What is idealization of mechanics in Engineering mechanics?

Answer 1

A number of ideal conditions are assumed to exist while applying the laws of mechanics of practical problems. in fact, without such assumptions, it is not feasible to arrive at practical solutions. The experience in the past centuries has shown that the following idealization could be made as they do not bring down the accuracy of the analytical results below the optimum level required by engineers to deal with practical diagram.

Continuum

A body consists of several particles. It is a well known fact that each particle can be sub-divided into molecules, atoms and electrons. It is not feasible to solve any engineering problem by treating a body as a conglomeration of such discrete particles. The body is assumed to consist of a continuous distribution of matter which will not separate even when various forces considered are acting simultaneously. In other words, we say the body is treated as a continuum.

Rigid Body

As already stated, in Civil Engineering, we treat a body as rigid, when the relative position of any two particles in the body do not change even after the application of a system of forces. For examples, let the body shown in figure (a) move to a position as shown in figure (b) when the system of forces F2 and F3 are applied. If the body is treated as a rigid body, the relative position of A to B is the same as A' and B', i.e.,

AB = A'B'

Particle

A particle may be defined as an object which has only mass and no size. Theoretically, such a body cannot exist; while dealing with the problems involving distances which are considerably larger compared to the size of the body, the size of the body may be neglected without sacrificing the accuracy, the example are as follows:

• A bomber aeroplane is a particle for a gunner operating from the ground.
• A ship in a mid sea is a particle in the study of relative motion from the control in a part.
• In the study of the movement of earth in celestial space, earth is treated as a particle.