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 over 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?
	On a horizontal table lies a wooden block of mass 500 g, which is set in motion by a weight of 300 g suspended on 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 pressing 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 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” 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

1. What is external and internal friction?
2. What type of friction is 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 coefficient of static friction?

1. In order for a body (a book lying on a table, a box standing on the floor, etc.) to move, a force must be applied to it. In this case, with a gradual increase in force, the body will remain at rest for some time, and at a certain value of the applied force, it will begin to move. The force generated by direct contact between two bodies is called friction force. This force is always directed along the contact surface.

A book lying on a table is affected in the vertical plane by the forces of gravity ​\(\vec(F)_t \) that balance each other, and elasticity (reaction of the support), in the horizontal plane the force applied to it \(\vec(F ) \) . Since the book remains motionless for some time, this means that another force acts in the horizontal plane, equal in absolute value to the force \(\vec(F) \) and directed in the opposite direction to it. This force is static friction force. The greater the force applied to the body (while it is not moving), the greater the static friction force.

The static friction force is equal in absolute value and directed oppositely to the force applied to a body at rest parallel to the surface of its contact with another body.

2. At a certain value of the force applied to the body ​\(\vec(F) \) ​ it starts to move. At the moment the bar starts moving, the static friction force has a maximum value \(\vec(F)_(tr.max) \) , which is equal to the sliding friction force. The greater the pressure force of the body on the contact surface of the bodies perpendicular to this surface (normal pressure force), the greater the maximum static friction force, i.e. ​\((F_(tr))_(max)=\mu N \) , where ​\(\mu \) ​ is the coefficient of friction.

The maximum static friction force is directly proportional to the force of normal pressure.

The static friction force prevents the body from starting to move. On the other hand, the force of static friction can be the cause of the acceleration of the motion of the body. So, when walking, the static friction force \\ (F_ (tr) \) , acting on the sole, tells us the acceleration. The force ​\(F \) ​, equal in absolute value to the static friction force and directed in the opposite direction, imparts acceleration to the support.

3. When a body moves, a friction force will also act on it, it is called sliding friction force. The force of sliding friction is the force acting when one body slides over the surface of another and is directed in the direction opposite to the movement of the body. It is slightly less than the maximum static friction force and is directed in the direction opposite to the movement of the body relative to the body in contact with it.

The sliding friction force is directly proportional to the normal pressure force: \((F_(tr))_(max)=\mu N \) . In this formula ​ \ (N \) ​ is the force of normal pressure, i.e. force acting perpendicular to the surface of the contacting bodies; ​\(\mu \) ​ - coefficient of friction. The coefficient of friction characterizes the surfaces of contacting bodies. It is determined experimentally and is given in tables.

Friction is caused by uneven surfaces. In the case of well-polished surfaces, the molecules located on the surfaces of bodies are located close to each other, and the forces of intermolecular interaction are quite large.

4. If a body rolls on the surface of another body, then the force of friction also acts on it. This is - rolling friction force. It is directly proportional to the force of normal pressure (support reaction) ​ \ (N \) ​ and inversely proportional to the radius ​ \ (R \) ​ of the rolling body: \(F_(set)=\mu\frac(N)(R) \)​, where ​\(\mu \) ​ is the coefficient of rolling friction.

5. There are a number of practical problems in which it is necessary to take into account the friction force. Of particular importance are the tasks associated with traffic. It is well known that in order to avoid accidents, a certain distance between cars should be maintained; in rainy weather or in icy conditions, it should be greater than in dry weather.

The distance that a car travels when braking to a complete stop is called the stopping distance. The braking distance is calculated using the formula ​\(s=\frac(v^2)(2a) \) .

Part 1

1. When measuring the coefficient of friction, the bar was moved along the horizontal surface of the table and the value of the friction force was obtained ​\(F_1 \) . Then a load was placed on the bar, the mass of which is 2 times greater than the mass of the bar, and the value of the friction force \(F_2\) was obtained. In this case, the friction force \ (F_2 \)

1) is equal to \(F_1 \)
2) 2 times more \(F_1 \)
3) 3 times more \(F_1 \)
4) 2 times less \ (F_1 \)

2. The table shows the results of measurements of the friction force and the normal pressure force in the study of the relationship between these quantities.

