Specific Gravity Nova question

[crazy person]

A bathtub duck floats in water with one thrid of its volume above the water line. What is its specific gravity?

The answr is 2/3.

How are they getting 2/3? I thought that if 1/3 of its volume that its above the water will be the same as 1/3 of its specific gravity, right? Specific gravity: p object/ pH2o ??? shouldn't the answer be 1/3 instead of 2/3 ??

Thanks guys !!!

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[brood910]

When an object is floating, percent submerged = specific gravity
It's because:

P0 x Vo x g = Pw x Vo x %submerged x g

that means, % submerged = Po/Pw = specific gravity.

 

[crazy person]

so maybe its a math thing then. are u plugging 1/3 for P0 and 1 for PH20 ???

so it should be 1/3 divided by 1 and that gives you 2/3 ??

The way they did it : pH20Vg -pvg .

Thanks !

 

[dudewheresmymd]

so maybe its a math thing then. are u plugging 1/3 for P0 and 1 for PH20 ???

so it should be 1/3 divided by 1 and that gives you 2/3 ??

The way they did it : pH20Vg -pvg .

Thanks !

Definitions:

Archmides' principle: mass object=buoyant force (Fb) = weight of water displaced
density object* volume object * g= density medium * volume of water displaced * g
therefore: density object/density medium = volume of water displaced/volume of object
density object/ density medium= volume of water displaced/volume of object = % submerged (is the key when solving these types of questions)

% submerged object (in other words how much of the object's total volume is below the water line?)= density object /density medium (in this case water), when the density of the medium in question is water as it is in this question, we refer to the ratio of density object/density water as the specific gravity of that object (what the question is asking for).

If they tell you 1/3 of an object's volume is above the water line then 2/3 of the object (100% of object volume -33.3% of objects volume above = 66.67% of objects volume below) MUST be below the water and therefore "submerged." Submerged refers to the %Volume of an object that is below the water line.

2/3 of object is submerged below water= density object/density medium(water) = specific gravity of the object!

 

[brood910]

so maybe its a math thing then. are u plugging 1/3 for P0 and 1 for PH20 ???

so it should be 1/3 divided by 1 and that gives you 2/3 ??

The way they did it : pH20Vg -pvg .

Thanks !

No. You dont bother with 1/3. That's % NOT submerged.
You just plug 2/3 into %submerged in the equation I provided.

 

[crazy person]

Oh I see ! Thanks

 

[crazy person]

No. You dont bother with 1/3. That's % NOT submerged.
You just plug 2/3 into %submerged in the equation I provided.

oh I see. Thanks