# Question #7a6ab

##### 1 Answer

The force exerted by the wedge is equal to

#### Explanation:

You're actually dealing with an *equilibrium problem*. However, the trick here is to distinguish between **translational equilibrium** and **rotational equilibrium**.

For example, let's assume that the first thing you want to determine is whether or not the plank is in *rotational equilibrium*.

In this case, equilibrium will be established if the **counterclockwise torque** caused by the boy is **equal** to the **clockwise torque** caused by the girl.

*Torque* is simply a term used to describe a force's tendency to induce rotation and is equal to

*length of the torque arm*, i.e. the distance from the fulcrum at which the force is applied.

So, in order to be at equilibrium, you need to have

Since *rotational equilibrium*.

Therefore, the force exerted by the fulcrum would be zero, right? Wrong. This is where **translational equilibrium** comes into play.

In order for a body to be at equilibrium, the vector sum of all the forces that are acting on that body must be equal to **zero**.

This implies that the two forces that push *downward*, i.e. the weights of the children, must be equal to the force pushing *upward*, i.e. the **reactive force** exerted by the fulcrum.

This implies that

I think the minus sign is optional, since it just signifies that this force is pointed upwards, as opposed to the other two forces which point downwards.