ARCHIMEDES' PRINCIPLE
In order to understand Archimedes' Principle, let us make the
following observations :
1. Let us take a brick and tie a length of cotton thread
around it. Any attempt to lift the brick by the cotton thread fails through the
breakage of the thread. But if the brick is immersed in water, it can be lifted
quite easily. Thus, the brick appears to weigh less in water than in air.
2. If you try to lift a large block of stone out of water, you
will notice that although it may be easily lifted while it is in water, it
seems to become much heavier as it comes out into the air. Thus, the large
block of stone appears to weigh less in water than in air.
3. Stone boulders are moved very easily by flood waters since
their apparent weight is less in water.
4. Heavy shingles pile up on a sea-beach due to the same
reason.
The apparent change of weight in the above observations may be
understood if a large piece of stone is hung from a spring balance and slowly
lowered into water. As it enters the water, the reading of the balance will
decrease and this decrease will continue as more and more of the stone is
submerged. Once the stone is completely submerged in water, the balance reading
will remain constant as the stone is lowered more deeply. On raising the stone
again, reverse changes of the balance readings take place until the stone is
completely out of water, when the original reading will be given once more.
This apparent loss in weight of a body immersed in a liquid,
which is due to upthrust experienced by the body, has beautifully been stated
by Archemedes' Principle and was discovered by the Greek scientist Archimedes
who lived in the third century BC. Archimedes' principle states that :
When a body is immersed partially or wholly in a liquid at
rest, it experiences an upthrust which is equal to the weight of the liquid
displaced. The apparent loss in weight of the body is equal to the upthrust on
the body.
In essence, Archimedes' Principle states that : (i) When a
body is immersed either partially or fully in a liquid , it experiences an
upthrust or buoyant force (FB). >
(ü) This upthrust (FB) is equal to the weight (W) of the
liquid displaced by the body, i.e., FB = W = V d, 8 ...(1)
where d, is the density of liquid in which the body is
immersed and V is the volume of the liquid displaced.
Clearly, FB depends upon : (a) volume of the liquid displaced
and (b) density of the liquid. (iii) The body appears to lose weight while in
the liquid and this apparent loss in weight is equal to the upthrust or the
weight of the liquid displaced by the body. (iv) apparent weight of the body in
the liquid actual weight of the body in air – weight of the liquid displaced by
the body.
NOTE
Like liquids, gases also exhibit the property of buoyancy.
Thus, if a body is immersed in a gas, it also experiences an upthrust. Thus,
Archimedes' principle is applicable to gases as well and we can, therefore,
replace the word 'liquid' by the more general term fluid (i.e., a liquid or a
gas) while stating this principle.
EXPERIMENTAL
VERIFICATION OF ARCHIMEDES' PRINCIPLE
(i) Place a
displacement can on a table with a beaker under its spout as shown in Fig. 4.6.
(ii) Pour water in the
can until it runs from the spout.
(iii) Another beaker
(previously dried and weighed) is placed in place of the first one after the
water ceases to drip in it.
(iv) A suitable body,
e.g., a piece of metal or a stone is suspended by a thin thread from the hook
of a spring balance and the weight of the body in air is measured.
(v) The body, which is
still attached to the balance, is then carefully lowered into the displacement
can. When it is completely immersed, its new weight is noted with the spring
balance.
(vi) The displaced
water is collected in the weighed beaker. When no more water drips from the
spout, the beaker and the water are weighed.
(vii) The difference
in the weights of beaker with water and the beaker alone, gives the weight of
the water collected (i.e., water displaced by the body).
It is found that weight of the water displaced by the body =
weight of the body in air - weight of the body in water -
Since weight of the body in air - weight of body in water =
apparent loss in weight of the body, it is clear that
apparent loss in weight of the body = weight of the water
displaced by the body. Thus, Archimedes' principle is verified in case of
water, Similar results are obtained if any other liquid is used.
PRACTICAL APPLICATIONS OF ARCHIMEDES' PRINCIPLE
Archimedes' Principle has many practical applications
and is used in : (i) designing ships and submarines. A ship is given such a
shape that as it sinks into water, it displaces a large volume and soon the
weight of the displaced water equals its own weight. The factor which makes it
possible for a ship to float is its shape. The density of the material of which
a ship is built is greater than that of sea-water. A submarine is so built that
it can float like an ordinary ship. It has two shells, one inside the other.
The inner shell is much stronger than the outer shell. The space between the
two shells is divided into chambers. When they are full of air, the submarine
floats. When the chambers are filled with water, the submarine
sinks. When it is required to rise to the surface, water is expelled from the
chambers by means of pumps driven by compressed air. This lightens the
submarine and it floats up.
(i)
determining
the purity of a sample of milk by using an instrument, called lactometer
(ii)
determining
the densities of liquids by using an instrument, called hydrometer.
(iii)
checking
the concentration (density) of sulphuric acid in acid batteries by using an
instrument battery hydrometer.
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