Definition 3.2.1. System.
A system is an object or collection of objects considered as a single group. Everything in a context can be considered as either internal or external to a system.
Section 3.2 Free-body Diagrams
Systems are crucial to understanding how to apply physics models. Often, how you decide to group objects into systems is a matter of convenience, but your choice of what is internal to a system will impact what forces you will consider to be important.
Representation 3.2.2. Free-body Diagram.
A Free-body Diagram is a way to represent the forces acting on an object. In a free-body diagram, each force should be labeled with information about the type of force and the objects involved. For example, in the symbol
\begin{equation*}
\vec{F}_{BC}^A
\end{equation*}
\(\vec{F}\) indicates that the symbol represents a force, the superscript \(A\) represents the type of force (such as \(G\) for gravity), \(B\) represents the system on which the force is acted, and \(C\) represents the system that is exerting the force. Additional relevant information such as the system of interest, the reference frame, and the direction of the acceleration are commonly written to the side of a free-body diagram, as in the simple example below.
Note 3.2.4. Alternate Notations.
Some physicists prefer to use alternate notation for forces. For example, you might decide to reverse the subscripts to say the force by \(B\) on \(C\text{.}\) Or, you might decide to use an expression like \(\vec{N}_{12}\) for a normal force. Any of these notations are useful, as long as (1) the notation indicates the type of force and the systems involved and (2) the notation is consistent across different forces.
One of the most important things to understand when drawing free-body diagrams is the difference between forces acting on a system (which appear on that system’s free-body diagram) and forces acted by a system, which would instead be represented on the free-body diagram for the other system. It is also important not to include things that are not forces, such as the velocity or acceleration of the system, which would instead be represented using a motion diagram. It is also helpful to include the force vectors acting on a system with relatively correct lengths as well as coordinate axes and any relevant angles.
Exercises Activities
1.
Choose an instant in the video of Dr. Paws from Figure 3.1.2 and use what you learned above to draw a free-body diagram for the system consisting only of the dog.
2.
The free-body diagram is one of the representational tools you will use most often throughout physics. Why do you think it might be such a valuable too? What features of the free body diagram do you think might be most helpful when you are solving future problems?
