NovaMath

Floating and sinking

Compare buoyancy and weight; submarine and hydrometer ideas.

Buoyancy (junior)Archimedes’ principle and floating/sinking.

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Floating and sinking

Float / sink conditions: compare Fb with G (or densities). Floating and suspended rest both have Fb = G, but immersion and density differ. Try submarine ballast and link to ships and hydrometers.

Memory cue: Fb ? G · float rest still Fb = G · submarine changes weight.

Key formulas

  • Immersed: Fb ? G → rise / suspend / sink
  • Solid: ρ_obj ? ρ_liq
  • At floating or suspended rest: Fb = G

How to use

  1. Read Related knowledge (map + conditions).
  2. Tune densities, drop again, watch force arrows and state.
  3. Switch to submarine, change ballast, watch average density and dive/surface.

Read next

Related knowledge

Read float/sink conditions → density rule → float vs suspend → apps — and compare Fb with G on the tank or submarine.

Mind map

1. Float / sink by forces

A fully immersed object feels downward weight G and upward buoyancy Fb. Comparing them predicts the motion.

  • Fb > G: rises, then floats; at floating rest still Fb′ = G.
  • Fb = G: can suspend at any depth in the liquid.
  • Fb < G: sinks; on the floor Fb + normal = G.
  • Fb ? GCompare Fb and G to decide rise, suspend, or sink.

2. Density rule (solid)

For a solid fully immersed, V_disp = V, so comparing densities is enough.

  • ρ_obj < ρ_liq: rises → floats.
  • ρ_obj = ρ_liq: suspends.
  • ρ_obj > ρ_liq: sinks.
  • Hollow objects (ships): denser materials can still float by increasing displaced volume.

3. Floating vs suspended

  • Same: at rest, Fb = G in both cases.
  • Floating: part above the surface, V_disp < V, ρ_obj < ρ_liq; usually at the free surface.
  • Suspended: fully immersed, V_disp = V, densities equal; can stay at any depth.
  • Pitfall: floating rest is still Fb = G — Fb > G only while rising.

4. Submarine idea

Submarines change their own weight (average density): flood tanks to dive, empty to surface. Once submerged, Fb is nearly fixed — weight changes.

  1. Switch to Submarine mode and drag ballast water.
  2. Watch effective density vs ρ_liq and rise / dive.

5. Applications

  • Ships: hollow hull increases V_disp. River → sea: same weight ⇒ same Fb, denser seawater ⇒ smaller V_disp (rides higher).
  • Balloons / airships: fill with gas lighter than air to rise on air buoyancy.
  • Hydrometer floats with Fb = G; denser liquid → less immersion. Scales denser downward.
  • Salt-water seed sorting: full seeds sink, shriveled ones float.

Applications

  • Float / suspend / sink rules guide life jackets and buoys.
  • Salt-water egg demos and separation processes use density vs buoyancy.

FAQ

Is buoyancy greater than weight when floating?

Only while rising. At floating rest, Fb equals G again (with V_disp < V).

How does a submarine dive?

Flood ballast tanks to increase weight; submerged Fb stays nearly fixed, so larger weight dives.

When floating, how do buoyancy and weight compare?

Floating/suspending: F_b = weight; sinking if F_b < weight.

Why can a hollow iron ship float?

Average density < water; displaced volume makes F_b = weight.

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