Friction is a phenomenon that we encounter in everyday life all the time. It is impossible to determine whether friction is harmful or beneficial. Taking even a step on slippery ice seems to be a difficult task; walking on a rough asphalt surface is a pleasure. Car parts without lubrication wear out much faster.
The study of friction, knowledge of its basic properties allows a person to use it.
The force of friction in physics
The force arising from the movement or attempt of movement of one body on the surface of another, directed against the direction of movement, applied to moving bodies, is called the force of friction. The modulus of the friction force, the formula of which depends on many parameters, varies depending on the type of resistance.
The following types of friction are distinguished:
slip;
rolling.
Any attempt to move a heavy object (cabinet, stone) from its place leads to tension. At the same time, it is not always possible to set the object in motion. Interferes with rest.
Resting state
The calculated static friction does not allow to determine it accurately enough. By virtue of the operation of Newton's third law, the magnitude of the static resistance force depends on the applied force.
As the force increases, the friction force also increases.
0 < F тр.покоя < F max
Does not allow nails driven into a tree to fall out; buttons sewn with thread are firmly held in place. Interestingly, it is the resistance of rest that allows a person to walk. Moreover, it is directed in the direction of human movement, which contradicts the general state of affairs.
slip phenomenon
With an increase in the external force that moves the body, to the value of the greatest static friction force, it begins to move. The force of sliding friction is considered in the process of sliding one body over the surface of another. Its value depends on the properties of the interacting surfaces and the force of the vertical action on the surface.
Calculation formula for the force of sliding friction: F=μР, where μ is the coefficient of proportionality (sliding friction), Р is the vertical (normal) pressure force.
One of the forces controlling the movement is the sliding friction force, the formula of which is written using the reaction force of the support. Due to the fulfillment of Newton's third law, the forces of normal pressure and the reaction of the support are the same in magnitude and opposite in direction: P \u003d N.
Before finding the friction force, the formula of which takes on a different form (F=μ N), the reaction force is determined.
The sliding resistance coefficient is introduced experimentally for two rubbing surfaces and depends on the quality of their processing and material.
Table. The value of the drag coefficient for various surfaces
| No. pp | Interacting surfaces | The value of the coefficient of sliding friction |
Steel + ice | ||
Leather + cast iron | ||
bronze+iron | ||
Bronze + cast iron | ||
Steel+steel |
The greatest force of static friction, the formula of which was written above, can be determined in the same way as the force of sliding friction.
This becomes important when solving problems to determine the strength of the driving resistance. For example, a book, which is moved by a hand pressed from above, slides under the action of the rest resistance force that arises between the hand and the book. The amount of resistance depends on the value of the vertical pressure force on the book.
rolling phenomenon
The transition of our ancestors from drags to chariots is considered revolutionary. The invention of the wheel is the greatest invention of mankind. that occurs when the wheel moves along the surface, is significantly inferior in magnitude to the sliding resistance.
The occurrence is associated with the forces of normal pressure of the wheel on the surface, has a nature that distinguishes it from sliding. Due to slight deformation of the wheel, different pressure forces arise in the center of the formed area and along its edges. This difference in forces determines the occurrence of rolling resistance.
The calculation formula for the rolling friction force is usually taken similarly to the sliding process. The difference is visible only in the values of the drag coefficient.
The nature of resistance
When the roughness of the rubbing surfaces changes, the value of the friction force also changes. At high magnification, two surfaces in contact look like bumps with sharp peaks. When superimposed, it is the protruding parts of the body that are in contact with each other. The total area of contact is insignificant. When moving or attempting to move bodies, the "peaks" create resistance. The magnitude of the friction force does not depend on the area of the contact surfaces.
It seems that two ideally smooth surfaces should experience absolutely no resistance. In practice, the friction force in this case is maximum. This discrepancy is explained by the nature of the origin of forces. These are electromagnetic forces acting between the atoms of interacting bodies.
Mechanical processes that are not accompanied by friction in nature are impossible, because there is no way to “turn off” the electrical interaction of charged bodies. The independence of the resistance forces from the mutual position of the bodies allows us to call them non-potential.
