Study of the dependence of friction force from the surface of the surface of contact bodies
We investigate, from which the friction force depends. To do this, we use a smooth wooden board, wooden bar and a dynamometer.
Picture 1.
First, check whether the friction force depends on the surface of the surface of contact bodies. Put the bar on the horizontally located board board with the largest surface area. Attaching the dynamometer to the bar, we will smoothly increase the force directed along the surface of the board, and note the maximum value of the friction force of rest. Then we will put the same bar on another line with a smaller surface area and again measure the maximum value of the friction force of rest. Experience shows that the maximum value of the friction force of the rest depends on the surface area of \u200b\u200bcontact bodies.
Repeating the same measurements with a uniform movement of the bar on the surface of the board, we are convinced that the stroke force of the slip also does not depend on the surface area of \u200b\u200bcontact bodies.
Study of the dependence of friction force from pressure force
We put on the first bar of the second same.
Figure 2.
By this, we will increase the strength perpendicular to the surface of the contact of the body and the table (it is called the power of pressure ~ $ \\ overline (P) $). If we again measure the maximum strength of rest friction, we will see that it has doubled. Putting on two bars the third, we discover that the maximum strength of friction of rest increased three times.
Based on such experiments, it can be concluded that the maximum value of the module of the friction force of the rest is directly proportional to the pressure force.
The interaction of the body and support causes deformation and body, and supports.
The strength of the elasticity of $ \\ overline (n) $ arising from the deformation of the support and the body acting on the body is called the power of the support reaction. According to the third law of Newton, the force of pressure and the strength of the support reaction is equal to the module and are opposite to the direction:
Figure 3.
Therefore, the previous conclusion can be formulated as follows: The module of the maximum strength of peace friction is proportional to the power of the support reaction:
The Greek letter $ \\ mu $ marked the proportionality coefficient called the friction coefficient (respectively resting or slipping).
Experience shows that the module of the friction force of $ F_ (MP) $, as well as the module of the maximum coarse friction force, is proportional to the module of the reaction force of the support:
The maximum value of the friction force of rest is approximately equal to the strength of the slip, the coefficients of friction and sliding are also approximately equal.
The dimensionless ratio of the $ \\ mu $ ratio depends:
- from the nature of rubbing surfaces;
- from the state of rubbing surfaces, in particular from their roughness;
- in the case of sliding, the friction coefficient is a speed function.
Example 1.
Determine the minimum value of the brake path of the car, which began braking on the horizontal section of the highway at the speed of $ 20 $ m / s. The friction coefficient is 0.5.
It is given: $ V \u003d 20 $ m / s, $ \\ mu \u003d $ 0.5 $.
Find: $ s _ (\\ min) $ -?
Solution: The brake path of the car will have the minimum value at the maximum value of the friction force. The module of the maximum friction force is:
\\ [(F_ (MP)) _ (\\ MAX) \u003d \\ Mu Mg \\]
The $ F_ (MP) $ for braking is directed opposite to the velocity of the $ \\ overline (V) _ (0) $ and the $ \\ overline (S) $ moving.
With a straight equilibrium movement, the projection of the movement of $ s_ (x) $ car on the axis parallel to the velocity vector $ \\ overline (V) _ (0) $ car is equal to:
Turning to modules of values, we get:
The time value can be found from the condition:
\ \
Then we get for the move module:
$ a \u003d \\ FRAC ((F_ (MP)) _ (\\ max)) (m) \u003d \\ FRAC (\\ Mu MG) (M) \u003d \\ Mu G $, then
$ S _ (\\ min) \u003d \\ FRAC (v_ (0) ^ (2)) (2 \\ Mu G) \\ APPROX $ 40 m.
Answer: $ s _ (\\ min) \u003d $ 40 m.
Example 2.
What force should be applied in a horizontal direction to a locomotive mass of $ 8 $ t to reduce its speed by $ 0.3 m / s for $ 5 $ seconds? The friction coefficient is $ 0.05. $
It is given: $ m \u003d $ 8000 kg, $ \\ delta v \u003d 0.3 $ m / s, $ \\ mu \u003d 0.05 $.
Find: $ F $ -?
Figure 4.
Write the body movement equation:
Sprogit on the axis x strength and acceleration:
Since $ F_ (MP) \u003d \\ MU MG $, A $ a \u003d \\ FRAC (V-V_ (0)) (T) \u003d \\ FRAC (\\ Delta V) (T) $, we get:
$ F \u003d M (\\ FRAC (\\ Delta V) (T) - \\ Mu G) \u003d 3440
The friction force occurs with the relative movement of two contacting bodies. Friction arising between the surfaces of various bodies call external friction. If friction is manifested between parts of the same body, it is called internal friction.
Depending on the nature of the relative movement of contacting solids distinguish friction of peace, friction slipand friction rolling.
The friction force of rest arises between fixed solid bodies when there are forces acting in the direction of the possible movement of the body.
The friction force of rest is always equal to the module and is directed oppositely, the parallel surface of contacting and seeking to lead this body in motion. The increase in this external force attached to the body leads to an increase in peace friction. The strength of friction of rest is aimed in the direction opposite to the possible movement of the body.
.
(2.14)
The strength of peace friction prevents the start of the movement. But there are cases when the force of friction of rest serves as the cause of the movement of the body. For example, man walking. When walking, the strength of friction of rest acting on the sole tells us acceleration. The sole does not slide back, and, it means that friction between her and the road is friction.
Slip friction forcesArguing when sliding one body differently directed along the surface of contacting bodies to the side opposite to movement. For the same solid bodies, the sliding friction force is approximately proportional to the force pressering one body to another, i.e., the power of the normal pressure of one body to another perpendicular to the surface on which these bodies come into contact:
. (2.15)
The proportionality coefficient is called sliding friction coefficient, depending on the material and the state of rubbing surfaces. When solving many practical tasks, you can consider the friction coefficient of constant value with acceptable accuracy.
Friction force acting on body in liquid or gas F V.Ter., as well as the friction force between solid surfaces is always directed opposite to the direction of the movement of the body and depends on the body velocity. At sufficiently low speeds we can assume that the friction force is proportional to the body velocity:
and at high speeds of movement - a square of speed:
(2.17)
The coefficients depend on the properties of fluid or gas and on the shape and size of the moving body.
Reduce friction force can be replaced by rolling: the use of wheels, rollers, ball and roller bearings. Rolling friction coefficienttens times less coefficient of slip friction. It is essential that rolling friction force is inversely proportional to the radius of a rolling body. In this regard, the transport intended for the movement of bad roads (all-terrain vessels), wheels have a large radius. Rolling friction force F TP.K. It is expressed by the formula:
, (2.18)
where N. - power of normal pressure, R. - Radius of a rolling body, μ - Rolling friction coefficient.
As already noted above, the grip friction force is always directed towards opposite the speed of movement. Therefore, the acceleration reported by the force of friction
Distinguish friction outdoor and domestic.
External friction It occurs with the relative movement of two contacting solids (sliding friction or friction of rest).Internal friction It is observed with the relative movement of parts of the same solid body (for example, liquid or gas).
Distinguish dry and liquid (or viscous) friction.
Dry friction It occurs between the surfaces of solid bodies in the absence of lubrication.
Liquid (viscous) is called friction between solid and liquid or gaseous medium or its layers.Dry friction, in turn, is divided into friction slip And friction rolling.
Consider the laws of dry friction (Fig. 4.5).
|
Fig. 4.5. |
 Fig. 4.6. |
We apply on the body lying on a fixed plane, external force, gradually increasing its module. Initially, the bar will remain immobile, it means that the outer force is backed by some force directed by a tangent of the rubbing surface opposite. In this case, there is a strength of rest friction.
It has been established that the maximum strength of friction of peace does not depend on the area of \u200b\u200bcontact bodies and is approximately proportional to the module forces of normal pressure N.:
μ 0 – the coefficient of friction of restdepending on the nature and state of rubbing surfaces.
When the module of the external force, and therefore, the peace friction force module will exceed the value F. 0, the body will start sliding on the support - friction of rest F. Tr. Pok will be replaced by friction slip F. SC (Fig. 4.6):
| F Tr \u003d μ N., | (4.4.1) |
Where μ is the friction coefficient of sliding.
