Question about Archimedes Principal

[ZeroXD]

Hi everyone,

im having some difficulties with a certain homework problem I'm on.
Up until now I've solved all buoyancy problems knowing its weight in air and its weight submerged in a liquid (generally water).

In this particular problem, it gives the weight of the block completely submerged in water as 25 Newtons, and the weight of the blocked cmpletely submerged in alcohol as 25.7 Newtons. Then it states the density of the alcohol is 806 kg/m^3. How would I go about solving for volume of the block?

thanks in advance.

 

[HallsofIvy]

Archimedes' principal states that an object, immersed in a liquid, displaces a volume of liquid equal to its own volume and its weight is reduced by the weight of the liquid displaced.

Let W be the (weight) density of water and A the (weight) density of alcohol.

Let V be the volume of the object and G its weight.

The weight of water displaced is WV so the weight of the object in water is G- WV= 25 Newtons.

The weight of alcohol displaced is AV so the weight of the object in alcohol is G- AV= 25.7 Newtons.

Since you know both W and A, you can eliminate G from the two equations and solve for V.