Simple Machines — How Does a Lever Work?
- 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.
- Effort. The force that is exerted by a person or machine to do something useful
- 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 (called the "effort"). 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.
You've Used a Lever Without Knowing It!
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.
In the diagram above, a force F1 acts downward on the lever at a distance d1 from the fulcrum.
"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, 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
© 2018 Eugene Brennan