RESEARCH PROJECT ON ARCHIMEDES PRINCIPLE

1. Acknowledgements
We would like to express our special thanks to our physics
teacher, Swapna Ma'am for their able guidance and support
in completing our investigatory project on "Verification of
Archimedes Principle".
We would like to extend our thanks of gratitude to our
Principal ma'am Mrs Dr. Manju Reji for the fruitful guidance
and for providing us with all the neccessary facilities that was
required to do this project.
We would also like to thank our parents and friends who
helped us with their valuable suggestions, guidance and
support for completing this project within the limited time
frame.
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2. Table of Content
2-3
4-6
Introduction
His Acheivements
7-9
10
What is the Archimedes
Principle
The Story behind the
principle's discovery
11
Applications/Uses of The
Principle
12-13
Buoyancy and the
Archimedes Principle
14-17
Verification of
Archimedes Principle
Experiment
Bibliography 18
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3. Introduction
Archimedes (c. 290-280 BC,
Syracuse – 212/211 BC,
Syracuse),was a legendary Greek
inventor and mathematician. His
main discoveries were
Archimedes' screw, an innovative
device for raising water, and the
hydrostatic or Archimedes'
principle.
His main interests were
mechanics, pure mathematics &
astronomy. Archimedes'
mathematical proof shows both
bold originality and rigor that
meets the highest standards of
modern geometry.
He resided in Syracuse for most
of his life but did live in Egypt for
his higher education. Archimedes
had a very close relationship with
the king of that time, Hieron II.
He was the master mind behind
the war machines used for
defense of Syracuse against the
siege laid by the Romans in 213
BCE.
His approximation to π did not
improve until the end of the
Middle Ages, and the translation
of his work had a significant
impact on 9th century Arabian
mathematicians & 16th and 17th
century European
mathematicians. In his hometown
of Syracuse, he was known as a
genius in the design of siege and
counterattack weapons. He was
killed by a Roman soldier during
the capture of the city.
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4. Introduction
These war machines were so
effective that they long delayed
the capture of the city. Unlike
other ancient scientists, far more
details are found about
Archimedes. Thus, he is credited
with the invention of the
Archimedes screw.
The story of him leaping from
the bath and running naked after
getting the idea behind the task
assigned to him and shouting
“Eureka!” (“I have found it”) is a
very popular moment in physics.
Equally there are stories where he said “Give me a place to stand and I
will move the Earth” and that a Roman soldier killed him because he
refused to leave his mathematical diagrams.
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5. His Acheivements
1.The Archimedes Principle
Archimedes’ principle states
that a body immersed in a
fluid is subjected to an
upwards force equal to the
weight of the displaced fluid.
2. The Claw of Archimedes
During the Roman invasion,
to defend themselves, he
created a hook that could
latch on to the enemy’s ship
and sink it. This was also
called the ‘iron hand’.
3. Evaluation of π
Archimedes was the one who
derived the approximate value of
π as 3.14 or 22/7.
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6. 5. The Law of Lever
It shows that if the distance a from the fulcrum to where the input
force is applied (point A) is greater than the distance b from
fulcrum to where the output force is applied (point B), then the
lever amplifies the input force.
His Acheivements
4. The Formula for Surface Area
and Volume of Sphere
Archimedes was able to calculate the surface area as well as the
volume of the sphere by first calculating the surface area of the
sphere using 6πr2. The volume is 2πr3. This made it easier for us
to calculate surface area and volume of any sphere.
6. Archimedes Screw
It was invented to pump water from a lower level to higher level.
It worked against the gravity. This helped many farmers to
irrigate their lands and is still used in modern days for various
purposes.
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7. This parabolic mirrored structure was used to concentrate sunlight
over a particular area on a ship which would then catch fire,
ultimately leading to the sinking of the ship. This was created as a
defense mechanism for his native land.
His Acheivements
6. Archimedes Death Ray
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8. Archimedes’ principle deals with the forces applied to an
object by fluids surrounding it. This applied force reduces
the net weight of the object submerged in a fluid. Let us
familiarize ourselves with Archimedes’ principle.
Archimedes’ principle states that:
“The upward buoyant force that is exerted on a body
immersed in a fluid, whether partially or fully submerged,
is equal to the weight of the fluid that the body displaces
and acts in the upward direction at the center of mass
of the displaced fluid”.
