DEFINITION

From the second equation:

Friction force:

Substituting the expression for the friction force into the first equation, we get:

When braking to a complete stop, the speed of the bus drops from value to zero, so the bus:

Equating the right-hand sides of the relations for accelerating a bus during emergency braking, we obtain:

where is the time until the bus stops completely:

Gravity acceleration m/s

Substituting the numerical values ​​of physical quantities into the formula, we calculate:

Answer The bus will stop in c.

EXAMPLE 2

Exercise	A small body was placed on an inclined plane making an angle with the horizon and released. What distance will the body travel in 3 s if the coefficient of friction between it and the surface is 0.2?
Solution	Let's make a drawing and indicate all the forces acting on the body. The body is acted upon by gravity, ground reaction force and friction force Let's choose a coordinate system, as shown in the figure, and project this vector equality on the coordinate axis: From the second equation:

The force of friction in terrestrial conditions accompanies any movement of bodies. It occurs when two bodies come into contact if these bodies move relative to each other. The friction force is always directed along the contact surface, in contrast to the elastic force, which is directed perpendicularly (Fig. 1, Fig. 2).

Rice. 1. Difference between the directions of friction force and elastic force

Rice. 2. The surface acts on the block, and the block acts on the surface

There are dry and non-dry types of friction. The dry type of friction occurs when solid bodies come into contact.

Let's consider a block lying on a horizontal surface (Fig. 3). It is acted upon by gravity and the ground reaction force. Let's act on the block with a small force , directed along the surface. If the block does not move, it means that the applied force is balanced by another force, which is called static friction force.

Rice. 3. Static friction force

Rest friction force () opposite in direction and equal in magnitude to the force tending to move a body parallel to the surface of its contact with another body.

As the “shearing” force increases, the block remains at rest, therefore, the static friction force also increases. With some sufficiently large force, the block will begin to move. This means that the static friction force cannot increase indefinitely - there is an upper limit beyond which it cannot be. The value of this limit is the maximum static friction force.

Let's apply pressure to the block using a dynamometer.

Rice. 4. Measuring friction force using a dynamometer

If the dynamometer acts on it with a force, then you can see that the maximum static friction force becomes greater with increasing mass of the block, that is, with increasing gravity and the support reaction force. If accurate measurements are taken, they will show that the maximum static friction force is directly proportional to the support reaction force:

where is the modulus of the maximum static friction force; N– ground reaction force (normal pressure); – coefficient of static friction (proportionality). Therefore, the maximum static friction force is directly proportional to the normal pressure force.

If you conduct an experiment with a dynamometer and a block of constant mass, while turning the block on different sides (changing the area of ​​contact with the table), you can see that the maximum static friction force does not change (Fig. 5). Consequently, the maximum static friction force does not depend on the contact area.

Rice. 5. The maximum value of the static friction force does not depend on the contact area

More accurate studies show that static friction is completely determined by the force applied to the body and the formula.

The force of static friction does not always prevent the movement of a body. For example, the static friction force acts on the sole of a shoe, imparting acceleration and allowing one to walk on the ground without slipping (Fig. 6).

Rice. 6. The force of static friction acting on the sole of a shoe

Another example: the static friction force acting on a car wheel allows you to start moving without slipping (Fig. 7).

Rice. 7. The force of static friction acting on a car wheel

In belt drives, the static friction force also acts (Fig. 8).

Rice. 8. The force of static friction in belt drives

If a body moves, then the friction force acting on it from the surface does not disappear; this type of friction is called sliding friction. Measurements show that the sliding friction force is almost equal in magnitude to the maximum static friction force (Fig. 9).

Rice. 9. Sliding friction force

The sliding friction force is always directed against the speed of movement of the body, that is, it impedes movement. Consequently, when a body moves only under the influence of friction, it imparts negative acceleration to it, that is, the speed of the body constantly decreases.

The magnitude of the sliding friction force is also proportional to the force of normal pressure.

where is the modulus of the sliding friction force; N– ground reaction force (normal pressure); – coefficient of sliding friction (proportionality).

Figure 10 shows a graph of the friction force versus the applied force. It shows two different areas. The first section, in which the friction force increases with increasing applied force, corresponds to static friction. The second section, in which the friction force does not depend on the external force, corresponds to sliding friction.

