Not given in the exam, recall it.
What it is for
Buoyant force (Archimedes' principle) is used in Pressure (SPM Physics Form 5). Keep the SI units in every line of working. Pressure
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| Fb | buoyant force | N |
| ρ | density of fluid | kg m⁻³ |
| V | volume of fluid displaced | m³ |
| g | gravitational acceleration | m s⁻² |
Rearrangements
ρ = Fb / (Vg)V = Fb / (ρg)
Worked example
Common trap
Understanding buoyant force (Archimedes' principle)
Fb is the buoyant (upthrust) force in newtons (N), ρ (rho) is the density of the fluid in kilograms per cubic metre (kg m⁻³), V is the volume of fluid displaced in cubic metres (m³), and g is the gravitational acceleration in metres per second squared (m s⁻²). Archimedes' principle says the upthrust on an object equals the weight of the fluid it displaces, and ρVg is exactly that weight.
The upthrust acts upward, opposing the object's weight.
Use the density of the fluid, not the object, and take V as the submerged volume, the volume of fluid pushed aside. Rearrange to find the fluid density with ρ = Fb / (Vg) or the displaced volume with V = Fb / (ρg).
A fully submerged object displaces its own whole volume.
A worked example, step by step
A metal block of volume V = 5.0 × 10⁻⁴ m³ is fully submerged in water of density ρ = 1000 kg m⁻³ (take g = 9.81 m s⁻²). Find the buoyant force on it.
- Write the formula: Fb = ρVg.
- Substitute with units: Fb = 1000 kg m⁻³ × 5.0 × 10⁻⁴ m³ × 9.81 m s⁻² = 4.905 N.
- Round: Fb = 4.9 N to two significant figures.
The unit check gives kg m⁻³ × m³ × m s⁻² = kg m s⁻² = N. Because the block is fully submerged, V is its entire volume. If the same block floated, only the submerged part would count, and the upthrust would equal the block's weight.
Common mistakes and how this is tested
The key trap is using the object's density instead of the fluid's, the upthrust depends on the fluid displaced, so ρ is always the fluid density. Another is using the whole object volume when the object only floats partly submerged; then V is just the submerged volume.
- Forgetting the answer is a force in newtons.
- Confusing the upthrust with the object's weight.
Questions ask you to calculate the buoyant force, explain why a ship floats or a submerged object feels lighter, or state Archimedes' principle. For the statement, say the buoyant force equals the weight of fluid displaced.
To decide floating or sinking, compare the upthrust with the object's weight.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)