Archimedes' Principle & Floating
A fluid pushes up on anything in it with the weight of the fluid it shoves aside.
Lesson at a glanceShow the key points
- Buoyant force: the resultant of the fluid's pressure forces on a submerged surface.
- Archimedes' principle: a body partly or fully immersed in a fluid at rest feels an upward buoyant force equal to the weight of the fluid it displaces (13.5).
- Proof: replace the body by fluid of the same shape; that fluid is in equilibrium, so the surrounding pressure forces balance its weight.
- Floatation: a body floats when the buoyant force equals its weight; it floats partly submerged if its average density is less than the fluid's, with submerged fraction ρ(body)/ρ(fluid).
- The principle assumes the fluid is at rest in an inertial frame.
A steel ship weighing thousands of tonnes floats, while a steel nail sinks. Lift someone in a swimming pool and they feel lighter. Both come down to one principle, which follows directly from the pressure forces we already understand.
The buoyant force
When a body is dipped partly or wholly into a fluid, the fluid pushes on every bit of its surface, perpendicular to the surface, with a force equal to the local pressure times the area. Deeper parts are pushed harder. The resultant of all these contact forces is the buoyant force, B.
Archimedes’ principle
This isn’t a separate law of nature; it follows from Newton’s laws. Imagine removing the body and filling the space it occupied with the same fluid. The fluid is now uniform and at rest, so this “substitute” fluid is in equilibrium. Only two forces act on it: its weight mg and the push B of the surrounding fluid. Hence
The surrounding fluid neither knows nor cares what fills the space: the substitute fluid and the original body have exactly the same boundary, so the pressure forces on them are identical. So the body feels the same B.
Floating
If the buoyant force equals the body’s weight, the body stays in equilibrium: it floats. A body whose average density is less than the fluid’s floats with only part of it submerged, just enough to displace its own weight of fluid:
A ship floats because its hull encloses lots of air, making its average density much less than water’s.
A wooden block 20 cm × 20 cm × 10 cm (density 600 kg/m³) floats in water with its large faces horizontal. How much of its 10 cm height sticks out?
A 2.0 kg stone of density 2500 kg/m³ hangs from a spring balance, fully under water. What does the balance read? (g = 10 m/s²)
- 1The buoyant force is the resultant of the fluid's pressure forces on a body.
- 2Archimedes: B = weight of fluid displaced, upward (for a fluid at rest in an inertial frame).
- 3A body floats when B equals its weight; if less dense than the fluid, the submerged fraction is ρ(body)/ρ(fluid).
- 4Apparent weight = true weight − buoyant force.
Check yourself
Keep exploring
Hand-picked videos, simulations and readings that explain this idea from a different angle.