The value of thrust force is given by the Archimedes law
which Archimedes of Syracuse of Greece discovered.
When an object is partially or fully immersed in a liquid,
the apparent loss of weight is equal to the weight of the
liquid displaced by it.
For example, a ship that is launched sinks into the ocean
until the weight of the water it displaces is just equal to its
own weight.
What exactly is the Archimedes
principle?
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9. If you look at the figure, the weight
due to gravity is opposed by the thrust
provided by the fluid. The object
inside the liquid only feels the total
force acting on it as the weight.
Because the actual gravitational force
is decreased by the liquid’s upthrust,
the object feels as though its weight is
reduced. The apparent weight is thus
given by:
What exactly is the Archimedes
principle?
Archimedes’ Principle Explanation -
Apparent weight= Weight of object (in the air) – Thrust force
(buoyancy)
Archimedes’ principle tells us that the weight loss is equal to the
weight of liquid the object displaces.
Archimedes’ Principle Formula -
In simple form, the Archimedes law states that the buoyant force on
an object is equal to the weight of the fluid displaced by the object.
Mathematically written as:
Fb = ρ x g x V
Where Fb is the buoyant force, ρ is the density of the fluid, V is the
submerged volume, and g is the acceleration due to gravity
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10. We know that the density is defined as:
Density(ρ)=Mass(M)/Volume(V)
What exactly is the Archimedes
principle?
Archimedes’ Principle Derivation -
Therefore, the mass of the displaced liquid can be written as follows:
Mass(M)=Density(ρ)Volume(V)
Now, the weight of the displaced liquid can be calculated as follows:
Weight=Mass x Acceleration due to gravity
Now, the weight of the displaced liquid can be calculated as follows:
Weight=Mass x Acceleration due to gravity
Weight=Mass x g = ρ x V x g
From Archimedes’ principle, we know that the apparent loss of
weight is equal to the weight of the water displaced therefore the
thrust force is given by the following equation:
Thrust Force = ρ x V x g
Now, the weight of the displaced liquid can be calculated as follows:
Weight=Mass x Acceleration due to gravity
Where ρ is the density of the liquid, V is the volume of liquid
displaced and g is the acceleration due to gravity.
The thrust force is also called the buoyant force because it is
responsible for objects floating. Thus, this equation is also called the
law of buoyancy.
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11. King Hieron II, The Then King of
Syracuse had commissioned a goldsmith
to make a crown of pure gold. For this
purpose, the king gave the goldsmith a
gold bar with the mass mB = 1 kg. The
goldsmith made him a crown of mass
mk = 1 kg. Although the king liked the
artistic design of the crown, he was
troubled by doubts as to whether it was
really made of gold or whether the
goldsmith had added cheaper silver and
taken the gold for himself. Therefore, he
commissioned Archimedes to devise a
The story behind The Discovery of
the Principle
method by which this could be determined without damaging the crown.
The story was first written down in the first century B.C. by Vitruvius, a
Roman architect.
Archimedes thought long and hard but could not find a method for proving
that the crown was not solid gold. Soon after, he filled a bathtub and noticed
that water spilled over the edge as he got in and he realized that the water
displaced by his body was equal to the weight of his body. Knowing that gold
was heavier than other metals the crown maker could have substituted in,
Archimedes had his method to determine that the crown was not pure gold.
". This is the story behind The Discovery of Archimedes Principle.
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12. The Archimedes principle is extremely useful for calculating the
volume of an object that doesn’t have a regular shape. The oddly
formed item can be submerged, and the volume of the fluid displaced
is identical to the extent of the item. It can also be used in calculating
the density of unique gravity of an item.
1.
Uses Of The Principle
2. Archimedes principle has proved to be useful in determining the
purity of substances.
Example: to measure the volume of an egg , which is an
irregularly shaped object, we can fill up a glass with water, put
an egg in the glass and measure the water that rises up (or spills
out), and hence we find the volume of the egg.
Example: Lactometer is an instrument that is
used to check the purity of milk. It works
according to Archimedes’ principle.
Lactometers measure the density of the milk,
which helps in finding the contents present
in milk and determine its purity. Milk is kept
undisturbed for a while until the cream
deposits on it, and then the lactometer is
placed in this milk sample, if the
lactometer floats it means that milk is pure,
but if the lactometer sinks, it means milk is
adulterated or impure.
