How to determine the moment of friction forces?

2024 Author: Angel Austin | [email protected]. Last modified: 2023-12-17 05:14

When they solve any problems in physics in which there are moving objects, they always talk about friction forces. They are either taken into account or they are neglected, but no one doubts the fact of their presence. In this article, we will consider what the moment of friction forces is, and also give problems to eliminate which we will use the knowledge gained.

The force of friction and its nature

Everyone understands that if one body moves on the surface of another in absolutely any way (slides, rolls), then there is always some force that prevents this movement. It is called dynamic friction force. The reason for its occurrence is related to the fact that any bodies have microscopic roughness on their surfaces. When two objects come into contact, their roughness begins to interact with each other. This interaction is both mechanical in nature (the peak falls into the trough) and occurs at the level of atoms (dipole attraction, van der Waals andothers).

When the bodies in contact are at rest, in order to set them in motion relative to each other, it is necessary to apply a force that is greater than that to maintain the sliding of these bodies over each other at a constant speed. Therefore, in addition to the dynamic force, the static friction force is also considered.

Properties of friction force and formulas for its calculation

The school physics course says that for the first time the laws of friction were stated by the French physicist Guillaume Amonton in the 17th century. In fact, this phenomenon began to be studied at the end of the 15th century by Leonardo da Vinci, considering a moving object on a smooth surface.

The properties of friction can be summarized as follows:

the force of friction always acts against the direction of movement of the body;
its value is directly proportional to the support reaction;
it does not depend on the contact area;
it does not depend on the movement speed (for low speeds).

These features of the phenomenon under consideration allow us to introduce the following mathematical formula for the friction force:

F=ΜN, where N is the reaction of the support, Μ is the coefficient of proportionality.

The value of the coefficient Μ depends solely on the properties of the surfaces that rub against each other. Table of values for some surfaces is given below.

For static friction, the same formula is used as above, but the values of the coefficients Μ for the same surfaces will be completely different (they are larger,than for sliding).

A special case is rolling friction, when one body rolls (does not slide) on the surface of another. For force in this case, apply the formula:

F=fN/R.

Here R is the radius of the wheel, f is the rolling coefficient, which, according to the formula, has the dimension of length, which distinguishes it from the dimensionless Μ.

Moment of force

Before answering the question of how to determine the moment of friction forces, it is necessary to consider the physical concept itself. The moment of force M is understood as a physical quantity, which is defined as the product of the arm and the value of the force F applied to it. Below is a picture.

Here we see that applying F to shoulder d, which is equal to the length of the wrench, creates a torque that causes the green nut to loosen.

Thus, the formula for the moment of force is:

M=dF.

Note that the nature of the force F does not matter: it can be electrical, gravitational or caused by friction. That is, the definition of the moment of the friction force will be the same as that given at the beginning of the paragraph, and the written formula for M remains valid.

When does frictional torque appear?

This situation occurs when three main conditions are met:

First, there must be a rotating system around some axis. For example, it can be a wheel moving on asph alt, or spinning horizontally on an axle.located gramophone music record.
Secondly, there must be friction between the rotating system and some medium. In the examples above: the wheel is subjected to rolling friction as it interacts with the asph alt surface; if you put a music record on a table and spin it, it will experience sliding friction on the surface of the table.
Thirdly, the resulting friction force should act not on the axis of rotation, but on the rotating elements of the system. If the force is central, that is, it acts on the axis, then the leverage is zero, so it will not create a moment.

How to find the friction moment?

To solve this problem, you must first determine which rotating elements are affected by the friction force. Then you should find the distance from these elements to the axis of rotation and determine what the friction force acting on each element is. After that, it is necessary to multiply the distances r_i by the corresponding values F_i and add up the results. As a result, the total moment of rotational friction forces is calculated by the formula:

M=∑r_iF_i.

Here n is the number of friction forces arising in the rotation system.

It is curious to note that although M is a vector quantity, therefore, when adding moments in scalar form, its direction should be taken into account. Friction always acts against the direction of rotation, so every moment M_i=r_iF_i will have one and the same sign.

Next, we will solve two problems where we useconsidered formulas.

Rotation of the grinder disc

It is known that when a grinder disk with a radius of 5 cm cuts metal, it rotates at a constant speed. It is necessary to determine what moment of force the electric motor of the device creates if the friction force on the metal of the disk is 0.5 kN.

Since the disk rotates at a constant speed, the sum of all moments of forces that act on it is equal to zero. In this case, we have only 2 moments: from the electric motor and from the friction force. Since they act in different directions, we can write the formula:

M₁- M₂=0=> M₁=M 2.

Since friction acts only at the point of contact of the grinder disk with the metal, that is, at a distance r from the axis of rotation, its moment of force is equal to:

M₂=rF=510^-2500=25 Nm.

Since the electric motor creates the same torque, we get the answer: 25 Nm.

Wood disc rolling

There is a disk made of wood, its radius r is 0.5 meters. This disc begins to roll on a wooden surface. It is necessary to calculate what distance it can overcome if its initial rotation speed ω was 5 rad/s.

The kinetic energy of a rotating body is:

E=Iω²/2.

Here I is the moment of inertia. The rolling friction force will cause the disc to slow down. The work done by it can be calculatedaccording to the following formula:

A=Mθ.

Here θ is the angle in radians that the disk can turn during its movement. The body will roll until all its kinetic energy is spent on the work of friction, that is, we can equate the written formulas:

Iω²/2=Mθ.

The moment of inertia of disk I is mr²/2. To calculate the moment M of the friction force F, it should be noted that it acts along the edge of the disk at the point of contact with the wooden surface, that is, M=rF. In turn, F=fmg / r (the reaction force of the support N is equal to the weight of the disk mg). Substituting all these formulas into the last equality, we get:

mr²ω²/4=rfmg/rθ=>θ=r 2^ω2^/(4fg).

Since the distance L traveled by the disk is related to the angle θ by the expression L=rθ, we get the final equality:

L=r³ω²/(4fg).

The value of f can be found in the table for rolling friction coefficients. For a tree-tree pair, it is equal to 1.510^-3m. We substitute all the values, we get: