# System Schema Introduction

#### Prerequisites

Newton's laws provide a framework in which we can build models of objects, how the interact, and how those interactions affect all their motions. In order to begin describing any physical system, we need to decide what we consider objects and what their interactions are.

In the physical world we experience every day, everything is made up of individual atoms (, and atoms are made up of electrons and nuclei, and nuclei are made up of protons and neutrons, and...). If we want to make a model of something happening, we need to model it as parts of appropriate size. For example, in the image below is shown a drawing of a child pulling itself up a rope with its hands. We can consider this phenomena at many levels: in terms of the pulls the child is exerting on the rope, in terms of the forces in the child's muscles that create its pull, in terms of the biochemistry in the nerve and muscle cells that result in the contraction of the muscle fibers, in terms of the molecular interactions in the rope that keep the rope together despite the fact that it is being pulled on.

In this class we will focus on the physical — the interaction of objects and what they do to each other. We'll leave the chemical and biological details for your other classes.

We need a tool that can help us articulate what model we are choosing to use as a working hypothesis for our description of a system. A useful representational tool for capturing important elements about the system we are trying to describe is the system schema.

It is easiest to understand the system schema by giving an example. Let's consider the child and the rope. The system schema consists of bubbles representing the objects we have decided to consider connected by two-way arrows indicating the interactions between those objects. We represent each object with a circle and a label. In the example situation, there could be many objects that seem to be relevant, but our job is to identify only those that influence the aspects of the situation we are currently interested in, in this case, the motion of the child up the rope. For example, would it matter if the child were wearing red shoes, blue shoes, or no shoes? No, so we can simplify and only identify the critical objects. In the example there are at least three important objects: the child, the rope, and the earth.

The next part of describing our situation is to identify the interactions between the objects. We represent these interactions with a two-headed arrow, and label the interaction. If the interaction is always taking place, the arrow is a solid line. If the interaction only takes place for a particular period of time, the arrow is a dashed line. In our example the child is always touching the rope, so that is a contact interaction between the child and the rope.

The rope is presumably hanging from something -- a tree, or a bridge, or a hook in the gymnasium ceiling. We now have a choice. How much are we interested in the rope? If our primary interest is the child, we only care that the rope is hanging. We might group the tree, building, or whatever it's attached to a "stuff connected to the earth."  So at this level of concern, we might treat whatever holds the rope us as part of the earth and label a contact interaction between the rope and the earth. Finally, the earth and the child are interacting. We know there is gravity, and to have a force there must be an interaction. If the child is hanging from the rope and not touching the ground, we identify that there is only a gravitational interaction between the earth and the child.

The final step in creating a system schema is to identify what objects are inside the system we are interested in describing. This is of primary importance when using the system schema in the context of energy, which we will discuss later in the semester. You identify the system with a dotted line around the objects of interest. In our example we will simply include all of the objects as part of our system. (This will be useful when we consider subsystems and the interaction of a subsystem with objects outside it, exchanging, for example, energy.)

Now we have a system schema. To use this representation to help draw a force diagram, start by identifying the object of interest.  In this case we'll choose the child. The object is represented by a dot in the force diagram. Now consider each interaction touching the object of interest. In our example there are two interactions with the child: the contact interaction with the rope and the gravitational interaction with the earth.

What we choose to include in our schema depends on what we want to do. Why did we include the earth if in this case the child isn't touching it? We did because the earth creates gravity that pulls on the child whether it is touching the earth or not. If the child released the rope it would fall. Why did we we simplify whatever the rope was connected to by calling it (indirectly) "the earth"? Because we were not thinking about analyzing the motion of the rope. If we wanted to worry about that (and whether the tree limb holding the rope might break) we would have to put in more detail.

Once we've drawn a system schema for our system, we can identify an object of interest. By object egotism, that object only responds to interactions it feels. Each interaction goes two ways between two objects. When we isolate a single object the relevant aspect of any interaction is the force it exerts on the object considered. We then draw a free-body diagram that indicates the forces acting on that object.

Vashti Sawtelle & Eric Brewe 8/20/12 revised by Joe Redish 8/21/18

Article 359