Calculating the Density of a Floating Block of Wood

In summary, the conversation discusses finding the density of a block of wood that is half submerged in water. The correct equation to use is Density = Mass/Volume, but the conversation mistakenly uses (Density of block/Density of water). The correct answer is 500 kg/m^3, but it was arrived at accidentally. The correct approach would be to use Archimedes' principle which states that the buoyant force on an immersed object is equal to the weight of the fluid displaced by the object.
  • #1
littlkj5
10
0

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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  • #2
Why did you divide the density of the block by the density of water? What did that get you?
 
  • #3
I found that the density equation was Density=Mass/Volume.
 
  • #4
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.
 
  • #5
so which equation would that be?
 
  • #6
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?
 
  • #7
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.
 
  • #8
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.
 

1. Why does wood float on water?

Wood floats on water because it is less dense than water. This means that its mass per unit volume is lower than that of water, making it more buoyant and able to float on the surface.

2. Can all types of wood float on water?

No, not all types of wood can float on water. Hardwoods, such as oak and cherry, are generally denser than water and will sink, while softwoods, such as pine and balsa, are less dense and can float.

3. How much weight can a piece of wood support when floating on water?

The amount of weight a piece of wood can support while floating on water depends on its size, shape, and type of wood. Generally, the larger and more buoyant the piece of wood, the more weight it can support. Additionally, wood that is less dense can support more weight than denser wood.

4. Why do some pieces of wood float higher on water than others?

The level at which a piece of wood floats on water is determined by its buoyancy, which is determined by its density and size. A larger, less dense piece of wood will float higher on the water's surface, while a smaller, denser piece of wood will float lower.

5. How does the shape of wood affect its ability to float on water?

The shape of wood can affect its ability to float on water in two ways. First, a piece of wood that is more streamlined and has less surface area will experience less resistance from the water, making it easier for it to float. Second, the shape of the wood can also affect its buoyancy, with wider and flatter pieces of wood being more buoyant than thinner and taller pieces.

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