Free Body Diagram (FBD)
The free body diagram (also known as FBD) is a simplified representation of an object (the body), and the forces acting on it. This body is called free because the diagram will show it without its surroundings; i.e. the body is “free” of its environment.
In other words we consider the forces (and only the forces) acting on the object of our interest. The object is seen as not connected to any other object – it is “free”.
The best way to explain the Free Body Diagram is to describe the steps required to construct one. Follow the procedure given below.
(1) Isolate the body (object) of interest.
This means creating an imaginary surface that separates our object from its surroundings. (2) Then draw all external force vectors for that body.
(3) Draw all mass times acceleration vectors for that body.
(4) Choose a convenient coordinate system common for all vectors.
Let’s construct a Free
body Diagram for a very simple situation.
The box of mass m on the floor:
The box is pulled downward by the force of gravity Fg and is prevented from accelerating toward the center of the Earth by the force of reaction FR exerted upwards by the floor against box’s lower surface. This situation is draw in part A of the Fig.1. The sketch is very suggestive. The force of Gravity is “pushing” downwards, the reaction force is “pushing” upwards.
But we can ask the question, where exactly are these forces situated?
We can assume that all forces exerted on the box in our example are concentrated at its center of gravity. On the part B of Fig.1 the small red circle points to the position of the center of gravity (CG) and two discussed forces are being concentrated at this point. Now we need to choose a convenient coordinate system for our Free Body Diagram sketched in part B of Fig.1. In this example the single axis parallel to the acting forces is the most convenient one. The direction of the axis can be up or down. Depending on this direction the force of gravity and that of reaction will have different signs.
For axis directed upwards:
Fg has a negative sign (-), FR has positive (+) sign.
For axis directed downwards:
Fg has a negative sign (+), FR has positive (-) sign.
Choosing absolute directions of forces on the FBD does not influence the result of calculation. Only the relative signs had to be correct. If you choose the coordinate axis upward and take Fg with (+) and FR with (-) signs, after solving the problem for which the FBD was drawn, you will get negative values for Fg and FR. The negative value of a vector (not only force) means that it is directed opposite to the direction chosen at the time of drawing the FBD. In our example of drawing FBD we chose a vertical y axis as our coordinate system.
Further examples of Free Body Diagrams are included in problems solutions.