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Testing a Gold Crown with Water — Archimedes' Buoyancy and the Eureka Method

创建者

Penny

2. 七月 2026

Testing a Gold Crown with Water — Archimedes' Buoyancy and the Eureka Method

King Hiero of Syracuse suspected his goldsmith had cut his crown with cheaper silver, but how do you check without melting it down? Around 250 BC Archimedes solved it in the bath: stepping in, he saw the water rise by his own volume and realised a submerged object displaces its own volume of water. Density — weight divided by volume — then betrays any cheating, because gold is far denser than silver. This blueprint reproduces both the famous displacement test and Archimedes' more precise underwater-balance method, and states the buoyancy principle that floats every ship.

中级

说明

Understand the problem

You must find whether a crown is pure gold without damaging it. The key is density — weight divided by volume. Pure gold is very dense (about 19.3 g/cm³); gold mixed with lighter silver (about 10.5 g/cm³) is less dense, so the same weight of it takes up more space.

The Eureka insight

When a solid is lowered into water it pushes aside — displaces — exactly its own volume of water. So even an oddly shaped crown's volume can be measured by how much water it displaces. This is what Archimedes realised watching the bath overflow.

Set up an equal-arm balance

Hang a balance scale, or make an equal-arm balance from a rod and string with a small pan on each end, so it swings level and can compare two weights precisely.

所需工具：

Balance Scale

Balance the crown against pure gold in air

On the balance, set the crown against an equal weight of known pure gold, in air, until the two sides hang exactly level. Now they weigh the same — the only question left is whether they take up the same volume.

此步骤所需材料：

Crude Lead Ingot (from galena smelting)1 个

所需工具：

Balance Scale

Submerge both in water

Lower both objects, still on the balance, into a vessel of water. Each is pushed up by a buoyant force equal to the weight of the water it displaces — the bulkier object is pushed up harder.

此步骤所需材料：

Water5 升

所需工具：

Clean Glass Jars with Lids

Cotton Kitchen String

Read the verdict

If the crown is pure gold it has the same volume as the gold and the balance stays level under water. If it is adulterated with lighter silver it is bulkier, displaces more water, is buoyed up more, and its side rises — proof the crown is not pure gold.

所需工具：

Balance Scale

Or measure density directly

The simpler displacement version: weigh the crown, then submerge it in a brim-full vessel and measure the overflow — that volume is the crown's volume. Density = weight ÷ volume. Compare to pure gold's 19.3 g/cm³; an adulterated crown reads lower.

所需工具：

Clean Glass Jars with Lids

State Archimedes' principle

Any body in a fluid is pushed up by a force equal to the weight of the fluid it displaces. That single law tells the crown from a fake, floats a loaded ship, and lifts a balloon — one of the oldest exact laws of physics, from around 250 BC.