Friction is a physical phenomenon with which a person fights to reduce it in any rotating and sliding parts of mechanisms, without which, however, it is impossible to move any of these mechanisms. In this article, we consider from the point of view of physics what is the rolling friction force .
What types of friction forces exist in nature?
First of all, let us consider what place rolling friction occupies among other friction forces. These forces result from the contact of two different bodies. It can be solid, liquid or gaseous. For example, a plane’s flight in the troposphere is accompanied by the presence of friction between its body and air molecules.
Examining exclusively solid bodies, they release the frictional forces of rest, sliding, and rolling. Each of us noticed: in order to move the boxes located on the floor, it is necessary to apply some force along the floor surface. The value of the force that will bring the box out of rest is modulo equal to the rest friction force. The latter acts between the bottom of the box and the floor surface.
As soon as the box has started its movement, it is necessary to apply constant force to keep this movement uniform. This fact is connected with the fact that the sliding friction force acts on the latter between the floor contact and the box. As a rule, it is several tens of percent less than rest friction.
If you put round cylinders of solid material under the boxes, then moving it becomes much easier. The rolling friction force will act on the cylinders rotating in the process of movement under the box . She is usually much smaller than the previous two forces. That is why the invention of the wheel by mankind has become a huge leap towards progress, because people got the opportunity to move much larger loads with the help of a small applied force.
Physical nature of rolling friction
Why does rolling friction force occur? This question is not easy. To answer it, you should consider in detail what happens to the wheel and the surface during the rolling process. First of all, they are not perfectly smooth - neither the surface of the wheel nor the surface on which it rolls. However, this is not the main reason for the appearance of friction. The main reason is the deformation of one or both bodies.
Any bodies, of whatever solid material they consist, are deformed. The greater the weight of the body, the greater the pressure it exerts on the surface, which means that it deforms itself at the point of contact and deforms the surface. In some cases, this deformation is so small that it does not exceed the elastic limit.
In the process of rolling the wheel, the deformed sections after the termination of contact with the surface restore their original shape. Nevertheless, these deformations are cyclically repeated with a new rotation of the wheel. Any cyclic deformation, even if it lies in the elastic limit, is accompanied by hysteresis. In other words, at the microscopic level, the shape of the body before and after deformation is different. The hysteresis of the deformation cycles in the process of rolling the wheel leads to a "dispersion" of energy, which is manifested in practice in the form of the appearance of rolling friction forces.
Perfect body swing
An ideal body in this case means that it is non-deformable. In the case of an ideal wheel, the area of its contact with the surface is zero (it touches the surface along the line).
Let us characterize the forces that act on the non-deformable wheel. Firstly, there are two vertical forces: body weight P and support reaction force N. Both forces pass through the center of mass (wheel axis), therefore they do not take part in creating the torque. For them you can write:
P = N
Secondly, these are two horizontal forces: the external force F, which pushes the wheel forward (it passes through the center of mass), and the rolling friction force f r . The latter creates a torque M. For them, we can write the following equalities:
M = f r * r;
F = f r
Here r is the radius of the wheel. These equalities contain a very important conclusion. If the friction force f r is infinitesimal, then it will still create a torque that will lead to the movement of the wheel. Since the external force F is equal to f r , then any infinitely small value of F will cause the wheel to roll. This means that if the rolling body is ideal and does not experience deformation during movement, then we can’t talk about any rolling friction force.
All existing bodies are real, that is, they undergo deformation.
Real body rolling
Now we will consider the situation described above only for the case of real (deformable) bodies. The contact area of the wheel and the surface will no longer be zero, it will have some finite value.
We will analyze the forces. Let's start with the action of vertical forces, that is, the weight and reaction of the support. They are still equal to each other, that is:
N = p
However, the force N now acts vertically upward not through the wheel axis, but is somewhat offset from it by a distance d. If we represent the area of contact of the wheel with the surface in the form of the area of a rectangle, then the length of this rectangle will be the thickness of the wheel, and the width will be 2 * d.
Now we turn to the consideration of horizontal forces. The external force F still does not create a torque and is equal to the friction force f r in absolute value, that is:
F = f r .
The moment of forces leading to rotation will create friction f r and the reaction of the support N. Moreover, these moments will be directed in different directions. The corresponding expression is:
M = N * d - f r * r
In the case of uniform motion, the moment M will be zero, therefore, we obtain:
N * d - f r * r = 0 =>
f r = d / r * N
The last equality, taking into account the above formulas, can be rewritten as follows:
F = d / r * p
In fact, we got the main formula for understanding the rolling friction force. Further in the article we will analyze it.
Rolling resistance coefficient
This coefficient has already been introduced above. A geometric explanation was also given. It is about the value of d. Obviously, the larger this value, the greater the moment creates the reaction force of the support, which prevents the movement of the wheel.
The rolling resistance coefficient d, in contrast to the coefficients of rest and sliding friction, is a dimensional quantity. It is measured in units of length. In the tables it is usually given in millimeters. For example, for train wheels rolling on steel rails, d = 0.5 mm. The value of d depends on the hardness of the two materials, on the load on the wheel, on temperature and some other factors.
Rolling friction coefficient
Do not confuse it with the previous coefficient d. The rolling friction coefficient is denoted by the symbol C r and calculated by the following formula:
C r = d / r
This equality means that the value of C r is dimensionless. Namely, it is given in a number of tables containing information on the type of friction under consideration. This coefficient is convenient to use for practical calculations, since it does not imply knowledge of the radius of the wheel.
The value of C r in the vast majority of cases is less than the coefficients of friction and rest. For example, for automobile tires moving on asphalt, the value of C r is within a few hundredths (0.01 - 0.06). However, it increases significantly with the movement of flat wheels on grass and sand (≈0.4).
Analysis of the obtained formula for the force fr
We write again the formula for the rolling friction force obtained above:
F = d / r * P = f r
It follows from the equality that the larger the diameter of the wheel, the less force F should be applied in order for it to start moving. Now we write this equality through the coefficient C r , we have:
f r = C r * P
As you can see, the friction force is directly proportional to the weight of the body. In addition, with a significant increase in weight P, the coefficient C r itself changes (it increases due to an increase in d). In most practical cases, C r lies within a few hundredths. In turn, the value of the sliding friction coefficient lies within a few tenths. Since the formulas are the same for the rolling and sliding friction forces, rolling is advantageous from an energy point of view (the force f r is less by an order of magnitude of the sliding force in most practical situations).
Rolling condition
Many of us have encountered the problem of slipping car wheels when driving on ice or on mud. Why is this happening? The key to the answer to this question lies in the ratio of the absolute values of the rolling friction forces and the rest. Once again, we write out the formula for rolling:
F ≥ C r * P
When the force F is greater than or equal to the rolling friction, then the wheel will begin to roll. However, if this force sooner exceeds the amount of static friction, then the wheel will slip earlier than its rolling.
Thus, the slippage effect is determined by the ratio of the coefficients of rest friction and rolling friction.
Ways to counteract the slipping of a car wheel
The rolling friction of the wheel of a car located on a slippery surface (for example, on ice) is characterized by a coefficient C r = 0.01-0.06. However, values of the same order are characteristic of the coefficient of rest friction.
To avoid the risk of wheel slippage, use a special "winter" rubber, in which metal spikes are screwed. The latter, crashing into the ice surface, increase the coefficient of friction of rest.
Another way to increase resting friction is to modify the surface on which the wheel moves. For example, by sprinkling it with sand or salt.