Interestingly, the friction force, the formula of which changes depending on the speed of the interacting bodies, is proportional to the square of the corresponding speed. This force refers to the force of viscous resistance in the fluid.
Movement in liquid and gas
The movement of a solid body in a liquid or gas, liquid near a solid surface is accompanied by viscous resistance. Its occurrence is associated with the interaction of fluid layers entrained by a solid body in the process of movement. Different layer speeds are a source of viscous friction. The peculiarity of this phenomenon is the absence of fluid static friction. Regardless of the magnitude of the external influence, the body begins to move while in the fluid.
Depending on the speed of movement, the resistance force is determined by the speed of movement, the shape of the moving body and the viscosity of the fluid. The movement in water and oil of the same body is accompanied by resistance of different magnitude.
For low speeds: F = kv, where k is a proportionality factor depending on the linear dimensions of the body and the properties of the medium, v is the speed of the body.
The temperature of the fluid also affects the friction in it. In frosty weather, the car is warmed up so that the oil warms up (its viscosity decreases) and helps to reduce the destruction of the engine parts in contact.
Increasing movement speed
A significant increase in the speed of the body can cause the appearance of turbulent flows, while the resistance increases sharply. What matters is: the square of the speed of movement, the density of the medium and the friction force takes on a different form:
F \u003d kv 2, where k is a proportionality factor depending on the shape of the body and the properties of the medium, v is the speed of the body.
If the body is given a streamlined shape, turbulence can be reduced. The body shape of dolphins and whales is a perfect example of the laws of nature that affect the speed of animals.
Energy Approach
The work of moving the body is prevented by the resistance of the medium. When using the law of conservation of energy, we say that the change in mechanical energy is equal to the work of friction forces.
The work of the force is calculated by the formula: A = Fscosα, where F is the force under which the body moves a distance s, α is the angle between the directions of force and displacement.
Obviously, the resistance force is opposite to the movement of the body, whence cosα = -1. The work of the friction force, the formula of which is A tr \u003d - Fs, is a negative value. In this case, it turns into internal (deformation, heating).
The force of friction is the amount with which two surfaces interact when moving. It depends on the characteristics of the bodies, the direction of movement. Due to friction, the speed of the body decreases, and soon it stops.
The friction force is a directed quantity, independent of the area of the support and the object, since with movement and an increase in the area, the reaction force of the support increases. This value is involved in the calculation of the friction force. As a result, Ftr \u003d N * m. Here N is the support reaction and m is a coefficient which is a constant value unless very precise calculations are needed. Using this formula, you can calculate the sliding friction force, which should definitely be taken into account when solving problems related to movement. If the body rotates on the surface, then the rolling force must be included in the formula. Then the friction can be found by the formula Froll = f*N/r. According to the formula, when a body rotates, its radius matters. The value of f is a coefficient that can be found, knowing what material the body and surface are made of. This is the coefficient that is in the table.There are three forces of friction:
- rest;
- slip;
- rolling.
Knowing the physical properties of bodies and the accompanying forces acting on an object, you can easily calculate the friction force.
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. The difference between the directions of the friction force and the elastic force
Rice. 2. The surface acts on the bar, and the bar acts on the surface
There are dry and non-dry types of friction. Dry type of friction occurs when solids come into contact.
Consider a bar lying on a horizontal surface (Fig. 3). It is affected by the force of gravity and the reaction force of the support. Let's act on the bar with a small force , directed along the surface. If the bar does not move, then the applied force is balanced by another force, which is called the static friction force.
Rice. 3. Force of static friction
The static friction force () opposite in direction and equal in magnitude to the force tending to move the body parallel to the surface of its contact with another body.
With an increase in the “shearing” force, the bar remains at rest, therefore, the static friction force also increases. With some, sufficiently large, force, the bar will begin to move. This means that the static friction force cannot increase to infinity - there is an upper limit, more than which it cannot be. The value of this limit is the maximum static friction force.
Let's act on the bar with a dynamometer.