Rice. 10. Graph of friction force versus applied force

The sliding friction coefficient is approximately equal to the static friction coefficient. Typically, the sliding friction coefficient is less than unity. This means that the sliding friction force is less than the normal pressure force.

The sliding friction coefficient is a characteristic of two bodies rubbing against each other; it depends on what materials the bodies are made of and how well the surfaces are processed (smooth or rough).

The origin of static and sliding friction forces is determined by the fact that any surface at the microscopic level is not flat; microscopic inhomogeneities are always present on any surface (Fig. 11).

Rice. 11. Surfaces of bodies at the microscopic level

When two bodies in contact attempt to move relative to each other, these discontinuities engage and prevent this movement. With a small amount of applied force, this engagement is sufficient to prevent the bodies from moving, so static friction arises. When the external force exceeds the maximum static friction, the engagement of the roughness is not enough to hold the bodies, and they begin to move relative to each other, while the sliding friction force acts between the bodies.

This type of friction occurs when bodies roll over each other or when one body rolls on the surface of another. Rolling friction, like sliding friction, imparts negative acceleration to a body.

The occurrence of rolling friction force is due to the deformation of the rolling body and the supporting surface. Thus, a wheel located on a horizontal surface deforms the latter. When the wheel moves, the deformations do not have time to recover, so the wheel has to constantly climb a small hill, which causes a moment of force that slows down the rolling.

Rice. 12. The emergence of rolling friction force

The magnitude of the rolling friction force is, as a rule, many times less than the sliding friction force, all other things being equal. Due to this, rolling is a common type of movement in technology.

When a solid body moves in a liquid or gas, a resistance force acts on it from the medium. This force is directed against the speed of the body and slows down the movement (Fig. 13).

The main feature of the drag force is that it arises only in the presence of relative motion of the body and its environment. That is, the static friction force does not exist in liquids and gases. This leads to the fact that a person can move even a heavy barge on the water.

Rice. 13. Resistance force acting on a body when moving in a liquid or gas

The modulus of the resistance force depends on:

From the size of the body and its geometric shape (Fig. 14);

Conditions of the body surface (Fig. 15);

Properties of liquid or gas (Fig. 16);

Relative speed of the body and its environment (Fig. 17).

Rice. 14. Dependence of the resistance force modulus on the geometric shape

Rice. 15. Dependence of the resistance force modulus on the state of the body surface

Rice. 16. Dependence of the modulus of resistance force on the properties of liquid or gas

Rice. 17. Dependence of the resistance force modulus on the relative speed of the body and its environment

Figure 18 shows a graph of the resistance force versus body speed. At a relative speed equal to zero, the drag force does not act on the body. As the relative speed increases, the drag force grows slowly at first, and then the growth rate increases.

Rice. 18. Graph of resistance force versus body speed

At low relative speeds, the drag force is directly proportional to the magnitude of this speed:

where is the relative speed; – resistance coefficient, which depends on the type of viscous medium, shape and size of the body.

If the relative speed is large enough, then the drag force becomes proportional to the square of this speed.

where is the relative speed; – resistance coefficient.

The choice of formula for each specific case is determined empirically.

A body weighing 600 g moves uniformly along a horizontal surface (Fig. 19). At the same time, a force is applied to it, the magnitude of which is 1.2 N. Determine the value of the coefficient of friction between the body and the surface.

Target: Consolidate acquired knowledge about friction and types of friction.

Progress:

1. Study the theoretical part
2. Fill out table 1.
3. Solve the problem using the option from Table 2.
4. Answer security questions.

Table 1

table 2

	A skater moves along a smooth horizontal ice surface by inertia of 80 m. Determine the friction force and initial speed if the skater’s mass is 60 kg and the friction coefficient is 0.015
	A body weighing 4.9 kg lies on a horizontal plane. What force must be applied to the body in the horizontal direction to impart to it an acceleration of 0.5 m/s 2 with a friction coefficient of 0.1?
	A wooden block with a mass of 500 g lies on a horizontal table, which is driven by a load with a mass of 300 g suspended from the vertical end of a thread thrown through a block attached to the end of the table. The coefficient of friction when the block moves is 0.2. With what acceleration will the block move?

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

The laws of friction in liquids and gases differ from the laws of dry friction. Friction in 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.

Formulas for solution:

Where "k" is the friction coefficient, "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 – final speed V – initial speed

Algorithm for solving a typical problem:

1. Briefly write down the conditions of the problem.

2. We depict the condition graphically in an arbitrary reference system, 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, 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 coordinate zero.

