# Levers

Levers were first described by the ancient Greek mathematician Archimedes in about 260 BC, and represent some of the earliest machines ever used by humans.

A lever is a simple machine consisting of a rigid bar that pivots about one point and that is used to move a load at a second point by a force applied at a third point. The pivot point on which the lever turns or is supported is known as the fulcrum.

A lever amplifies an input force to provide a greater output force, which is said to provide leverage. The ratio of the output force to the input force is the mechanical advantage of the lever.

All levers are one of three classes depending on the relative position of the load, effort and fulcrum:

The load is the object you are trying to move.
The effort is the force applied to move the load.
The fulcrum is the point where the load is pivoted.

#### Class 1 levers

A class 1 lever has the load and the effort on opposite sides of the fulcrum. Examples of a class-one lever are a pair of pliers and a crowbar.

#### Class 2 levers

A class 2 lever has the load and the effort on the same side of the fulcrum, with the load nearer the fulcrum. Examples of a class-two lever are a pair of nutcrackers or a wheelbarrow.

#### Class 3 levers

A class 3 lever also has the load and the effort on the same side of the fulcrum, but with the effort nearer the fulcrum. This means that a class 3 lever does not have the mechanical advantage of a class 1 or class 2 lever, so more force is put in the effort than is applied to the load.

These levers are good for grabbing something small, fiddly or dirty, or picking up something that could be squashed or broken if too much pressure is applied. The common example of class 3 levers is a pair of tweezers or tongs.

These cases are described by the mnemonic FLE123 where the fulcrum is in the middle for the class 1 lever, the load is in the middle for the class 2 lever, and the effort is in the middle for the class 3 lever.

#### Mechanical Advantage

In the example (Class 1 Lever) shown the fulcrum is at the center of the lever. This lever provides no mechanical advantage and the force needed to lift the weight is equal to the weight itself.

However, if you want to lift a weight that is heavier than the force applied you can move the fulcrum closer to the weight to be lifted. This affects the force required in the following way:

w x d1 = f x d2

Where:

w = weight
d1 = distance from fulcrum to weight
f = force needed
d2 = distance from fulcrum to point where force is applied

In this example the fulcrum has been moved towards the weight so that the weight is 1 meter from the fulcrum. This means that the force can now be applied 2 meters from the fulcrum.

If you needed to calculate the force needed to lift the weight then you can rearrange the formula.

w x d1 = f x d2 can be rearranged to f = (w x d1)/d2
f = (10 x 1)/2 (10/2 is the same as 5/1, the force required is 5 Kg)

#### Example Question

How much force is required to lift the weight?

A) 40lbs B) 50lbs C) 60lbs D)70lbs

Answer
C – 60lbs is needed to lift the weight. It can be calculated like this:
f = (w x d1)/d2
f = (80 x 9)/12
f = (720)/12
f = 60 lbs

In practice, levers are used to reduce the force needed to move an object, in other words to make the task easier. However, in mechanical aptitude questions it is possible that you will see questions where the fulcrum has been placed closer to the force then the weight. This will mean that a force greater than the weight will be required to lift it.

You may see more complex questions involving levers, where there is more than one weight for example. In this case you need to work out the force required to lift each weight independently and then add them together to get the total force required.

#### Key Points

• A lever consists of a rigid bar that pivots about a fulcrum and that is used to move a load at a second point by a force applied at a third point.
• All levers are one of three classes depending on the relative position of the load, effort and fulcrum.
• A class 1 lever has the load and the effort on opposite sides of the fulcrum.
• A class 2 lever has the load and the effort on the same side of the fulcrum, with the load nearer the fulcrum.
• A class 3 lever has the load and the effort on the same side of the fulcrum, with the effort nearer the fulcrum.
• In practice, levers are normally used to reduce the force needed to move an object, in other words to make the task easier.
• However, in mechanical aptitude tests you may see questions where the fulcrum has been placed such that a force greater than the weight will be required to lift it.