# Principle of Flotation- Archimedes’ Principle

“Archimedes” Principle states that when a body is
wholly or partially immersed in a fluid it appears to suffer a loss in mass
equal to the mass of the fluid it displaces.

### Relative Density

The relationship between weight and volume is called

*density*. It is defined as ‘mass per unit volume’. One metric tonne of fresh water has a volume of one cubic metre. Therefore it has a density of 1.000 tonnes/m^{3}. Salt water on the other hand, is heavier. One cubic metre of salt water weighs 1.025 tonnes, and so salt water has a density of 1.025 tonnes/m^{3}.
The relative
density (or specific gravity) of a substance is defined as the ratio of the
weight of the substance to the weight of an equal volume of fresh water. In
other words, it is simply a comparison of the density of a substance with the
density of fresh water.

__Density of Substance__

^{R.D.}

^{ = }Density of Fresh Water

This is a pure number and has no units. The R.D. of sea water is therefore 1.025.

# Relationship Between Weight and Buoyancy

Suppose we have a body or block that measures 1 cubic
metre and weighs 4000 kg. If we now
lower the block into fresh water, it will displace 1 cubic metre of fresh water
- which, as we now know, weighs 1000 kg.
In other words, there is a force acting

*upwards*of 1000 kg and a force acting*downwards*of 4000 kg: the resultant force has to be 3000 kg*downwards.*That is, the block will sink.
If we take the same 4000kg block and mould it into a
hollow box with a volume of 5 cubic metres, and then place it in fresh water,
it has sufficient volume to displace 5 cubic metres of fresh water. If the box were now completely submerged, it
would experience an upward force of 5000 kg.

However, the downward force of the box is still only
4000 kg, thus the resultant force will be 1000 kg upwards. In this case the box will rise out of the
water to a level where the forces are equal and opposite, that is, with 4 cubic
metres under water, and 1 cubic metre still outside water.

Thus for a body to (just) float in water, its weight
must be exactly balanced by the force of buoyancy. If the volume of the body is further
increased, it will float with a certain amount outside the water.

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