How far a cube sinks below the waterlevel

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In summary, the wood cube has a density of 700 kg/m^3 and floats levelly in water. The distance from the top of the wood to the water surface can be determined using the buoyancy equation. To have the wood cube's top just at water level, a mass of 8.9 kg needs to be placed on top of it. This can be found by using the density equation and setting it equal to the density of water.
  • #1
justinram22
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Homework Statement


A wood cube .30m on each side has a density of 700 kg/m^3 and floats levelly in water. (a) What is the distance from the top of the wood to the water surface? (b) What mass has to be placed on top of the wood so that its top is just at the water level.


Homework Equations


I assume the buoyancy equation.


The Attempt at a Solution


I figured out part (a) no problem, but seem to be having difficulty with part (b).

I assume it has to be:
Density=(mass/volume)?
When i do that I get 18.9, where the back of the book says 8.9

Thanks guys so much! Hope once I actually get good at physics I can come back and help people similar to myself!
 
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  • #2
How much would the wooden block weigh if its density was the same as the density of water?
 
  • #3
Sorry, but I'm still lost?

So

1000=(mass/.027)
mass=27?

Thanks!
 
  • #4
27 what?
 
  • #5
27kg

Which is not what they had in the back of the book (they had 8.9).

Thanks You again!
 
  • #6
How much does a cube of water weigh which is 0.30 m on each side?
 

1. What factors determine how far a cube sinks below the water level?

The main factors that determine how far a cube sinks below the water level are its density, volume, and the density of the water. The denser the cube and the larger its volume, the further it will sink. Additionally, the density of the water will also play a role in determining the depth of sinking.

2. Does the shape of the cube affect how far it sinks below the water level?

Yes, the shape of the cube can affect how far it sinks below the water level. A cube with a larger surface area will displace more water, causing it to sink deeper. On the other hand, a cube with a smaller surface area will displace less water and therefore sink less.

3. How does the weight of the cube impact its sinking depth?

The weight of the cube plays a significant role in its sinking depth. A heavier cube will sink deeper than a lighter cube, assuming they have the same volume and density.

4. Is there a limit to how far a cube can sink below the water level?

Yes, there is a limit to how far a cube can sink below the water level. This limit is known as the buoyant force, which is the upward force exerted by the water on the cube. Once the buoyant force is equal to the weight of the cube, it will stop sinking and reach a state of equilibrium.

5. Why does a cube sink in water in the first place?

A cube sinks in water because of the force of gravity. The weight of the cube pulls it down, while the buoyant force of the water pushes it up. If the weight of the cube is greater than the buoyant force, it will sink below the water level. However, if the buoyant force is greater, the cube will float on top of the water.

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