Fence posts are often set in concrete to keep them stable, which is great ... until you have to remove them. I've seen people dig all around the concrete to free the post, but that is way more digging than I want to do. Instead, you can make a long lever to remove it without any digging at all!
What Is a Lever?
A lever is just a stiff arm that can pivot around some point (the fulcrum) so you can apply a force to one part of the arm and get out a force from another part of the arm. This can be used to change the magnitude or the direction of a force, making a small force large or an upward force downward.
This mechanism hinges on (sorry, couldn't resist) the idea of rotational equilibrium. As long as the arm is at rest or moving at a consistent speed, the total torque on the arm must be zero because its angular acceleration is zero. When you use a lever to lift something, these conditions are typically met exactly or at least approximately.
If we use the fulcrum as our axis of rotation for the calculation, then the force from the fulcrum does not contribute to the total torque on the system, only the input and output forces do. This means that the torque caused by the input force must be equal to the torque caused by the output force (but in the opposite direction).
Technical note: More accurately, the torque from the input force must be equal in magnitude to the torque from the third law pair force to the output force. If we use the lever to lift a rock, we're talking about the force that the rock applies to the lever, not the force the lever applies to the rock. These two forces will be equal in size, as described by Newton's Third Law of Motion.
How to Calculate the Magnitude of the Torque
The magnitude of the torque here is equal to the magnitude of the force multiplied by the distance from the pivot to the location of the force. If the two distances are different, the forces must be different, as well, to make the torques equal. For example, if the input force is 2 meters from the fulcrum, but the output force is only 1 meter from the fulcrum, the output force must have 2 times the magnitude of the input force.
There are three classes of levers. A first-class lever has the fulcrum in the middle of the two forces, like a teeter-totter. A second-class lever places the output force in the middle, with the input force on one side and the fulcrum on the other. The lever in the video below is a second-class lever, as is something like a wheelbarrow. A third-class lever has the input force in the middle, with the output force on one side and the fulcrum on the other. A lacrosse stick and a human forearm are examples of a third-class lever. The image below summarizes these three types. Note that both arrows could be flipped to the opposite direction for each class of lever.
Diagram credit: Andrew Bennett
How to Apply Our Knowledge of Levers to the Fence Post Problem
To lift a post out of the ground requires a huge amount of force. To achieve this without special machinery, we simply need to place the input force much farther from the fulcrum than the output force. In the video below, I applied a force to the lever a distance 10 times that of the output force on the post, making the output force 10 times that of the input force.
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More Physics Life Hacks
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