Lever
The mathematics of moving the world
Summary
A lever is a rigid bar that turns around a pivot point (the fulcrum). The longer the effort arm, standing away from the load, the less force you need to lift the load. The balance condition: W·d_W = F·d_F. Use the sliders to change the weight of the load and the lengths of the arms, and see how the force you need changes.
In depth
The ancient Greek mathematician and engineer Archimedes (c. 287–212 BC) is known as the first person to set out the mathematics of the lever systematically. In a lever system, balance is reached through equal moments (torques): the moment of the load must equal the moment of the effort, that is, W·d_W = F·d_F. From this, the force needed is F = W·(d_W/d_F). How many times longer the effort arm is than the load arm directly gives the mechanical advantage. It is not free: for every factor of force you gain, you have to move that much further; the end you push moves MA times as far as the load.
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