Upthrust, floating and sinking · Grade 7
When something is put in a liquid it pushes some liquid aside, and the liquid pushes back up with a force called upthrust. If the upthrust can balance the weight, the object floats. Whether something floats depends on its density compared with the liquid, not just on how heavy it is.
Key facts
- Upthrust is an upward force from a fluid on any object in it.
- Archimedes’ principle: upthrust = weight of fluid displaced = ρ(fluid) × V(displaced) × g.
- A floating object: upthrust = weight.
- Objects less dense than the liquid float; denser ones sink.
- Apparent weight in water = real weight − upthrust.
- Fraction of a floating object under the surface = ρ(object) ÷ ρ(liquid).
Worked examples
Example 1
A stone weighs 8.0 N in air and 5.0 N in water. Find the upthrust and the stone’s volume. (ρ water = 1,000 kg/m³, g = 9.8 N/kg)
Answer: 3.0 N; 306 cm³
Example 2
A block of mass 120 g and volume 150 cm³ is put in water. Does it float? What fraction is under water?
Answer: It floats, with 4/5 (80%) under water.
Example 3
A raft has volume 0.60 m³ and mass 180 kg. What extra mass can it carry before it is fully submerged in fresh water?
Answer: 420 kg