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SHEENA ( 5GAMMA)

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ArChImEdEs PrInCiPlE

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ARCHIMEDES BIBLIOGRAPHY

Greek mathematician, physicist, and inventor. He is famous for his work in geometry (on the circle, sphere, cylinder, and parabola), physics, mechanics, and hydrostatics. He lived most of his life in his native Syracuse, where he was on intimate terms with the royal family.

  • Few facts of his life are known, but tradition has made at least two stories famous. In one story, he was asked by Hiero II to determine whether

 'A crown was pure gold or was alloyed with silver?'

Archimedes was perplexed, until one day, observing the overflow of water in his bath, he suddenly realized that since gold is more dense (has more weight per volume) than silver, a given weight of gold represents a smaller volume than an equal weight of silver and that a given weight of gold would therefore displace less water than an equal weight of silver.

  • Delighted at his discovery, he ran home without his clothes, shouting Eureka, which means I have found it. He found that Hiero's crown displaced more water than an equal weight of gold, thus showing that the crown had been alloyed with silver (or another metal less dense than gold). In the other story he is said to have told Hiero, in illustration of the principle of the lever, Give me a place to stand, and I will move the world.

Archimedes Contributions

Hydrostatics: Archimedes is credited with the first proof involving hydrostatics. While bathing Archimedes realized a basic principle of hydrostatics, that a solid heavier than fluid will, when weighted in the fluid, be lighter than its true weight by the weight of the fluid displaced. This realization began his study of this new field of mathematics.

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Fluid Mechanics
D. Archimedes' Principle

Key Concepts

  • A buoyant force is exerted on an object submersed in a fluid. The pressure beneath the object is larger than the pressure above. The resultant force on the object is upward, opposing the force of gravity.
  • The apparent change in (or loss in) weight of an object immersed in a liquid is due to the buoyant force. (The buoyant force on an object in a gas is negligible in most applications.)
  • When an object is partially or fully submerged, the buoyant force, or apparent loss in weight, is equal to the weight of the fluid displaced. (Archimedes' principle).
  • The apparent weight equals the actual weight minus the buoyant force.
  • A floating object displaces its own weight of fluid. The buoyant force is equal to the weight of the object.
  • A floating object has an average density which is less than the density of the fluid in which it is florating.

     

     

    Archimedes' principle is the law of buoyancy. It states that "any body partially or completely submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body." The weight of an object acts downward, and the buoyant force provided by the displaced fluid acts upward. If these two forces are equal, the object floats. Density is defined as weight per volume. If the density of an object exceeds the density of water, the object will sink. Example : submarines

     

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Archimedes Principle APPLICATION : HYDROMETER

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  • Archimedes Principle states that the buoyant force on a submerged object is equal to the weight of the fluid that is displaced by the object.

 

Archimedes principle APPLICATIONS :

Hot air balloons rise into the air because the density of the air (warmer air) inside the balloon is less dense than the air outside the balloon (cooler air). The balloon and the basket displaces a fluid that is heavier than the balloon and the basket, so it has a buoyant force acting on the system. Balloons tend to fly better in the morning, when the surrounding air is cool.

  • Floating Log:

The log floats because its density is less than that of water.

  • Sinking Rock.

The rock sinks because its density is greater than that of water.

  • Floating Ship.

The ship floats because the average density is less than that of water.

 

 

 

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Question :

 A balloon weighing 80 kg has a capacity of 1200 m3. If it is filled with helium, how great a payload can it support? The density of helium is 0.18 kg/ m3 and the density of air is 1.30 kg/ m3. Express your answer in newtons.

 

Answer:

Steps to complete the problem:

  1. List all of the variables given.

Mass of balloon = 80 kg
Volume of balloon = 1200 m3
Density of Helium = .18 kg/m3
Density of Air = 1.3 kg/m3

  1. Determine the the total mass that can be lifted by the helium balloon.

Mass lifted = mass of the volume of fluid displaced

Mass = (1200 m3)( 1.3 kg/m3)

Mass = 1560 kg

The total amount that can be lifted = 1560 kg (including balloon, helium and payload)

 

 

  1. Determine the mass that is displaced.
    1. Determine the mass of helium.

(1200 m3)*(.18 kg/m3) = 216 kg

    1. Subtract the mass of the balloon and mass of the 1200 m3 volume of helium from the total mass that can be lifted.

1560 kg - 80 kg - 216 kg = 1264 kg

  1. Determine the Force required to lift the displace volume of 1200 m3.

F = mg (where g is gravity)

F = (1264 kg) * (9.8 m/s2)

F = 12,387 Newtons

 

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Archimedes Principle 

  • The fluid exerts a force on the object

  • If you measure the buoyant force and the weight of the displaced fluid, you find:

-An object in a fluid is supported by a buoyant force equal to the weight of fluid it displaces

What determines if a object will sink or float?

  • A floating object displaces fluid equal to its weight
  • A sinking object displaces fluid equal to its volume

How will an object float?

The denser the object, the lower it will float.

Example: ice floating in water.

Equations :

W=rVg

Vi/Vw=rw/ri

rw = 1024 kg/m3 and ri = 917 kg/m3

 

Consider a pipe of cross sectional area, A with a fluid moving through it with velocity, v

  1. Mass must be conserved
  2. If the density is constant then,

    Av= constant = R = volume flow rate

Because the amount of fluid going in must equal the amount of fluid going out
 

 

If density of object is less than density of fluid: Object rises (accelerates up)

If density of object is greater than density of fluid: Object sinks. (accelerates down).  

 

QUESTION AND ANSWER!!!!

Question : A huge ship floats over water but a small nail sinks into water . Explain why ?

Answer : Floating of a huge ship or sinking of a nail is according to Archimedes principle.
A huge ship displaces water whose weight is greater than the weight of ship & the upward thrust on the ship balances its weight. That's why ship floats over water surface. On the other hand nail displaces water whose weight is less than the weight of the nail. Due to this reason nail sinks into water.

 

With the help of Archimedes principle we conclude that:
(1) A body will float over a liquid if displaces liquid whose weight is greater than the weight of body .
(2) A body will sink in a liquid if it displaces liquid whose weight is less than the weight of body.

 

Question:
If a penny is tossed into the ocean will it displace more or less water than the same penny placed on the deck of a boat?

Answer:
The penny placed on the deck will displace more water.

The penny in the ocean will displace its volume while the penny on the deck will displace its mass. We know that the penny is more dense than water because it sinks to the bottom of the ocean.

Approximate density of a pure copper penny: 8.92 g/mL
Approximate density of water: 1 g/mL

Approximate volume of a penny: 0.360 mL
Approximate weight of a penny: 3.21 g

When the penny is placed on the deck it must displace its weight in the water. Therefore the penny must displace 3.21 g of water, which is equivalent to 3.21 mL of water. The penny at the bottom of the ocean is only displacing 0.360 mL of water. So more water will be displaced due to the weight of the penny than its volume.

We know,

If we allow Vp and Vw to represent unit areas and decrease the volume to account for less mass,

where

result,    or,

The volume of the displaced water is more than the volume of the penny.

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