Calculating the Density of a Floating Block of Wood

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Homework Help Overview

The problem involves calculating the density of a block of wood that floats with half of its volume submerged in water, where the density of water is given as 1000 kg/m³. The original poster attempts to relate the densities of the block and water to find the block's density.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the density of the block and the density of water, with some questioning the reasoning behind dividing the densities. Others reference Archimedes' principle as a potential framework for understanding buoyancy.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the assumptions made by the original poster. Some guidance has been offered regarding the application of Archimedes' principle and the need for clarity in the calculations presented.

Contextual Notes

There is a noted confusion regarding the use of a density value (500 kg/m³) that was not provided in the problem statement, leading to questions about its relevance and the calculations performed.

littlkj5
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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
 
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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.
 
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.
 
so which equation would that be?
 
littlkj5 said:
I tried 500 kg/m3 divided by 1000 kg/m3

Chi Meson said:
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?
 
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.
 
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.
 

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