Simple Machines — How Does a Lever Work?

Updated on December 1, 2018
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Eugene is a qualified control/instrumentation engineer Bsc (Eng) and has worked as a developer of electronics & software for SCADA systems.

A lever can magnify force.
A lever can magnify force. | Source

Glossary

  • Force. This can be thought of as a "push" or "pull". Examples are lifting a weight, sliding something, a magnet pulling a piece of iron, the tension in a spring and the effects of pressure acting on the walls of a gas cylinder.
  • Fulcrum. The point at which a lever pivots.
  • Mechanical advantage. A simple machine can magnify a force. The degree to which the force is magnified is called the mechanical advantage.

The Lever — One of the Six Classical Simple Machines

The lever is one of the six simple machines which were defined by Renaissance scientists, also including the wheel, the inclined plane, the screw, the wedge and the pulley. Levers are great because they give a mechanical advantage. This means that they can produce a greater force than that which you apply to them. You have used a lever in some shape or form without actually realizing it. So for instance scissors, nut crackers, pliers, hedge shears, bolt cutters and lopping shears all employ levers in their design. A prybar or crowbar is a lever also, and when you prise open the lid of a tin with the handle of a spoon, you are using "the law of the lever" to create a greater force. A long handle on a wrench provides more "leverage". A claw hammer also acts as a lever when pulling out nails. A see-saw is also a lever.

Levers can increase a force. I.e they give a mechanical advantage.
Levers can increase a force. I.e they give a mechanical advantage.

You've Used a Lever Without Knowing It!

Using the handle of a spoon to open a tin. The spoon acts as a lever, creating a larger force to lift the lid. The fulcrum is the rim of the tin
Using the handle of a spoon to open a tin. The spoon acts as a lever, creating a larger force to lift the lid. The fulcrum is the rim of the tin | Source

How Levers Work - An Analysis

In the diagram below, two forces act on the lever. This is a schematic or diagram, but it symbolically represents any of the real life levers mentioned above.

The lever pivots at a point called a fulcrum represented by the black triangle (in real life, this could be the screw holding the two blades of a scissors together). A lever is said to be balanced when the lever doesn't rotate and everything is in equilibrium (e.g. two people of equal weight sitting on a see-saw, at equal distances from the pivot point).

What is the Moment of a Force?

To understand how levers work, we need to understand the concept of moment of a force. The moment of a force about a point is the magnitude of the force multiplied by the perpendicular distance from the point, to the line of direction of the force.

Moment of a force.
Moment of a force. | Source
Forces on a lever.
Forces on a lever. | Source

In the diagram above, a force F1 acts downward on the lever at a distance d1 from the fulcrum.

When balanced:

"The sum of the clockwise moments equals the sum of the counter-clockwise moments"

Another force F2 at distance d2 from the fulcrum acts downwards on the lever. This balances the effects of F1 and the lever is stationary, i.e. there is no net turning force.

So for F1, the moment is F1d1

and for F2, the moment is F2d2

And when the lever is balanced, i.e. not rotating and static:

F1d1 = F2d2

Imagine if F1 is the active force and is known. F2 is unknown but must push down on the lever to balance it.

Rearranging the equation above

F2 = F1(d1/d2)


So F2 must have this value to balance the force F1 acting down on the right hand side.

Since the lever is balanced, an equivalent force equal to F2 (and due to F1), shown in orange, must be pushing upwards on the left side of the lever.

If the distance d2 is a lot smaller than d1 (which would be the case with a crowbar or pliers), the term (d1/d2) in the equation above is greater than unity and F2 becomes greater than F1. (a long handled crowbar can easily produce a ton of force).

This is intuitively correct since we know how a long crowbar can create a lot of force for lifting or prying things, or if you put your fingers between the jaws of a pliers and squeeze, you know all about it!

If F2 is removed and the lever becomes unbalanced, the upwards force due to the force F1 on the right is still F1(d1/d2). This force magnifying effect or mechanical advantage of a lever is one of the features that makes it so useful.

When the lever is balanced, the force F1 produces an equivalent force of magnitude F2  (shown in orange). This balances F2 (shown in blue) acting downwards
When the lever is balanced, the force F1 produces an equivalent force of magnitude F2 (shown in orange). This balances F2 (shown in blue) acting downwards | Source
From "The World of Wonder" a children's science periodical from the 1930s
From "The World of Wonder" a children's science periodical from the 1930s | Source
Using a crowbar to pry up a heavy rock
Using a crowbar to pry up a heavy rock | Source
A bolt cutters
A bolt cutters | Source
Pliers and side cutters
Pliers and side cutters | Source

© 2018 Eugene Brennan

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