The world around us would not be so stable if there were no frictional force of rest. Houses, cars, objects on tables and shelves, and even the person himself, could not stand in one place and would constantly slide off. In the article, we will open the question that this is the force of rest friction.
Horizontal item
Before answering the question that this is the rest friction force, we study the position of the body on a horizontal surface in terms of dynamics.
Everyone knows that if you put a glass of water on the table, then it will rest in its place until someone takes it again. What forces act on the glass? Of course, gravity or body weight. Its value is directly proportional to the mass, and the vector is directed downward vertically.
At first glance, it may seem that no force exerts any effect on the glass. However, if this were so, then he would have fallen through the table due to the action of gravity. So, there is some opposition to this force, which is equal in magnitude to it and opposite in direction. This counteraction is the support reaction. We will denote it by the letter N.
The physical cause of the reaction of the support is the elastic force acting on the body from the side of the deformed surface (the surface of the table acts vertically upwards on a glass of water). In most cases, these deformations are not visible to the naked eye, but they are always present, no matter how small the body weight is, and no matter how hard and durable the surface material is.
Thus, the mathematical record of the glass on the table looks like this:
N = m * g
External force
We continue to consider the above example from the point of view of physics. Suppose we wanted to move a glass of water from one corner of the table to another. To do this, some external force must be applied. Moreover, if it is applied vertically down or up, then we will not achieve the movement of the glass along the surface of the table. That is, the force should be parallel to the plane of the table.
When a small parallel force is applied, you will notice that the glass continues to be at rest. The reaction forces of the support and body weight are directed perpendicular to the surface; therefore, they do not exert counteraction to the external parallel force. The force of rest friction is responsible for this counteraction. This is the interaction that appears only in the case of an external parallel force. Recall that if you do not touch the glass, then only the body weight and the reaction of the table surface act on it.
Thus, the resting friction force is the force that occurs in the contact area of two solid surfaces and prevents any relative displacement of these surfaces.
Why does this power appear?
We examined how rest friction manifests itself by the example of a glass of water on a table. Nevertheless, the question remains: why does this power exist?
At rest, the friction force is mainly due to the presence of roughness on the surfaces of mechanical contact. Microscopic roughness is always present on any surface, even perfectly polished. Microscopic depressions of one surface fall on the peaks of another, which leads to a simple mechanical engagement of bodies. It is to overcome this linkage that an external force tangential to the surface is directed.
There is another reason for the rest friction, which begins to play an increasingly important role, the more smooth the contact surfaces. This is the electrochemical interaction of atoms and molecules of different bodies. This reason becomes obvious if you polish two metal sheets, then attach them to each other and try to move.
Maximum resting friction
When the physics teacher asks the pupils the question, according to which formula, the force of rest friction is calculated (in the 7th grade, they begin to study friction), then they together name the following expression:
F t = µ * N
Where µ is a certain coefficient. Such an answer of schoolchildren cannot be considered 100% correct. The fact is that the maximum possible magnitude of the force in question is determined by this formula, but it can be even less, which most often happens in practice.
It should be remembered that the rest friction force is a variable characteristic. Always, when the body is at rest, its value is equal in magnitude to the force external to the surface tangent to the surface. When the body begins to move, then talking about static friction is no longer possible (a different type of friction appears - sliding). The above expression for F t allows one to calculate the static friction at the moment the body begins to move.
Coefficient of friction µ
In the formula for the maximum force F t , the coefficient of rest friction force was introduced - the value µ. It is dimensionless because the reaction of the N support is measured in Newtons.
This coefficient cannot be theoretically determined, since it depends on a large number of factors: surface materials, quality of their processing (roughness), surface cleanliness, temperature, microscopic structure and some others. In this regard, the value of µ is measured experimentally. For example, if you attach a dynamometer to the glass in the example above and measure the maximum force F t , then, knowing the mass of the glass with water, you can determine µ.
The values of the coefficient µ are entered in special tables for each pair of contact surfaces. So, in our example, glass moves along a tree. The corresponding µ is 0.25.
Next, we give an example of solving two problems in which it will be clear that this is the rest friction force, and how it works in practice.
The task of determining the change in friction
It is known that a glass of water with a total mass of 400 grams stands on a horizontal table. The table is tilted 5 o to the horizon. How does static friction change with this? Will the glass begin to slide across the table?
Since the glass initially stands on a horizontal table, the rest friction is zero. When the table is tilted, a component of the gravity vector parallel to its surface appears. It is equal to:
F = m * g * sin (α)
Since the rest friction force is equal to the value of F, we obtain that its change as a result of the slope will be 0.34 N.
Now we will answer the second question of the problem. When tilted by 5 o maximum rest friction force is equal to:
F t = μ * m * g * cos (α)
We get the value of F t = 0.98 N. Since this value is greater than the calculated rest friction force, the glass will not move on the table at an angle of inclination of 5 o .
The task of determining the work of rest friction
In physics, work is called the scalar product of the displacement vector and the force vector. When the body is at rest, the module of its movement is equal to zero. The latter means that the force in question cannot do the work (it acts only at rest).
Now imagine the following situation: two bars lie on top of each other. The lower force is affected by the force F, which brings it into uniform acceleration with acceleration a. The upper bar is relatively stationary relative to the lower one. Since the upper bar also moves with acceleration a, and only the rest friction force acts on it, it turns out that it does a positive job. What is this job equal to? During the movement t, the static friction force does the work:
A = F t * l = F * a * t 2/2
Note that if the value of F turns out to be greater than the maximum value of F t , then the upper block will slide off the surface of the lower one.