Friction law formula. Friction
Friction forces are called tangential interactions between bodies in contact, arising from their relative movement. Friction coefficient μ is a dimensionless quantity.
Rolling friction is manifested when the body rolls on the support, and it is much less than sliding friction. It has been experimentally established that the force of friction depends on the pressure force of the bodies on each other (reaction force of the support), on the materials of the rubbing surfaces, and on the speed of relative movement.
It is also possible to classify friction by its area. And the greater the normal reaction force, the greater the friction force. It shows exactly how the force of sliding friction depends on the force of the normal reaction (or, one might say, on the weight of the body), what proportion of it it is.
Friction coefficient, formula
So, for example, wooden objects rub against each other with a coefficient of 0.2 to 0.5 (depending on the type of wooden surfaces). The strength of the normal support reaction depends on the weight of the body. It is equal to it in modulus, but opposite in direction.
See what "Sliding Friction Force" is in other dictionaries:
COEFFICIENT OF FRICTION, a quantitative characteristic of the force required to slide or move one material over the surface of another. Dry friction forces are the forces that arise when two solid bodies come into contact in the absence of a liquid or gaseous layer between them. The static friction force cannot exceed a certain maximum value (Ftr)max.
Usually the coefficient of friction is less than unity. When a solid body moves in a liquid or gas, a viscous friction force arises. Friction forces also arise when a body rolls. However, rolling friction forces are usually quite small. When solving simple problems, these forces are neglected.
Accounting for the shape of the guides. Reduced coefficient of friction
The existence of a friction force is explained by the interaction of irregularities on the surfaces of bodies. It always exists, since absolutely smooth bodies do not exist. The static friction force is the minimum force that must be applied in order for the body to start moving.
The support reaction force is directed perpendicular to the line of motion, and the body weight is directed perpendicular to the horizon. If there is no liquid or gaseous layer (lubrication) between the bodies, then such friction is called dry. Otherwise, the friction is called "liquid".
However, most often this dependence is weakly expressed, and if greater measurement accuracy is not required, then "k" can be considered constant. Boundary, when the contact area may contain layers and areas of various nature (oxide films, liquid, etc.) - the most common case in sliding friction.
Traction force formula
In the latter case, the interactions between bodies are called friction forces. In real movements, friction forces of greater or lesser magnitude always arise. The body moves uniformly and rectilinearly when an external force balances the friction force arising during the movement.
The combination of three varieties of nominative meanings in the word friction is curious. The mechanics term friction has been used to characterize social relations. Plain bearing - a support or guide of a Mechanism or machine (See Machine), in which friction occurs when the mating surfaces slide.
The shape of the guides also affects the friction force in the translational pair. As can be seen, in this case, to a large extent, it is possible to influence the magnitude of the friction force by changing the angle between the planes of the guides (here, β is half the angle of the wedge).
Answers to questions in the natural sciences and mathematics
When small (close to zero) angles are used, the friction force increases to very large values (as the wedge angle tends to zero, the friction force tends to infinity). The unit of force is N (newton). The source of traction force are external influences. In the case of a car, this is the friction force of the wheels on the road surface, in the case of a ship, the force of the water jet thrown by the propeller.
Examples of solving problems on the topic "Traction Force"
The magnitude of this force weakly depends on the magnitude of the velocity, therefore, when solving problems, it is considered to be constant in magnitude. Solution. Three forces act on the bar: gravity mg, support reactions N and friction force Ffr (Fig. The last relation allows in practice to determine the value of the coefficient of friction.
We have found the functional dependence of the thrust force on the angle α. Obviously, F will be the smallest for highest value denominator. Problem 98-15. The body A is placed on a non-smooth plate BC, which can be rotated around the hinge B. The coefficient of friction / between the body A and the plate BC is known.
A replaceable plate 6 is inserted into the recess of the board 4 (shaded in the figure). We have repeatedly come across in our discussions with friction forces from one side or another (see here >>>, here >>> and here >>>.) Let's consider a few more "blunders" related to friction forces. The coefficient μ depends on the materials of the rubbing bodies and on the state of the contacting surfaces.
As is known, the friction force acts along the surface of the bodies in contact and is directed in the direction opposite to the relative motion of the body (possible motion in the case of static friction). In addition, the coefficient of friction depends on the speed. The force of static friction at the moment of the beginning of sliding. The rolling friction force depends on the radius of the rolling object. Regarding the friction force, it is only known in advance that it is directed along an inclined plane.
And acts on the body in the direction opposite direction slip.
The negative consequences of sliding friction in mechanisms are not only a decrease in efficiency, but also the wear of mechanisms.