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

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

6. Solve the equations in general form.

7. Substitute the quantities into the general solution and calculate.

8. Write down the answer.

Theoretical part
Friction is the resistance of bodies in contact to movement relative to each other. Friction is accompanied by every mechanical movement, and this circumstance has a significant 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 unevenness of the rubbing surfaces of bodies and the molecular interaction between them. If we go beyond mechanics, we should say that friction forces are of electromagnetic origin, like elastic forces. Each of the above two causes of friction manifests itself to varying degrees in different cases. For example, if the contacting surfaces of solid rubbing bodies have significant unevenness, then the main term in the friction force arising 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 movement of bodies relative to each other may not occur 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 component 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 static friction forces at the junction of two contacting bodies. If you look at the surface of bodies under a microscope, you will see micro-irregularities, 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 microroughness is similar. With this type of interaction, all horizontal components of the interaction force balance each other, and all 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” to the left of the pattern. The first body will press on the second. The intensity of this pressure is characterized by 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 force R (support reaction). Force R

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

After considering the interaction of bodies, two points should be noted.
1) When two bodies interact 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 Fst (Ftr in the case of motion).
2) Forces N and F Tp have the same nature (electromagnetic interaction); It couldn’t be otherwise, since these are components of the same force R.
The replacement of sliding friction with rolling friction is very important in modern technology 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 along a horizontal plane. Experience has established that the rolling friction force is calculated by the formula:

where F is the rolling friction force; k-coefficient of rolling friction; P is the pressure force of a 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 a rolling body, the less obstacle the uneven surface of the support poses to it.
Note that the rolling friction coefficient, in contrast to the sliding friction coefficient, 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 known as viscosity). External friction is a type of friction 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 the type of friction that occurs during mutual movement. Layers of liquid or gas between them generate tangential forces that prevent such movement.

External friction is divided into static friction (static friction) and kinematic friction. Static friction occurs between fixed solid bodies when they try to move one of them. Kinematic friction exists between mutually touching moving solid bodies. Kinematic friction, in turn, is divided 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 of an electromagnetic nature, i.e. Friction forces are based on the electrical forces of interaction between molecules. They depend on the speed of movement of bodies relative to each other.
There are 2 types of friction: dry and liquid.
1. Fluid 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 liquid (gas):
Ftr= k1v,
where k1 is the resistance coefficient, depending on the shape, size of the body and the environment. Determined empirically.

At high speeds:
Ftr= k2v,
where k2 is the resistance coefficient.
2. Dry friction is a force that arises when bodies come into direct contact, and is always directed along the contact surfaces of electromagnetic bodies precisely by breaking molecular bonds.
Rest friction.
Let's consider the interaction of a block with the surface of a table. The surface of the contacting bodies is not absolutely flat. The greatest force of attraction occurs between atoms of substances located at a minimum distance from each other, that is, on microscopic protrusions. The total force of attraction of atoms and bodies in contact is so significant that even under the influence of an external force applied to the block parallel to the surface of its contact with the table, the block remains at rest. This means that the block is acted upon by a force equal in magnitude to the external force, but in the opposite direction. This force is the static friction force. When the applied force reaches a maximum critical value sufficient to break the bonds between the protrusions, the block begins to slide along 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 magnitude to the support reaction force N.
The maximum static friction force is proportional to the normal pressure force:

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 coefficient of static friction.

The maximum value of the static friction force is proportional to the modulus of the force F d of the pressure produced by the body on the support.
The value of the static friction coefficient can be determined as follows. Let the body (flat block) lie on the inclined plane AB (Fig. 3). Three forces act on it: the force of gravity F, the static friction force Fп and the support reaction force N. The normal component Fп of the force of gravity represents the pressure force Fд produced by the body on the support, i.e.
FН=Fд. The tangential component Ft of gravity is a force tending to move a 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 it is clear that Ft = Fsin = mgsin; Fн=Fcos = mgcos.
we get
fн=sin/cos=tg.
By measuring the angle at which the body begins to slide, you can use the formula to calculate the value of the coefficient of static friction fп.

