In a special section of physics - dynamics, when they study the motion of bodies, they consider the forces acting on the moving system. The latter can perform both positive and negative work. Consider in this article what the work of friction force is and how it is calculated.
The concept of work in physics
In physics, the concept of "work" is different from the ordinary idea of this word. Under the work understand the physical quantity, which is equal to the scalar product of the force vector by the displacement vector of the body. Suppose that there is some object on which the force F¯ acts. Since other forces do not act on it, the vector of its displacement l¯ in the direction coincides with the vector F¯. The scalar product of these vectors in this case will correspond to the product of their modules, that is:
A = (F¯ * l¯) = F * l.
The value A is the work of the force F¯ to move the object to a distance l. Given the dimensions of the quantities F and l, we find that the work is measured in newtons per meter (N * m) in the SI system. However, the unit N * m has its own name - this is the joule. This means that the concept of work coincides with the concept of energy. In other words, if a force of 1 Newton moves the body 1 meter, then the corresponding energy costs are equal to 1 Joule.
What is the friction force?
The study of the work of the friction force is possible if you know what kind of force in question. Friction in physics is a process that prevents any movement of one body over the surface of another when these surfaces are brought into contact.
If we consider exclusively solid bodies, then for them there are three types of friction:
These forces act between contacting surfaces and are always directed against the movement of bodies.
The static friction prevents the occurrence of the movement itself, sliding friction manifests itself in the process of movement, when the surfaces of the bodies glide along each other, and rolling friction exists between the body that rolls along the surface and the surface itself.
An example of the action of resting friction is a car that stands on a hand brake on a hillside. Sliding friction manifests itself when a skier moves in the snow or a skater moves on ice. Finally, rolling friction acts while the car wheels are moving along the road.
The forces for all three types of friction are calculated by the following formula:
F t = μ t * N.
Here N is the force support reaction , μ t is the friction coefficient. Force N shows the magnitude of the impact of support on the body perpendicular to the plane of the surface. As for the parameter µ t , it is measured experimentally for each pair of rubbing materials, for example, wood-wood, steel-snow, and so on. The measured results are collected in special tables.
For each friction force, the coefficient µ t has its own value for the selected pair of materials. Thus, the coefficient of rest friction is greater than that for sliding friction by several tens of percent. In turn, the rolling coefficient is 1-2 orders of magnitude less than that for sliding.
Friction force work
Now, having become acquainted with the concepts of work and with the types of friction, you can go directly to the topic of the article. Let us examine in order all types of friction forces and see what work they perform.
Let's start with the friction of rest. This species manifests itself when the body does not move. Since there is no motion, it means that its displacement vector l¯ is equal to zero. The latter means that the work of the static friction force is also zero.
Sliding friction, by its definition, acts only when the body moves in space. Since the force of this type of friction is always directed against the movement of the body, it means that it does a negative job. The value of A can be calculated by the formula:
A = -F t * l = -µ t * N * l.
The work of the sliding friction force is aimed at slowing down the movement of the body. As a result of this work, the mechanical energy of the body goes into heat.
Friction rolling, like sliding, also involves body movement. The rolling friction force does a negative job, slowing down the initial rotation of the body. Since we are talking about the rotation of the body, it is convenient to calculate the value of the work of this force through the work of its moment. The corresponding formula is written as:
A = -M * θ, where M = F t * R.
Here θ is the angle of rotation of the body as a result of rotation, R is the distance from the surface to the axis of rotation (wheel radius).
Task with sliding friction force
It is known that a wooden block is located on the edge of an inclined wooden plane. The plane to the horizon is tilted at an angle of 40 o . Knowing that the coefficient of sliding friction is 0.4, the length of the plane is 1 meter, and the mass of the bar corresponds to 0.5 kg, it is necessary to find the work of sliding friction.
We calculate the sliding friction force. It is equal to:
F t = m * g * cos (α) * μ t = 0.5 * 9.81 * cos (40 o ) * 0.4 = 1.5 N.
Then the corresponding work A will be equal to:
A = -F t * l = -1.5 * 1 = -1.5 J.
Task with rolling friction force
It is known that the wheel swept along the road for some distance and stopped. The diameter of the wheel is 45 cm. The number of revolutions of the wheel before stopping is 100. Considering the rolling coefficient equal to 0.03, it is necessary to find what the work of the rolling friction force is. The mass of the wheel is 5 kg.
First, we calculate the moment of rolling friction:
M = F t * R = µ t * m * g * D / 2 = 0.03 * 5 * 9.81 * 0.45 / 2 = 0.331 N * m.
If the number of revolutions made by the wheel is multiplied by 2 * pi radians, then we get the angle of rotation of the wheel θ. Then the formula for the work has the form:
A = -M * θ = -M * 2 * pi * n.
Where n is the number of revolutions. Substituting the moment M and the number n from the condition, we obtain the desired work: A = - 207.87 J.