Rolling friction occurs between the spherical body and the surface on which it rolls. The growth force of rolling is subject to the same laws as the stroke of the sliding, but the coefficient of friction μ; It is much smaller here.
Read more Consider the force of friction of sliding on the inclined plane (Fig. 4.7).
There are three forces on the body located on an inclined plane with dry friction: the strength of gravity, the normal force of the reaction of the support and the power of dry friction. The strength is the resultant forces and; It is directed down, along the inclined plane. From fig. 4.7 it can be seen that
| F \u003d Mg. sin α N \u003d Mg. COS α. |
 Fig. 4.7. |
- The body remains fixed on the inclined plane. The maximum angle of inclination α is determined from the condition ( F. TR) Max \u003d F. or μ. mG. cosα \u003d mG. SINα, therefore, Tg α max \u003d μ, where μ is the coefficient of dry friction. F. Tr \u003d μ. N. = mG. cosα
F \u003d Mg. sinα.
With α\u003e α max body will roll with acceleration
a \u003d g. (sinα - μ cosα),
F. SK \u003d. mA. = F - F. Tr.
If additional force F. Vn, directed along the inclined plane, is applied to the body, the critical angle α max and the acceleration of the body will depend on the size and direction of this external force.
What is friction coefficient in physics and what is it connected with? How to calculate this value? What is numerically equal to the friction coefficient? These and some other issues that affect the main topic, we will give answers during the article. Of course, we will analyze and concrete examples where we face a phenomenon in which the friction coefficient appears.
What is friction?
Friction is one of the types of interactions occurring between material bodies. There is a process of friction between two bodies when they are in contact with one or another surface area. Like many other types of interaction, friction exists exclusively with a light-up to the third Newton law. How does it work in practice? Take two absolutely any body. Let it be two wooden arrangements of medium sizes.
Let's start conducting their friend by a friend, carrying out contact in the squares. You will notice that to move them relative to each other will become much more difficult than just move them in the air. Here, the friction coefficient starts playing its role. In this case, we absolutely calmly say that friction force can be described by the third Newton law: it applied to the first body will be equal to numerically (module, as they like to speak in physics) the same friction attached to the second body . But we will not forget that in the third law of Newton there is a minus that says that the forces though equal to each other in the module, but are directed in different directions. Thus, the strength of friction is a vector.
Nature of friction strength
Slip friction force
Previously, it was said that if the external force exceeds a certain maximum value allowed for the corresponding system, then the bodies included in such a system will come into motion relative to each other. Will one body be moved or two, or more - all this does not matter. It is important that in this case there is a strong stroke force. If we talk about her direction, it is directed to the side, which is opposite to the direction of sliding (or movement). It depends on what relative speed have bodies. But this is if you go into different kinds of physical nuances.
It should be noted that in most cases it is customary to consider the force of friction of the slip independent on the speed of one body relative to the other. It is also in no way connected with the maximum value of the friction force of rest. A huge number of physical problems are solved precisely with the use of a similar behavior model, which makes it possible to significantly facilitate the decision-making process.
What is the coefficient of friction slip?
This is nothing more than a proportionality coefficient that is present in the formula describing the process of application of the friction force to one or another body. The coefficient is a dimensionless value. In other words, it is expressed exclusively by numbers. It is not measured in kilograms, meters or something else. Almost in all cases, the friction coefficient is numerically less than one.
What does it depends on?
The sliding friction coefficient of two factors depends: on what material the bodies are made, which undergo contact, and also from how their surface is treated. It can be embossed, smooth, and some special substance can be applied to it, which will be or reduced, or increase friction.
How is friction?
It is aimed aside, which is opposite to the direction of movement of two or more touching bodies. The direction vector is applied by a tangent line.
If contact occurs between solid body and liquid
In the event that the solid body with liquid (or some gas volume) occurs, we can talk about the emergence of the so-called viscous friction force. It, of course, is numerically significantly less than the power of dry friction. But its direction (vector of action) is preserved the same. In the case of viscous friction, they do not have to talk about peace.
The corresponding force with the velocity of the body is associated. If the speed is small, the force will be proportional to the speed. If high, then it will be proportional to the square of speed. The coefficient of proportionality will be inextricably linked with what form have the bodies between which contact occurs.
