Kinetic and potential energy

One of the characteristics of any system is its kinetic and potential energy. If any force F exerts an effect on the resting body in such a way that the latter comes into motion, then the work dA takes place. In this case, the value of the kinetic energy dT becomes higher the more work is done. In other words, we can write the equality:

DA = dT

Given the path dR traversed by the body, and the developed velocity dV, we use Newton's second law for the force:

F = (dV / dt) * m

An important point: this law can be used if an inertial frame of reference 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 velocity of displacement V and mass m, is:

T = ((V * V) * m) / 2

It can be concluded that the kinetic energy is determined by the speed and mass, in fact representing a function of motion.

Kinetic and potential energy allows us to describe the state of the body. If the first, as already mentioned, is directly related to the movement, 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 the gravitational interaction. But if the trajectory is also important, then the force is dissipative (friction).

In simple terms, the potential energy is an opportunity to do the work. Accordingly, this energy can be considered in the form of work, which must 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 work is done by decreasing dP. For the known function dP, it is possible to determine not only the modulus of the force F, but also the vector of its direction.

The change in kinetic energy is always connected with the potential energy. This is easy to understand if we recall the law of conservation of the energy of the system. The total value of T + dP when moving the body always remains unchanged. Thus, the change in T always occurs in parallel with the change in dP, they seem to flow into each other, transforming.

Since the kinetic and potential energies are interrelated, their sum is the total energy of the system under consideration. With regard to molecules, it is an internal energy and is always present, as long as there is at least thermal motion and interaction.

When performing calculations, the frame of reference is chosen and any arbitrary moment taken as the initial one. Precisely determine the value of the potential energy can only be in the zone of action of such forces that, when the work is done, do not depend on the trajectory of the displacement of any particle or body. In physics, such forces are called conservative. They are always interrelated with the law of conservation of total energy.

An interesting point: in a situation where external influences are minimal or leveled, any system studied always tends to such a state when its potential energy tends to zero. For example, a thrown ball reaches its potential energy limit at the top point of the trajectory, but at the same instant it starts moving downward, converting the accumulated energy into motion, into the work being done. It should once again be noted that for potential energy there is always an interaction of at least two bodies: thus, in the ball example, the gravity of the planet influences it. The kinetic energy can be calculated individually for each moving body.