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Buoyancy and Archimedes' Principle

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What you learned

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drag-and-terminal-velocityCompare buoyant support with velocity-dependent fluid drag

Key takeaway

  1. Buoyant force follows the weight of displaced fluid, so displaced volume is the live quantity to watch.
  2. A free-floating block settles where buoyant force equals weight, which turns into the density-ratio submerged fraction.
  3. Denser fluid can support the same block with less submerged volume because each displaced volume unit weighs more.
  4. Once a uniform block is fully submerged in a uniform fluid, moving deeper changes absolute pressure but not buoyant force.

Common misconception

Heavier objects always sink because buoyancy depends directly on mass.

Buoyant force depends on fluid density, gravity, and displaced volume, not on the object's mass alone.

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Read next

Keep the sequence moving with the most relevant follow-up concept.

  1. Read nextCompare buoyant support with velocity-dependent fluid dragdrag-and-terminal-velocity
    1. Read nextContrast static-fluid pressure differences with moving-fluid pressure tradeoffsBernoulli's Principle
    2. Read nextReview the pressure difference that causes the upward pushPressure and Hydrostatic Pressure

Start with the pressure difference, package it as displaced-fluid weight, then use the density ratio only for a freely floating balance.

  1. Pressure difference across the block

    The deeper bottom of the block feels more fluid pressure than the shallower top.

  2. Archimedes' principle

    The buoyant force equals the weight of the displaced fluid.

  3. Floating fraction at balance

    For a floating block, the submerged fraction is set by the density ratio.

Worked examples

Buoyancy worked examples

Open examples when you want to see the same idea walked through step by step.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
Use the live bench values. First find the buoyant force from displaced volume, then compare it with the block's weight to decide whether the current depth is a free-float balance.

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Example 1 of 2
Frozen valuesUsing frozen parameters

For the current block with , , and displaced volume , what buoyant force should Archimedes' principle predict?

Fluid density

1e3 kg/m³

Gravity

9.8 m/s²

Displaced volume

0.05 m³

1. Read the displaced volume from the submerged part of the block

The block currently has submerged, so the displaced-fluid column is showing .

2. Use $F_b = \rho_f g V_{\mathrm{disp}}$

Using , the current state gives .

3. Interpret the result as the weight of the displaced fluid

That same is the weight of the displaced fluid, which is why the displaced-fluid cue and the buoyant-force arrow stay synchronized.

Predicted buoyant force

The block is only partly submerged, so pushing it deeper would increase the displaced volume and the buoyant force.

Archimedes checkpoint

A uniform block is already fully submerged in a uniform fluid. You pull it 0.5 m deeper without changing the fluid or the block's volume. What happens to its buoyant force?

Make a prediction before you reveal the next step.

Decide whether deeper means more buoyancy once the whole block is already underwater.

Check your reasoning against the live bench.

The buoyant force stays the same.
The top and bottom pressures both increase, but their difference stays the same because the fluid density and the block's height are unchanged. The displaced volume also stays the same, so the buoyant force does not change.

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