Scale Diagram

Contents

Key Stage 4

Meaning

A scale diagram is a method used to add vectors by drawing them as arrows whose length and direction are accurately drawn to represent the magnitude and direction of the vector.

About Scale Diagrams

Scale diagrams use a 'scale' to show how the units of the vector are represented by a single unit of length (cm or mm). For example 100N = 1cm, so an arrow of 5cm represents a force of 500N.

Scale diagrams can be used to add forces, displacements, velocities or accelerations.

Examples

The two vector forces drawn to a 'scale' on a Scale Diagram. This scale is 1N = 1cm. The two forces can be added by placing the start of one vector force at the end of the other. This Scale Diagram shows that the two forces cancel one another out so the net force is zero.

The two vector forces drawn to a 'scale' on a Scale Diagram. This scale is 1N = 1cm. The two forces can be added by placing the start of one vector force at the end of the other. This Scale Diagram shows that the two arrows add to make a length of 6.1cm, which represents 6.1N, in a direction of 35° down from the horizontal.

A boat is being pulled by two separate tug boats attached by a cable. The tension in each cable is 5000N.	The tug boats and cables are replaced by vector forces from the boat.	The two forces are redrawn in a a Scale Diagram with scale is 1000N = 1cm placing the start of one vector force at the end of the other.
This Scale Diagram shows that the two arrows add to make a length of 9.4cm, which represents 9400N, in a direction of 90° from the North which is an Easterly direction.