How to represent the force of friction. What is friction force, formulas

Target: To consolidate the knowledge gained about friction and the types of friction.

Working process:

1. Study the theoretical part
2. Complete table 1.
3. Solve the problem according to the option from table 2.
4. Answer security questions.

Table 1

table 2


	A skater drives on a smooth horizontal ice surface with an inertia of 80 m. Determine the friction force and initial speed if the mass of the skater is 60 kg and the coefficient of friction is 0.015
	A body of mass 4.9 kg lies on a horizontal plane. What force must be applied to the body in the horizontal direction to give it an acceleration of 0.5 m / s 2 with a friction coefficient of 0.1?
	A wooden block of mass 500 g rests on a horizontal table, which is set in motion by a weight of 300 g suspended from the vertical end of a thread thrown over a block fixed at the end of the table. The coefficient of friction during the movement of the bar is 0.2. With what acceleration will the block move?

Friction force is the force that occurs between the surfaces of contacting bodies. If there is no lubrication between the surfaces, then the friction is called dry. The dry friction force is directly proportional to the force that presses the surfaces against each other and is directed in the direction opposite to the possible movement. The coefficient of proportionality is called the coefficient of friction. The pressing force is perpendicular to the surface. It is called the normal support reaction.

The laws of friction in liquids and gases differ from the laws of dry friction. Friction in a liquid and gas depends on the speed of movement: at low speeds it is proportional to the square, and at high speeds it is proportional to the cube of the speed.

Solution formulas:

Where "k" is the coefficient of friction, "N" is the normal reaction of the support.

Newton's second law and equations of motion in vector form. F=ma

According to Newton's third law N = - mg

expression for speed

Equations of motion for uniformly accelerated kinematic motion

; 0 - V = a t where 0 is the final speed V is the initial speed

Algorithm for solving a typical problem:

1. Briefly write down the condition of the problem.

2. We depict the condition graphically in an arbitrary reference frame, indicating the forces acting on the body (point), including the normal reaction of the support and the friction force, the speed and acceleration of the body.

3. We correct and designate the reference system in the figure by introducing the origin of time and specifying the coordinate axes for forces and acceleration. It is better to direct one of the axes along the normal reaction of the support, and start counting the time at the moment the body (point) is at the coordinate zero.

4. We write in vector form Newton's second law and the equations of motion. The equations of motion and speed are the dependences of displacement (path) and speed on time.

5. We write in the same equations in scalar form: in projections on the coordinate axes. We write down the expression for the friction force.

6. We solve equations in a general form.

7. Substitute the values in the general solution, calculate.

8. Write down the answer.

Theoretical part
Friction is the resistance of bodies in contact to movement relative to each other. Friction accompanies every mechanical movement, and this circumstance has an essential consequence in modern technical progress.
The force of friction is the force of resistance to the movement of bodies in contact relative to each other. Friction is explained by two reasons: the roughness of the rubbing surfaces of bodies and the molecular interaction between them. If we go beyond the limits of mechanics, then it should be said that the forces of friction are of electromagnetic origin, as well as the forces of elasticity. Each of the above two causes of friction in different cases manifests itself to a different extent. For example, if the contacting surfaces of solid rubbing bodies have significant irregularities, then the main term in the friction force that arises here will be due precisely to this circumstance, i.e. unevenness, roughness of the surfaces of rubbing bodies. Bodies moving with friction relative to each other must touch the surfaces or move one in the environment of the other. The motion of bodies relative to each other may not arise due to the presence of friction if the driving force is less than the maximum static friction force. If the contacting surfaces of solid rubbing bodies are perfectly polished and smooth, then the main term of the friction force arising in this case will be determined by the molecular adhesion between the rubbing surfaces of the bodies.

Let us consider in more detail the process of the emergence of sliding and rest friction forces at the junction of two contacting bodies. If you look at the surfaces of bodies under a microscope, you will see microroughnesses, which we will depict in an enlarged form (Fig. 1, a). Let us consider the interaction of contacting bodies using the example of one pair of irregularities (ridge and trough) (Fig. 3, b). In the case when there is no force trying to cause movement, the nature of the interaction on both slopes of microroughnesses is similar. With this nature of the interaction, all the horizontal components of the interaction force balance each other, and all the vertical ones are summed up and make up the force N (support reaction) (Fig. 2, a).

