Mechanics

# Relationship between work and kinetic energy

Turbine transforms the kinetic energy of the winds into electrical energy.

Consider a body of mass m, with negligible dimensions, moving with velocity v1, and which, from a certain instant on, is subjected to a resultant force F in the same direction as the velocity and which acts for a certain time.
During the application of this force, the body undergoes a displacement d, and its velocity becomes v2.

The action of the force F gives the body a certain acceleration and this causes a change in its velocity. In other words, the kinetic energy of the body varies.
It can be shown that the amount of energy transferred by the force F, that is, the work done by the force F during the displacement d, is equal to the change in the kinetic energy of the body. Soon:

Such a result is known as the kinetic energy theorem, and it can be applied even when the magnitude of the resultant force is not constant.

Theorem:
The work of the resultant forces acting on a body, in a given displacement, measures the change in kinetic energy that occurs in that displacement.

– If the resultant performs motor work (τ > 0), the kinetic energy increases.
– If the resultant does resistant work (τ < 0), the kinetic energy decreases.
– If the kinetic energy has not changed between two positions, it means that the resultant of the forces acting on the body has done zero work.