02 Buoyant Force.pptx

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Learning Objective

Understand

the source of

liquid pressure.

Develop

an equation to

calculate liquid pressure.

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Why do these two objects have the same buoyant force?

Force

=

Pressure

·

Area

Pressure

=

Force

Area

Buoyant Force

=

ΔP

·

A

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Archimedes Principle

http://www.briantaylor.com/images/Archimedes7_framed.jpg

(287-212 BCE)

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The Story of

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“I know of no way,” was the answer.

But Archimedes was not the man to say that anything was impossible. He took great delight in working out hard

problems, and when any question puzzled him he would keep studying until he found some sort of answer to it. And so,

day after day, he thought about the gold and tried to find

some way by which it could be tested without doing harm to the crown.

One morning he was thinking of this question while he was getting ready for a bath. The tub was full to the very

edge, and as he stepped into it a quantity of water flowed out upon the stone floor. A similar thing had happened a

hundred times before, but this was the first time that Archimedes had thought about it.

“How much water did I displace by getting into the tub?” he asked himself. “Anybody can see that I displaced a

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“Now suppose, instead of putting myself into the tub, I had put Hiero’s crown into it, it would have displaced a volume of water equal to its own volume. Ah, let me see! Gold is much denser than silver. Ten pounds of pure gold would not make so great a volume as say seven pounds of gold mixed with three pounds of silver. If Hiero’s crown is pure gold it will

displace the same volume of water as any other ten pounds of pure gold. But if it is part gold and part silver it will displace a larger volume. I have it at last! Eureka! Eureka!

Forgetful of everything else he leaped from the bath.

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The crown was tested . It was found to displace much more water than ten pounds of pure gold displaced.

The guilt of the goldsmith was proved beyond a doubt. But whether he was punished or not, I do not know, neither does it matter. The simple discovery which Archimedes made in the his bathtub was worth far more to the world than

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TITLE:

OBJECTIVE:

APPARATUS:

Determine the relationship

between the

buoyant force

,

and the

weight of the water

displaced

PART 1 PART 2

Buoyant Force

EQUALS

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OUT of Water =

20 N

IN water =

13 N

Weight of Water Displaced = 7 N

Buoyant Force = 7 N

?

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𝑭

𝒃

=

(

ρ ∙

𝑽

)

𝒈

𝑭

𝒃

=

(

𝒎

)

𝒈

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http://www.briantaylor.com/images/Archimedes7_framed.jpg

(287-212 BCE)

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ρ_gold = 19,320 kg/m3 ρ

silver = 10,490 kg/m3

Assume Gold had a mass of 2.00 kg.

2.00 kg

19,320 kg/m3

V_gold =

0.30 kg 10,490 kg/m3

V_silver =

1.70 kg

19,320 kg/m3

V_gold = = 8.799 x 10-5 m3

= 2.860 x 10-5 _m3

= 10.352 x 10-5 m3

Assume Crown had 1.70 kg of Gold and 0.30 kg of Silver.

= 11.659 x 10-5 m3

= 103.52 cm3

= 87.99 cm3

= 28.60 cm3

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10 lbs Pure Gold 10 lbs Pure Gold

10 lbs. 10 lbs.

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10 lbs Gold Mixed with Silver _{10 lbs Pure Gold}

10 lbs. 10 lbs.

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The Death of Archimedes

(287-212 BCE)

http://www-groups.dcs.st-and.ac.uk/~history/PictDisplay/Archimedes.html

The Roman invader, Marcus Marcellus, captured Syracuse. Having heard of Archimedes, he forbade harm to him.

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Archimedes Principle

Buoyant Force

EQUALS

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Find the buoyant

force on the ball.

Weigh the ball in

water AND out of

water.

OR

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2.8 cm

Volume

_ball

= 4/3·

π

·Radius

3

Volume

_ball

= 4/3·

π

·2.8

3

Volume

_ball

= 92 cm

3

V

_{water displaced}

= 92 cm

3

ρ =

V

m

m = ρ ·V

mass = 1 · 92 cm

g 3

cm3

mass

= 92 g

ρ

_water

= 1

_cmg3

buoyant force =.092(9.8) = .90 N

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http://www.cotedazur-holiday.com/Photos/Swimming%20Pool.jpg

Is it hard to

push

an

empty

five gallon bucket under

water?

How hard?

http://i.ehow.com/images/GlobalPhoto/Articles/2101895/nano-5g-bucket_Full.jpg

5.0 gal

8.3 lbs

= 42 lbs

gal

42 lbs

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http://www.thecarycompany.com/containers/drums.html

≈200 gallons of water displaced.