A different picture of the interaction of bodies is obtained when a force begins to act on one of the bodies. In this case, the contact points will be predominantly on the “slopes” left in the figure. The first body will put pressure on the second. The intensity of this pressure is characterized by the force R. The second body, in accordance with Newton's third law, will act on the first body. The intensity of this action is characterized by the force R (support reaction). The force R

can be decomposed into components: the force N, directed perpendicular to the contact surface of the bodies, and the force Fsc, directed against the action of the force F (Fig. 2, b).

After considering the interaction of bodies, two points should be noted.
1) In the interaction of two bodies, in accordance with Newton's third law, two forces R and R" arise; for the convenience of taking it into account when solving problems, we decompose the force R into components N and Fsc (Ftr in the case of motion).
2) The forces N and F Tp are of the same nature (electromagnetic interaction); it could not be otherwise, since these are components of the same force R.
In modern technology, the replacement of sliding friction by rolling friction is of great importance in order to reduce the harmful effects of friction forces. The rolling friction force is defined as the force required for uniform rectilinear rolling of a body on a horizontal plane. It has been established by experience that the rolling friction force is calculated by the formula:

where F is the rolling friction force; k is the coefficient of rolling friction; P is the pressure force of the rolling body on the support and R is the radius of the rolling body.

From practice it is obvious, from the formula it is clear that the larger the radius of the rolling body, the less obstacle the unevenness of the support surface renders to it.
Note that the coefficient of rolling friction, in contrast to the coefficient of sliding friction, is a named value and is expressed in units of length - meters.
Sliding friction is replaced by rolling friction, in necessary and possible cases, by replacing plain bearings with rolling bearings.

There is external and internal friction (otherwise called viscosity). This type of friction is called external, in which forces arise at the points of contact of solid bodies that impede the mutual movement of the bodies and are directed tangentially to their surfaces.

Internal friction (viscosity) is a type of friction, consisting in the fact that with mutual displacement. Layers of liquid or gas between them there are tangential forces that prevent such a movement.

External friction is divided into rest friction (static friction) and kinematic friction. Friction of rest arises between fixed solid bodies when any of them are trying to move. Kinematic friction exists between mutually touching moving rigid bodies. Kinematic friction, in turn, is subdivided into sliding friction and rolling friction.

Friction forces play an important role in human life. In some cases he uses them, and in others he fights them. Friction forces are electromagnetic in nature.
Types of friction forces.
Friction forces are electromagnetic in nature, i.e. friction forces are based on the electric forces of interaction of molecules. They depend on the speed of movement of bodies relative to each other.
There are 2 types of friction: dry and liquid.
1. Liquid friction is a force that arises when a solid body moves in a liquid or gas, or when one layer of liquid (gas) moves relative to another and slows down this movement.

In liquids and gases, there is no static friction force.
At low speeds in a liquid (gas):
Ftr= k1v,
where k1 is the drag coefficient, depending on the shape, size of the body and on the light in the medium. Determined by experience.

At high speeds:
Ftr= k2v,
where k2 is the drag coefficient.
2. Dry friction is a force arising from direct contact of bodies, and is always directed along the contact surfaces of electromagnetic bodies precisely by breaking molecular bonds.
Friction of rest.
Consider the interaction of the bar with the surface of the table. The surface of the bodies in contact is not absolutely even. The greatest force of attraction occurs between atoms of substances that are at a minimum distance from each other, that is, on microscopic protrusions. The total force of attraction of the atoms of the bodies in contact is so significant that even under the action of an external force applied to the bar parallel to the surface of its contact with the table, the bar remains at rest. This means that a force acting on the bar is equal in absolute value to the external force, but oppositely directed. This force is the static friction force. When the applied force reaches the maximum critical value sufficient to break the bonds between the protrusions, the bar begins to slide on the table. The maximum static friction force does not depend on the surface contact area. According to Newton's third law, the normal pressure force is equal in absolute value to the support reaction force N.
The maximum static friction force is proportional to the force of normal pressure:

where μ is the static friction coefficient.

The coefficient of static friction depends on the nature of the surface treatment and on the combination of materials that make up the contacting bodies. High-quality processing of smooth contact surfaces leads to an increase in the number of attracted atoms and, accordingly, to an increase in the static friction coefficient.

