des Principle Lecture

8/6/2019 des Principle Lecture

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A little history In the first century BC, the Romanarchitect Vitruvius related a story of how Archimedes,

the Greek scientist, discovered that a goldsmith had

tried to cheat King Hiero II

The king had given the goldsmith a particular amount

of gold to melt down and make into a crown. When

the crown was made and returned to the king, the

king was suspicious that the goldsmithhad stolen some of the gold and replaced

it with an equal weight of silver.

The king turned to Archimedes for help


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The Great Philosopher Archimedes

Archimedes think for

days, weeks and

months trying to solve

the problemhis

body got smelly and

he decided to take abath


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Thats it! Its the overflow of water


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Ive found it! Ive found it!


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Yesss! Ive found it!

Oh..er..sorry, forgot

about the clothes..he he

he


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Archimedes Experiment

Eureka

can


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Upthrust

= 0.67 0.40 N= 0.27 N

Weight of liquid

displaced

= 0.37 0.10 N

= 0.27 N

= Upthrust


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Archimedes Principle

Says that:

When a body is fully or partially

submerged in a fluid, a buoyant forceor upthrust, U from the surrounding

fluid acts directed upwards under the

body and has a magnitude equal to theweight of the fluid that has been

displaced by the body


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V

Density of

liquid,

U = mg

Since m = V, U= Vg

U

Upthrust

V

W

U

weight of the liquid

displaced by object


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Upthrust

U= Vg

Density

of liquid

displaced

x

Volume

of liquid

displaced

x

Gravit-

ational

field

Upthrust =


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Upthrust and density of the displaced liquid

= 40 N

= 24 N

= 12 NUpthrust of solid in water

= 40 24 N

= 16 N

Upthrust of solid in liquid

= 40 12 N

= 28 N

If density of water is 1000 kg m-3

and g is 9.8 N kg-1, calculate the

density of the liquid.


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Law of floatation

U = WU < W

U


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Law of floatationA floating body in a liquid displaces its own

weight.

U

U

V

W = U = Vg

Weight of body = weight of liquid displaced = upthrust

W = Vg

V

W


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Law of floatation

The weight of the displaced water equals the upward

force and this equals the weight of the ship.

W

U

U


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A ship floating in the ocean is a familiar sight. But is all

that water really necessary? Can an ocean vessel float

in the amount of water than a swimming pool contains?

How MuchWater is Needed to Float a Ship?


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Water Bridge in Germany


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This is a channel-bridge over the River Elbe

and joins the former East and West Germany,

as part of the unification project. It is locatedin the city of Magdeburg, near Berlin. The

photo was taken on the day of inauguration.

Did this bridge have to be designed towithstand the additional weight of ship and

barge traffic, or just the weight of the water?

Six years to build the bridge, cost 500 Million

Euros, and 918 meters across.....


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It only needs to be designed to withstand

the weight of the water!

Why?

A ship always displaces an amount of water

that weighs the same as the ship, regardlessof how heavily a ship may be loaded.

Answer:


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Submarines


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Surface and Submerge

U

U

U


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How do submarines dive & surface?

Does the upthrust change? ____!

A sub has ballast tanks that can be filled with

______ or _____.

To dive, a sub must become heavier, so the tanksallow _______ in while venting ____ out.

To surface, a sub must become lighter. A supply of

compressed air in the sub is used to force ______

back out of the ballast tanks.

NO

water air

water air

water


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Hot Air Balloon

The weight of the air

displaced is equal to

the upward force and if

greater than the weight

of the balloon, theballoon will accelerate

upwards.

If the weight of the

displaced air is lessthan the weight of the

balloon, the balloon will

accelerate towards the

ground.


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Hot Air Balloons

If balloon is floating (notaccelerating up or down):

________U!

(includes the weight of

the balloon, the basket,the riders, and the __________ balloon!)

Wtotal

airinside the


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How does a balloon accelerate up?

Heaters heat the air Astemperature , pressure __.

Some of the air escapes out

the bottom of the balloon,since air will move from

_____ to ____ pressure.

Thus, the weight of theballoon ____. The upward

buoyant force is now greater

than the downward weight.

high low


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How does a balloon accelerate down?

Heaters are turned off,causing the air to cool As

temperature , pressure __.

Air from the outside entersthis lower pressure area,

___________ the total weight

of the balloon. The upwardbuoyant force is now less

than the downward weight.

increasing


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Exercise:

1. Weight of an object in air is 2.8 N and 1.7 N

when submerged in a liquid of density 880 kgm-3. Calculate (i) the upthrust and (ii) thedensity of the object.

2. A ship floats with one-third of its hull

submerged in seawater. If the mass of the shipis 2.45 x 104 kg, calculate (i) the upthrustacting under the hull, (ii) the volume ofseawater displaced. (Density of seawater is

950 kg m-3

)3. A block of wood of size 20 cm x 18 cm x 15 cm

floats in water which shows only the topsurface of the wood. What is the weight of the

wood? (Density of water = 1000 kg m

-3

)


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4. A balloon floats still in air as shownin the figure. The balloon is filled

with a gas of density 0.18 g cm-3.Calculate (i) the tension in thestring, (ii) volume of the balloon.

5. A hydrometer is an instrument todetermine the density of liquids. If itfloats in water with the submergepart 18 cm from the surface andfloats in a cooking oil with the

submerge part 15 cm, what isdensity of the oil? (Density of wateris = 1000 kg m-3)

250 gm

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