Rice. 4. Measuring the friction force with a dynamometer
If the dynamometer acts on it with a force, then it can be seen that the maximum static friction force becomes greater with an increase in the mass of the bar, that is, with an increase in the force of gravity and the reaction force of the support. If accurate measurements are taken, they will show that the maximum static friction force is directly proportional to the reaction force of the support:
where is the modulus of the maximum static friction force; N– support reaction force (normal pressure); - coefficient of static friction (proportionality). Therefore, the maximum static friction force is directly proportional to the force of normal pressure.
If we conduct an experiment with a dynamometer and a bar of constant mass, while turning the bar on different sides (changing the area of contact with the table), we can see that the maximum static friction force does not change (Fig. 5). Therefore, 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 static friction force does not always prevent the body from moving. For example, the static friction force acts on the sole of the shoe, while imparting acceleration and allowing you to walk on the ground without slipping (Fig. 6).
Rice. 6. Force of static friction acting on the sole of the shoe
Another example: the static friction force acting on the wheel of a car allows you to start moving without slipping (Fig. 7).
Rice. 7. The static friction force acting on the car wheel
In belt drives, the static friction force also acts (Fig. 8).
Rice. 8. Force of static friction in belt drives
If the body is moving, then the friction force acting on it from the side of the surface does not disappear, this type of friction is called sliding friction. Measurements show that the force of sliding friction is practically equal in magnitude to the maximum force of static friction (Fig. 9).
Rice. 9. Force of sliding friction
The force of sliding friction is always directed against the speed of the body, that is, it prevents movement. Consequently, when the body moves only under the action of the friction force, it imparts negative acceleration to it, that is, the speed of the body is constantly decreasing.
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– support reaction force (normal pressure); – coefficient of sliding friction (proportionality).
Figure 10 shows a graph of the dependence of the friction force on the applied force. It shows two different areas. The first section, in which the friction force increases with an increase in the applied force, corresponds to static friction. The second section, where the friction force does not depend on the external force, corresponds to sliding friction.
Rice. 10. Graph of the dependence of the friction force on the applied force
The coefficient of sliding friction is approximately equal to the coefficient of static friction. Typically, the coefficient of sliding friction is less than unity. This means that the sliding friction force is less than the normal pressure force.
The coefficient of sliding friction 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 due to the fact that any surface at the microscopic level is not flat, there are always microscopic inhomogeneities on any surface (Fig. 11).
Rice. 11. Surfaces of bodies at the microscopic level
When two bodies in contact are subjected to an attempt to move relative to each other, these inhomogeneities are hooked 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, then the engagement of the roughness is not enough to hold the bodies, and they begin to shift 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 the body.
The occurrence of the rolling friction force is due to the deformation of the rolling body and the supporting surface. So, 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 climb a small hill all the time, which causes a moment of forces that slows down the rolling.
Rice. 12. Occurrence of rolling friction force
The magnitude of the rolling friction force, as a rule, is many times less than the sliding friction force, all other things being equal. Due to this, rolling is a common type of movement in engineering.
When a solid body moves in a liquid or gas, a resistance force acts on it from the side of the medium. This force is directed against the speed of the body and slows down the movement (Fig. 13).
The main feature of the resistance force is that it occurs only in the presence of relative motion of the body and its environment. That is, the static friction force in liquids and gases does not exist. This leads to the fact that a person can move even a heavy barge that is on the water.
Rice. 13. Resistance force acting on a body when moving in a liquid or gas
The resistance force modulus depends on:
From the size of the body and its geometric shape (Fig. 14);
Conditions of the body surface (Fig. 15);
Properties of a liquid or gas (Fig. 16);
The relative speed of the body and its environment (Fig. 17).
Rice. 14. Dependences of the modulus of resistance force on the geometric shape
Rice. 15. Dependences of the resistance force modulus on the state of the body surface
Rice. 16. Dependences of the resistance force modulus on the properties of a liquid or gas
Rice. 17. Dependences of the resistance force modulus on the relative velocity of the body and its environment
Figure 18 shows a graph of the dependence of the resistance force on the speed of the body. At a relative velocity equal to zero, the drag force does not act on the body. With an increase in the relative velocity, the resistance force first grows slowly, and then the growth rate increases.
Rice. 18. Graph of the dependence of the resistance force on the speed of the body
At low values of the relative speed, the drag force is directly proportional to the value of this speed:
where is the value of the relative velocity; - resistance coefficient, which depends on the type of viscous medium, the 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 value of the relative velocity; is the drag coefficient.