The maximum value of the static friction force is proportional to the modulus of force F d of the pressure exerted by the body on the support.
The value of the static friction coefficient can be determined as follows. Let the body (flat bar) lie on an inclined plane AB (Fig. 3). Three forces act on it: gravity F, static friction force Fp and support reaction force N. The normal component Fp of gravity is the pressure force Fd produced by the body on the support, i.e.
FН=Fд. The tangential component Ft of gravity is the force tending to move the body down an inclined plane.
At small angles of inclination a, the force Ft is balanced by the static friction force Fp and the body is at rest on the inclined plane (the support reaction force N according to Newton's third law is equal in magnitude and opposite in direction to the force Fd, i.e., it balances it).
We will increase the angle of inclination a until the body begins to slide down the inclined plane. In this moment
Fт=FпmaxFrom fig. 3 shows that Ft=Fsin = mgsin; Fn \u003d Fcos \u003d mgcos.
we get
fн=sin/cos=tg.
Having measured the angle at which the sliding of the body begins, it is possible to calculate the value of the coefficient of static friction fp by the formula.

Rice. 3. Friction of rest.
sliding friction

Sliding friction occurs when the relative movement of the contacting bodies.
The force of sliding friction is always directed in the direction opposite to the relative speed of the bodies in contact.
When one body begins to slide over the surface of another body, the bonds between the atoms (molecules) of the initially immobile bodies are broken, and friction decreases. With further relative motion of bodies, new bonds are constantly formed between atoms. In this case, the sliding friction force remains constant, slightly less than the static friction force. Like the maximum static friction force, the sliding friction force is proportional to the normal pressure force and, therefore, to the support reaction force:
, where is the coefficient of sliding friction (), depending on the properties of the contacting surfaces.

Rice. 3. Sliding friction

test questions

What is external and internal friction?
What type of friction is static friction?
what is dry and liquid friction?
What is the maximum static friction force?
How to determine the value of the coefficient of static friction?

Definition 1

The friction force is the force that appears at the moment of contact between two bodies and prevents their relative movement.

The main reason that provokes friction lies in the roughness of the rubbing surfaces and the molecular interaction of these surfaces. The friction force depends on the material of the contacting surfaces and on the force of their mutual pressing.

The concept of friction force

Based on simple friction models (based on Coulomb's law), the friction force will be considered directly proportional to the degree of normal reaction of the contacting and rubbing surfaces. If considered as a whole, then the processes of the friction force cannot be described only by simple models of classical mechanics, which is explained by the complexity of the reactions in the zone of interaction of rubbing bodies.

Friction forces, like elastic forces, have an electromagnetic nature. Their occurrence becomes possible due to the interaction between the molecules and atoms of the bodies that are in contact.

Remark 1

Friction forces differ from elastic and gravitational forces by the fact that they depend not only on the configuration of the bodies (on their relative position), but also on the relative velocities of their interaction.

Varieties of friction force

Provided that there is a relative motion of two bodies in contact with each other, the friction forces arising in such a process are divided into the following types:

Sliding friction (represents the force arising as a result of the translational movement of one of the interacting bodies relative to the second and acting on this body in a direction that will be opposite to the direction of sliding).
Rolling friction (represents the moment of forces that can occur under the conditions of the rolling process of one of the two bodies in contact with the other).
Friction at rest (it is considered a force that arises between two interacting bodies, while it becomes a serious obstacle to the occurrence of relative motion. Such a force is overcome in order to set these contacting bodies in motion relative to each other. This type of friction appears during microdisplacements (for example, during deformation ) of the contacting bodies With an increase in effort, an increase in the friction force will also begin.
Spinning friction (is the moment of force that occurs between the contacting bodies under the conditions of rotation of one of them in relation to the other and directed against rotation). It is determined by the formula: $M=pN$, where $N$ is the normal pressure, $p$ is the spinning friction coefficient, which has the dimension of length.

It was experimentally established that the friction force is independent of the surface area along which the bodies are in contact, and proportional to the normal pressure force with which one body will act on the second.

Definition 2

The constant value represents the coefficient of friction, while depending on the nature and condition of the rubbing surfaces.

In certain situations, friction is useful. Examples can be given with the impossibility of human walking (in the absence of friction) and the movement of vehicles. At the same time, friction can also have a detrimental effect. So, it provokes wear of the contacting parts of the mechanisms, additional fuel consumption for vehicles. Various lubricants (air or liquid cushions) serve as a means of countering this. Another effective way is to replace sliding by rolling.

Basic calculation formulas for determining the friction force

The calculation formula for the sliding friction force will look like this:

$m$-proportionality coefficient (sliding friction),
$P$ is the vertical (normal) pressure force.

The sliding friction force is one of the forces controlling the movement, and its formula is written using the reaction force of the support. Based on the operation of Newton's third law, the forces of normal pressure, as well as the reaction of the support, are equal in magnitude and opposite in direction:

Before determining the friction force, the formula of which will be written as follows: $F=mN$, the reaction force is determined.

