Representing a force with a vector

Why a simple number is not enough

To fully describe a force, it is not enough to say "there is a force of 10 newtons". You also need to specify:

• its point of application (where it acts),
• its direction (the line along which it acts),
• its sense (which way it pushes or pulls),
• its value (its magnitude, in newtons, symbol N).

This is why a force is represented by an arrow, called a force vector.

The force vector

A force vector is written with an arrow above a letter, for example F (vector F). On a diagram:

• the origin of the arrow = the point of application,
• the line carrying the arrow = the direction,
• the arrow itself = the sense,
• the length of the arrow = the value (with a scale chosen in advance).

Example with a scale

If we choose the scale 1 cm -> 5 N, then a force of 20 N will be represented by an arrow 4 cm long (20 / 5 = 4).

Force	Length of the arrow (scale 1 cm -> 5 N)
10 N	2 cm
25 N	5 cm
40 N	8 cm

The unit of force: the newton

The magnitude of a force is measured in newtons, denoted N, in honor of the physicist Isaac Newton. It is measured with a device called a dynamometer.

Classic pitfall to avoid

A common mistake is to forget one of the four elements of the vector (point of application, direction, sense, value) when drawing a force. An arrow without a specified scale, or badly placed on the object, does not correctly describe the force. Also remember never to confuse the length of the line with the actual magnitude in newtons: it is the scale that links the two.