## Three Forces in Equilibrium

There are several equivalent ways of saying that three forces are in equilibrium. Of course the forces must act on the same object.

1. The net force in any direction is zero.

Consider the three forces show acting at a point.

Resolving vertically gives 13 cos 22.62 ° -12=0

Resolving horizontally gives -13 sin 22.62 ° +5=0

2.We can add any two forces, and the resultant will be equal in magnitude and opposite in direction to the third force. To show this first resolve the forces into horizontal and vertical components.

Force (N) | Horizontal | Vertical |

13 | -13 sin 22.62 ° =-5 | 13 cos 22.62 ° =12 |

5 | 5 | 0 |

12 | 0 | -12 |

Adding the first and second force gives a vertical force of +12, equal and opposite to the third force of -12.

Adding the first and third force gives a horizontal force of -5, equal and opposite to the second force of +5.

Adding the second and third force gives a horizontal force of 5 and a vertical force of -12, equal and opposite to the first force of -5 horizontally and +12 vertically.

3. We can draw a vector triangle with the sides representing the forces. The triangle will be closed. All the forces will follow each other around the triangle in the same direction.

We can move the forces to follow on from each other and get the diagram below.

All the requirements for the forces to be balanced are satisfied.