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# Specific Gravity – The REST of the story… - PowerPoint PPT Presentation

Eureka!. Specific Gravity – The REST of the story…. AKA “Owl” Archimedes saved his life by taking a bath!. Hiero of Syracuse (really!)…. challenged Archimedes. to determine if his new crown was made of pure gold.

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### Specific Gravity – The REST of the story…

AKA

“Owl” Archimedes saved his life by taking a bath!

### Hiero of Syracuse (really!)…

challenged Archimedes

to determine if his new crown was made of pure gold.

### Archimedes realized (eventually) that the crown would weigh LESS when weighed in water!

F LESS when weighed in water!g

FT

FT

=

Fg

### Has the gravity stopped pulling as hard on the crown? LESS when weighed in water!

Fg

F LESS when weighed in water!g

FT

### No! So…

FT

>

Fg

F LESS when weighed in water!g

F?

FT

### Therefore…

F?

FT

+

=

Fg

F LESS when weighed in water!g

F?

FT

### This new force is called…

Oh, BOY!

F?

FT

+

=

Fg

F LESS when weighed in water!g

F?

FT

### the BUOYANT force!

Oh, BOY!

F?

FT

+

=

Fg

F LESS when weighed in water!g

FB

FT

### the BUOYANT force!

Oh, BOY!

FB

FT

+

=

Fg

F LESS when weighed in water!g

FB

FT

Hmm...

FB

FT

+

=

Fg

### Does the fluid exert any force on the cylinder? LESS when weighed in water!

F LESS when weighed in water!B = |Fup| - |Fdown|

### Because h2 > h1, the force up is greater than the force down.

= PbotAbot - PtopAtop

= ρgh2Abot – ρgh1Atop

{ Abot = Atop }

= ρgA(h)

h1

= ρgV

h2

h = h2 - h1

|F LESS when weighed in water!B|= Fgfluid

= ρfluidgV

= mfluidg

Remember that:

h1

{ ρ = m/V }

h2

h = h2 - h1

{ m = ρV }

### So | F LESS when weighed in water!B |= | Fgfluid |

Oh, BOY!

h1

h2

h = h2 - h1

Is this LESS when weighed in water!

always true?

h1

h2

h = h2 - h1

### Let’s consider a still fluid: LESS when weighed in water!

The fluid was there already, and if we encase it in a plastic bag that has the same density as the fluid, it will continue to be there.

### | F LESS when weighed in water!B |= | Fgfluid |

Oh, BOY!

So the buoyant force on an object equals the weight of the fluid displaced, regardless of the shape of the object.

### In all cases, negative):Fnet = Fgobject + FB

F negative):net = Fgobject + FB

### If Fnet is positive, then the object is positively buoyant and it will rise upward.

FB

Fg

F negative):net = Fgobject + FB

FB

Fg

### If F negative):net is zero, then the object is neutrally buoyant and it will neither rise nor sink while it is under the surface.

Fnet = Fgobject + FB

FB

Fnet = 0 N

Fg

ALWAYS negative):

upward

FB

FB

Fg

Fg

FB

Fg

float negative):

(i.e. The object would displace enough fluid such that Fnet = ________.

0 N

F negative):g

FB

FT

Hmm...

FB

FT

+

=

Fg

F negative):g

FB

FT

Oh, yeah...

### Remember that SG = ρo/ρf

FB

FT

+

=

Fg

SG = negative):mo/Vo/mf/Vf

SG = mo/mf

### So… SG = ρo/ρf

SG = mog/mfg

SG = Fgo/Fgf

SG = Fgo/|FB|

SG = Fgo/ΔFgo

Eureka! negative):

So… Archimedes realized that an object’s specific gravity (relative to the fluid used) equaled the weight of the object out of the water divided by the change of weight that occurred when the object was submerged in the fluid!

Oh, BOY!

SG = Fg/ΔFg

SG = negative):Fgo/ΔFgo

SG = Fgo/|Fgo– Fgo’|

SG = ρoVo/ρfVf

### Note:

SG = ρo/ρf

If the fluid involved is water at 4ºC, then this ratio is the specific gravity for the object, not just a relative SG.

|F negative):B| = |Fg|

ρo = 0.2 g/mL

### For floating objects, objects sink enough that:

ρf.Vdisplaced.g=ρo.Vo.g

Vdisplaced/Vo = ρo/ρf

So 80% of the ball is above the water.

ρ negative):1/ρ2 = V2/V1

### Hydrometers follow:

ρ1/ρ2 = A2h2/A1h1

ρ1/ρ2 = h2/h1

h2/h1

Ex. .8/1= .8 /1

If placed into a denser fluid: .8/2= x /1

ρ negative):1/ρ2 = V2/V1

### Hydrometers follow:

x = 0.4

ρ1/ρ2 = A2h2/A1h1

ρ1/ρ2 = h2/h1

Ex. .8/1= .8 /1

.8/2= x /1