Dry friction

Kvant 1970, No. 1 p. 37-43 Tag C7KG

Rough automatic draft, low quality: expect mistakes and awkward wording. It will be replaced by a better translation. Original →

We interact with the trainer at every step. It would be more accurate to say that without training we cannot take a single step. But despite the large role that friction plays in our lives, a properly complete picture of the origin of friction has not yet been created, and this question remains unclear. This is not even due to the fact that friction is of a complex nature, but rather to the fact that experiments with friction are very sensitive to surface treatment and are therefore difficult to reproduce.

Here’s an example. The English physicist Hardy studied the dependence of the friction force between glass plates on temperature. He carefully treated the plates with bleach and washed them with water, removing fats and dirt. Friction increased with temperature. The routine was repeated many times, and each time approximately the same results were obtained. But one day, my plastic

Above: copy from figure Leonardo da Vinci.

tiniki, Gardin rubbed them with his fingers. Try not to change depending on the temperature. Having wiped the plates, Gardin, as he himself believes, removed a very thin layer of glass from them, which had changed its properties due to interaction with bleach and water.

When talking about trenium, three somewhat distinct physical phenomena are distinguished: resistance when a body moves in a liquid or gas - it is called liquid trenni; the resistance that occurs when a body slides on some surface is a sliding trene, or a dry trene; and the resistance that occurs when a body rolls is called rolling friction. This article is about dry training.

The first studies of friction that we know of were carried out by Leonardo da Vinci approximately 450 years ago. He measured the strength of friction acting on wooden parallelepids, sliding along the board, and, by placing the bars on different faces, he determined the dependence of the strength of friction on the area of support. But Leonardo da Vinci’s works were not published. They became known after the classical laws of friction in the 17th and 18th centuries. rediscovered by French scientists Amonton and Coulomb.

These laws are: 1) the force of friction $F$ is directly proportional to the force $N$ of the normal pressure of the body on the surface on which the body moves: $F = kN$ , where $k$ is a dimensionless coefficient called the friction coefficient; 2) friction strength does not depend on the contact area between surfaces; 3) the friction coefficient depends on the properties of the rubbing surfaces; 4) the strength of friction does not depend on the speed of the body.

Three hundred years of friction research have confirmed correctly the first three laws proposed by Amonton and Coulomb. Only the last one, the fourth, turned out to be incorrect. But this became clear much later, when railways appeared and drivers noticed that when braking the train did not behave as the engineers had predicted.

Amonton and Coulomb declared the origin of friction to be quite simple. Both surfaces are uneven and covered with small humps and depressions. When moving, the protrusions cling to each other, and therefore the body rises and falls all the time. In order to rotate the body up the “hills”, a certain force must be applied to it. If the protrusions are larger, then more force is needed. But this explanation contradicts one very important phenomenon: energy is processed on the train. A cube sliding along a horizontal surface stops. His energy is spent on trenna. And when rising and falling, the body does not waste its energy. Remember the American Mountain ride. When the sled rolls down the hill, its potential energy turns into kinetic energy, and the speed of the sled increases, and when the sled reaches a new height, the kinetic energy, on the contrary, turns into potential energy. The energy of the sled is reduced due to the training, but not due to the ascent and descent. The situation is similar when one body moves over the surface of another. Here, the loss of energy on trenna also cannot be associated with the fact that the protrusions of one body climb onto the protuberances of another.

There are still objections. For example, simple experiments on changing the friction silite between polished glass plates showed that with improved polishing of surfaces, the friction silite initially does not change, and then increases, and does not decrease, as would be expected based on the model of the phenomenon proposed by Amonton and Coulomb.

The friction mechanism is much more complex. Due to the irregularities, they only touch at certain points at the tops of the protrusions. Here, the molecules of the contacting bodies approach at distances commensurate with the distance between the molecules in the bodies themselves, and are specialized. A strong bond is formed, which will be inserted when you press on the body. At

With the movement of the body, connections constantly arise and break. In this case, molecular vibrations occur. Energy is wasted on these vibrations.

The actual contact area is generally from one to two thousand square microns. It practically does not depend on the size of the body and is determined by the suitability of the surface, their treatment, temperature and the force of normal pressure. If you press on the body, the protrusions become compressed, and the area of actual contact increases. The friction force also increases.

With significant surface roughness, mechanical substitution between the “kholams” begins to play a large role in increasing the friction force. When they move, they become crushed, and at the same time vibrations of the molecules also arise.

The experience with polished glass plates is now clear. While the surfaces were “rough”, the number of contacts was small, but after good polishing it increased. Another example can be given of increasing friction with improving the surface. If you take two metal bars with clean polished surfaces, they will fit together. The trains here become very large, since the actual contact area is large. The forces of molecular cohesion, which are responsible for trene, turn two bars into a monolith!

