Fluid statics specific gravity question

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Homework Help Overview

The problem involves a block of wood with a specific gravity of 0.6 that is modified to float in water by replacing part of it with a denser substance of specific gravity 6.5. The goal is to determine the mass of wood that was replaced.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between the volume and mass of the wood and the substance being added. Questions arise about how to derive the volume of wood removed and the implications of specific gravity in the context of buoyancy.

Discussion Status

Some participants have provided guidance on calculating the mass of the remaining wood and the mass of the substance filling the cavity. There is ongoing exploration of the equations involved, with various interpretations of the problem being discussed.

Contextual Notes

Participants note the challenge of understanding the problem due to a lack of instruction from their teacher, which may affect their confidence in approaching the calculations.

oates151
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Homework Statement



A block of wood with a specific gravity of .6 with a volume of 100 cm^3 is made to just float in H2O by hollowing out some of the wood and replacing it with a substance of specific gravity of 6.5. How many grams of wood were replaced.


Homework Equations



Not totally sure - possibly Fbuoy=(weightdensity) x (volume)

The Attempt at a Solution



.6(100) + .65(100-v)= 1, but i definitely think I took the wrong approach.
 
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Hi oates151, welcome to PF.
When you remove v volume of wood, the mass of the remaining wood is =...?
If you fill the space by the other substance, what is the mass of the other substance?
 
I'm unsure how to find those two specific questions you have asked. How do you derive the volume of wood taken out with the new specific gravity? My teacher has been out sick and I am trying to learn this since all my other classmates want to just fool around while he's out so forgive my ignorance.
 
If you remove a volume of v from the wood, the remaining mass = 0.6(100 - v) g.
The mass of the substance filled in the cavity = 6.5*v g
Now the weigh of the block = ...?
What is the weight of the displaced water?
Equate these two and find v.
 
Okay, so I do the following:

6.5V + .6(100-v)=100 and get v=6.78

then I just take 6.78 x 6.5 and get 44.07 as the removed mass?
 
then I just take 6.78 x 6.5 and get 44.07 as the removed mass?
This is wrong.
Removed mass is equal to volume of removed wood*density of wood.
 
Okay, so that would make it 6.78 x 100g/100cm^3 making the mass of the object 6.78 g?
 

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