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Simple Machines · Question 12 of 20

Levers

"Give me a place to stand and I will move the Earth." Archimedes wasn't bragging about strength — he was bragging about geometry.

Plate XV — Torque vs torque F₁·r₁ = F₂·r₂
Slide the fulcrum toward the rock until your small push wins the argument.
100 kg30 kg push1.7 m2.3 m
FIG. XV — TORQUE VS TORQUE
Fulcrum position 1.7 m from the rock
Slide it toward the rock — your side of the argument gets longer.
Rock 100 kg
Your push 30 kg
Rock's torque
1,648N·m
Your torque
683N·m
Push to balance
72.4kg
The seesaw doesn't care how strong you are — it cares about push × distance from the pivot. Slide the fulcrum close to the rock and suddenly your little push, working on a long arm, out-argues a boulder.
The short answer

Push down far from the pivot and you can lift something heavy close to it — a lever trades a long, easy push for a short, strong lift.

What's actually happening

A lever is a rigid bar resting on a pivot — the fulcrum — and it runs on one rule: what matters is not how hard you push, but how hard you push times how far from the pivot you push. That product is torque, the turning power. A small force far from the fulcrum can out-torque a huge force close to it, which is why a child at the end of a seesaw can lift a parent sitting near the middle.

The price is distance, as always. Push down one metre on your long side of the lever and the short side rises only a fraction of that — exactly the inverse of the force multiplication. Ten times the force, one-tenth the lift. The work in equals the work out; the lever just changes the currency from "moving far" to "pushing hard". Archimedes' boast about moving the Earth was mathematically sound — he'd just need a lever arm light-years long and a very long afternoon.

Once you know the pattern you find levers everywhere, in three flavours: fulcrum in the middle (seesaw, pliers, scissors), load in the middle (wheelbarrow, bottle opener, nutcracker), and effort in the middle (tweezers, your own forearm). That last class multiplies distance instead of force — your bicep pulls a short distance with great force near your elbow so your hand can sweep fast and far. Your body chose speed over strength at almost every joint.

Try it at home A coin-powered crane
  1. 1Balance a 30 cm ruler on a pencil at its midpoint, then place a stack of four coins on one end.
  2. 2Slide the pencil fulcrum toward the coin stack and balance the stack with a single coin on the long side.
  3. 3Measure the two arms. The single coin sits roughly four times further from the pencil than the stack — force times distance balancing force times distance.