You can do the following experiment at home. Place the glass on a glass plate and tie a string to the stem and drain the glass. Then wet the glass and stem of the glass with water, which will remove any grease or dirt. Put it out again. Now this is much more difficult to do. Clean contact glass - glass is not easy to break. If you look closely at the surface, you may even notice scratches. It turns out that tearing out pieces of glass is easier than breaking contact!

The friction model we considered is quite crude. We did not dwell here on the diffusion of molecules, that is, on the penetration of molecules of one body into another, on the role of electronic charges arising on contacting surfaces, on the role and mechanism of action of a lubricant. These questions are largely unclear and explanations controversial. One can only be surprised that with such complexity, the training is described only by a simple law: $F = kN$ . And although the friction coefficient $k$ is not very constant and varies somewhat from one point on the surface to another, for many surfaces that we often encounter in technology, it is possible to make fairly good estimates of the expected friction force.

Dry training has one essential feature: rest training. If in a liquid or gas a friction occurs only when a body moves and the body can be moved by applying even a very small force to it, then with a dry friction the body begins to move only when the projection of the force $F$ applied to it onto the plane tangent to the surface on which the body lies becomes greater than a certain value. Until the body begins to slip, the friction force acting on it is equal to the tangential component of the applied force and is directed in the opposite direction. As the applied force increases, friction also increases until it reaches a maximum value equal to $kN$ , at which sliding begins. The training doesn’t change any more.

This is often forgotten when solving problems. To the question “what is the force on a table weighing 30 kg standing on the floor if the friction coefficient is 0.4,” the majority confidently answers: “12 kg,” which is incorrect. The friction force is zero, otherwise the table would move in the direction of the friction force, since there are no other horizontal forces.

So, if the body is finished, then in order to drain it from its place, a force must be applied to the body that is greater than the maximum possible static friction force, which is determined by the strength of the molecular bonds. But what happens if the body is already moving? What force must be applied so that the body begins to move in another direction? It turns out, as small as you like. This is due precisely to the fact that the force cannot be greater than the maximum force of static friction.

Try a simple experiment. Take a book and place it with one edge on top of another thicker book. The result is an inclined plane. Now place a matchbox with a thread attached to this plane. If the box slips, then reduce the tilt of the plane by taking a thicker book stand. Pull the string of selection boxes. At the same time, it is also pushed down! Reduce the inclination of the plane and pull the thread again. Same picture. The box slips even at very small angles of inclination of the plane. For some reason, the friction force, equal to the one holding the boxes on the plane, became very small.

Let’s try to understand what’s going on here. If the box were moving only horizontally, then parallel to the edge of the inclined plane a friction force equal to $kN$ would act on it. In order for the box not to slide down, a friction force must act upward on it, equal in magnitude to the projection of the weight of the box on the inclined plane. The resultant of these two friction forces is greater than $kN$ , but this cannot be. This means that the box should slide off the inclined plane.

Take a block, attach a thread to it and, placing the block on a horizontal plane, pull the thread at a constant speed $v_1$ . By applying a force perpedicular to $v_1$ to the block, it can also be made to move in this direction with a constant speed $v_2$ . The friction force will be equal to $kN$ and directed opposite to the speed $v$ of the movement of the block relative to the plane

$F_1 = F_{\text{tp}} \cos \beta, \quad F_2 = F_{\text{tp}} \sin \beta,$

where $\beta$ is the angle between vectors $v_1$ and $v$ , and $tg \beta = \frac{v_2}{v_1}$ .

The $F_1$ component of the friction force is balanced by the tension force of the thread, and the $F_2$ “lateral” force applied to the bar. Because

$\sin \beta = \frac{tg \beta}{\sqrt{1 + tg^2 \beta}},$

That

$F_2 = F_{\text{tp}} \frac{v_2}{\sqrt{1 + \left(\frac{v_2}{v_1}\right)^2}} = F_{\text{tp}} \frac{v_2}{\sqrt{v_1^2 + v_2^2}}.$

If $v_2 \ll v_1$ , then the angle $\beta$ is small and $\sin \beta \approx tg \beta$ .

In this case, $F_2 = F_{\text{tp}} \mathrm{tg} \beta = kN \frac{v_2}{v_1}$ , and the component of the friction force, affecting the “sideways” movement of the block, turns out to be proportional to the speed of this movement. The picture turns out to be the same as at low speeds with liquid friction. This means that a block moving in a certain direction can also be made to move in a perpendicular direction with an arbitrarily small force.

An interesting conclusion can now be drawn for a box moving along an inclined plane. Here $F_2 = P \sin \alpha$ , and $N = P \cos \alpha$ (P is the weight of the box, $\alpha$ is the angle of inclination of the plane to the horizon). Then

$P \sin \alpha = k \cdot P \cos \alpha \frac{v_2}{\sqrt{v_1^2 + v_2^2}},$

where

$v_2 = v_1 \frac{tg \alpha}{\sqrt{k^2 - tg^2 \alpha}}.$

(This is true, of course, only for $tg \alpha < k$ , since at large angles of inclination of the plane to the horizon, the boxes are no longer held on the plane by the force of friction.)

