Any movement of the body in space, which leads to a change in its total energy, is associated with work. In this article, we will consider what kind of value this is, in which mechanical work is measured, and how it is indicated, and we will also solve an interesting problem on this topic.
Work as a physical quantity
Before answering the question of what is measured by mechanical work, we will get acquainted with this quantity. According to the definition, the work is a scalar product of force by the displacement vector of the body that this force caused. Mathematically, we can write the following equality:
A = (F¯ * S¯).
Parentheses indicate scalar product. Given its properties, in explicit form, this formula can be rewritten as follows:
A = F * S * cos (α).
Where α is the angle between the force and displacement vectors.
From the recorded expressions it follows that the work is measured in Newtons per meter (N * m). As you know, this value is called the joule (J). That is, in physics, mechanical work in units of work Joules is measured. One Joule corresponds to such work, in which a force of one Newton, acting parallel to the movement of the body, leads to a change in its position in space by one meter.
As for the designation of mechanical work in physics, it should be noted that for this they most often use the letter A (from it. Ardeit - labor, work). In English literature, you can find the designation of this value with the Latin letter W. In Russian literature, this letter is reserved to indicate power.
Work and energy
Analyzing the question of what mechanical work is measured in, we saw that its units coincide with those for energy. This coincidence is not accidental. The fact is that the physical quantity in question is one of the ways energy is manifested in nature. Any movement of bodies in force fields or in their absence requires energy costs. The latter go to change the kinetic and potential energy of bodies. The process of this change is characterized by the work performed.
Energy is a fundamental characteristic of bodies. It is stored in isolated systems, it can be transformed into mechanical, chemical, thermal, electrical and other forms. Work is only a mechanical manifestation of energy processes.
Work in gases
The above expression for the operation is basic. Nevertheless, this formula may be unsuitable for solving practical problems from various fields of physics, therefore, other expressions derived from it are used. One such case is gas work. It is convenient to calculate it using the following formula:
A = ∫ V (P * dV).
Here P is the pressure in the gas, V is its volume. Knowing what mechanical work is measured in, it is easy to prove the validity of the integral expression, indeed:
Pa * m 3 = N / m 2 * m 3 = N * m = J.
In the general case, pressure is a function of volume; therefore, the integrand can take an arbitrary form. In the case of an isobaric process, the expansion or contraction of the gas occurs at a constant pressure. In this case, the work of the gas is equal to the simple product of the quantity P and the change in its volume.
Work when the body rotates around an axis
Rotation is widespread in nature and in technology. It is characterized by the concepts of moments (force, momentum and inertia). To determine the work of external forces that caused the body or system to rotate around a certain axis, you must first calculate the moment of force. It is calculated as follows:
M = F * d.
Where d is the distance from the force vector to the axis of rotation, it is called the shoulder. The torque M, which led to the rotation of the system by an angle θ around a certain axis, performs the following work:
A = M * θ.
Here M is expressed in N * m, and the angle θ in radians.
The task of physics on mechanical work
As stated in the article, work is always accomplished by one or another force. Consider the following interesting problem.
The body is on a plane that is inclined to the horizon at an angle of 25 o . Sliding down, the body gained some kinetic energy. It is necessary to calculate this energy, as well as the work of gravity. Body weight is 1 kg, the path traveled along the plane is 2 meters. The sliding friction resistance can be neglected.
It was shown above that only the part of the force that is directed along the movement performs the work. It is easy to show that in this case the following part of gravity will act along the displacement:
F = m * g * sin (α).
Here α is the angle of inclination of the plane. Then the work is calculated as follows:
A = m * g * sin (α) * S = 1 * 9.81 * 0.4226 * 2 = 8.29 J.
That is, gravity does a positive job.
Now we determine the kinetic energy of the body at the end of the descent. To do this, recall the second Newtonian law and calculate the acceleration:
a = F / m = g * sin (α).
Since the sliding of the body is uniformly accelerated, we are entitled to use the appropriate kinematic formula to determine the time of motion:
S = a * t 2/2 =>
t = √ (2 * S / a) = √ (2 * S / (g * sin (α))).
The speed of the body at the end of the descent is calculated as follows:
v = a * t = g * sin (α) * √ (2 * S / (g * sin (α))) = √ (2 * S * g * sin (α)).
The kinetic energy of the translational motion is determined using the following expression:
E = m * v 2/2 = m * 2 * S * g * sin (α) / 2 = m * S * g * sin (α).
We got an interesting result: it turns out that the formula for kinetic energy exactly matches the expression for the work of gravity, which was obtained earlier. This indicates that all the mechanical work of the force F is aimed at increasing the kinetic energy of the sliding body. In fact, due to the friction forces, the work A always turns out to be more than the energy E.