Maths questions - buoyancy

englishpremier

englishpremier

englishpremier

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It seems the mathematicians are out in force on the forum today, so I have a fairly basic question.

Let's say there are two sealed fibreglass cubes. Each empty cube weighs 1kg and has a volume of 1m3

The first cube (a) is filled with air at standard atmospheric pressure at sea level, on a day where the temp is 25c. The second cube (b) is filled with a two part foam with a density of 40kg/m3.

Both boxes are left to float in seawater. The average density of which is 1025kg.

Which box will float higher in the water?

If we then add a 100kg weight on top of the boxes which box will have more of an effect on?

P.S Neither of the boxes are on a treadmill :p

Edit - changed the box weight otherwise it would it sink. lol
 
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The cubes will displace an amount of water equal to their weight.

The 1kg cube filled with air will weigh 1kg (at sea level) and displace 1kg of water.
The 1kg cube filled with 40kg of foam will displace 41kg of water.

Add 100kg weight on top of each cube and the first will then displace 101kg of water and the second 141kg of water.
 
touch said:
The cubes will displace an amount of water equal to their weight.

The 1kg cube filled with air will weigh 1kg (at sea level) and displace 1kg of water.
The 1kg cube filled with 40kg of foam will displace 41kg of water.

Add 100kg weight on top of each cube and the first will then displace 101kg of water and the second 141kg of water.
Click to expand...
Was just about to post this.

They are identical size, one is give or take 101kg and the other is roughly. 140kg. Therefore the second will be lower as it's heavier.

Bit like saying you have two identical boats. One has a flock* of elephants and the other has a magpie on it, which is lower.

*Flock of elephants is definitely the correct phrasing.
 
Okay so cutting through the fancy stuff,

2 boxes. Each 1 kg in mass, and volume of 1 m^3

One filled with air, the other foam, density of 40 kg/m^3

Density of air ~ 1.2 kg/m^3.

  • One has a mass of ~ 2.2 kg
  • The other 41 kg
So box of air will float higher

Adding 100 kg weight to both will have equal effect - it'll make both boxes displace 100 kg more water.
 
MrRockliffe said:
Density of air ~ 1.2 kg/m^3.
Click to expand...

If you include the density of air, you also need to consider buoyancy from the atmosphere.
So the 1kg box with 1m^3 of air in it has a mass of 2.2kg (as you said) but it's also displacing 1m^3 of atmosphere at sea level (1.2kg) so it'll only "weigh" 1kg.
 
kinobestew123 said:
If you fill box 1 with 10kg of something that floats and box 2 with 10kg of something that sinks, what happens then?
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The density of the thing inside the box is irrelevant, it's about the weight of it. Obviously something denser will have a higher weight per volume of that stuff. But putting in something less dense than seawater won't make the thing 'more buoyant', as you are just replacing air in the cube with something presumably heavier.
 
touch said:
I simplified my calculations by ignoring the density of air because it becomes confusing.

If you include the density of air, you also need to consider buoyancy from the atmosphere.
So the 1kg box with 1m^3 of air in it has a mass of 2.2kg (as you said) but it's also displacing 1m^3 of atmosphere at sea level (1.2kg) so it'll only "weigh" 1kg.
Click to expand...

Very true - thankfully no vacuums :p

kinobestew123 said:
If you fill box 1 with 10kg of something that floats and box 2 with 10kg of something that sinks, what happens then?
Click to expand...

If the boxes have the same volume, one can't float and the other sink assuming the same mass (as you've filled the boxes).

I.e. if they're both full, and weigh 10KG, the resultant density is 10 kg/m^3, regardless of what is in them (excluding the box itself)
 
MrRockliffe said:
If the boxes have the same volume, one can't float and the other sink assuming the same mass (as you've filled the boxes).

I.e. if they're both full, and weigh 10KG, the resultant density is 10 kg/m^3, regardless of what is in them (excluding the box itself)
Click to expand...

Yeah you have to consider the density of the object as a whole. If you jump in a pool, you float or sink based on your whole body's buoyancy. The lighter bits in you don't float while the heavier bits sink.
 
dl8860 said:
The density of the thing inside the box is irrelevant, it's about the weight of it. Obviously something denser will have a higher weight per volume of that stuff. But putting in something less dense than seawater won't make the thing 'more buoyant', as you are just replacing air in the cube with something presumably heavier.
Click to expand...

Makes sense. Where does surface area come in to it. For example, if I have a 10kg block of metal, it will sink. But if I turn it into a boat shape, it will float even though it still weighs exactly 10kg.
 
The reason I was asking, was due to a discussion on a boating forum.

Some boats are built with watertight chambers designed to keep the vessel afloat it it takes on water. Some owners fill the chambers with foam then seal them up again. My argument was that unless the chamber was breached, the foam (which is lighter than seawater) is not helping to increase buoyancy, and that weight of it, compared to a sealed unfilled chamber will have a negative impact on the vessel. i.e it will sit lower in the water.
 
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