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Archimedes Guide

PhysicsIntermediateReading time: 3 min

Overview

Why does a massive steel ship float on the ocean while a small pebble sinks to the bottom? Over 2,000 years ago, Archimedes discovered the secret of displacement and buoyancy in a bathtub. In this experiment, you will use the 'Weighing Method' to verify Archimedes' Principle and uncover the core factors determining buoyancy: Is it the liquid's density? The displaced volume? Or the depth of immersion?

Background

There is a famous legend about the discovery of Archimedes' Principle. The King of Syracuse asked a goldsmith to make a pure gold crown, but he suspected the goldsmith had mixed in some silver. Archimedes pondered this problem until one day, while taking a bath, he noticed water overflowing from the tub. He realized the relationship between volume and displacement, and excitedly ran naked into the street shouting 'Eureka!' (I have found it!). He used the water displacement method to measure the volume of the irregular crown and determined its authenticity. Although this story may be apocryphal, it vividly demonstrates that scientific discoveries often stem from keen observation of everyday details.

Key Concepts

Buoyancy (FbuoyF_{buoy})

The upward force exerted by a fluid (liquid or gas) on an object immersed in it. The direction is always vertically upward.

Weighing Method

Fbuoy=G−FpullF_{buoy} = G - F_{pull}

A method to measure buoyancy by measuring the object's weight in air and then in liquid. The difference between the two is the buoyant force.

Archimedes' Principle

Fbuoy=GdisplacedF_{buoy} = G_{displaced}

The buoyant force on an object immersed in a fluid is equal to the weight of the fluid that the object displaces.

Formulas & Derivation

Archimedes' Principle Formula

Fbuoy=ρliquidgVdisplacedF_{\text{buoy}} = \rho_{\text{liquid}} g V_{\text{displaced}}
The magnitude of the buoyant force is determined only by the density of the liquid ρliquid\rho_{\text{liquid}} and the volume of the fluid displaced by the object VdisplacedV_{\text{displaced}}, and is independent of the object's own density.

Experiment Steps

  1. 1

    Measure Weight in Air (GG)

    Observe the reading of the spring dynamometer when the metal block is not touching the liquid surface. Record the weight of the metal block GG.
  2. 2

    Explore Displaced Volume (VdisplacedV_{displaced})

    Slowly drag the stand downwards. Observe how the dynamometer reading changes as the metal block goes from touching the water surface to being fully submerged. What does this indicate about the relationship between buoyancy and the volume of displaced liquid?
  3. 3

    Explore Immersion Depth (hh)

    After the object is fully submerged, continue to drag it downwards for a certain distance. Note whether the dynamometer reading changes. Does this refute the incorrect intuition that 'buoyancy increases with depth'?
  4. 4

    Explore Liquid Density (ρliquid\rho_{liquid})

    Keep the depth constant and switch the liquid to 'Brine' (concentrated salt water). You will find that the dynamometer reading decreases. Does this mean the buoyancy has increased or decreased? How does the 'density' of the environment affect buoyancy?

Learning Outcomes

  • Confirm that buoyancy is directly proportional to VdisplacedV_{\text{displaced}} and ρliquid\rho_{\text{liquid}}.
  • Master the experimental skill of calculating buoyancy using the 'Weighing Method'.
  • Correct the intuitive misconception that 'buoyancy increases as an object enters deeper'.
  • Deeply understand the specific physical meaning of Archimedes' Principle.

Real-world Applications

  • Ship Engineering: Generating huge displacement by increasing the volume of the hollow part of the hull to produce enough buoyancy to lift a 10,000-ton ship.
  • Submarines: Changing their own weight by taking in and discharging water in ballast tanks to achieve surfacing or diving (while buoyancy remains basically unchanged).
  • Hot Air Balloons: Heating the air inside the balloon to decrease its density, using the buoyancy generated by the surrounding cold air to ascend.
  • Hydrometers: Using the floating principle to measure the density of various liquids.

Common Misconceptions

Misconception
The deeper an object is buried in a liquid, the greater the buoyancy it receives.
Correct
Incorrect. Before being fully submerged, buoyancy indeed increases with depth (because VdisplacedV_{\text{displaced}} is increasing); but after being fully submerged, since VdisplacedV_{\text{displaced}} no longer changes, buoyancy remains constant.
Misconception
Heavier objects must receive greater buoyancy than lighter objects.
Correct
Incorrect. Buoyancy is only related to the 'volume of displaced liquid', and has no direct relationship with the object's mass, density, or shape. An iron block is heavier than a wood block, but if their volumes are the same, the buoyancy they receive when fully submerged is the same.

Further Reading

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