Lever

• 1. Introduction

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  A lever is a beam or rigid rod pivoted at a fixed hinge, and with one of them a person can claim to move the world. The Greek mathematician Archimedes is credited with the boast "Give me a lever (long enough and a fulcrum on which to place it), and I shall move the world". His earliest surviving writings about the device date from the third century BC. Yet by then the lever was already ancient. Renaissance scientists would later count it among six simple machines. This is the story of a rigid body that rotates on a single point, and how that one point lets a small push become a large one. What did the lever lift before Archimedes named its law? Why does moving something farther cost you force? And why does a wheelbarrow and a fishing rod belong to the same family as a seesaw?

• 2. Light, Easy, Nimble

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  Around 1300 the word "lever" entered English, carrying a meaning at odds with the heavy loads it shifts. It sprang from the stem of the verb lever, meaning "to raise". That verb reaches back to the Latin levare, which itself comes from the adjective levis, meaning "light", as in not heavy. The word's deepest root is the Proto-Indo-European stem legwh-, meaning "light", "easy", or "nimble". The same stem gave English the word "light", the antonym of "heavy". So a tool prized for hauling obelisks owes its name to the idea of weightlessness.

• 3. Before Archimedes

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  Autumn Stanley argues that the digging stick can be considered the first lever, a claim that would position prehistoric women as the inventors of lever technology. The next known cultural evidence comes from ancient Egypt around 5000 BC, where the mechanism appeared in a simple balance scale. In ancient Egypt around 4400 BC, a foot pedal worked the earliest horizontal frame loom. In Mesopotamia, modern Iraq, around 3000 BC, builders invented the shadouf, a crane-like device that uses a lever mechanism. In ancient Egypt, workmen used the lever to move and uplift obelisks weighing more than 100 tons. The proof sits in the stone itself. Recesses in the large blocks and the handling bosses could serve no purpose other than for levers.

• 4. The Law Of The Lever

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  The ideal lever does not dissipate or store energy, meaning no friction in the hinge and no bending in the beam. In that case the power into the lever equals the power out. As the lever rotates around the fulcrum, points farther from the pivot move faster than points closer to it. Because power is the product of force and velocity, a force applied farther out must be smaller than the force nearer in. This is the law of the lever, as discussed by Archimedes. If the distance from the fulcrum to the input force is greater than the distance to the output force, the lever amplifies the input force. If that distance is smaller, the lever reduces it. The relationship holds even though the horizontal distances shrink as the lever tilts away from the horizontal. Treating velocity this way inside a static problem is an application of the principle of virtual work.

• 5. Effort, Load, Fulcrum

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  Levers are classified by the relative positions of the fulcrum, the effort, and the resistance, also called the load. By convention the input force is the effort and the output force is the load. In a Class I lever the fulcrum sits between the effort and the resistance, as in a seesaw, a crowbar, a pair of scissors, a balance scale, a pair of pliers, and a claw hammer pulling a nail. Its mechanical advantage may be greater than, less than, or equal to 1. In a Class II lever the resistance sits between the effort and the fulcrum, as in a wheelbarrow, a nutcracker, a bottle opener, a wrench, a pair of bellows, and a car's brake pedal. Its load arm is shorter than its effort arm, so its mechanical advantage is always greater than 1, earning the name force multiplier. In a Class III lever the effort sits between the resistance and the fulcrum, as in a hoe, a pair of tweezers, a hammer, a pair of tongs, a fishing rod, and the mandible of a human skull. Its effort arm is shorter, so its advantage is always less than 1, making it a speed multiplier. The mnemonic fre 123 fixes the order: f between r and e for the first class, r between f and e for the second, e between f and r for the third.

• 6. Levers In Series

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  A compound lever comprises several levers acting in series, where the resistance from one acts as the effort for the next. The applied force passes down the chain from one lever to the next. Scales, nail clippers, and piano keys all work this way. The most intimate example sits inside the head. The malleus, incus, and stapes are small bones in the middle ear, connected as compound levers. Together they transfer sound waves from the eardrum to the oval window of the cochlea.