Chapters 5 and 6 considered forces acting on a single object that we modeled as a particle. FIGURE 7.3a shows a diagrammatic representation of single-particle dynamics. We can use Newton’s second law, $\vec{a}=\vec{F}{}_{\text{net}}\text{/}m$, to determine the particle’s acceleration.

FIGURE 7.3 Single-particle dynamics and a model of interacting objects.

We now want to extend the particle model to situations in which two or more objects, each represented as a particle, interact with each other. For example, FIGURE 7.3b shows three objects interacting via action/reaction pairs of forces. The forces can be given labels such as $\vec{F}{}_{\text{A on B}}$ and $\vec{F}{}_{\text{B on A}}$. How do these particles move?

We will often be interested in the motion of some of the objects, say objects A and B, but not of others. For example, objects A and B might be the hammer and the nail, while object C is the earth. The earth interacts with both the hammer and the nail via gravity, but in a practical sense the earth remains “at rest” while the hammer and nail move. Let’s define the system as those objects whose motion we want to analyze and the environment as objects external to the system.

FIGURE 7.3c is a new kind of diagram, an interaction diagram, in which we’ve enclosed the objects of the system in a box and represented interactions as lines connecting objects. This is a rather abstract, schematic diagram, but it captures the essence of the interactions. Notice that interactions with objects in the environment are called external forces. For the hammer and nail, the gravitational force on each—an interaction with the earth—is an external force.