Archimedes' principle and its uses
A body fully or partly in a fluid feels an upward force equal to the weight of the fluid it displaces. Ships, hydrometers and lactometers use this.
The principle
Archimedes' principle: when a body is fully or partly immersed in a fluid, it feels an upward force equal to the weight of the fluid displaced by it. 'Displaced' means pushed out of the way. A larger volume under the fluid pushes away more fluid, so it feels a larger upthrust. A denser fluid also gives a larger upthrust.
Activity: loss of weight of a stone in water
You need a stone, a thread, a spring balance, and a bucket or beaker of water.
- 1Tie the stone to the spring balance and note its weight in air.
- 2Lower the stone slowly into the water and watch the reading.
- 3★Observe: the reading falls as more of the stone goes under water.
- 4Once the stone is fully under, lower it further. Observe: the reading does not change any more.
- 5Conclude: water pushes the stone up. The fall in the reading is the buoyant force. It stops growing once the whole stone is under.
- 6To check the principle, use a can filled to its spout. Collect the water the stone pushes out and weigh it. Its weight equals the fall in the reading.
★ key step
Worked example: buoyant force from two readings
A metal piece weighs 5.0 N in air and 3.2 N when fully under water. Find the buoyant force on it, and the volume of water it displaces. (g = 9.8 m s⁻²; density of water 1000 kg m⁻³)
- Buoyant force = weight in air − weight in water = 5.0 N − 3.2 N = 1.8 N.
- By Archimedes' principle, the weight of the water displaced = buoyant force = 1.8 N.
- Mass of the displaced water = 1.8 N ÷ 9.8 m s⁻² ≈ 0.184 kg = 184 g.
- Since 1 g of water fills 1 cm³, its volume is about 184 cm³. This is also the volume of the metal piece.
Buoyant force 1.8 N upward; the displaced water weighs 1.8 N and has a volume of about 184 cm³
Uses of Archimedes' principle
- Ships and boats are designed to displace enough water to balance their weight with the load.
- Submarines take in water to sink and pump it out to rise. This changes their weight while the upthrust stays the same.
- A hydrometer is a weighted glass float that sinks less in a denser liquid. A scale on its stem shows the density.
- A lactometer is a hydrometer for milk. Watered milk is less dense, so the lactometer sinks deeper and shows that the milk is impure.
- Life jackets and rubber tubes add a large volume, so the upthrust keeps a person afloat.
How to draw the loss of weight experiment
- Draw a stand with a spring balance hanging from it, showing the pointer and scale.
- Draw a thread from the hook down to a stone.
- Draw a beaker of water below, with the stone fully under the surface and not touching the bottom.
- Beside it, draw the same balance with the stone in air, showing a higher reading.
- Label: spring balance, pointer, scale, thread, stone, water, beaker.
Milk collection centres in villages check milk with a lactometer: watered milk lets it sink deeper. Every boat on a river floats by displacing water equal to its own weight.
2 marks: “State Archimedes' principle.” When a body is fully or partly immersed in a fluid, it feels an upward force equal to the weight of the fluid displaced by it.
2 marks: “A stone weighs 2.4 N in air and 1.5 N in water. Find the buoyant force on it, and the weight of water it displaces.” Buoyant force = 2.4 − 1.5 = 0.9 N. By Archimedes' principle, the water displaced also weighs 0.9 N.
3 marks: “How does a lactometer test the purity of milk? Name one more use of Archimedes' principle.” A lactometer is a weighted float. It sinks to a depth that depends on the density of the milk. Watered milk is less dense, so the lactometer sinks deeper. Another use: designing ships and submarines (or the hydrometer).
Push water aside and you are pushed up by its weight: that is Archimedes' 'Eureka'.