longer depends on the geometric dimensions of the rod. Young's moduli of various substances are given in reference tables.