Mechanical Advantage of a Lever

Also known as law of the lever · class 1 lever

MA = \frac{d_e}{d_l}

MA =

de =

dl =

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Balance the torques about a pivot — F_e·d_e = F_l·d_l — and the force multiplication falls out as the ratio of the arms. A 1.2 m crowbar with its fulcrum 0.3 m from the load gives MA = 4, so 200 N of effort lifts 800 N. Archimedes summed it up around 250 BC with "give me a place to stand and I will move the Earth", and the three lever classes still classify tools today: a seesaw (class 1), a wheelbarrow (class 2), and tweezers or a human forearm (class 3, where MA is deliberately less than 1 to trade force for speed and range).

Nothing is free — the effort end must travel the same factor further, so a MA of 4 means moving your hand 4 cm to raise the load 1 cm, and the work in equals the work out. Real levers fall short of the ideal because friction at the pivot and flex in the bar eat a few percent, which is why the actual mechanical advantage measured from forces is always a little below this ideal value computed from lengths.

Mechanical Advantage of a Lever

MA = \frac{d_e}{d_l}

Where

$MA$ = Mechanical advantage
$d_e$ = Effort arm length
$d_l$ = Load arm length

Missing one of these? Work it out first, then come back

Mechanical advantage — Kinetic Friction Force (f = μₖN), Maximum Static Friction (f = μₛN)
Effort arm length — Torque, Torque with a Lever Arm (τ = rF sin θ)
Load arm length — Torque, Torque with a Lever Arm (τ = rF sin θ)