# Vector diagrams

Two forces can be added together to find a resultant force.

In the diagram of a toy trailer below, when two children pull on the handle, one with a force of 3 newtons (N) to the left and one with a force of 4 newtons (N) to the right, the combined effect of the two forces is to pull the trailer to the right with a resultant force of 4 – 3 = 1 newton (N).

### Example

What would be the resultant force on the trailer if both children pulled to the right?

Resultant force = 4 + 3 = 7 N to the right

In the diagram of a toy trailer below, when two children pull on the handle, one vertically with a force of 3 newtons (N) and one horizontally with a force of 4 newtons (N), the combined effect of the two forces is to pull the trailer upwards away from the ground and to the right.

The sum of these two forces can be found using a vector diagram. The two forces are represented by the adjacent sides of a parallelogram, the lengths of the sizes being proportional to the size of the forces.

The resultant force is represented in size and direction by the diagonal of the parallelogram.

Draw a parallelogram to scale, in which two adjacent sides each represent a force. Try to choose a simple scale, for example 1 cm = 1 N. For the toy trailer example above, draw:

• a horizontal line representing the 4 N force
• a vertical line representing the 3 N force
• arrow heads to show the direction in which each force acts
• complete the parallelogram
• measure the length of the diagonal
• use the same scale to convert this length to the resultant force
• measure the angle of the resultant force to the horizontal

The diagonal of the parallelogram shows that the resultant force is 5 newtons (N) acting at an angle of 37° to the horizontal.