Regularity ​\(\mu=N/F_(tr) \) ​ is fulfilled for normal pressure force

1) only 0.4 N to 2.0 N
2) only 0.4 N to 3 N
3) only 0.4 N to 4.5 N
4) only 2.0 N to 4.5 N

3. When measuring the friction force, the bar was moved along the horizontal surface of the table and the value of the friction force \(F_1 \) was obtained. Then the bar was moved, putting it on the table with a face, the area of ​​which is 2 times larger than in the first case, and the value of the friction force \(F_2\) was obtained. Friction force \(F_2 \)

1) is equal to \(F_1 \)
2) 2 times more \(F_1 \)
3) 2 times less \ (F_1 \)
4) 4 times less \ (F_1 \)

4. Two wooden blocks of mass ​\(m_1 \) ​ and \(m_2 \) slide along a horizontal, identically treated table surface. The sliding friction force \(F_1 \) and \(F_1 \) acts on the bars, respectively. It is known that ​\(F_2=2F_1 \) . Therefore, ​\(m_1 \) ​

1) \(m_1\)
2) \(2m_2\)
3)\(m_2/2\)
4) the answer depends on the value of the coefficient of friction

5. The figure shows graphs of the dependence of the friction force on the force of normal pressure. Compare the friction coefficient values.

1) ​\(\mu_2=\mu_1 \) ​
2) ​\(\mu_2>\mu_1 \) ​
3) \(\mu_2<\mu_1 \)
4) \(\mu_2>>\mu_1 \)

6. The student performed an experiment to measure the friction force acting on two bodies moving along horizontal surfaces. The mass of the first body ​\(m_1 \) , the mass of the second body ​\(m_2 \) ​, and ​\(m_1 =2m_2 \) . He got the results presented in the figure in the form of a diagram. What conclusion can be drawn from the analysis of the chart?

1) normal pressure force ​\(N_2=2N_1 \) ​
2) normal pressure force \ (N_1 \u003d N_2 \)
3) coefficient of friction ​\(\mu_1=\mu_2 \) ​
4) coefficient of friction ​\(\mu_2=2\mu_1 \) ​

7. Two cars of the same mass are moving one on an asphalt road, and the other on a dirt road. The diagram shows the friction force values ​​for these vehicles. Compare the friction coefficient values ​​(​\(\mu_1 \) ​ and \(\mu_2 \) ).

1) ​\(\mu_2=0.3\mu_1 \) ​
2) \(\mu_2=\mu_1 \)
3) \(\mu_2=1.5\mu_1\)
4) \(\mu_2=3\mu_1\)

8. The figure shows a graph of the dependence of the friction force on the force of normal pressure. What is the coefficient of friction?

1) 0,5
2) 0,2
3) 2
4) 5

9. A sled weighing 3 kg slides along a horizontal road. The sliding friction force of their runners on the road is 6 N. What is the coefficient of sliding friction of the runners on the road?

1) 0,2
2) 0,5
3) 2
4) 5

10. When a body weighing 40 kg moves along a horizontal surface, a sliding friction force of 10 N acts. What will the sliding friction force become when the body mass decreases by 5 times?

1) 1 N
2) 2 N
3) 4 N
4) 5 N

11. Establish a correspondence between the physical quantity (left column) and the nature of its change (right column) with an increase in the mass of the bar moving along the table. In your answer, write down the numbers of the selected answers in a row.

PHYSICAL QUANTITY
A. Force of friction
B. Coefficient of friction
B. Normal pressure force

CHARACTER OF VALUE CHANGE
1) decreases
2) increases
3) does not change

12. From the statements below, choose two correct ones and write down their numbers in the table.

1) The static friction force is greater than the force applied to the body.
2) The rolling friction force is less than the sliding friction force for the same body mass.
3) The coefficient of sliding friction is directly proportional to the force of normal pressure.
4) The force of friction depends on the area of ​​support of a moving body with its surface equally processed.
5) The maximum static friction force is equal to the sliding friction force.

Part 2

13. The car, having a speed of 72 km / s, starts to slow down with the engine off and travels a distance of 100 m. What is the acceleration of the car and the braking time?

Answers

Definition

By the force of friction called the force that occurs during the relative movement (or attempt to move) of bodies and is the result of resistance to the movement of the environment or other bodies.

Friction forces arise when bodies (or their parts) in contact move relative to each other. In this case, the friction that appears during the relative movement of the contacting bodies is called external. The friction that occurs between the parts of one solid body (gas, liquid) is called internal.

The friction force is a vector that has a direction along the tangent to the rubbing surfaces (layers). In this case, this force is directed towards counteracting the relative displacement of these surfaces (layers). So, if two layers of liquid move over each other, while moving at different speeds, then the force that is applied to the layer moving at a higher speed has a direction that is opposite to the movement. The force that acts on the layer that moves at a lower speed is directed along the motion.

Types of friction

The friction that occurs between the surfaces of solids is called dry. It occurs not only when sliding surfaces, but also when trying to cause movement of surfaces. This creates a static friction force. External friction that appears between moving bodies is called kinematic.

The laws of dry friction indicate that the maximum force of static friction and the force of sliding friction do not depend on the area of ​​the contact surfaces of the contacting bodies subject to friction. These forces are proportional to the modulus of the normal pressure force (N), which presses the rubbing surfaces:

where is the dimensionless coefficient of friction (at rest or sliding). This coefficient depends on the nature and condition of the surfaces of rubbing bodies, for example, on the presence of roughness. If friction occurs as a result of sliding, then the coefficient of friction is a function of speed. Quite often, instead of the coefficient of friction, the angle of friction is used, which is equal to:

The angle is equal to the minimum angle of inclination of the plane to the horizon, at which a body lying on this plane begins to slide under the influence of gravity.

