The Law of the Lever — Archimedes' Balance of Weight and Distance

'Give me a place to stand and I will move the Earth,' said Archimedes of the lever. Around 250 BC he proved the exact law behind it: a weight balances another when each weight multiplied by its distance from the pivot is equal. That simple rule — weight times distance on one side equals weight times distance on the other — lets a small effort lift an enormous load, and underlies the crowbar, the balance scale, the oar and the seesaw. This blueprint builds a lever and fulcrum and demonstrates the law by measurement.

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Understand the law

A lever is a rigid bar that turns on a pivot called the fulcrum. Archimedes' law says it balances when the weight on one side times its distance from the fulcrum equals the weight times distance on the other: W1 × d1 = W2 × d2. Each 'weight times distance' is called a moment.

Build a lever and fulcrum

Rest a straight rigid beam across a fixed fulcrum — a triangular block or a firm edge — so the beam can tip freely both ways. Mark equal distance graduations along the beam from the fulcrum.

このステップの材料:

Dowel Rod1 個

Hardwood Block1 個

必要な工具:

Cotton Kitchen String

Balance equal weights

Hang or set equal weights the same distance from the fulcrum on each side. The beam should sit level. This confirms your fulcrum is central and the beam itself is balanced.

必要な工具:

Ankle Weight Set (Adjustable, DIY)

Balance a heavy weight with a light one

Put a heavy weight close to the fulcrum and a lighter weight far out on the other arm. Slide the light weight in or out until the beam balances — the small far weight holds up the big near one.

必要な工具:

Ankle Weight Set (Adjustable, DIY)

Verify the numbers

Measure and multiply. For example, 4 units of weight at 10 cm balances 1 unit at 40 cm, because 4 × 10 = 40 = 1 × 40. The two moments are equal — exactly as Archimedes' law predicts.

必要な工具:

Cotton Kitchen String

Read off the mechanical advantage

The ratio of the two arm lengths is the force multiplier. A long effort arm and a short load arm let a small push raise a big load: effort = load × (load arm ÷ effort arm). Doubling the effort arm halves the effort needed.

Why it could 'move the Earth'

Because the law has no built-in limit, a long enough lever on a firm enough fulcrum could balance any weight at all — the point Archimedes was making. In practice the only limits are the length and stiffness of the bar.

Spot levers everywhere

The same rule works a crowbar prising a rock, a seesaw, an oar against its rowlock, a wheelbarrow, and the balance scale of a market. Each trades distance for force by weight × distance.