1. General Provisions
The main reason for sliding friction is that the surfaces of the bodies that are in contact are rough; as a result, when moving one body on the surface of another, a force is needed to overcome the resistance of the microscopic irregularities of these surfaces. In addition to surface roughness, friction phenomena are also influenced by the forces of intermolecular interaction between two bodies.
where - Dimensionless quantity, which is called the static friction coefficient or the static coefficient of friction.
The friction force during movement is less than the static friction force and the coefficient of friction of motion (dynamic coefficient of friction) is less than the static coefficient of friction:
2. Friction angle
Often, during engineering calculations, no distinction is made between static and dynamic friction coefficients and their values \u200b\u200bare determined for the corresponding materials from tables of tangents of the angle φ 0, formed by the reaction R rough surface with normal N to the surface because μ = tan φ.
Corner φ 0 called friction angle.
3. Friction cone
Consider a body in a state of ultimate equilibrium on a rough surface. Depending on the action of given forces, the direction of the limiting reaction F0 may change. The locus of all possible reaction directions F0 in boundary conditions forms a conical surface - friction cone. We bring all the active forces acting on the body into one resultant R, which forms an angle α with the normal to the surface. Such a force does a double action - its normal component determines the reaction of the surface N and, as a consequence, the limiting force of friction , The tangential component of the force R trying to overcome this power. With increasing strength R both components will increase proportionally. So the state of rest or motion of the body does not depend on the modulus of force R and is determined only by the angle of its application α.
When the body is in equilibrium, And in order for the body to start moving, it is necessary and sufficient that the resultant of the active forces R was outside the cone of friction.
See also
Notes
- DSTU 2823-94 Wear resistance of friction, wear and lubricant products. Terms and Definitions.
Sources
- Sivukhin D.V. General course of physics - M.: Nauka, 1979. - T. I. Mechanics. - S. 101-102. - 520 s.
- Kindrachuk M. V., Labunets V. F., Pashechko M. I., Korbut E. V. tribology: textbook / MON. - Kyiv: NAU-print, 2009. - 392 p. ISBN 978-966-598-609-6
- Theory of mechanisms and machines / A. S. Korenyako; Ed. M. K. Afanasiev. - K .: Vishcha school. Main publishing house, 1987. - 206 p.
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 factor which is a constant 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 resistance that arises when trying to move one body over the surface of another is called sliding friction. The occurrence of friction is primarily due to the roughness of the contacting bodies. The study of all factors affecting friction is a very complex physical and mechanical problem, the consideration of which is beyond the scope of the course of theoretical mechanics.
7.1. Laws of sliding friction
In engineering calculations, they usually proceed from empirically established patterns called the laws of sliding friction.
When trying to move one body over the surface of another in the plane of contact of the bodies, friction force, which can take any value from zero to ultimate friction force .
The limiting friction force is numerically equal to the product static coefficient of friction to normal pressure or normal response.
The value of the limiting force of friction in a fairly wide range does not depend on the area of contact during friction of the surfaces.
It should be noted that the value of the friction force will be equal only when the shear force acting on the body reaches such a value that, with the slightest increase, the body begins to move (slide). The equilibrium that takes place when the friction force is , we will call limit equilibrium.
7.2. Rough surface reaction. Friction angle. friction cone
Consider a body of weight lying on a horizontal rough plane. Let a horizontal force be applied to the body, under the influence of which the body is at rest. In this case, the force must be balanced by another force, equal in magnitude and directed in opposite side- sliding friction force (Fig. 7.1).
Rice. 7.1
Consequently, the total reaction of a rough surface is composed of two components: the normal reaction and the friction force perpendicular to it. As the friction force increases from zero to , the total reaction of the rough surface will change from to , and the angle from zero to . The largest angle that the total reaction of a rough surface makes with the normal is called friction angle(Fig. 7.2a).
If the vector of the total reaction of a rough surface is rotated around the normal, then it will describe the surface of a cone (Fig. 7.2b), called friction cone. By constructing a cone of friction, it is possible to determine the equilibrium of the body. For the equilibrium of a body lying on a rough surface, it is necessary and sufficient that the force acting on the body passes inside the friction cone (or along its generatrix through the top of the cone).
Rice. 7.2
If a force is applied to a body lying on a rough surface, forming an angle α with the normal (Fig. 7.3), then the body will move only if the shear force is greater limit value friction.
Rice. 7.3
Since and , then . The shift condition is the inequality or , because , That . Hence, no force forming an angle with the normal , unable to move the body. This condition explains the well-known phenomenon in engineering practice of jamming and self-braking of bodies.
7.3. Guidelines for the study of equilibrium conditions of bodies in the presence of friction
The study of the equilibrium of bodies, taking into account friction, is reduced to the consideration of the limit positions of equilibrium.