The law of friction is considered more accurate, which takes into account the forces of attraction between the molecules of bodies that are subjected to friction:

where S is the total contact area of ​​the bodies, p 0 is the additional pressure caused by the forces of molecular attraction, is the true coefficient of friction.

The friction between a solid body and a liquid (or gas) is called viscous (liquid). The force of viscous friction becomes equal to zero if the velocity of the relative motion of the bodies vanishes.

When a body moves in a liquid or gas, the resistance forces of the medium appear, which can become significantly greater than the friction forces. The magnitude of the sliding friction force depends on the shape, size and condition of the body surface, the speed of the body relative to the medium, the viscosity of the medium. At not very high speeds, the friction force is calculated using the formula:

where the minus sign means that the friction force has a direction opposite to the direction of the velocity vector. With an increase in the velocities of bodies in a viscous medium, the linear law (4) turns into a quadratic one:

The coefficients and are essentially dependent on the shape, dimensions, state of the surfaces of the bodies, and the viscosity of the medium.

In addition, rolling friction is distinguished. As a first approximation, rolling friction is calculated using the formula:

where k is the coefficient of rolling friction, which has the dimension of length and depends on the material of the bodies subject to contact and the qualities of the surfaces, etc. N is the force of normal pressure, r is the radius of the rolling body.

Friction force units

The basic unit of measurement of the friction force (as well as any other force) in the SI system is: [P]=H

In GHS: [P]=dyn.

Examples of problem solving

Example

Exercise. A small body rests on a horizontal disk. The disk rotates about an axis that passes through its center, perpendicular to the plane with an angular velocity . At what distance from the center of the disk can the body be in equilibrium if the coefficient of friction between the disk and the body is ?

Decision. Let us depict in Fig. 1 the forces that will act on a body placed on a rotating disk.

According to Newton's second law, we have:

In the projection onto the Y-axis, from equation (1.1) we get:

In the projection on the X axis we have:

where the acceleration of the motion of a small body is equal in modulus to the normal component of the total acceleration. We find the rest frictions as:

we take into account the expression (1.2), then we have.

The friction force arises at the point of contact between two bodies and prevents the mutual movement of these bodies relative to each other. It is always directed opposite to the movement of bodies or the direction of application of an external force. If the bodies are stationary. As a result of friction, mechanical energy is converted into thermal energy.

Friction is divided into friction of rest and friction of motion. The friction of motion is in turn divided into rolling friction and sliding friction. Friction occurs when bodies in contact try to move relative to each other.

Formula 1 - Force of friction.

N - Support reaction force.

Mu - Coefficient of friction.

Friction of rest, as the name implies, occurs when an outside force is applied to the bodies, seeking to displace them relative to each other. But there is no movement yet. There is no movement precisely because it is prevented by the rest friction force. At the moment when the external force exceeds the static friction force, the sliding friction force will arise.

The cause of the friction force is the unevenness on the surface of the contacting bodies. Even if the surfaces appear smooth, in fact, at high magnification, the surface is rough. So it is precisely these irregularities on the surface of two bodies that cling to each other.

Figure 1 - Contact surfaces.

It would seem that if the surfaces are polished to a mirror finish, then the friction between them should, if not completely disappear, then certainly fall to a minimum value. But in practice, it turns out it's not so simple. In the case of very smooth surfaces, another friction-increasing factor appears. This is intermolecular attraction. With very fine processing of the material, the molecules of the substance of two bodies are so close to each other that such strong forces of attraction arise that they prevent the bodies from moving relative to each other.

Of course, the magnitude of the friction force is also affected by the force that presses the bodies against each other. The higher it is, the higher the friction force. If you roll in the winter, empty sleds in the snow come out easily enough. If a child is sitting on the sled, it will be more difficult to drag them. Well, if an adult sits in them, you will think twice whether it is worth dragging them at all. In all these cases, the quality of the surface of the sledge runners and the surface of the snow is unchanged. But the force of gravity is different, which leads to an increase in the friction force.

In addition to sliding friction, there is also a rolling friction force. Again, the essence of the phenomenon is hidden in the name. That is, this is the friction that occurs during the rolling of one object on the surface of another. Rolling friction is many times less than sliding friction.

Imagine a metal ball rolling on a table surface. Due to the deformation of the table, and the ball itself, the place of contact between them is not a point, but a certain surface. As a result, the point of application of the support reaction is shifted slightly forward from the center of equilibrium. And the reaction of the support is a little back. As a result, the normal part of the reaction of the support is compensated by the force of gravity, and the tangential component is the rolling friction force.