The choice of formula for each specific case is determined empirically.
A body of mass 600 g moves uniformly along a horizontal surface (Fig. 19). In this case, a force is applied to it, the value of which is 1.2 N. Determine the value of the coefficient of friction between the body and the surface.
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
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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 |
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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? |
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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 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 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?
Let's put experience
Let's push the block lying on the table, giving it some initial speed. We will see that the bar slides on the table and its speed decreases to a complete stop (Figure 17.1 shows successive positions of the bar at regular intervals). As you already know from the basic school physics course, the sliding friction force acting on it from the side of the table slows down the bar.
The forces of sliding friction act on each of the contacting bodies when they move relative to each other.
These forces act on each of the contacting bodies (Fig. 17.2). They are equal in absolute value and opposite in direction, because they are connected by Newton's third law. 
When the block slides on the table, we do not notice the sliding friction force acting on the table from the side of the bar, because the table is attached to the floor (or a rather large static friction force acts on the table from the floor, which will be discussed later).
If you push a bar lying on the cart, then under the action of the sliding friction force acting on the cart from the side of the bar, the cart will move with acceleration, and the speed of the bar relative to the cart will decrease.
1. How many times is the acceleration of the bar relative to the table in this experiment greater than the acceleration of the cart relative to the table, if the mass of the bar is 200 g and the mass of the cart is 600 g? The friction between the trolley and the table can be neglected.
The forces of sliding friction are directed along the contact surface of the bodies. The friction force acting on each body is directed opposite to the speed of this body relative to another body.
The forces of sliding friction are mainly due to the engagement and destruction of the irregularities of the contacting bodies (these irregularities are exaggerated in Figure 17.3 for clarity). Therefore, usually the smoother the surfaces of the bodies in contact, the less the friction force between them. 
However, if the contact surfaces are made very smooth (for example, if they are polished), then the sliding friction force may increase due to the action of intermolecular forces of attraction.
Let us find out what the force of sliding friction depends on.
What does the force of sliding friction depend on?
Let's put experience
Using a dynamometer, we will pull the bar along the table at a constant speed (Fig. 17.4, a), applying a horizontally directed force to it ex. 
When moving at a constant speed, the acceleration of the block is zero. Consequently, the sliding friction force acting on the bar from the side of the table is balanced by the elastic force acting on the bar from the side of the dynamometer. This means that these forces are equal in absolute value, that is, the dynamometer shows the modulus of the friction force.
Let's repeat the experiment by placing another similar bar on the bar (Fig. 17.4, b). We will see that the sliding friction force has doubled. We now note that in this experiment (compared to the experiment with one bar) the force of the normal reaction also doubled.
By changing the normal reaction force, one can make sure that the modulus of the sliding friction force Ftr is proportional to the modulus of the normal reaction force N:
F tr.sk \u003d μN. (one)
As experience shows, the force of sliding friction practically does not depend on the relative speed of movement of the contacting bodies and on the area of their contact.
The coefficient of proportionality μ is called the coefficient of friction. It is determined from experience (see Lab 4). It depends on the material and the quality of the processing of the contacting surfaces. On the flyleaf of the problem book (under the cover) approximate values of the coefficient of friction for some types of surfaces are given.
The coefficient of friction of tires on wet asphalt or on ice is several roses less than the coefficient of friction of tires on dry asphalt. Therefore, the braking distance of the car is significantly increased during rain or ice. A road sign warns drivers about a slippery road (Fig. 17.5). 
2. A body of mass m moves along a horizontal surface. Friction coefficient between body and surface μ.
a) What is the force of sliding friction?
b) With what modulus of acceleration does the body move if only the force of gravity, the force of normal reaction and the force of sliding friction act on it?
3. A block lying on the table was given a speed of 2 m/s, and it went to a stop of 1 m (stopping distance). What is the coefficient of friction between the bar and the table?
4. We can approximately assume that the sliding friction force acts on the car during braking. Estimate the stopping distance of the car on dry pavement and on ice at an initial speed of 60 km/h; 120 km/h Compare the found values with the classroom length.
