Lets start with the principle itself:
Archimedes’ Principle – A fluid exerts an upward buoyant force on an object, fully or partially immersed in the fluid, that is equal to the weight of the fluid displaced by the object.
Some Key Definitions
Weight – the force acting on an object due to gravity, found by multiplying the mass of the object by the acceleration due to gravity, g.
Fluid – a phase of matter including liquids, gases and plasmas.
Buoyant Force – the upward force exerted by a fluid on any object either partially or fully immersed in the fluid.
Buoyant Force
In any fluid pressure increases with depth. As a result of this the pressure exerted on an object submersed in a fluid is greater at the bottom of the object than at the top, as seen in the diagram below. The results in a net upwards force – the buoyant force.
Formula
Archimedes’ principle gives rise to the flowing equation:
Where:
- Fb = buoyant force (units = N)
- ρ is the density of the fluid (units = kgm-3)
- g is the acceleration due to gravity (units = ms-2)
- V is the volume of the displaced fluid (units = m3)
Please let me know in the comments, if you would like an explanation of how this formula can be derived.
When an object is fully or partially immersed in a fluid it appears to weigh less. For example, a person appears to weigh less in water. This apparent weight is equal to the weight of the person minus the weight of the water displaced by the person. From the principle we can see that the force giving rise to this apparent weight loss is the buoyant force.
Sink Or Float?
The net force acting on an object determines whether it sinks or floats.
We know there are two forces acting on the object. The weight of the object and the buoyancy force. The below images show 3 different scenarios. Remember here that the buoyant force is equal to the weight of the fluid displaced by the object (Archimedes’ Principle).
In the diagrams: Fb is the buoyant force and W is the weight of the object.
Image 1 – The weight of the object is less than the weight of the fluid it has displaced. The buoyancy force is therefore greater than the weight of the object. The net force is positive and so the object rises. When it reaches the surface, the object will float.
Image 2 – The weight of the object is equal to the weight of the fluid it has displaced. The buoyancy force is therefore equal to the weight of the object. The net force is zero, the object is neutrally buoyant and stays where it is.
Image 3 – The weight of the object is more than the weight of the fluid it has displaced. The buoyancy force is therefore less than the weight of the object. The net force is negative and so the object sinks.
Key points to note:
- The buoyant force is equal to the weight of the displaced fluid NOT the weight of the object. The weight of the object is not necessarily the same.
- The buoyant force is dependent on the volume of the object immersed in the fluid and density of the fluid NOT the density of the object. This can be seen in the formula.
As always if you have any questions please leave them in the comments below. Or feel free to contact me on Instagram or Pinterest.
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