Energies and powers (mechanical system)

Introduction

This section deals with the stored energy and the power dissipated in a mechanical system in motion.

Power: definition (reminder)

The instantaneous power developed by a force F (a torque G) is equal to the product of the values of the force (of the torque) and the instantaneous velocity.

(translating motion) (rotating motion)

Regarding exerted forces

Among the forces which are exerted upon the mechanical system, one can distinguish:

  • the conservative forces, which derive from a potential energy (see the following section)
  • the non conservative forces, which can be:
    • the forces of system interaction with an external operator, which can produce an increase or a decrease of the mechanical energy
    • the forces caused by constraints (i.e. the forces of contact with another system, for example forces of friction if the object is moving in a fluid medium), which, by opposing the motion, yield a decrease (loss) of mechanical energy

Elastic potential energy: definition

The potential mechanical energy of a mechanical system is the energy that the system possesses by:

  • its position (potential energy of the gravity)
  • its shape (elastic potential energy*)
Note: * By compressing a spring and then releasing it a rapid reversal to the original shape occurs, making it possible to propel an object. During the compression of the spring work is carried out over it, therefore; it accumulates elastic potential energy which can then be released as another form.

Example:

Let us consider a system consisting of a mass m subjected to the action of gravity and suspended from a spring of elastic constant k.

In this case, the system potential energy is equal to the sum:

  • of a potential energy of gravity: mgx
  • of a potential elastic energy: kx2 /2

Stored energy

In the cases we are interested in the mechanical energy stored as the potential elastic energy. This is expressed as:

(translating motion) (rotating motion)

Dissipated power

The forces or torques that results in the dissipation of energy are the forces or torques yielded by the constraints (friction forces/torques).

(translating motion) (rotating motion)