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Specific Gravity – The REST of the story…PowerPoint Presentation

Specific Gravity – The REST of the story…

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## PowerPoint Slideshow about ' Specific Gravity – The REST of the story…' - donovan-dease

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

### Hiero of Syracuse (really!)…

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

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

### To keep this simple, let’s look at a cylinder in water. LESS when weighed in water!

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

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

### Since the fluid was at rest…

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

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

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

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

### If Fnet is negative, then the object is negatively buoyant and it will sink downward.

### 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.

### Please note also, if Fnetwere positive, the object would simply __________ if it were not held below the surface.

### So… SG = ρo/ρf

### Note:

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

### Hydrometers follow:

### Hydrometers follow:

AKA

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

challenged Archimedes

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

Fg

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

= 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 }

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.

Oh, BOY!

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

F negative):net = Fgobject + FB

FB

Fg

F negative):net = Fgobject + FB

FB

Fg

Fnet = Fgobject + FB

FB

Fnet = 0 N

Fg

float negative):

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

0 N

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

SG = mo/mf

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

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

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

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

x = 0.4

ρ1/ρ2 = A2h2/A1h1

ρ1/ρ2 = h2/h1

Ex. .8/1= .8 /1

.8/2= x /1

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