Physical System

Defines what a physical system is, its boundary and surroundings, and how correct delimitation changes problem formulation.

Conceptual context

Before applying any law of physics, a prior question must be answered: what exactly are we analyzing? A well-defined $S_{tipo}$ together with its $F$ is the conceptual tool that answers this question. The choice of what to include inside the system and what to leave outside is not a minor detail: it determines which interactions are internal, which are exchanges with the $E$, and which conserved quantities must be tracked. Without this definition, no balance equation has physical meaning.

🟢 Essential level

Imagine analyzing a bouncing ball. You can decide your system is only the ball, or the ball plus the floor.

The difference is not trivial: if you include only the ball, the floor's force is external and appears in the force balance. If you include both, that force is internal and disappears from the external balance. The $F$ acts as a membrane separating what you analyze from its surroundings, the $E$. The $X_{\int}$ quantifies everything crossing that membrane: mass, energy, momentum. Choosing the boundary well simplifies the problem and avoids sign errors. The $S_{tipo}$ encodes in one category what can cross the boundary: nothing (isolated), only energy (closed), or mass and energy (open).

A combustion engine is a good example of an open system: fuel and air go in, exhaust gases and mechanical energy come out, so neither the mass nor the energy inside the engine stays constant on its own. The balance only closes if those inflows and outflows are explicitly accounted for.

🔵 Formal level

Basic formulas

A physical system is defined by three inseparable elements:

Definition of physical system

Content C is the set of included objects, the $F$ F delimits the system from the $E$ E, and the $S_{tipo}$ determines what can cross F. The formal classification is:

Classification of system type according to its exchanges

— Isolated: $X_{\int}$ of mass and energy is zero. All internal extensive quantities are conserved.

— Closed: $X_{\int}$ of mass is zero; energy may be exchanged as heat Q or work W.

— Open: $X_{\int}$ of both mass and energy is possible.

Real student questions

Does the $F$ have to be physical or can it be imaginary?

It can be entirely imaginary. A control volume in fluid dynamics is a conceptual $F$ with no real wall. What matters is consistency throughout the analysis.

What happens if I include the agent applying the force inside the system?

The contact force becomes internal and disappears from the external force balance. The result is an incomplete balance that appears correct but ignores the most important interaction in the problem.

Why does the $S_{tipo}$ change the numerical result?

Because it changes which $X_{\int}$ terms appear in the balance. Treating an open system as closed omits mass flows and yields an incorrect energy balance.

Final synthesis

A physical system is the analyst's conscious choice of what to include in the analysis. The $F$ separates the internal from the external. The $S_{tipo}$ summarizes what can cross that boundary. The $X_{\int}$ quantifies the flows. Without this well-defined triad, no conservation law can be applied unambiguously.