Calculating the Density of a Floating Block of Wood

[littlkj5]

Homework Statement

A block of wood of uniform density floats so that exactly half of its volume is underwater. The density of water is 1000 kg/m3. What is the density of the block?

Homework Equations

The Attempt at a Solution

I tried 500 kg/m3 divided by 1000 kg/m3

 

[Chi Meson]

Why did you divide the density of the block by the density of water? What did that get you?

 

[littlkj5]

I found that the density equation was Density=Mass/Volume.

 

[emg333]

I think you use Archimedies ' principle for this= the buoyant force on an immersed object has the same magnitude as the weight of the fluid displaced by the object.

 

[littlkj5]

so which equation would that be?

 

[Chi Meson]

I tried 500 kg/m3 divided by 1000 kg/m3

Why did you divide the density of the block by the density of water? What did that get you?

I found that the density equation was Density=Mass/Volume.

Density = m/V, but that is NOT what you did above. You divided the "density of the block of wood" over "the density of water." THAT is what (500 kg/m^3)/(1000 kg/m^3) is. First of all, what made you pick "500 kg/m^3" anyway? It's not given information. It is in fact the answer to the question, but it appears to be accidental. Again my question is, why did you make that division?

 

[littlkj5]

I did this because it said half of its volume is underwater so therefore I assume it was 500. So then I did the division. I guess I over thought the question. More than what was needed.

 

[Chi Meson]

You still might need to explain why a density that is half of water will be half-submerged. Find Archimedes' principle and read it aloud. You also should understand that the division you did is NOT the same as the formula you stated.