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13. Buoyancy: The tendency of a body to float or to
rise when submerged in a fluid is known as
buoyancy. All liquids and gases in the
presence of gravity exert an upward force
known as the buoyant force on any object
immersed in them. Buoyancy results from the
differences in pressure acting on opposite
sides of an object immersed in a static
fluid.An object sinks in water if its density is
greater than that of water and floats in water if
its density is less than that of water.
Buoyancy and Archimedes Principle
Relating Archimedes Principle and
Buoyancy:Archimedes's principle states
that the buoyant force on an object is
equal to the weight of the fluid
displaced by the object. This means,To
determine the buoyant force on an
object, we will only have to find the
weight of the fluid displaced by the
object.
.:Loss in weight of body = Weight of
liquid displaced by the body = Buoyant
force exerted on the body.
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14. When a ship floats, it displaces some water below it. A part of the ship's
hull will remain immersed in water. Here the volume once occupied by
water is now occupied by the ship.
The principle is, in order to remain afloat, the mass of the whole ship
should be less (or equal to) than the mass of the quantity of water
displaced by the ship.
More heavier the ship, more water it displaces.
How does a Ship Float? : The structure of the ship is very important when it
comes to floating. The design of the ship must ensure that it can displace
water equal to the ship's own weight, as stated by Archimedes' principle.
There are three basic concepts that explain how and why a ship can float:
The hull of a ship contains an adequate quantity of air which makes the ship
less dense than water, which satisfies the law of flotation.The density of the
ship—including the cargo, crew, and components—must be less than the
density of water in order for the ship to float on top of the water. The air in
the hull makes the density of the ship lower than the density of water.
Buoyancy and Archimedes Principle
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15. 500 ml beaker filled with tap water
500 ml beaker filled with saturated salt solution
Overflow can
250 ml beaker
Weighing scale
Wooden base
Rectangular copper block (S1)
Spring balance
1.
2.
3.
4.
5.
6.
7.
8.
To verify the archimedes principle
Verification Of Archimedes Principle
Experiment
Objective -
Apparatus Required -
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16. Hang a spring balance on an iron stand using a clamp.
Note the least count of the spring balance.
Take one of the solid blocks (S1) and weigh it by hanging it on
the hook of the spring balance using a thread. Find the weight of
the solid in air (Wa) and note it.
Take two beakers (each of 250 ml) and mark them as A and B.
Weigh them on a balance separately and note down the mass of
beaker A and B.
Take an overflow can and fill it with water to the brim of the
outlet and place beaker A below the overflow outlet of the can to
collect the displaced water. Now, start lowering the metallic block
(S1), still attached to the spring balance into the water of the
overflow can.
Note the loss of weight of the metallic block as it gets completely
immersed in the water. Weigh beaker A which contains the
displaced water and note the mass. To find the mass of the water
displaced, subtract the initial mass of beaker A (without
displaced water) from the present mass of the beaker A
(containing displaced water).
1.
2.
3.
4.
5.
6.
(weight of Beaker A + Displaced water) - weight of empty beaker A =
Weight of water displaced by completely immersing block (S1)
Verification Of Archimedes Principle
Experiment
Proceedure -
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17. 7. Repeat the experiment using the metallic block S1 by completely
immersing it in the strong salty water in the overflow can. Note
the loss in weight S1 by immersing it in the strong salt solution.
Find the mass of the salt solution displaced and collected in the
beaker.
(weight of Beaker B + Displaced salt solution ) - weight of empty
beaker A = Weight of salt solution displaced by completely immersing
block (S1)
Verification Of Archimedes Principle
Experiment
Observations -
Weight of metallic block S1 in air = .....850.... g wt.
Mass of empty beaker = .....110....... g.
Weight of the block (S1) after immersed in solution =
....750... g wt.
New mass displayed in the digital balance = .....210.... g.
Loss of weight of block in air = ...100.... g wt.
Mass of water displaced (m) = ....100... g.
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18. Verification Of Archimedes Principle
Experiment
Experiment done virtually*
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19. Bibliography
https://www.ancienthistorylists.com/people/top-
contributions-archimedes/
https://www.britannica.com/biography/Archimedes
https://byjus.com/
http://amrita.olabs.edu.in/?sub=1&brch=1&sim=72&cnt=4
https://www.scienceworld.ca/resource/egg-volume-relay/
https://studiousguy.com/archimedes-principle-
applications/
1.
2.
3.
4.
5.
6.
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