0.2 Force, momentum and impulse

If we draw a box around the two trailers they can be considered a closed system or unit. When we look at the forces on this closed system the following forces will apply (we assume drag forces are absent):

• The force of the car pulling the unit (trailer A and B)
• The force of friction between the wheels of the trailers and the road (opposite to the direction of motion)
• The force of the Earth pulling downwards on the system (gravity)
• The force of the road pushing upwards on the system

These forces are called external forces to the system.

The following forces will not apply:

• The force of A pulling B
• The force of B pulling A
• The force of friction between the wheels of the car and the road (opposite to the direction of motion)

We can also draw a box around trailer A or B, in which case the forces will be different.

If we consider trailer A as a system, the following external forces will apply:

• The force of the car pulling on A (towards the right)
• The force of B pulling on A (towards the left)
• The force of the Earth pulling downwards on the trailer (gravity)
• The force of the road pushing upwards on the trailer
• The force of friction between the wheels of A and the road (opposite to the direction of motion)

Force diagrams

If we look at the example above and draw a force diagram of all the forces acting on the two-trailer-unit, the diagram would look like this:

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 ${}_1$ for example) indicates a bigger force than a shorter arrow (F ${}_f$ ). 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. A free body diagram for the two-trailer-system will therefore look like this:

Finding the resultant force

The easiest way to determine a resultant force is to draw a free body diagram. Remember from Chapter [link] that we use the length of the arrow to indicate the vector's magnitude and the direction of the arrow to show which direction it acts in.