A cube of some substance floats

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In summary, the density of the unknown cube can be calculated by taking 57% of the density of mercury, which is 13,594 kg/m3. Therefore, the density of the cube is 0.57 x 13,594 kg/m3 = 7,754.58 kg/m3. This is because the cube is displacing 57% of the weight of mercury, which is equivalent to its own weight.
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Homework Statement


A cube of some unknown material floats in a pool of mercury. 43% of the cube is above the surface. Find the density of the cube.

Homework Equations


Fb=pVg
d=m/V

The Attempt at a Solution


So I Googled the density of mercury and found that it is 13,594 kg/m3. I also know that 57% of the cube is underwater.

mg=pVg
m=pV
m=p(.57V)

d=m/V
d=p(.57V)/V
d=.57pHg

Is that correct?
 
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That is correct. If an object displaces 57% of the weight of mercury then that means it's own weight is 57% of that of the weight of mercury in the same volume. This means then that it's density is 57% that of mercury.
 

1. What is the substance that the cube is made of?

The substance that the cube is made of is typically a type of plastic, such as polystyrene or polyurethane foam. These materials have a low density and are able to float on water.

2. How does the density of the cube affect its ability to float?

The density of the cube is a key factor in determining whether it will float or sink. If the density of the cube is less than the density of the liquid it is placed in (usually water), it will float. If the density is greater, it will sink.

3. Why do some substances float while others sink?

This is due to the density of the substance. Materials with a lower density have more empty space between their molecules, making them less dense and able to float. Materials with a higher density have less empty space, making them more dense and likely to sink.

4. Can the shape of the cube affect its ability to float?

Yes, the shape of the cube can play a role in its ability to float. A cube with a larger surface area will displace more water and be more likely to float. A cube with a smaller surface area may not displace enough water and will sink.

5. What other factors can influence the floating of a cube?

Aside from density and shape, other factors that can influence the floating of a cube include the temperature and salinity of the liquid it is placed in. These can affect the density and buoyancy of the liquid, potentially impacting the floating of the cube.

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