At small angles of inclination of the plane to the horizon (such that $tg \alpha \ll k$ )

$v_2 = v_1 \frac{tg \alpha}{k},$

that is, the speed of sliding of the box is proportional to the speed of its movement parallel to the oblique edge

plane and the tangent of the angle of the overhead plane to the horizon.

This conclusion can be easily verified experimentally. Since in uniform motion the path traversed by the body is proportional to the speed, the ratio of the speed $v_2$ to $v_1$ will be equal to the ratio of the segments that the box will travel in these directions.

The phenomenon in question is quite common and occurs quite often. For example, it is known that when the electric motor brakes sharply, the transmission belt often slips off the pulleys. This happens because when the driver brakes, the belt begins to slip relative to the pulleys, and a small force is enough to push the belt to the side.

Since there is usually a slight misalignment in the installation of the pulleys and belt, this force is a component of the belt tension force. Here are more examples. When they want to pull a nail out of the wall without placing kleshes, they bend it and drag it, simultaneously turning it around its axis. For the same reason, when braking sharply, it automatically loses control: the car “skids”. The wheels slip on the road, and the lateral force arises due to the unevenness of the road.

Let us now dwell on the last Amonton-Coulomb law: the friction force does not depend on the speed of the body. This is not entirely true.

The question of the dependence of friction force on speed is of very important practical importance. And although the experiments here have many specific difficulties, they pay off using the information obtained, for example, in the theory of cutting metals, in calculating the movement of bullets and shells in the barrel, etc.

Obviously they believe that in order to move a body from its place, more force must be applied to it than in order to drag the body. In most cases, this is due to contamination of the surface of the working bodies. For example, for pure metals such a jump in the friction force is not observed. Experiences with the movement of a bullet in

barrel showed that with increasing bullet speed, the magnitude of the friction force first kills quickly, then it decreases more and more slowly, and at speeds greater than 100 m/sec, it begins to increase. A graph of friction force versus speed is shown at figure. This can be roughly explained by the fact that a lot of heat is released at the point of contact. At a speed of about 100 m/sec, the temperature at the point of contact can reach several thousand degrees, and a layer of molten metal forms between the surfaces. The trene becomes liquid. At high speeds, the liquid train is proportional to the square of the speed.

It is interesting that the friction force of the bow on the string has approximately the same dependence on speed. That is why we can serve playing bowed instruments - violin, cello, viola.

With a uniform movement of the bow, the string is carried away by it and stretched. Along with the tension of the string, the friction force between the bow and the string increases. When the magnitude of the friction force becomes the maximum possible, the string begins to slip relative to the bow. If the friction force did not depend on the relative speed of the bow and string, then obviously the deviation of the string from the equilibrium position would not change.

But when slipping, the friction decreases. Therefore, the string begins to move towards the equilibrium position. At the same time, the relative speed of the string increases, and this further decreases the friction force. When the string, having vibrated, moves in the opposite direction, its speed relative to the bow decreases, and the bow again grabs the string. Everything repeats itself. This is how the string vibrates. These vibrations do not die out, since the energy lost by the string during its movement is each time replenished by the work of the friction force, which confirms the string to the position at which the string breaks.

With this we can and will end the article on dry friction - a phenomenon whose nature we do not yet understand well, but we can describe with the help of laws that are fulfilled with satisfactory accuracy. This gives us the opportunity to explain many physical phenomena and make calculations necessary when building machines.

TASKS

Why does the car turn when its front wheels turn?
Place the stick horizontally on your outstretched index fingers. Slowly move your right hand towards your left. Why does the stick also move, and in such a way that its balance is not disturbed?
Draw a graph of the dependence of the friction force acting on a block located on an inclined plane on the angle of inclination of the plane to the horizon.
Draw a graph of the dependence of the friction force acting on a block located on a horizontal surface on the angle,

which is the force applied to this block with the horizon. The force applied to the block is less than the weight of the block, and the angle varies from 0 to $\frac{\pi}{2}$ .

Pipes that break during drilling can be lifted using the device shown at figure. Rods $AB$ and $AC$ are hingedly attached to the cable at point $A$ . The lifting of the pipe is carried out due to the friction of the rods on the pipe. Find conditions under which pipes of any weight can be lifted using such a device. The cable is, of course, strong enough.
A small cube of mass $m$ lies on a rough plane inclined to the horizon at an angle $\alpha$ . Friction coefficient $k=2tg\alpha$ . Determine the minimum force $F$ (see figure) with which the cube must be pushed to start moving.
A flywheel of radius $R=20$ cm is mounted on a horizontal axis of radius $r=2$ cm. Having secured the axis, the flywheel can be removed by pulling it with a force of $F=100$ kg. To make it easier to remove the flywheel, a force of $F_1=8$ kg is applied to its rim, creating a rotational moment relative to the axis. With what minimum force $F_2$ should you pull the flywheel along the axis?
Why does a poorly lubricated door squeak?