1. We select the body (system of bodies), the balance of which should be considered.
2. Arrange all active forces acting on a rigid body (system of bodies).
3. We represent the coordinate system.
4. We release the body from bonds, replacing their action with reaction forces. The reaction of a rough surface is represented as a normal reaction and a friction force.
5. We compose the equilibrium equations for the selected body (system of bodies).
6. Solving the resulting system of equations, we determine the desired values.
Example. Homogeneous staircase AB weighing R rests with its lower end on a horizontal rough floor, and with its upper end on a rough vertical wall. The coefficient of friction of the stairs on the floor and the wall is the same and equal. Determine gender reactions NA and walls NB, as well as the largest angle α between the wall and the ladder in the equilibrium position (Fig. 7.4).
Rice. 7.4
Solution. The study of the equilibrium of bodies, taking into account the forces of friction, is reduced to the consideration of the limiting positions of equilibrium.
So, when studying the equilibrium of the ladder AB, resting on a non-smooth floor and wall, the angle of inclination α should be considered limiting, with its increase, the balance of the stairs will be disturbed.
Let's show on the diagram the forces acting on the stairs and draw up the equations for the balance of forces (Fig. 7.4):
Where
From equation (1):
From equation (2):
From equation (3):
Answer: in order for the ladder to be in balance, it is necessary that the angle of inclination to the wall does not exceed the angle 
.
7.4. Equilibrium of a rigid body in the presence of rolling friction
If the body under consideration has the shape of a skating rink and, under the action of applied active forces, can roll along the surface of another body, then due to the deformation of the surfaces of these bodies, reaction forces can arise at the point of contact that prevent not only sliding, but also rolling. Examples of such rollers are various wheels, such as, for example, on electric locomotives, wagons, motor vehicles, balls and rollers in ball and roller bearings and so on.
Let a cylindrical roller be on a horizontal plane under the action of active forces. The contact of the roller with the plane due to deformation actually occurs not along one generatrix, as in the case of absolutely rigid bodies, but along a certain area. If the active forces are applied symmetrically with respect to the average section of the rink, that is, they cause the same deformations along its entire generatrix, then only one average section of the rink can be studied. This case is discussed below.
Between the skating rink and the plane on which it rests, friction forces arise if a force is applied to the axis of the rink (Fig. 7.5), which tends to move it along the plane.
Rice. 7.5
Consider the case when the force is parallel to the horizontal plane. It is known from experience that when the modulus of force changes from zero to a certain limit value, the roller remains at rest, i.e. the forces acting on the roller are balanced. In addition to active forces (weight and force), the reaction of the plane is applied to the rink, the balance of which is being considered. From the condition of equilibrium of three non-parallel forces it follows that the reaction of the plane must pass through the center of the rink ABOUT, since two other forces are applied to this point.
Therefore, the application point of the reaction WITH must be displaced by some distance δ from the vertical passing through the center of the wheel, otherwise the reaction will not have a horizontal component necessary to satisfy the equilibrium conditions. We decompose the reaction of the plane into two components: the normal component and the tangential reaction, which is the friction force (Fig. 7.6).
Rice. 7.6
In the limit position of the balance of the rink, two mutually balanced pairs will be applied to it: one pair of forces with a moment (where r- the radius of the roller) and the second pair of forces that keeps the roller in balance.
Moment of a couple called rolling friction moment, is determined by the formula:
From (1) it follows that in order for pure rolling (without slip) to take place, it is necessary that the rolling friction force 
was less than the maximum sliding friction force:
Where f- coefficient of sliding friction.
Thus, pure rolling (without slip) will be if .
Rolling friction occurs due to the deformation of the roller and the plane, as a result of which the contact between the roller and the plane occurs along a certain surface, displaced from the lower point of the roller in the direction of possible movement.
If the force is not directed horizontally, then it should be decomposed into two components directed horizontally and vertically. The vertical component should be added to the force , and we again come to the scheme of the action of the forces shown in Fig. 7.6.
The following approximate laws have been established for the largest moment of a pair of forces preventing rolling:
1. The largest moment of a pair of forces that prevents rolling does not depend on the radius of the roller in a fairly wide range.
1. limit value moment is proportional to normal pressure and equal to it normal reaction: .
The coefficient of proportionality δ is called rolling friction coefficient at rest or friction coefficient of the second kind. The coefficient δ has the dimension of length.
3. The coefficient of rolling friction δ depends on the material of the rink, the plane and the physical condition of their surfaces. The coefficient of friction during rolling in the first approximation can be considered independent of the angular velocity of the roller and its sliding speed on the plane. For the case of a wagon wheel rolling along a steel rail, the rolling friction coefficient is δ=0.5mm.
The laws of rolling friction, as well as the laws of sliding friction, are valid for not very large normal pressures and not too easily deformed roller and plane materials.
