Levers

A lever is a rigid bar that pivots about a fixed point, or fulcrum. It is one of the six classical simple machines and is used to amplify force or distance. When the lever is in equilibrium, the moments (torques) produced by the input force and the output load balance: F_in × d_in = F_out × d_out, where d_in is the distance from the fulcrum to the point where the input force is applied and d_out is the distance from the fulcrum to the load. The lever thus changes the direction of the applied force and, depending on arm lengths, can reduce the effort required or increase the speed and distance of the load.

Levers are classified into three classes: first class, second class, third class. In a first-class lever, the fulcrum lies between the effort and the load (examples: seesaw, crowbar). In a second-class lever, the load is between the fulcrum and the effort (examples: wheelbarrow, nutcracker). In a third-class lever, the effort is between the fulcrum and the load (examples: forearm during a biceps curl, tweezers). The mechanical advantage depends on arm lengths: MA = d_in/d_out; if d_in > d_out, MA > 1, enabling larger loads; if d_in < d_out, MA < 1, moving the load farther or faster than the effort.

History and use: The concept dates to ancient Greece and earlier, with Archimedes articulating the principle of the lever. Levers are fundamental in tools and machinery, appearing in construction, medicine, and daily life. In real systems, friction at the fulcrum and structural limits reduce ideal performance, but the lever remains a foundational example of how physics enables mechanical work to be done more efficiently.