Levers explained: moments, balance and the three classes

Levers are one of the four areas NEIEP names for the EIAT's mechanical comprehension section, and they appear on almost every mechanical aptitude test. The good news is that one idea — the turning effect, or moment — answers nearly all of them.

The parts of a lever

• The pivot (or fulcrum): the point the lever turns about.
• The load: the weight or resistance being moved.
• The effort: the force you apply.

The one idea: turning effect = force × distance

A force applied to a lever has a turning effect about the pivot, called a moment. Its size is the force multiplied by its distance from the pivot:

moment = force × distance from the pivot

This is why the same force does more when it is further out. Pushing a door near its handle is easy; pushing it right next to the hinges is hard, because the distance is tiny.

Will it balance?

A beam balances when the turning effects on each side are equal. Work out force × distance on the left, then on the right:

• 10 lb placed 3 ft left of the pivot: 10 × 3 = 30.
• 15 lb placed 2 ft right of the pivot: 15 × 2 = 30.

They match, so the beam balances — even though the weights are different. If one side's total is bigger, that side goes down.

The trap in test questions is to look at which weight is heavier. Always multiply by the distance first.

How much effort do you need?

Turn the balance rule around to find the effort needed. A 60 lb load sits 2 ft from the pivot, and you push down 6 ft from the pivot on the other side:

Load's turning effect: 60 × 2 = 120. You need the same: effort × 6 = 120, so the effort is 20 lb.

The further from the pivot you push, the less force you need. The trade-off is distance: your end of the lever moves further than the load does. Here your hand moves three times as far as the load.

Mechanical advantage

Mechanical advantage is how many times the lever multiplies your force. For an ideal lever:

mechanical advantage = load ÷ effort = effort distance ÷ load distance

In the example above, 60 ÷ 20 = 3, and 6 ft ÷ 2 ft = 3. Real levers lose a little to friction and bending, but test questions almost always treat them as ideal.

The three classes of lever

Levers are grouped by where the pivot, load and effort sit relative to each other.

• First class — pivot in the middle. Effort on one side, load on the other. Examples: a seesaw, a crowbar, a pair of scissors. Can multiply force or distance depending on where the pivot sits.
• Second class — load in the middle. The pivot is at one end and the effort at the other. Examples: a wheelbarrow, a nutcracker, a bottle opener. Always multiplies force.
• Third class — effort in the middle. The pivot is at one end and the load at the other. Examples: tweezers, a fishing rod, your forearm lifting something in your hand. Needs more force than the load, but moves the load further and faster.

A simple way to remember it: ask what is in the middle. Pivot, load or effort gives first, second or third class.

Practice

Our mechanical comprehension practice includes balance questions and lever-effort questions drawn to scale, so you can practice multiplying out the turning effects instead of guessing from the picture.