Lever

Physics

A lever is a rigid bar that pivots on a fulcrum to multiply force or change its direction, as in a seesaw, crowbar, or wheelbarrow.

Visualization

Definition

A lever is a stiff bar that turns around a fixed point called the fulcrum, so pushing down on one end can lift a heavy load on the other end. The three classes differ in where the fulcrum, effort, and load sit: first class (a seesaw, fulcrum in the middle), second class (a wheelbarrow, load in the middle), and third class (tweezers or a fishing rod, effort in the middle), and the ideal mechanical advantage equals the effort arm length divided by the load arm length. A lever is in rotational equilibrium when the net torque about the fulcrum is zero, $F_{\text{effort}}\, r_{\text{effort}} = F_{\text{load}}\, r_{\text{load}}$, where $r$ is the perpendicular distance from the fulcrum to the line of action; this is the law of the lever, first stated by Archimedes. Mechanical advantage is $r_{\text{effort}}/r_{\text{load}}$, and a value greater than $1$ multiplies force while a value less than $1$ multiplies displacement and speed. Work in equals work out for an ideal lever, since both ends sweep arcs proportional to their radii.

Example

A seesaw is a lever: a small kid far from the middle can lift a bigger kid sitting close to the middle. A crowbar $1.2\ \text{m}$ long with its fulcrum $0.1\ \text{m}$ from the load end has a mechanical advantage of $1.1 / 0.1 = 11$, so a $100\ \text{N}$ push lifts an $1{,}100\ \text{N}$ rock (ignoring friction). A $2\ \text{kg}$ meter stick balanced at its center has a $0.5\ \text{kg}$ mass hung at the $10\ \text{cm}$ mark; to balance, an unknown mass at the $80\ \text{cm}$ mark must satisfy $0.5 \times 40 = m \times 30$, so $m = 0.67\ \text{kg}$. The stick's own weight acts at the pivot and contributes no torque.

Key Insight

The farther from the fulcrum you push, the less force you need, so a long crowbar beats a short one every time. Your forearm is a third-class lever: the biceps pulls close to the elbow and the hand moves far away, which costs force but gains speed and reach, exactly what throwing needs. The lever is the physical picture behind torque. Every wrench, door handle, and bicycle pedal is a lever in disguise, and every one of them obeys the same rule: torque equals force times lever arm.