Abstract:

The energy and its theorem of conservation are concepts widely treated in the undergraduate texts of Physics because they provide an alternative method to the Newton's laws to solve questions of the Mechanics. The definition of the energy, that commonly appears in many textbooks rely on the definition of another physical magnitude: work. This concept is more abstract than the definition of force; making this procedure of introducing the energy more far away to the student.
In this article, we recover two approaches on the energy and the theorem of conservation that, for the lack of mathematical artifices and simplicity seems of special usefulness for undergraduate students. We owe them to two great Physicists: Lev Davidovich Landau that showed us that a physical magnitude during the frictionless motion of a particle along a curve keeps constant taking only into account the Newton's laws; whereas Johanes Bernouilli demonstrated the relation between work and speed from the superposition principle.