Force and Free Diagrams

Force Diagrams

Force diagrams are sketches of the physical situation you are dealing with, with arrows for all the forces acting drawn on the system. For example, if a block rests on a surface then there is a force from gravity pulling the block down and there is a normal force acting on the block from the surface. The normal force and the force of gravity have the same magnitude in this situation. The force diagram for this situation is:

The length of the arrows are the same to indicate that the forces have the same magnitude.

Another example could be a the same block on a surface but with an applied force, \(\vec{F}_L\), to the left of \(\text{10}\) \(\text{N}\) and an applied force, \(\vec{F}_R\), to the right of \(\text{20}\) \(\text{N}\). The weight and normal also have magnitudes of \(\text{10}\) \(\text{N}\).

It is important to keep the following in mind when you draw force diagrams:

• Make your drawing large and clear.

• You must use arrows and the direction of the arrow will show the direction of the force.

• The length of the arrow will indicate the size of the force, in other words, the longer arrows in the diagram (\({F}_{R}\) for example) indicates a bigger force than a shorter arrow (\({F}_{L}\)). Arrows of the same length indicate forces of equal size (\({F}_{N}\) and \({F}_{g}\)). Use “little lines” like in maths to show this.

• Draw neat lines using a ruler. The arrows must touch the system or object.

• All arrows must have labels. Use letters with a key on the side if you do not have enough space on your drawing.

• The labels must indicate what is applying the force (the force of the car) on what the force is applied (on the trailer) and in which direction (to the right)

• If the values of the forces are known, these values can be added to the diagram or key.

Free Body Diagrams

In a free-body diagram, the object of interest is drawn as a dot and all the forces acting on it are drawn as arrows pointing away from the dot. We can redraw the two force diagrams above as free body diagrams: