Simple Machines: How Does a Lever Work?

What Is a Lever?

A lever is a simple device that works by changing the input force needed to do work and move something. Some levers do this by magnifying the force applied to them. In this tutorial, we'll explore how levers are used in our everyday lives and then learn the simple physics of how they work.

The Lever: One of the Six Classical Simple Machines

The lever is one of the six simple machines which were defined by Renaissance scientists hundreds of years ago.

Six Classical Simple Machines

• Lever
• Wheel
• Inclined plane
• Screw
• Wedge
• Pulley

You've used a lever in some shape or form without actually realizing it. So for instance scissors, nutcrackers, pliers, hedge shears, bolt cutters and lopping shears all use 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're 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 and wheelbarrow are also levers.

What Is a Force?

To understand how a lever works, we first need to learn about forces. A force can be thought of as a "push" or "pull". A force is required for example to lift a weight or slide it on a surface.

Examples of Forces

• A forklift lifting a load
• Tension in a spring when you pull on it
• A magnet pulling a piece of iron
• Air in a balloon, football or tire, pushing outwards on its walls
• The force of gravity keeping things on the ground
• Air or water resisting the movement of a car, aircraft or ship. This is called drag.

An active force results in a reactive force, so for instance when you pull on a spring, this is the active force. The tension in the spring is the reactive force pulling back.

What Does Mechanical Advantage Mean?

A simple machine can magnify a force. The degree to which the force is magnified is called the mechanical advantage. Levers are great because they can increase mechanical advantage and generate much larger forces. For example a hammer or crowbar can easily produce a ton of force for pulling out nails, lifting a rock or prising up boards.

What Are the Parts of a Lever?

In general, levers can be actual tools or components in a machine, but they also appear in our bodies and in nature. A lever is made up of several parts:

• Beam: The physical lever itself is made of materials such as wood, metal or plastic, bone in humans and animals etc., which can pivot or move on the fulcrum.
• Effort: The force that is exerted on the lever
• Fulcrum: The point at which a lever pivots or hinges
• Load: The object that is acted on by the lever.

Examples of Levers in Everyday Life

• Crowbars and prybars
• Pliers
• Scissors
• Bottle openers
• Bolt cutters
• Nut crackers
• Claw hammer
• Wheel barrow
• Parts of machines such as engines and production machines in factories
• Bones and joints in your body

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Three Classes of Levers

The class of a lever depends on the position of the effort, fulcrum and load.

First Class Lever

The effort is on one side of the lever and the load is on the other side. The fulcrum is in the middle. Moving the fulcrum closer to the load increases the mechanical advantage and increases the force on the load.

Examples: Scissors, pliers, hammer

Second Class Lever

The effort is on one side of the lever and the fulcrum is on the other side with the load between the effort and fulcrum. Keeping the effort in the same position and moving the load closer to the fulcrum, increases the force on the load.

Examples: nutcracker, wheelbarrow

Third Class Lever

The fulcrum is on one end of the lever, the load is on the other side and the effort is between the load and fulcrum. A third class lever has less of a mechanical advantage than the other two types because the distance from the load to the fulcrum is greater than the distance from the effort to the fulcrum.

Examples: human arm, broom, sporting equipment (e.g. baseball bat)

Examples of Levers

The Physics of How Levers Work

What Is the Moment of a Force?

To understand how levers work, we first 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. So in the diagram below, if the magnitude of the force is F and the distance is d, the the moment = Fd

In the 2nd diagram below, two forces act on a 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).

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

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

When balanced:

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

So for F1, the clockwise moment is F1d1

and for F2, the counter-clockwise moment is F2d2

So the clockwise moments = the anticlockwise moments

and

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.

Dividing both sides of the equation by d2 and switching the left and right gives:

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, we can think of there being an equivalent force equal to F2 (and due to F1), shown in orange in the diagram below, 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.

The Law of the Lever

We can summarise the above reasoning into a simple equation known as the law of the lever:

Mechanical advantage = F2/F1 = d1/d2

d1 is called the effort arm and d2 the load arm. If F1 is the effort and F2 is the load, then:

Interesting Fact: We Have Levers in Our Body!

Many of the bones in your body act as third class levers. For instance in your arm, the elbow is the pivot, the biceps muscle creates the effort acting on the forearm and the load is held by a hand. The small bones in the ear also form a lever system. These bones are the hammer, anvil and stirrup and act as levers to magnify sound coming from the eardrum.