Any movement of a body in space, which leads to a change in its total energy, is associated with work. In this article, we will consider what this quantity is, what mechanical work is measured in, and how it is denoted, and we will also solve an interesting problem on this topic.
Work as a physical quantity
Before answering the question of what mechanical work is measured in, let's get acquainted with this value. By definition, work is the scalar product of the force and the displacement vector of the body that this force caused. Mathematically, we can write the following equality:
A=(F¯S¯).
Round brackets indicate dot product. Given its properties, explicitly this formula will be rewritten as follows:
A=FScos(α).
Where α is the angle between the force and displacement vectors.
From the written expressions it follows that work is measured in Newtons per meter (Nm). As is known,this quantity is called a joule (J). That is, in physics, mechanical work is measured in units of work Joules. 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 the letter A is most often used for this (from German ardeit - labor, work). In English-language literature, you can find the designation of this value with the Latin letter W. In Russian-language literature, this letter is reserved for power.
Work and energy
Determining the question of how mechanical work is measured, we saw that its units coincide with those for energy. This coincidence is not accidental. The fact is that the considered physical quantity is one of the ways of manifestation of energy in nature. Any movement of bodies in force fields or in their absence requires energy costs. The latter are used to change the kinetic and potential energy of bodies. The process of this change is characterized by the work being done.
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.
Working in gases
The expression written above to workis basic. However, this formula may not be suitable for solving practical problems from different areas of physics, so other expressions derived from it are used. One such case is the work done by the gas. It is convenient to calculate it using the following formula:
A=∫V(PdV).
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:
Pam3=N/m2m3=N m=J.
In the general case, pressure is a function of volume, so the integrand can take an arbitrary form. In the case of an isobaric process, the expansion or contraction of a gas occurs at a constant pressure. In this case, the work of the gas is equal to the simple product of the value P and the change in its volume.
Work while rotating the body around the axis
The movement of rotation is widespread in nature and technology. It is characterized by the concepts of moments (force, momentum and inertia). To determine the work of external forces that caused a body or system to rotate around a certain axis, you must first calculate the moment of force. It is calculated like this:
M=Fd.
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 through an angle θ around some axis, does the following work:
A=Mθ.
Here Mis expressed in Nm and the angle θ is in radians.
Physics task for mechanical work
As it was said in the article, the work is always done by this or that force. Consider the following interesting problem.
The body is on a plane that is inclined to the horizon at an angle of 25o. Sliding down, the body acquired some kinetic energy. It is necessary to calculate this energy, as well as the work of gravity. The mass of a body is 1 kg, the path traveled by it along the plane is 2 meters. Sliding friction resistance can be neglected.
It was shown above that only the part of the force that is directed along the displacement does work. It is easy to show that in this case the following part of the force of gravity will act along the displacement:
F=mgsin(α).
Here α is the angle of inclination of the plane. Then work is calculated like this:
A=mgsin(α)S=19.810.42262=8.29 J.
That is, gravity does positive work.
Now let's determine the kinetic energy of the body at the end of the descent. To do this, remember the second Newtonian law and calculate the acceleration:
a=F/m=gsin(α).
Since the sliding of the body is uniformly accelerated, we have the right to use the corresponding kinematic formula to determine the time of movement:
S=at2/2=>
t=√(2S/a)=√(2S/(gsin(α))).
The speed of the body at the end of the descent is calculated as follows:
v=at=gsin(α)√(2S/(gsin(α)))=√(2Sgsin(α)).
The kinetic energy of translational motion is determined using the following expression:
E=mv2/2=m2Sgsin(α)/2=mSgsin(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 friction forces, the work A always turns out to be greater than the energy E.