Density

_water

= 8.3 lbs/gal

1700 pounds of water displaced.

1700 pounds of buoyant force.

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1700 lbs.

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Which object experiences a

larger

Buoyant Force?

Which object displaces a

greater

Weight of Fluid?

Buoyant Force

EQUALS

Weight of Fluid

Displaced

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larger

Buoyant Force?

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larger

Buoyant Force?

greater

Weight of Fluid?

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Buoyant Force

Buoyant Force

Weight

Net Force

Which object experiences a

larger

Buoyant Force?

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Buoyant Force

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Buoyant Force

Weight

Net

Force Buoyant _Force

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Buoyant Force

Weight

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Pb

1 kg

Al

1 kg

1 kg Lead or 1 kg of Aluminum

Buoyant Force

Buoyant Force

Net Force Net Force

Which object experiences a

larger

Buoyant Force?

greater

Weight of Fluid?

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Pb

1 kg

Al

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1 liter of Lead or 1 liter of Aluminum

Pb 1 liter 11.3 kg Al 1 liter 2.70 kg

Weight

Net Force

Buoyant Force

larger

Buoyant Force?

greater

Weight of Fluid?

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Buoyant Force

EQUALS

Weight of Fluid

Displaced

When FLOATING, Weight of Fluid

Displaced

EQUALS

weight of the object

.

When FLOATING,

Buoyant Force

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Floating

Submerged

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Falkirk Wheel

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The tubs stay balanced because the water level in

each tub is the same and the boats displace a weight

of water equal to their own weight.

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Buoyant Force is the SAME at all depths.

Buoyant Force

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Weight

Buoyant

Force

1.00 gal

8.29 lbs

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http://sargentwelch.com/product.asp_Q_pn_E_WL1136%5FEA_A_Equal+Mass+Metal+Cylinder+Set%2C+BASIX_E_

Zinc Lead Aluminum Tin Copper

ρ ≡

m

V

Which one weighs more?

If submerged in water

(or any fluid)

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WHY

does an object that is

MORE DENSE

than the fluid it is in

SINKS

,

while an object that is

LESS DENSE

FLOATS

.

An object that is

MORE DENSE

SINKS

.

An object that is

LESS DENSE

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Water

1.0 kg

Pine Wood

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Pine Wood

.50 kg

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Net

Force

Weight

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http://www.discountstationers.com/DScom_Featured_Beverages.htmhttp://www.discountstationers.com/DScom_Featured_Beverages.htm

Sugar is not very “sweet”.

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http://www.underwater.org/mermaid/belize/images/turtle1-800.jpg

Weight of Turtle

Sand Pushing Up

Buoyant Force

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Mercury

Steel

7.8 kg

Mercury

13.5 kg

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http://fy.chalmers.se/~asa/asadeadsea.html

Fresh Water

Would this man displace

a greater weight of water

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Short Kayak Long Kayak

200 lbs 200 lbs

= 24 gallons 200 lbs 1 gal

8.3 lbs.

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Waterline for no heel

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http://www.online-pets-supply.com/dog-apparel/dog-life_jacket.htm

http://shop.lifejackets.co.uk/acatalog/Lifejacket_Orange_Foam.html

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http://www.ice-queen.org/ice_berg.htm

Weight

of

Iceberg

Weight

of

Water Displaced

EQUALS

mass

ice

=

mass

water

= densitywater·Volumewater

density_ice·Volume_ice

= density_water·Volume_water

density_ice·Volume_ice

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http://www.rosssea.info/pix/big/Commonwealth-Glacier-Face.jpg http://theexperiencejunkie.com/wp-content/uploads/2010/05/Antarctica-Iceberg.jpg

Which melting

ice would

contribute to

rising sea

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http://www.swimmingpoolservices.com/myimages/rect-indoor.jpg

http://www.coolest-furniture.com/wp-content/uploads/2007/10/boattub.jpg

Would the water level in the pool raise, fall, or stay

the same if the water were dumped out of the boat

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http://www.s-t.com/daily/08-00/08-27-00/h01ho200.htm

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http://www.coolstuffcheap.com/mul14galther.html

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Which object has a greater

buoyant force?

2.0 Newton Hollow Sphere

2.0 Newton

Hollow Sphere _{Solid Sphere}_{Solid Sphere}2.0 Newton2.0 Newton

2.0 Newtons 2.0 Newtons LESS than 2.0 Newton LESS than 2.0 Newton

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http://www.cee.cemr.wvu.edu/images/students/cc4.jpg

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Photo by: Gabuchan