Rice. 3. Static friction.
Sliding friction

Sliding friction occurs when relative movement of contacting bodies occurs.
The sliding friction force is always directed in the direction opposite to the relative speed of the contacting bodies.
When one body begins to slide over the surface of another body, the bonds between the atoms (molecules) of the initially motionless bodies are broken, and friction decreases. With further relative motion of bodies, new connections between atoms are constantly formed. 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

Control questions

1. What is external and internal friction?
2. What kind of friction is called static friction?
3. What is dry and liquid friction?
4. What is the maximum static friction force?
5. How to determine the value of the static friction coefficient?

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

Friction forces are of an electromagnetic nature, just like elastic forces. The friction between the surfaces of two solids is called dry friction. The friction between a solid and a liquid or gaseous medium is called viscous friction.

Distinguish static friction, sliding friction And rolling friction.

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

The force of static friction 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 surface of contact, tending to move the object from its place.

The greater the force tending to move the body from its place, the greater the static friction force. However, for any two contacting bodies it has a certain 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- ground reaction force.

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

Sliding friction. If we apply a force to the body that exceeds the maximum force of static friction, the body will move and begin to move. Rest friction 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 = μN.

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

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

F tr.kach = μ kach N,

Where μ quality- rolling friction coefficient.

Because the μ quality<< μ , under the same loads, the rolling friction force is much less than the sliding friction force.

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

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

The resistance force of a medium appears only during the movement of a 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.

Sliding friction force- force that arises between contacting bodies during their relative motion.

It has been experimentally established that the friction force depends on the force of pressure of bodies on each other (support reaction force), on the materials of the rubbing surfaces, and on the speed of relative movement. Since no body is absolutely smooth, the friction force Not depends on the contact area, and the true contact area is much smaller than the observed one; In addition, by increasing the area, we reduce the specific pressure of bodies on each other.

The quantity characterizing the rubbing surfaces is called friction coefficient, and is most often denoted by the Latin letter k (\displaystyle k) or Greek letter μ (\displaystyle \mu ). It depends on the nature and quality of processing of the rubbing surfaces. In addition, the coefficient of friction depends on speed. However, most often this dependence is weakly expressed, and if greater measurement accuracy is not required, then k (\displaystyle k) can be considered constant. To a first approximation, the magnitude of the sliding friction force can be calculated using the formula:

F = k N (\displaystyle F=kN)

K (\displaystyle k)- sliding friction coefficient,

N (\displaystyle N)- the strength of the normal support reaction.

Friction forces are the tangential interactions between contacting bodies that arise during their relative movement.

Experiments with the movement of various bodies in contact (solids on solids, solids in liquid or gas, liquids in gas, etc.) with different states of the contact surfaces show that friction forces appear during the relative movement of the contacting bodies and are directed against the relative velocity vector tangentially to the contact surface. In this case, mechanical motion is always converted to a greater or lesser extent into other forms of motion of matter - most often into a thermal form of motion, and the interacting bodies are heated.

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✪ Lesson 67. Friction force

✪ Friction force

✪ Statics. Sliding friction. Lecture (28)

Subtitles

Types of sliding friction

If there is no liquid or gaseous layer (lubricant) between the bodies, then such friction is called dry. Otherwise, friction is called "fluid". A characteristic feature of dry friction is the presence of static friction.

According to the physics of interaction, sliding friction is usually divided into:

• Dry, when interacting solids are not separated by any additional layers/lubricants - a very rare case in practice. A characteristic feature of dry friction is the presence of a significant static friction force.
• Dry with dry lubricant (graphite powder)
• Liquid, during the interaction of bodies separated by a layer of liquid or gas (lubricant) of varying thickness - as a rule, occurs during rolling friction, when solid bodies are immersed in a liquid;
• Mixed, when the contact area contains areas of dry and liquid friction;
• Boundary, when the contact area may contain layers and areas of different nature (oxide films, liquid, etc.) is the most common case of sliding friction.

Friction can also be classified by its area. The frictional forces that arise during the relative movement of various bodies are called forces external friction. Friction forces also arise during relative movement of parts of the same body. Friction between layers of the same body is called internal friction.

Measurement

Due to the complexity of the physicochemical processes occurring in the zone of frictional interaction, friction processes fundamentally cannot be described using the methods of classical mechanics. Therefore, there is no exact formula for the friction coefficient. Its assessment is made on the basis of empirical data: since, according to Newton’s first law, a body moves uniformly and rectilinearly when an external force balances the friction force arising during movement, then to measure the friction force acting on the body it is enough to measure the force that must be applied to the body so that it moved without acceleration.