The answers you get will surprise you. Probably, you will become more careful on the road during rain and especially ice.
2. Force of static friction
Let's put experience
Try to move the cabinet (Fig. 17.6). It will stay still even if you apply quite a lot of force to it.
What force balances the horizontally directed force applied by you to the cabinet? This is the static friction force acting on the cabinet from the side of the floor. 
The forces of static friction arise when you try to move one of the contacting bodies relative to the other in the case when the bodies remain at rest relative to each other. These forces prevent the relative motion of bodies.
5. Does the static friction force act on the floor from the side of the cabinet (Fig. 17.6)?
The causes of the static friction force are similar to the causes of the sliding friction force: the presence of irregularities on the contacting surfaces of the bodies and the action of intermolecular forces of attraction.
We will gradually increase the horizontal force applied to the cabinet. Upon reaching a certain value, the cabinet will move and begin to slide on the floor. Consequently, the modulus of the static friction force Ftr.pok does not exceed a certain limit value, called the maximum static friction force.
Experience shows that the maximum static friction force is slightly greater than the sliding friction force. However, to simplify the solution of school problems, it is assumed that the maximum static friction force is equal to the sliding friction force:
F tr.pok ≤ μN. (2)
If the body is at rest, then the static friction force tr.pok balances the force directed along the contact surface of the bodies and tending to move the body.
Therefore, in this case
F tr.pok = F. (3)
Please note: the static friction force satisfies two relationships - inequality (4) and equality (5). From them follows the inequality for the force that cannot move the body:
If F > μN, then the body will begin to slide, and sliding friction fats will act on it. In this case
F tr \u003d F tr.sk \u003d μN.
Relations (3) and (5) are illustrated by a graph of the dependence of the friction force Ftr on the force F applied to the body (Fig. 17.7). 
6. A horizontal force equal in magnitude to F is applied to a bar with a mass of 1 kg lying on the table. The coefficient of friction between the bar and the table is 0.3. What is the friction force acting on the bar from the side of the table if F = 2 N? F = 5 N?
7. A tractor pulls a bunch of logs weighing 10 tons horizontally with a force of 40 kN. What is the acceleration of the bundle if the coefficient of friction between the logs and the road is 0.3? 0.5?
8. A bar with a mass of 1 kg located on the table is pulled by a horizontal spring with a stiffness of 100 N/m. Friction coefficient 0.3. What is the elongation x of the spring if the bar is at rest? moving at a speed of 0.5 m/s?
Can friction be a driving force?
Taking a step, a person pushes the road back, acting on it with the force of static friction mp1: after all, the sole during the push rests relative to the road (this is sometimes indicated by a clear imprint of the sole) (Fig. 17.8, a). According to Newton's third law, from the side of the road a person is affected by the same modulus static friction force tr2 directed forward. 
The static friction force also accelerates the car (Fig. 17.8, b). When a wheel rolls without slipping, its lowest point is at rest relative to the road. The driving wheel of the car (driven by the engine) pushes the road back, acting on it with the static friction force mp1. According to Newton's third law, the road with an atom pushes the wheel (and with it the car) forward by the static friction force mp2. It is this force that is often called the traction force.
9. What is the purpose of making locomotives (electric and diesel locomotives) very massive?
10. The coefficient of friction between the tires of the driving wheels of the car and the road is 0.5. Assume that air resistance can be neglected.
a) With what maximum possible acceleration can a car move if all its wheels are driving?
b) Would the maximum possible acceleration of the car increase or decrease if only the front or only the rear wheels were driven? Justify your answer.
Hints. The acceleration of the car is due to the action of the static friction force from the side of the road. 
Additional questions and tasks
11. Figure 17.9 shows graphs of the dependence of the sliding friction force on the normal reaction force when moving three different bars on the table. Between which bar and the table is the coefficient of friction the greatest? What is it equal to?
12. On the table is a stack of four identical books weighing 500 g each (Fig. 17.10). The coefficient of friction between book covers is 0.4. What horizontally directed force must be applied in order to hold the remaining books:
a) move book 4?
b) move books 3 and 4 together?
c) pull out book 3?
d) pull out book 2?
