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Concept module

Buoyancy and Archimedes' Principle

Use one immersed-block bench to connect pressure difference, displaced fluid, and the density balance behind floating, sinking, and neutral buoyancy.

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Starter track

Step 4 of 50 / 5 complete

Fluid and Pressure

Earlier steps still set up Buoyancy and Archimedes' Principle.

1. Pressure and Hydrostatic Pressure2. Continuity Equation3. Bernoulli's Principle4. Buoyancy and Archimedes' Principle+1 more steps

Previous step: Bernoulli's Principle.

Start from track beginning

Why it behaves this way

Explanation

Buoyancy is not a separate magic force that appears without a cause. It is the upward result of fluid pressure being larger on deeper parts of an immersed object than on shallower parts. This page deliberately reuses the pressure and hydrostatic-pressure language so buoyancy grows out of the same fluid-statics story instead of replacing it.

Archimedes' principle packages that pressure-difference story into one compact rule: the buoyant force equals the weight of the displaced fluid. On this bench the displaced-fluid column, the buoyant-force arrow, and the response graphs all come from the same submerged volume, so the equation stays tied to what the learner can actually see.

Floating and sinking depend on density balance, not mass alone. A large object can still float if its average density stays below the fluid density because both weight and buoyant force scale with volume. This bounded model keeps one rectangular block, one uniform fluid, and one immersion control so displaced volume, floating level, and the fully-submerged-deeper case stay visually honest without turning into a ship-design sandbox.

Key ideas

01Archimedes' principle says the buoyant force equals the weight of the displaced fluid, so displaced volume is the quantity to watch.

02While the block is only partly submerged, pushing it deeper increases displaced volume and therefore increases the buoyant force.

03A freely floating block settles where weight and buoyant force balance, so the required submerged fraction is the density ratio $\rho_{obj}/\rho_f$.

04Once the whole block is submerged in one uniform fluid, moving it deeper raises both the top and bottom pressures together but does not change their difference, so the buoyant force stays the same.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the current bench directly. The same block, fluid, and immersed depth that you can see on the stage now drive both worked examples, so Archimedes' principle stays attached to the live model.

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View plans

Frozen valuesUsing frozen parameters

For the current block with $ρ_{f} = 1 e 3 kg/ m^{3}$ , $g = 9.8 m/ s^{2}$ , and displaced volume $V_{disp} = 0.05 m^{3}$ , what buoyant force does Archimedes' principle predict?

ρ_{f}

Fluid density

1e3 kg/m^3

g

Gravity

9.8 m/s²

V_{d i s p}

Displaced volume

0.05 m^3

1. Read the displaced volume from the submerged part

The block currently has

0.65 m

submerged, so the displaced-fluid column is showing

V_{disp} = 0.05 m^{3}

2. Apply Archimedes' principle

Using

F_{b} = ρ_{f} g V_{disp}

, the current state gives

F_{b} = 509.6 N

3. Interpret the result as displaced-fluid weight

That same

509.6 N

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

Current buoyant force

F_{b} = 509.6 N, V_{disp} = 0.05 m^{3}

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 larger buoyancy once the whole object is already underwater.

Check your reasoning against the live bench.

The buoyant force stays the same.

Both the top and bottom pressures rise when the block is moved deeper, but their difference stays the same because the block's height and the fluid density are unchanged. The displaced volume also stays the same, so Archimedes' principle gives the same buoyant force.

Common misconception

Heavy objects sink because buoyancy only depends on the object's mass.

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

Weight and buoyant force both scale with volume, so floating versus sinking is really about average density compared with the fluid.

Quick test

Reasoning

Question 1 of 4

Use the displaced-fluid and force-balance story, not memory alone. These checks focus on what buoyancy means physically.

A block has average density $600 kg/ m^{3}$ and floats in water of density $1000 kg/ m^{3}$ . About what fraction of its volume must be submerged at balance?

Use the live bench to test the result before moving on.

Accessibility

The stage shows one rectangular block in a fluid tank. The block can sit partly above the surface or fully under the fluid depending on the bottom-depth slider. A readout panel reports object density, fluid density, displaced volume, weight, buoyant force, and any extra support needed to hold the current depth.

Guided overlays can show the weight and buoyant-force arrows on the block, a side column with the same displaced-fluid volume as the submerged part, a dashed free-float balance line for the current density ratio, and pressure samples at the top and bottom of the displaced part of the block.

Graph summary

The force-depth graph keeps the block's weight flat while the buoyant-force curve rises with submersion and then levels off after full submersion.

The force-fluid-density graph shows that denser fluid raises buoyant force at the same depth. The required-fraction graph shows how much of the block must be submerged for balance and marks the full-submersion limit at 1.

Carry pressure into buoyancy and back

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Review the pressure sourceFluids

Buoyancy and Archimedes' Principle

Fluid and Pressure

Explanation

Step through the frozen example

For the current block with ρf​=1e3kg/m3, g=9.8m/s2, and displaced volume Vdisp​=0.05m3, what buoyant force does Archimedes' principle predict?

A block has average density 600kg/m3 and floats in water of density 1000kg/m3. About what fraction of its volume must be submerged at balance?

Keep this idea moving

Pressure and Hydrostatic Pressure

Bernoulli's Principle

Continuity Equation

For the current block with $ρ_{f} = 1 e 3 kg/ m^{3}$ , $g = 9.8 m/ s^{2}$ , and displaced volume $V_{disp} = 0.05 m^{3}$ , what buoyant force does Archimedes' principle predict?

A block has average density $600 kg/ m^{3}$ and floats in water of density $1000 kg/ m^{3}$ . About what fraction of its volume must be submerged at balance?