What you’re referring to is called the cantilever effect. It’s basically the first tool ever created.
In nature, everything is about balance. This is where the phrase action = reaction comes into play. If you push against something, the same force pushes back. By introducing a lever, you get a force applied at some distance from a rotationpoint. Again this has to be in balance, so if you use a lever against something, the force you apply at the length of the lever is balanced against the counter force on the arm at the length of that arm that it pressed against.
If you choose the place where you push to be farther away from the rotation point compared to the position where the counter force is applied, you increase the force. Think of this as you look at a see-saw. When you move farther back from the center, the force of gravity can easier move you down.
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