Summary:
This class studies continuous bodies in physics. It starts with point-like objects but shows how Newtonian mechanics explains that objects formed by many particles can simulate the continuity of nature. It reviews Newton’s laws to understand motion and causes in particles. It highlights that conglomerated bodies acquire unique properties and are classified into solids, liquids, and gases based on their reaction to external forces.

Learning Objectives:
Upon completing this class, the student will be able to:

1. Understand how the possible states of relative motion between points of matter can reproduce the states of matter.
2. Recognize the new properties that emerge from particles when they form a conglomerate.
3. Understand the connection between the mechanics of particles and that of continuous media.

TABLE OF CONTENTS:
CONTINUOUS BODIES IN PHYSICS
HOW CAN WE UNDERSTAND CONTINUOUS BODIES IN PHYSICS?
THE PHYSICS OF THE CONTINUUM

Continuous Bodies in Physics

In physics, we often begin by studying point-like objects and idealized systems before tackling more complex and realistic ones. Although nature does not present point-like objects, this approach makes sense because it allows us to address concepts more simply and understandably. Newtonian mechanics, for instance, was developed before the physics of the continuum, so it is important to have some familiarity with its laws to understand how continuous objects, which are composed of a large number of tiny particles, can “simulate” the continuity we observe in nature.

Reminder of Newton’s Laws

Physics studies the phenomena that change in nature, because without change, there is no possible perception. Therefore, it is important to recall the fundamental concepts of Newtonian mechanics, which allow us to understand the motion of particles and their causes, as well as position, momentum, and their variations.

Position and momentum are attributes of matter, referring to the location and movement of an object in space. All objects with mass have a position and a state of motion.

Let’s recall Newton’s three laws.

• FIRST LAW: Law of Inertia:
  In the absence of an external action, every body preserves its state of motion.
• SECOND LAW: Law of Force and Masses:
  If the state of motion of a body changes, it will be due to the action of a force, and this is equivalent to the variation of the state of motion over time.

  \displaystyle\vec{F}= \frac{d\vec{p}}{dt}

• THIRD LAW: Law of Action and Reaction:
  To every “action” force, there corresponds another “reaction” force, of equal magnitude but opposite direction.

How Can We Understand Continuous Bodies in Physics?

A continuous body is a conglomerate of point-like objects; the branch of a tree or the blood in our body is composed of particles so tiny in size and large in number that, when put together, they resemble a “continuity.”

Bodies formed by a conglomerate acquire qualities that their parts do not possess individually.

• The position of each particle relative to the others produces the shape of the body.
• The state of motion of the entire body is due to the collective state of motion of all the particles as a whole.
• And the possibilities of relative motion between the points of matter produce the states of matter.

All these things are susceptible to change. Thus, based on these physical characteristics, we can classify bodies according to how they change in response to the action of an external force.

Types of Continuous Bodies in Physics

Continuous bodies are classified as follows:

Those in which the relative position between their particles tends to remain constant in the absence of external forces.

On one hand, in solids the relative position between the particles that make them up tends to remain constant unless an external force is applied. Bodies made of steel, wood, bones, or rubber fall into this classification. The relative position between the particles is sustained by two types of forces: on one hand, we have restorative forces, which oppose any force that attempts to move the particles from their relative position, and dissipative forces, which release the energy introduced by the action of the external force until it disappears. Restorative forces are responsible for a spring oscillating after being disturbed, while dissipative forces are responsible for an iron bar heating up when bent.

And those in which, on the contrary, the relative position between their particles varies even in the absence of external forces.

In contrast, in fluids the relative position between the particles changes even if no external forces are exerted and even when the body maintains its shape. The air confined in a bottle or the water in a bucket are of this nature. The restorative forces that keep each part in place are almost non-existent, and the dissipative forces are responsible for the phenomenon of viscosity.

These are classified into two types:

Liquid Bodies:

There are internal forces strong enough to preserve the average relative distance, but not the position, between the particles, making the substance collectively tend to maintain a constant volume.

Gaseous Bodies:

In the absence of restrictions, they do not have a fixed volume. The particles move freely in the available space. When contained in a container, every point inside it represents a possible position for the gas particles.

The main difference between solids and fluids is that solids tend to preserve their shape, while fluids do not. When a solid changes shape, it either tries to return to it or heats up (at least one of the two), and it can even break; in contrast, fluids offer little resistance to the movement of their particles and, unlike solids, adapt to the container that holds them.

The Physics of the Continuum

This science deals with the study of continuous bodies in some of the states we have just described and their physical properties; but as we have seen, it is assumed that the number and size of the particles that make up the body are such that they make it behave as a continuous object. In this science, although we talk about “forces between particles,” their nature, whether electromagnetic, quantum origin, or simple collisions, is not detailed; instead, it is a collective analysis. The detailed analysis of such situations, where the types of forces between particles are considered, is more typical of statistical mechanics. From this science, others emerge depending on the type of body studied and the focus given to that study.

• Physics of the Continuum
  • Solid Mechanics
    Studies the behavior of solid materials under various types of deformation stresses.
  • Fluid Mechanics
    • Hydrodynamics: Studies the behavior of liquids
    • Pneumatics: Studies the behavior of gases