One of the characteristics of any system is its kinetic and potential energy. If any force F exerts an effect on a body at rest in such a way that the latter comes into motion, then work dA takes place. In this case, the value of the kinetic energy dT becomes the higher, the more work is completed. In other words, we can write the equality:
dA = dT
Given the path dR traveled by the body and the speed dV developed, we use Newtonโs second law for force:
F = (dV / dt) * m
An important point: this law can be used if an inertial reference system is taken. The choice of system affects the value of energy. In the international SI system, energy is measured in joules (j).
It follows that the kinetic energy of a particle or body, characterized by a speed of movement V and mass m, will be:
T = ((V * V) * m) / 2
It can be concluded that kinetic energy is determined by speed and mass, actually representing a function of motion.
Kinetic and potential energy allow us to describe the state of the body. If the first, as already mentioned, is directly related to motion, then the second is applied to the system of interacting bodies. Kinetic and potential energy are usually considered for examples when the force connecting the bodies does not depend on the trajectory of motion. In this case, only the initial and final positions are important. The most famous example is gravitational interaction. But if the trajectory is important, then the force is dissipative (friction).
In simple terms, potential energy is an opportunity to do work. Accordingly, this energy can be considered in the form of work that needs to be done to move the body from one point to another. I.e:
dA = A * dR
If the potential energy is denoted as dP, then we get:
dA = - dP
A negative value indicates that the job is due to a decrease in dP. For the well-known function dP, it is possible to determine not only the modulus of force F, but also the vector of its direction.
A change in kinetic energy is always associated with potential. This is easy to understand if we recall the law of conservation of energy of the system. The total value of T + dP when moving the body always remains unchanged. Thus, a change in T always occurs in parallel with a change in dP, as if they flow into each other, transforming.
Since kinetic and potential energy are interconnected, their sum represents the total energy of the system in question. In relation to molecules, it is internal energy and is always present as long as there is at least thermal motion and interaction.
When performing the calculations, the reference system and any arbitrary moment taken as the initial one are selected. Accurately determine the value of potential energy is possible only in the zone of action of such forces, which when completing work do not depend on the trajectory of movement of any particle or body. In physics, such forces are called conservative. They are always interconnected with the law of conservation of full energy.
An interesting point: in a situation where external influences are minimal or leveled, any system under study always tends to its state when its potential energy tends to zero. For example, a thrown ball reaches the limit of its potential energy at the top of the trajectory, but at the same instant begins to move down, converting the accumulated energy into movement, into the work being performed. It is worth paying attention once again that for potential energy there always occurs an interaction of at least two bodies: for example, in the example with a ball, the planetโs gravity influences it. Kinetic energy can be calculated individually for each moving body.