Fluid statics specific gravity question

[oates151]

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.

 

[rl.bhat]

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?

 

[oates151]

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.

 

[rl.bhat]

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.

 

[oates151]

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?

 

[rl.bhat]

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.

 

[oates151]

Okay, so that would make it 6.78 x 100g/100cm^3 making the mass of the object 6.78 g?