Remark 2

The drag coefficient during the sliding process is introduced experimentally for rubbing surfaces, while it will depend on the material and the quality of processing.

The maximum force of static friction is determined similarly to the force of sliding friction. This is important for solving problems of determining the strength of the driving resistance. An example can be given with a book moved by a hand pressed against it. So, the sliding of this book will be carried out under the influence of the rest resistance force between the book and the hand. In this case, the amount of resistance will depend on the indicator of the force of vertical pressure on the book.

The fact that the friction force is proportional to the square of the corresponding speed will be interesting, and its formula will begin to change, depending on the speed of movement of the interacting bodies. This force can be attributed to the force of viscous resistance in a liquid.

Depending on the speed of movement, the resistance force will determine the speed of movement, the shape of the moving body or the viscosity of the fluid. The movement in oil and water of the same body is accompanied by resistance of different magnitude. For low speeds it looks like this:

$k$ – coefficient of proportionality, depending on the linear dimensions of the body and the properties of the medium,
$v$ is the speed of the body.

Everyone knows how difficult it is to move heavy objects on any surface. This is due to the fact that the surface of a solid body is not perfectly smooth and contains a lot of notches (they have different sizes, which decrease during grinding). When two bodies come into contact, the notches interlock. Let a small force (F) be applied to one of the bodies, directed tangentially to the contacting surfaces. Under the influence of this force, the notches will deform (bend). Therefore, there will be an elastic force directed along the contacting surfaces. The elastic force acting on the body, to which the force F is applied, compensates for it and the body will remain at rest.

static friction force – force arising at the boundary of contiguous bodies in the absence of their relative motion.

The static friction force is directed tangentially to the surface of the bodies in contact (Fig. 10) in the direction opposite to the force F, and is equal to it in magnitude: Ftr = - F.

With an increase in the force modulus F, the bending of the hooked notches will increase and, in the end, they will begin to break and the body will begin to move.

sliding friction force – is the force that occurs at the boundary of contacting bodies during their relative motion.

The sliding friction force vector is directed opposite to the velocity vector of the body relative to the surface on which it slides.

A body sliding on a solid surface is pressed against it by the force of gravity P directed along the normal. As a result, the surface sags and an elastic force N appears (normal pressure force or support reaction), which compensates for the pressing force P (N = - P).

The greater the force N, the deeper the engagement of the notches and the more difficult it is to break them. Experience shows that the modulus of the sliding friction force is proportional to the force of normal pressure:

The dimensionless coefficient μ is called the coefficient of sliding friction. It depends on the materials of the contacting surfaces and the degree of their grinding. For example, when skiing, the coefficient of friction depends on the quality of the lubricant (modern expensive lubricants), the surface of the ski track (soft, loose, compacted, icy), one or another state of snow depending on temperature and air humidity, etc. A large number of variable factors makes itself coefficient is not constant. If the coefficient of friction lies between 0.045 - 0.055, the slip is considered good.

The table shows the values of the coefficient of sliding friction for various contacting bodies.

Coefficients of sliding friction for various cases

The role of the friction force in many cases is positive. It is thanks to this force that the movement of man, animals and land transport is possible. So, when walking, a person, tensing the muscles of the supporting leg, pushes off the ground, trying to move the sole back. This is prevented by the static friction force directed in the opposite direction - forward (Fig. 11).

Over 300 years ago. The question is not the most difficult, but it will take a little attention and patience to understand it.

A special section of mechanics is devoted to the study of the friction force - the so-called mechanics of frictional interaction (or - tribology).

The force of friction is the force with which bodies in contact and moving relative to each other interact with each other. It is the force of friction that prevents the free movement of contacting bodies.

Types of Friction and Friction Forces

Where does the static friction force come from?

If we look at the surface of the floor and the legs of the cabinet under a microscope, we will find multiple microscopic bumps of unimaginable shapes.

When the bodies rest on each other, the tubercles engage with each other, due to which the bodies remain in an immobilized state.

The impact on one of the bodies or on both bodies at once to move them relative to each other will lead to deformation of the tubercles, which will cause the electromagnetic repulsion of molecules, which underlies the static friction force.

If physical efforts are applied smoothly, up to a certain critical moment, the static friction force will be equal in absolute value to the force with which we are trying to move the cabinet.

sliding friction force

At the moment when the cabinet still moves, the static friction force will reach its maximum value.

At this moment, the tubercles are destroyed and, as a result, the cabinet begins slide.

Photo 1. Wheels and other devices are used to reduce the force of sliding friction.