These laws make it possible not to consider the deformations of the rink and the plane, considering them to be absolutely rigid bodies touching at one point. At this point of contact, in addition to the normal reaction and the friction force, a couple of forces must also be applied to prevent rolling.
In order for the roller not to slip, the following condition must be met:
In order for the roller not to roll, the condition must be satisfied
What is the coefficient of friction in physics and what is it related to? How is this value calculated? What is the numerical value of the coefficient of friction? We will give answers to these and some other questions that the main topic touches upon in the course of the article. Of course, we will analyze concrete examples, where we are faced with a phenomenon in which the coefficient of friction appears.
What is friction?
Friction is one of the types of interactions that occur between material bodies. There is a process of friction between two bodies when they come into contact with one or another surface area. Like many other types of interaction, friction exists solely with an eye to Newton's third law. How does it work out in practice? Let's take two absolutely any bodies. Let it be two medium-sized wooden bars.
Let's start to lead them past each other, making contact over the areas. You will notice that moving them relative to each other will become noticeably more difficult than just moving them in the air. This is where the coefficient of friction begins to play its role. IN this case we can absolutely calmly say that the friction force can be described by Newton's third law: it, applied to the first body, will be numerically (in modulus, as they like to say in physics) the same friction force applied to the second body. But let's not forget that there is a minus in Newton's third law, which says that the forces, although they are equal in absolute value, are directed in different directions. Thus, the friction force is vector.
The nature of the friction force
sliding friction force
Earlier it was said that if an external force exceeds a certain maximum value allowed for the corresponding system, then the bodies included in such a system will move relative to each other. Whether one body will move or two, or more - all this is unimportant. It is important that in this case there is a force of sliding friction. If we talk about its direction, then it is directed in the direction that is opposite to the direction of sliding (or movement). It depends on what relative speed the bodies have. But this is if you go into all sorts of physical nuances.
It should be noted that in most cases it is customary to consider the force of sliding friction to be independent of the speed of one body relative to another. It also has nothing to do with maximum value static friction force. Great amount physical problems are solved precisely by using a similar behavior model, which makes it possible to significantly facilitate the solution process.
What is the coefficient of sliding friction?
This is nothing but the coefficient of proportionality, which is present in the formula that describes the process of applying the friction force to a particular body. The coefficient is a dimensionless quantity. In other words, it is expressed exclusively in numbers. It is not measured in kilograms, meters or something else. In almost all cases, the friction coefficient is numerically less than unity.
What does it depend on?
The coefficient of sliding friction depends on two factors: on what material the bodies that are in contact are made of, and also on how their surface is treated. It can be embossed, smooth, and some special substance can be applied to it, which will either reduce or increase friction.
How is the force of friction directed?
It is directed to the side that is opposite to the direction of movement of two or more contacting bodies. The direction vector is applied along the tangent line.
If contact occurs between a solid and a liquid
In the event that a solid body contacts a liquid (or some volume of gas), we can talk about the emergence of a force of so-called viscous friction. It, of course, will be numerically much less than the force of dry friction. But its direction (the vector of action) remains the same. In the case of viscous friction, one cannot speak of rest.
The corresponding force is related to the speed of the body. If the speed is small, then the force will be proportional to the speed. If high, then it will be proportional to the square of the speed. The coefficient of proportionality will be inextricably linked with the shape of the bodies between which there is contact.
Other cases of friction force occurrence
This process also takes place when a body is rolling. But usually they are neglected in problems, since the rolling friction force is very, very small. This, in fact, simplifies the process of solving the corresponding problems, while maintaining a sufficient degree of accuracy of the final answer.
internal friction
This process is also called in physics by the alternative word "viscosity". In fact, it is an offshoot of transference phenomena. This process is characteristic of fluid bodies. And we are talking not only about liquids, but also about gaseous substances. The property of viscosity is to resist the transfer of one part of a substance relative to another. In this case, the work necessary to move the particles is logically performed. But it is dissipated in the surrounding space in the form of heat.
The law that determines the force of viscous friction was proposed by Isaac Newton. It happened in 1687. The law still bears the name of the great scientist. But all this was only in theory, and experimental confirmation was obtained only at the beginning of the 19th century. Corresponding experiments were carried out by Coulomb, Hagen and Poiseuille.
So, the force of viscous friction, which affects the liquid, is proportional to the relative velocity of the layers, as well as the area. At the same time, it is inversely proportional to the distance at which the layers are located relative to each other. The coefficient of internal friction is a coefficient of proportionality, which in this case is determined by the type of gas or liquid substance.
Another coefficient will be determined in a similar way, which takes place in situations with the relative motion of two currents. This is, respectively, the coefficient of hydraulic friction.
