You've actually already learned about equilibrium, you just didn't know that we were talking about it!

- Equilibrium is any situation where the net force acting on an object is zero.
- We call it equilibrium because all the forces acting on the object equal out and cancel each other.
- Some situations of equilibrium are easy, others are more difficult, as the following images show.

Each of these situations shown in **Figure 1** could be solved by you back in "Net Forces", but we can also do problems that you will have to use vectors for.

Example 1: A 10 kg sign is being held up by two wires that each make a 30° angle with the ground. **Determine** the tension (force) in each of the wires.

The diagram to the right shows what this would look like. The tension is a force in the wires that acts along the length of the wires.

- Basically, these wires are wasting some of their effort by pulling sideways against each other.
- The only force that the sign actually needs to hold it up is a force pulling up.
- Since everything else is equal, we can assume that each wire is holding up half of the weight of the sign.
- We can do our calculations for one wire, and then say that the other wire is the same (since they are just mirror images of each other).
F

_{g }= mg

= (10) (9.81)

F_{g}_{ }= 98.1 NsinΘ = opp / hyp

sinΘ = 1/2 F_{g}/ F_{T}

F_{T}= (1/2 F_{g}) / sinΘ

= (49.05) / sin 30° = 98.1 NThe tension in

eachwire of the sign is 98 N [30° from the horizontal].

In some situations you may already have a couple of forces acting on an object and want to know what third force would cancel them out.

- This third force that would do the cancelling out is called the equilibrant.
- The equilibrant is a vector that is the exact same size as the
**resultant**would be, but the equilibrant points in exactly the opposite direction. - For this reason, an equilibrant touches the other vectors head-to-tail like any other vector being added.

Example 2: Two forces are pushing an object along the ground. One force is 10 N [W] and the other is 8.0 N [S]. **Sketch** a diagram showing the equilibrant of these two forces, and **determine** the equilibrant.

If you look at the sketch you'll see that the equilibrant is the exact opposite of what you would draw for a resultant.

The equilibrant takes you right back to where you started. The net force... zero!

It would almost be the same if you went for a walk and followed this as a path. You'd end up back where you started and your displacement would be zero.

Calculate the equilibrant...

c^{2}= a^{2}+ b^{2}= 10^{2}+ 8^{2}

c = 13 NCalculate the angle where the 8.0 N force and the equilibrant touch...

tanΘ = opp/adj = 10 / 8

Θ = 51°

The equilibrant is 13 N [N51°E].