Theory of operation
The principle of the lever tells us that the above is in static equilibrium, with all forces balancing, if F1D1 = F2D2.
The principle of leverage can be derived using Newton's laws of motion, and modern statics. It is important to note that the amount of work done is given by force times distance. To use a lever to lift a certain unit of weight with a force of half a unit, the distance from the fulcrum to the spot where force is applied must be exactly twice that of the distance between the weight and the fulcrum. For example, to cut in half the force required to lift a weight resting 1 meter from the fulcrum, we would need to apply force 2 meters from the other side of the fulcrum. The amount of work done is always the same and independent of the dimensions of the lever (in an ideal lever). The lever only allows to trade force for distance.
The point where you apply the force is called the effort. The effect of applying this force is called the load. The load arm and the effort arm are the names given to the distances from the fulcrum to the load and effort, respectively. Using these definitions, the Law of the Lever is:
Load arm X load force = effort arm X effort force. If, for example, a 1 gram feather were balanced by a one kilogram rock, the feather would be 1000 times further from the fulcrum than the rock; if a 1 kilogram rock were balanced by another 1 kilogram rock, the fulcrum would be in the middle.