Levers
Levers
Levers are a simple machine that consist of a rigid arm (bar or beam), and a pivot point called a fulcrum (full-krum). A lever used an effort force to move a load force.
Generally speaking, the effort arm is longer than the load arm, which, when applying force to the effort arm makes it easier to move the load.
Classes of Lever
There are three classes of levers, which are determined by which element of the lever is in the middle.
You can remember which class of lever is which with the saying 123FLE.
First class levers have the Fulcrum in the middle.
Second class levers have the Load in the middle.
Third class levers have the Effort in the middle.
Mechanical Advantage of a Lever
Mechanical advantage is always calculated as $ \frac{\text{Load}}{\text{Effort}} $, but each simple machine has it's own calculation to work out the ideal mechanical advantage. The IMA of a lever is calculated with:
$$ \frac{\text{Effort Distance from Fulcrum}}{\text{Load Distance from Fulcrum}} $$
A moment of a Lever
A moment is the turning effect generated when a force (effort) is applied to a lever to rotate it about the fulcrum. A moment is calculated by multiping the force in newtons applied to the lever, by the perpendicular distance in meters. The result is given in newton-meters. A small force applied to a long lever arm can produce a significant moment.
$$ \text{Moment} = \text{Force} \times \text{Distance} $$
Law of the Lever
In the 3rd century BCE, Archimedes developed a formula for the principle of the lever: "Effort times effort arm equals load times load arm".
This can be expressed with the following formula.
$$ \text{F}_\text{effort} \times \text{d}_\text{effort} = \text{F}_\text{load} \times \text{d}_\text{load} $$
Subscripts, the small characters below the base line beneath variables, indicate different versions of the same variable.
In the equation above, the full label is used to show the different forces and distances. Generally, you would not use an entire label, just a letter or number to indicate the different versions.
$$ \text{F}_\text{e} \times \text{d}_\text{e} = \text{F}_\text{l} \times \text{d}_\text{l} $$ $$ \text{F}_1 \times \text{d}_1 = \text{F}_2 \times \text{d}_2 $$
In practice, this means that a lever can reach equilibrium when the two opposing forces just balance each other. The moments on both sides of the fulcrum are equal.
Example
In the example here you can see the forces labelled on each side of the diagram.
$$ 30\text{N} \times 10\text{m} = 10\text{N} \times 30\text{m} $$
You may get a question asking for the minimum force to move a load. The minimum force to move a load is considered the force to reach equilibrium. This kind of equation would usually provide three known variables (commonly, two distances and one load), and one unknown variable.
You would use linear equation processes to resolve the unknown variable.