A new type of friction force arises - sliding friction force. This force arises from the interaction of surfaces sliding on each other.

This force is manifested at the moment of physical movement (sliding) of the legs of the cabinet on the floor or when the skate of a hockey player or skater slides on the surface.

If we translate what is happening to the "hillocks", when sliding, there is a break in the bonds between the molecules concentrated in different hillocks.

When objects are stationary - that is, when the force of static friction is acting - such discontinuities do not occur.

"Model of hillocks" is conditional. It is designed to present complex things in simple language.

The same processes can be explained by deeper scientific terms, the understanding of which will require special training from the reader.

The simplest physical laws related to the force of friction

The answer to the question, what is the force of friction, can be obtained not only by studying theoretical positions, but also by solving practical problems.

To solve problems related to the calculation of the values of the friction force, we need some scientific facts characterizing the friction force.

For example, the vector of the sliding friction force applied to the body from the side of the sliding surface is always directed in the opposite direction from the direction of the object's velocity vector.

If the direction of velocity changes, the direction of the sliding friction force will also change. The dependence of the friction force on velocity is an important distinguishing feature inherent in this force (which, for example, is not present in the force of gravity or the force of elasticity).

The simplest model of dry friction is characterized by the action of the following laws:

. The sliding friction force is equal to the maximum value of the static friction force.

. The coefficient of friction does not depend on the area of the interacting surfaces, nor on the speed of the interacting objects relative to each other.

. There is a directly proportional relationship between the reaction force of the support and the absolute value of the sliding friction force, calculated by the formula: f = µN.

The coefficient of proportionality µ is called coefficient of friction.

Physicists have calculated friction coefficients for tens of thousands of pairs of materials.

For example, static friction coefficient for the pair "rubber - dry asphalt" is 0.95, and sliding friction coefficient for the same pair varies from 0.5 to 0.8.

By changing the properties of interacting objects, it is possible to influence the magnitude of the friction force that occurs during their interaction.

For example, improving the external shape of racing cars or the tread pattern of the tires used allows you to increase their speed by reducing the force of sliding friction.

Friction occurs when bodies are in direct contact, preventing their relative motion, and is always directed along the contact surface.

Friction forces are electromagnetic in nature, as are elastic forces. The friction between the surfaces of two solid bodies is called dry friction. Friction between a solid body and a liquid or gaseous medium is called viscous friction.

Distinguish static friction, sliding friction and rolling friction.

Friction of rest- occurs not only when one surface slides over another, but also when trying to cause this sliding. Friction at rest keeps the loads on the moving conveyor belt from slipping, keeps nails driven into the board, etc.

The static friction force is a force that prevents the occurrence of movement of one body relative to another, always directed against a force applied from the outside parallel to the contact surface, seeking to move the object from its place.

The greater the force tending to move the body, the greater the static friction force. However, for any two bodies in contact, it has some maximum value (F tr.p.) max, more than which it cannot be, and which does not depend on the area of contact of the surfaces:

(F tr.p.) max = μ p N,

where μ p- static friction coefficient, N- support reaction force.

The maximum static friction force depends on the materials of the bodies and on the quality of the processing of the contacting surfaces.

Sliding friction. If we apply a force to the body that exceeds the maximum static friction force, the body will move and begin to move. Friction at rest will be replaced by sliding friction.

The sliding friction force is also proportional to the normal pressure force and the support reaction force:

F tr \u003d μN.

rolling friction. If the body does not slide on the surface of another body, but, like a wheel, rolls, then the friction that occurs at the point of their contact is called rolling friction. When the wheel rolls along the roadbed, it is constantly pressed into it, so there is always a bump in front of it, which must be overcome. This is what causes rolling friction. Rolling friction is less, the harder the road.

The rolling friction force is also proportional to the support reaction force:

F tr.qual = μ qual N,

where μ quality- coefficient of rolling friction.

Insofar as μ quality<< μ , at the same load, the rolling friction force is much less than the sliding friction force.

The causes of the friction force are the roughness of the surfaces of the contacting bodies and the intermolecular attraction at the points of contact of the rubbing bodies. In the first case, seemingly smooth surfaces actually have microscopic bumps that, when sliding, catch on each other and interfere with movement. In the second case, attraction is manifested even with well-polished surfaces.

A solid moving in a liquid or gas is affected by medium resistance force, directed against the speed of the body relative to the environment and slowing down the movement.

The resistance force of the medium appears only during the movement of the body in this medium. There is nothing like the static friction force here. On the contrary, objects in water are much easier to move than on a hard surface.