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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.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Match object density against fluid density, then move the same block deeper or shallower. The submerged volume, displaced-fluid cue, and force balance stay tied to one static fluid model.

Graphs

Switch graph views without breaking the live stage and time link.

Force balance vs bottom depth

Weight stays fixed for the same block, while buoyant force rises with submersion and then plateaus once the block is fully submerged.

bottom of block below surface (m): 0.15 to 1.8force (N): 0 to 1.02e3

Object weightBuoyant force

Hover or scrub to link the graph back to the stage.bottom of block below surface (m) / force (N)

Controls

Adjust the physical parameters and watch the motion respond.

Object density

ρ_{o bj}

650 kg/m^3

Changes the block's weight without changing its outer volume.

Fluid density

ρ_{f}

1e3 kg/m^3

Changes how much each displaced cubic meter of fluid weighs.

Gravity

g

9.8 m/s²

Scales both the block's weight and the buoyant force together.

Bottom depth

h_{b o tt o m}

0.65 m

Moves the bottom of the block deeper or shallower below the fluid surface.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Show

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

ObservationPrompt 1 of 1

While the block is still partly submerged, pushing the bottom deeper fills more of the displaced-fluid column and lengthens the buoyant-force arrow.

Try this

Start from Wood in water, then raise the bottom-depth slider toward 0.9 m.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

ρ_{o bj}

Object density

650 kg/m^3

Changes the block's weight and therefore the submerged fraction needed for floating balance.

Graph: Required submerged fraction vs object densityGraph: Force balance vs bottom depthOverlay: Force balanceOverlay: Free-float level

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use one prompt at a time. Each one keeps buoyancy tied to pressure differences and displaced volume rather than turning the page into a rule shelf.

ObservationPrompt 1 of 1

Graph: Force balance vs bottom depth

While the block is still partly submerged, pushing the bottom deeper fills more of the displaced-fluid column and lengthens the buoyant-force arrow.

Try this

Start from Wood in water, then raise the bottom-depth slider toward 0.9 m.

Why it matters

It shows that buoyant force follows displaced volume, not hidden mass inside the block.

Control: Bottom depthGraph: Force balance vs bottom depthOverlay: Displaced fluidOverlay: Force balanceEquation

h_{b o tt o m}

Equation

ρ_{f}

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

3 visible

Overlay focus

Force balance

Shows the object's weight, the buoyant-force arrow, and any extra support needed to hold the current depth.

What to notice

At balance the upward buoyant force matches the downward weight.
If the current depth is not a free-float depth, an extra support arrow appears to show what would be needed to hold the block there.

Why it matters

It keeps floating and sinking tied to force balance instead of memorized object labels.

Control: Object densityControl: Fluid densityControl: Bottom depthGraph: Force balance vs bottom depthGraph: Force balance vs fluid densityEquation

ρ_{o bj}

Equation

ρ_{f}

Equation

h_{b o tt o m}

Challenge mode

Use the live bench, not memory alone. These challenges keep Archimedes' principle tied to density balance and displaced volume on the same stage.

0/2 solved

MatchStretch

0 of 5 checks

Same block, less submersion in brine

Start from Wood in water, switch to compare mode, leave Setup A alone, and tune only Setup B until the same block balances with a noticeably smaller submerged height in denser fluid.

Compare modeGuided start2 hints

Suggested start

Setup A stays fixed as the water baseline. Edit only Setup B.

Pending

Stay in compare mode while editing Setup B.

Explore

Pending

Keep Setup A at its water-baseline buoyant force.

Pending

Raise Setup B's fluid density to about brine level.

Pending

Make Setup B only about half submerged.

Pending

Keep Setup B balanced too.

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

A block with density 650 kg/m^3 and fixed volume 0.08 m^3 weighs 509.6 N. With its bottom 0.65 m below the surface, 0.65 m of the block is submerged, so it displaces 0.05 m^3 of fluid. In a fluid of density 1e3 kg/m^3 at 9.8 m/s², Archimedes' principle gives a buoyant force of 509.6 N, which matches the weight of the displaced fluid. The pressure difference from top to bottom is 6.37 kPa. At this depth the buoyant force and weight are already balanced, so the block could stay here without extra support. The block is only partly submerged, so pushing it deeper would displace more fluid and raise the buoyant force.

Equation detailsDeeper interpretation, notes, and worked variable context.

Pressure difference across the block

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

Δ P = ρ_{f} g Δ h

ρ_{f}

Fluid density 1e3 kg/m^3

g

Gravity 9.8 m/s²

h_{b o tt o m}

Bottom depth 0.65 m

Archimedes' principle

The buoyant force equals the weight of the displaced fluid.

F_{b} = ρ_{f} g V_{disp}

ρ_{f}

Fluid density 1e3 kg/m^3

g

Gravity 9.8 m/s²

h_{b o tt o m}

Bottom depth 0.65 m

Object weight

The block's own weight depends on its average density, its volume, and gravity.

W = ρ_{obj} g V_{obj}

ρ_{o bj}

Object density 650 kg/m^3

g

Gravity 9.8 m/s²

Floating fraction at balance

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

\frac{V _{disp}}{V _{obj}} = \frac{ρ _{obj}}{ρ _{f}}

If the density ratio is larger than 1, even full submersion is not enough and the block sinks.

ρ_{o bj}

Object density 650 kg/m^3

ρ_{f}

Fluid density 1e3 kg/m^3

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 2 compact tasks ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

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

Short explanation

What the system is doing

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.

Live buoyancy checks

Solve the exact state on screen.

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.

Live valuesFollowing current 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?

Prediction prompt

Decide whether deeper means larger buoyancy once the whole object is already underwater.

Check your reasoning

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?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

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 moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Review the pressure sourceFluids

Buoyancy and Archimedes' Principle

See each variable before you move it.

Force balance

Same block, less submersion in brine

Fluid and Pressure

What the system is doing

Solve the exact state on screen.

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 moving through the concept map.

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?