13.11 Conservation of energy  (Page 2/7)

Mechanical system

System types are defined with respect to “energy” and “matter”. However, we are required to know about the role of external force on a system in mechanics. Remember internal forces within a system sum up to zero. Does external force anyway change the system type?

In order to answer this question, we seek to know what does an external force do? For one, it tries to change the motion of the system and hence does the work. So if we apply the force on an isolated system, work will change energy of the system – even if system is isolated! Actually, there is nothing wrong in the definition of an isolated system. It says that energy and matter both are not exchanged. We know that work is just a form of “energy” is transit. Hence, work on the system is also barred by the definition.

We have actually brought this context with certain purpose. Our mechanical system is more akin to the description as given above. We need to know the role of force. Now, the question is what would we call such a system – a closed system or an isolated system.

Here, we consider an example of mechanics to bring out this point. Let us consider a block, which slides down a rough incline. Here, “Earth-incline-block” system is an isolated system as shown in the figure with an enclosed area.

“earth-incline-block” system

Let us, now, consider an external force, which pushes the block up as shown in the figure. The work by force increases potential energy of the system, may increase kinetic energy of the block (if brought up with an acceleration) and produces heat in the isolated system.

In the nutshell, an external force on an isolated system is equivalent to “closed system”, which allows exchange of energy with surrounding only via work by an external force. So it is a special case of “closed” system. Remember that energy exchange in “closed” system takes place either as “energy” or “work”. In our mechanical context, the “closed” system allows exchange of energy as “work” only.

Interpretation of system type

The definitions of three system types are straight forward, but its physical visualization is not so easy. In the following paragraphs, we bring out important points about a system type.

1: Any system on Earth is linked with it – whether we say so or not. We have seen that “potential energy” of a particle as a matter of fact belongs to the system of “Earth – particle” system – not only to the particle. Since Earth is comparatively very large so that its mechanical energy does not change due to motion of a particle, we drop the Earth reference. It means if we draw a boundary for a system constituting particles only – we implicitly mean the reference to Earth and that Earth is part of the system boundary.

2: We should emphasize that system is not bounded by a physical boundary. We can understand this point by considering a “particle”, which is projected vertically up from the surface of Earth. What would be the type of this “Earth-particle” system? It is an “open” system, if we think that particle is dragged by air. Drag is a non-conservative force. It takes out kinetic energy and transfers the same as heat or sound energy. The system, therefore, allows exchange of energy with the air, which physically lies in between “particle” and “Earth” of the system. However, if we assert that there is negligible air resistance, then we are considering the system as an isolated system. Clearly, it all depends what attributes we assign to the boundary in accordance with physical process.