Other cases of friction force
This process takes place and when combating any body. But usually they neglect them in the tasks, since the growth of rolling friction is quite and very small. This, in fact, simplifies the process of solving the corresponding tasks, although it remains a sufficient degree of accuracy of the final response.
Internal friction
This process is also called in physics with an alternative word "viscosity". In fact, it is a branch of transfer phenomena. This process is peculiar to fluid bodies. Moreover, it is not only about liquids, but also about gaseous substances. The viscosity property lies in resistance when transferring one part of the substance relative to the other. At the same time, the work required for the movement of particles is logical. But it dissipates in the surrounding space in the form of heat.
The law that determines the strength of viscous friction was proposed by Isaac Newton. It happened in 1687. The law and to today wears the name of the great scientist. But all this was only in theory, and the experimental confirmation was obtained only at the beginning of the 19th century. The relevant experiments were put on a pendant, Hagen and Poazeil.
So, the strength of viscous friction, which has an impact on fluid, is proportional to the relative speed of the layers, as well as the area. At the same time, it is inversely proportional to that distance on which the layers are placed relative to each other. The internal friction coefficient is the proportionality coefficient, which in this case is determined by the gas variety or liquid substance.
Another coefficient will be determined in a similar way, which takes place in situations with the relative movement of two flows. This, respectively, the hydraulic friction coefficient.
Corner and cone friction.Many challenges on the balance of the body on the rough surface in the presence of friction force, it is convenient to solve geometrically. For this purpose, the concept of the angle and cone of the friction is used.
Let the solid body under the action of active forces are on the rough surface in the limiting state of equilibrium, i.e. Such a state, when the friction force reaches its greatest value at a given value of a normal reaction (Fig. 8.4). In this case, the complete reaction of the rough surface is rejected from normal to the total tangent plane of rubbing surfaces to the largest angle.
The angle φ between the total reaction of the rough body and the direction of the normal reaction is called the friction angle. The angle of friction φ depends on the coefficient of friction, i.e.
consequently, Tgφ \u003d ƒ, i.e. the tangent of the friction angle is equal to the coefficient of slip friction.
The friction cone is called the cone described by a complete reaction around the direction of the normal reaction. It can be obtained by changing the active forces so that the body on the rough surface is in the limit positions of equilibrium, striving to exit equilibrium in all possible directions lying in the total tangent plane of contacting surfaces. If the friction coefficient in all directions is the same, then the friction cone is circular.
If unequal, then the cone of the friction of the necrow, for example, in the case when the properties of contacting surfaces are different (due to a certain direction of the fibers or, depending on the direction of surface treatment of the body, if the processing occurs on a planer machine, etc.).
For the equilibrium of the body on the rough surface, it is necessary and enough that the line of action of the resultant active forces acting on the body passed inside the cone of the friction or in the limit state by forming it through its vertex (Fig. 8.5).
The body cannot be output from the equilibrium of any module for active force if its line of action passes inside the friction cone, i.e. A.<φ.
If the line of action of the equal active forces does not pass inside the friction cone or by forming it, i.e. a. \u003e φ (Fig. 8.5), the body on a rough surface cannot be in equilibrium, q\u003e F.
Task 1.On the body located on a rough horizontal surface, the force at an angle but \u003d 10 °. Determine whether the body will be out of the equilibrium position if the friction coefficient f.\u003d 0.2 (Fig. 4).
Decision. For a balanced flat system of converging strength, two equilibrium equations can be made:
Find from (2)
,
.
Since, then 
, or 
. Then.
Since the force is applied at an angle, less friction angle, the body will not come out of the equilibrium position.
Task 2.Body weighing 100. N. Hold on a rough inclined plane by force T.(Fig. 5). Slip friction coefficient between body and plane f.\u003d 0.6. Determine the value of power T. When the body is equilibrium on the plane, if a. \u003d 45 °.
Decision. Two cases of body equilibrium are possible and, accordingly, two limit strength values T. With two directions of friction force:
,
where is the coefficient that takes into account the direction of movement, \u003d ± 1.
Make up for a flat arbitrary system of forces two equilibrium equations.
