Find the force of friction. Friction force formula

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 bar 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 side, 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
We will use a dynamometer to pull the bar on the table with constant speed(Fig. 17.4, a), applying a horizontally directed force to it control.

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 (cf. laboratory work four). 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. O slippery road drivers warns road sign(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?

The friction force occurs 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 goes into heat.

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 a third-party 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 external force exceeds the force of static friction, there will be a force of sliding friction.

The cause of the friction force is the unevenness on the surface of the contacting bodies. Even if the surfaces look 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 case of very smooth surfaces There is another factor that increases friction. 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 support reaction is compensated by the force of gravity, and the tangential component is the rolling friction force.

Friction- one of the types of interaction of bodies. It occurs when two bodies come into contact. Friction, like all other types of interaction, is subject to Newton's third law: if a friction force acts on one of the bodies, then the same modulus, but directed in opposite side force acts on the second body. Friction forces, like elastic forces, have electromagnetic nature. They arise as a result of the interaction between atoms and molecules of adjoining bodies.

Dry friction forces called the force that occurs when two people come into contact solids in the absence of a liquid or gaseous layer between them. They are always directed towards tangent to adjacent surfaces.

Dry friction that occurs when bodies are at relative rest is called static friction. The static friction force is always equal in magnitude to the external force and is directed in the opposite direction (Fig. 1.1.6).

The static friction force cannot exceed a certain maximum value (F tr) max . If the external force is greater than (F tr) max , relative slip occurs. The force of friction in this case is called sliding friction force. It is always directed in the direction opposite to the direction of motion and, generally speaking, depends on the relative velocity of the bodies. However, in many cases, approximately the force of sliding friction can be considered independent of the magnitude of the relative velocity of the bodies and equal to the maximum force of static friction. This dry friction force model is used to solve many simple physical problems (Fig. 1.1.7).

Experience shows that the force of sliding friction is proportional to the force normal pressure body on the support, and consequently, the reaction force of the support

The coefficient of proportionality μ is called coefficient of sliding friction.

Friction coefficient μ is a dimensionless quantity. Usually the coefficient of friction is less than unity. It depends on the materials of the contacting bodies and on the quality of the surface treatment. When sliding, the friction force is directed tangentially to the contacting surfaces in the direction opposite to the relative speed (Fig. 1.1.8).

When a rigid body moves in a liquid or gas, viscous friction force. The force of viscous friction is much less than the force of dry friction. It is also directed in the direction opposite to the relative velocity of the body. With viscous friction, there is no static friction.

The force of viscous friction strongly depends on the speed of the body. At sufficiently low speeds F tr ~ υ, at high speeds F tr ~ υ 2 . In this case, the coefficients of proportionality in these ratios depend on the shape of the body.

Friction forces also arise when a body rolls. However, since rolling friction forces usually quite small. When solving simple problems, these forces are neglected.

1. In order for a body (a book lying on a table, a box 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 acted upon in the vertical plane by the balancing forces of gravity ​\(\vec(F)_t \) , 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 (as long as it does not move), the more power rest friction.

The static friction force is equal in absolute value and directed opposite 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. It - 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 bars mass ​\(m_1 \) ​ and \(m_2 \) slide along the horizontal, equally processed 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